FROM THE FIELD

OF CATALYSIS.

Dm. Turbaba,

Extraordinary Professor of the Tomsk Technological Institute
of Emperor Nicholas II.

Tomsk.

Steam Typo-Lithography of P. I. Makushin, Blagoveshchensky Lane, own house.

1901.

Instead of a Preface

In February 1888 I reported to the Physico-Chemical Section of the Society of Experimental Sciences at Kharkov University the following work of mine. Since during 1888 the proceedings of this section were not printed, and indeed I did not print this work of mine at all thereafter, and since it is the direct beginning of the work done by me in Leipzig in 1899–1900, I reproduce it here, instead of a preface, in the form in which I once reported it.

“My first task was to study the dissociation of paraldehyde. Paraldehyde with a melting point of 10.5° and a boiling point of 124°–125° was taken for these experiments.

I studied the dissociation by determining the vapor density of pure paraldehyde in Hofmann’s apparatus.

At 100° (in water vapor), at 132° (in amyl alcohol vapor), and at 165° (in cumene vapor), instead of the theoretical density of paraldehyde, equal to 4.56, there were obtained, at the very beginning of heating, densities respectively equal to 4.41—4.46—4.48. Exactly the same height of the mercury column in the inner tube of the Hofmann apparatus, i.e. the same density, is also maintained during the whole three hours of subsequent heating. Consequently, the differences of the observed densities from the theoretical one should be ascribed to experimental errors, and not to an incipient decomposition of paraldehyde. In view of these data, I cast doubt on Weidenbusch’s statement (see Beilstein¹) that paraldehyde, already when distilled under ordinary pressure, i.e. at 124°, partly passes into aldehyde. Did Weidenbusch’s paraldehyde perhaps contain some amount of some volatile catalyst? Then his attitude toward distillation is quite understandable.

At \(184^\circ\) (in aniline vapor) a clear, although very slow, decomposition of paraldehyde begins: after two hours of heating the density had decreased to 4.12, which, assuming the decomposition of the paraldehyde particles only into 3 particles of aldehyde, corresponds to 14.5% decomposition \(\left(=\frac{4.56-4.12}{4.56-1.52}\times100\right)\). Judging by the rate of decomposition, approximately the same at the beginning of the experiment as after 2 hours of heating, one must conclude that there can be no question of proximity to the limit of decomposition.

At \(210^\circ\) (in ethyl benzoate vapor) the decomposition is still faster: after 2 h. 15 min. of heating the density fell to 3.70; but here a carbonaceous deposit on the walls of the inner tube of Hofmann’s apparatus already indicates deep decomposition of the paraldehyde particles, carbonization. In view of the latter phenomenon and the closeness of the temperatures \(184^\circ\) and \(210^\circ\), it is hardly possible to suppose that the decomposition of paraldehyde at \(184^\circ\) represents only the splitting of its particle into three particles of aldehyde; it is incomparably more probable to suppose that, if the latter reaction does occur, then alongside it there is also a deep decomposition of the paraldehyde particle.

If, however, at temperatures of \(100\)—\(165^\circ\), it is still possible to observe pure decomposition (only into aldehyde), then paraldehyde would have to be subjected to heating at these temperatures for a very, very long time.

Leaving aside the study of the vapor density of pure paraldehyde, I took up the study of the behavior of its vapor at \(100^\circ\) toward various reagents in the same Hofmann apparatus.

On the basis that \(H_2SO_4\), \(HCl\), \(COCl_2\) (Kekule und Zincke Lieb. Ann. 1872) polymerize aldehyde and decompose paraldehyde upon heating, I set myself the task of testing whether it might be a general property of all polymerizers of aldehyde, i.e., to convert aldehyde into paraldehyde at ordinary temperature and, conversely, at a higher temperature (e.g. \(100^\circ\)) to decompose paraldehyde into three particles of aldehyde, whether it is characteristic only of one and the same substances?

If the substances are arranged under two headings \(\alpha\) and \(\beta\), then

\[ \begin{array}{llllllllll} \alpha & HCl; & HNO_3; & H_2SO_4; & COCl_2; & SO_2; & (CN)_2; & ZnCl_2; & CaCl_2; & ? \\ \hline \beta & HCl; & HNO_3; & H_2SO_4; & COCl_2; & ?; & ?; & ?; & ?; & HgBr_2 \end{array} \]

it turns out (as was known before my experiments) that the substances under heading \(\alpha\) polymerize aldehyde at ordinary temperature, while the substances under heading \(\beta\) decompose paraldehyde at a higher temperature. Consequently, guided by my hypothesis, I had to study

action at \(100^\circ\) of \(SO_2\), \((CN)_2\), \(CaCl_2\), and \(ZnCl_2\) on paraldehyde, and on aldehyde the action of \(HgBr_2\) at ordinary temperature.

1) With sulfurous acid I carried out 5 experiments. Its amount, compared with paraldehyde, was from 22 to 68 times smaller than that of paraldehyde; moreover, a different rate of decomposition was always obtained. I have not elucidated the cause of this different rate by a sufficient number of experiments \(^{2}\).

The limit of decomposition in all 5 experiments was evidently close to \(100\%\), i.e. to complete decomposition of the paraldehyde, although it was not reached in any one experiment.

2) Molten calcium chloride slowly decomposes paraldehyde at \(100^\circ\).

3) Zinc chloride at \(100^\circ\) produces a very rapid decrease in the density of paraldehyde vapor, which is very soon accompanied by a side reaction (resinification?).

4) Cyanogen, whether dry or moist, does not act on paraldehyde during 2 hours’ heating: the height of the mercury column is exactly the same after two hours’ heating as at the beginning of the experiment.

Thus it turned out that cyanogen alone does not fall under rubric \(\beta\). I therefore verified Lieben’s statement about the polymerization of aldehyde by cyanogen. I carried out the polymerization of aldehyde by introducing, into a tube containing saturated aldehyde vapor over mercury at room temperature, various substances. In such experiments it turned out that \(SO_2\), \(CaCl_2\), \(ZnCl_2\), and \(HgBr_2\) after several days very greatly reduce the elasticity of aldehyde vapor, while cyanogen, whether dry or moist, does not act.

Further, by my experiments I added mercuric chloride \((HgCl_2)\) and boric acid to rubrics \(\alpha\) and \(\beta\). The experiments with the latter substance are especially interesting. Boric acid, dried over sulfuric acid, after 50 minutes’ heating with paraldehyde at \(100^\circ\) brings its density to 1.58 (the theoretical density of aldehyde is \(=1.52\)).

Molten boric anhydride after 5–10 minutes at \(100^\circ\) decomposes \(90\%\), after 20–25 minutes \(100\%\) of the paraldehyde, and with further heating for an hour does not change the height of the mercury column at all (the density found is 1.53).

Meanwhile, at ordinary temperature boric acid (ignited to remove sulfuric acid, recrystallized from solution, and pressed between filter paper) does not act on aldehyde; but it is worth it for several

\(^{2}\) This different rate is now quite clear, owing to the influence of the different mass of catalyst \((SO_2)\). The numerical data of these experiments, unfortunately, have been lost, so that the rate curve cannot be traced.

dehydrate it, for example, dry it at \(100^\circ\), since it acts strongly on aldehyde, rapidly diminishing, at ordinary temperature, the elasticity of its saturated vapor, and the more rapidly the higher the temperature to which it has been heated.

Consequently, \(B(OH)_3\) is a substance indifferent toward aldehyde, while the aldehyde is polymerized and decomposed (at \(100^\circ\)) by the anhydrides of this substance.

Thus the headings \(\alpha\) and \(\beta\) are now represented as follows:

\(\alpha\)	\(\beta\)
HCl	HCl
HNO\(_3\)	HNO\(_3\)
H\(_2\)SO\(_4\)	H\(_2\)SO\(_4\)
COCl\(_2\)	COCl\(_2\)
SO\(_2\)	SO\(_2\)
ZnCl\(_2\)	ZnCl\(_2\)
CaCl\(_2\)	CaCl\(_2\)
HgBr\(_2\)	HgBr\(_2\)
HgCl\(_2\)	HgCl\(_2\)
Anhydrides \(B(OH)_3\)	Anhydrides \(B(HO)_3\)

Consequently I can say with great probability that, first, only those substances which at low temperature condense aldehyde will, at higher temperature, bring it back to its original state; secondly, that these phenomena of polymerization of aldehyde and depolymerization of paraldehyde apparently represent a model of the contact action of substances.

Note. Geuther and Cartmell (Lieb. Ann. 112, 16), refuting Fehling’s earlier observation, showed that absolutely pure aldehyde is not polymerized by the action of low temperature alone. In exactly the same way it is not polymerized by the action of pressure alone, not exceeding a pressure of 200 atmospheres. (I carried out the compression of pure aldehyde in Kalete’s simple apparatus for converting gases into the liquid state.) I add further that at \(100^\circ\) water, acetic acid, pumice, dried SiO\(_2\), and HgJ\(_2\) prove to be completely indifferent to paraldehyde, while toward aldehyde at ordinary temperature only “gypsum” is indifferent.

Thus, this work at the beginning of 1888 enabled me, relying on experiment, to express that relation between the polymerizers of aldehyde and the depolymerizers of paraldehyde which is now a direct consequence of the theoretical considerations supplied by thermodynamics for this class of chemical phenomena. It is precisely at the present time\(^1\) accepted that, for

\(^1\) Van’t Hoff Vorlesungen I, 210, 1898.

reactions limited by a boundary. This boundary is not changed by the presence of catalytic substances; only the rate is changed (increased or decreased). “Catalysts, in a word, act in such a way that they impart to the process another unit of time, leaving everything else unchanged”¹.

Van’t Hoff (loco stato) writes: “From this inability of contact substances of this kind to produce a change in the reaction boundary, it necessarily follows that the contact substance which accelerates one of two reactions leading to equilibrium must also accelerate the other, the reverse of the first.”

Koelichen², putting such reasoning into mathematical form, gives for the rate of a reaction obtained as the result of two rates of opposite reactions the expression:

\[ K_1 C_1^{n_1} C_2^{n_2} C_3^{n_3}\ldots - K_2 C_1'^{\,n_1'} C_2'^{\,n_2'}\ldots = -\frac{dC}{dt}, \]

(\(C_1 C_2 C_3 - C_1' C_2' C_3'\ldots\)—active masses, and \(n_1\ n_2\ n_3\ n_1'\ n_2'\ldots\)—known numerical coefficients in the Guldberg—Waage equation), which, upon attainment of equilibrium, reduces to

\[ \frac{C_1^{n_1} C_2^{n_2} C_3^{n_3}\ldots} {C_1'^{\,n_1'} C_2'^{\,n_2'} C_3'^{\,n_3'}\ldots} = \frac{K_2}{K_1} = K \]

From the presence of the catalyst, the expression for the reaction rate changes insofar as the rate coefficients \(K_1\) and \(K_2\) also include factors for the concentration of the catalyst. The reaction equation will thus remain essentially unchanged; only the rate constants acquire other numerical values, greater or smaller, according as we are dealing with a catalyst that accelerates or retards the reaction. The question is asked whether the action of a catalyst on both opposite reactions is the same or not in quantitative respect?

In the first case, the equilibrium constant, equal to the ratio of both rate constants, will remain unchanged; in the second, because of the addition of the catalyst, it becomes greater or smaller. The fundamental laws of energetics necessarily lead us to the conviction that the latter case is impossible. For, if two opposite reactions were changed to different extents, the equilibrium of the system would change. This change could be obtained, without any compensation, in the form of work at the expense of the heat of the surrounding medium, by combining in a cyclic process one reaction with the addition of a catalyst and the reverse one without a catalyst, which contradicts the second fundamental principle of energetics.

The above-cited references give the necessary first conclusion, obtained by me empirically in 1888, concerning the connection of the accelerators (catalysts) of the reversible reaction

\[ (\mathrm{CH}_3 \ \mathrm{COH})_3 = 3 \ \mathrm{CH}_3 \ \mathrm{COH}, \]

for the rate of which we have

\[ \frac{dc}{dt} = K_1 Cp - K_2 Ca^3; \]

and at equilibrium

\[ K = \frac{K_1}{K_2} = \frac{Ca^3}{Cp} \]

where \(K_1\) and \(Cp\) are the rate constant of decomposition and the active mass of paraldehyde, and \(K_2\) and \(Ca\) are the rate constant of formation of aldehyde and its active mass.

In order to derive, from the above-stated propositions of Kantorff, Ostwald, and Kelichen, as a consequence, the relation between the catalysts of the above-mentioned reversible reaction that I observed in 1888, it is only necessary to establish the following: 1) in view of the present conception of catalysis (catalysts do not cause chemical reactions, but only change their rates), the formulation of the relation I observed should now be changed thus: only those substances which at a lower temperature accelerate the condensation of aldehyde into paraldehyde will, at a higher temperature, accelerate the conversion of the latter into its initial state; 2) in the liquid phase at ordinary temperature, the equilibrium state in the above-mentioned reaction is such that the active mass of paraldehyde very greatly predominates over that of aldehyde, which was known even before my work of 1888; whereas at \(100^\circ\) in the vapor phase we have the complete reverse (although Hofmann’s method of determining vapor density gives, as a limit, one hundred percent decomposition of paraldehyde, theoretically, especially taking into account the low accuracy of this method, one must assume not 100% decomposition of paraldehyde, but a somewhat smaller, though close, number); 3) substances, being catalysts of the known reaction at ordinary temperature, generally do not lose this capacity at a higher temperature (and conversely), especially if this higher temperature is not far removed from the first, ordinary one; such, in my experiments, is the temperature of \(100^\circ\).

It now follows directly that substances which, like cyanogen, at ordinary temperature do not affect the value \(K_2\) of the above equation, i.e. do not increase the rate of aldehyde formation, will not at the same temperature affect \(K_1\) either, i.e. will not accelerate the decomposition of paraldehyde; consequently, even at \(100^\circ\) they will not cause an acceleration of the decomposition of paraldehyde. Conversely, substances, such as sulfurous anhydride, which affect \(K_2\) at ordinary temperature, will at the same temperature also affect \(K_1\) according to the present view of catalysis, and consequently, according to the references

the 2nd and 3rd will also cause, at \(100^\circ\), the decomposition (acceleration of decomposition) of paraldehyde into aldehyde almost completely.

At intermediate temperatures, one should expect, at equilibrium, a still greater equality of the active masses of these two substances. I began to seek such an equilibrium in October 1899 in the Leipzig laboratory of Prof. Ostwald; moreover, this very reaction—the catalysis of paraldehyde, which has very many catalysts, and of quite varied nature—offered the first opportunity to examine experimentally, on a broad scale, the theoretical requirement: the nature of the catalyst does not affect the limit of a reversible reaction, but only its rate.

It is precisely the catalysis of paraldehyde that should lead to a considerable expansion of the original volume, in view of the great difference in the specific gravities of aldehyde and paraldehyde; it was necessary to determine this expansion of the volume of paraldehyde with the most varied catalysts and to see whether, when the limit of catalysis is reached, it would be the same, whatever the nature of the chosen catalyst. My experiments confirmed the predictions of the theory; I describe them and devote to them the first chapter of the present work.

CHAPTER ONE.

On the paraldehyde taken for the experiments.

At the beginning of the work, for purification I subjected the paraldehyde (preparation from Kahlbaum) to distillation with a dephlegmator (the fraction boiling at \(121^\circ\)—\(123^\circ\) was collected) and to repeated freezing out. This latter operation gave ever higher and higher values for the melting point of the paraldehyde thus purified. I stopped the freezing out when I obtained paraldehyde with a melting point equal to \(12.50^\circ\)* C. (the thermometer was normal, as everywhere below). The last preparation contained no water (since the reaction with ignited copper sulfate, which is sensitive for the detection of water, did not reveal any), and only a negligible quantity of aldehyde: such paraldehyde, not only at ordinary temperature but even on heating with solid caustic potash, gives only traces of yellow coloration; whereas small quantities of aldehyde added to such paraldehyde, even at ordinary temperature, and especially on heating, give, under the action of solid caustic potash, an abundant formation of a brown coloration—aldehyde resin. A portion of paraldehyde of this preparation, melting at \(12.20^\circ\), had at \(15^\circ\) the specific gravity

\[ S_{\frac{15^\circ}{4^\circ}} = 0.9983. \]

[A similar notation—\(S_{\frac{15^\circ}{4^\circ}}\)—for the specific gravity, measured or calculated at a known temperature (\(15^\circ\)) and referred to water of greatest density, is adopted throughout below.]

In subsequent periods of my work, for the purification of commercial paraldehyde (from Kahlbaum) I carried out the following three operations:

1) distillation of the paraldehyde alone with a dephlegmator; the fraction boiling below \(121^\circ\) was set aside for obtaining aldehyde; the very small fraction boiling above \(123^\circ\) was discarded;

2) distillation of the middle fraction obtained after the first operation, boiling at \(121\)—\(123^\circ\), over metallic sodium, whereby, besides the removal of water, the conversion of aldehyde into brown nonvolatile products is achieved, as well as the removal of many catalysts (if such happened to be contained in the commercial paraldehyde);

* Temperatures everywhere in this work are given according to the Celsius thermometer.

3) repeated freezing out of the portion purified by distillation over sodium. The last operation once gave, successively, portions with melting points of 11.80°—12.55°—12.61°. Of these, the last portion was fused down further, by half, and then the fused (liquid) part froze at 12.58°, and the remaining (solid) part at 12.57°. [On the basis of the latter data, I take as the melting point of very pure paraldehyde the number 12.58° C. (with an error of 0.05°), i.e. at least 0.5° higher than that given by Lieben (see Beilstein), who had, judging from the melting point, less pure paraldehyde than the preceding investigators, e.g. Kekulé and Zincke].

The specific gravity of such paraldehyde

$$ S\frac{15.7^\circ}{4^\circ} = 0.99753 $$

or

$$ S\frac{15.0^\circ}{4^\circ} = 0.99817 $$

(taking Perkin’s expansion data, see Beilstein) immediately after preparation. But when this purest paraldehyde stood at room temperature (20°) for 1 month and 8 days, its specific gravity was

$$ S\frac{50.5^\circ}{4^\circ} = 0.9584, $$

and that which had stood for 1 month and 20 days:

$$ S\frac{17.4^\circ}{4^\circ} = 0.9963 $$

and

$$ S\frac{50.5^\circ}{4^\circ} = 0.9581, $$

and, reducing according to Perkin’s expansion data, I obtain

$$ S\frac{15.7^\circ}{4^\circ} = 0.99768, $$

which shows that the attraction of moisture, and in general alteration during storage in air in such a vessel (a flask with a cap), did not occur (or was negligibly small). On the basis of these measurements, throughout the whole of this work I used paraldehyde stored in similar vessels. Further, the same paraldehyde gave specific gravities

$$ S\frac{30.0^\circ}{4^\circ} = 0.98170 $$

and

$$ S\frac{30.03^\circ}{4^\circ} = 0.98155, $$

Consequently,

$$ -\frac{ds}{dt}, $$

the coefficient of change of density with temperature, within the limits

$$ 15^\circ - 30^\circ = 0.00116 $$

$$ 30^\circ - 50^\circ = 0.00115 $$

therefore

$$ S\frac{25.0^\circ}{4^\circ} = 0.98746 $$

and

$$ S\frac{35.0^\circ}{4^\circ} = 0.97014. $$

In all the experiments described below I worked with paraldehyde melting at 12.2°—12.4°.

Concerning Troeger’s indication¹ that paraldehyde is capable, when stored at ordinary temperature, of passing almost entirely into aldehyde (within a year), I shall cite the following 2 observations.

1) Paraldehyde, melting at 12.58°, was sealed in a tube and placed in a thermostat at 50.5° on December 7, 1899. On February 20, 1900,

¹ Berlin. Berichte 25, 3316.

the melting point was found to be 12.32°. This tube, opened again on May 1, and consequently subjected to heating up to 50.5° for \(4^{2}/_{3}\) months, gave a melting point \(=12.22^\circ\).

Having again sealed the paraldehyde in the tube and kept it continuously at 50.5° for another three months, I determined, in Beckmann’s apparatus, a melting point \(=12.10^\circ\). Thus the melting temperature fell by only 0.48°, upon heating to 50.5° for \(7^{2}/_{3}\) months.

Thermodynamics (see van’t Hoff, Vorlesungen, Die Chemische Statik, 47) permits one to derive the following equation:

\[ -\frac{\Delta t}{a}\, m=\frac{0.02\,T^{2}}{W}, \]

where \(-\frac{\Delta t}{a}\) is the lowering, in degrees Celsius, of the freezing point of a one-percent solution of some substance having in such a solution molecular weight \(=m\); \(T\) and \(W\) are the temperature, reckoned from absolute zero, and the latent heat of fusion of the pure solvent.

Applying this equation to the present case, i.e., wishing to determine how much aldehyde was formed in the paraldehyde taken over \(7^{2}/_{3}\) months, corresponding to a lowering of the freezing point of paraldehyde by 0.48°, I must take \(T\) equal to \(273+12.58\), i.e. 285.58°, and \(m\) equal to 44 (which is the molecular weight aldehyde has both in the vapor state and in solutions of many solvents); finally, for \(W\), with a high degree of probability, one may take (approximately) 40 calories. (Landolt’s physico-chemical tables give, for the latent heat of fusion:

Substance	Latent heat of fusion
Formic acid	57.38 calories
Acetic acid	44.34 calories
Glycerin	42.5 calories
Lauric acid	44.9 calories
Beeswax	42.3 calories

Then the preceding equation gives for \(\frac{\Delta t}{a}\) the value

\[ \frac{0.02\times(285.58^\circ)^2}{40\times44}, \]

equal to 0.93° Celsius.

Consequently, the amount of aldehyde causing a lowering of the freezing point of paraldehyde by 0.48° will be approximately equal to \(0.5\%\) aldehyde.

(The preceding calculation was made on the assumption that the observed lowering of the freezing point of paraldehyde by 0.48° was caused only by the formation of aldehyde. I omit proving—qualitatively and quantitatively—the presence of this \(1/2\%\) aldehyde, because this observation did not constitute the direct aim of my investigation and was made incidentally. I must mention here that this paraldehyde, throughout the entire experiment (\(7^{2}/_{3}\) months), retained colorlessness and homogeneity, but when it was poured out of the opened ...

tubes into Beckmann’s apparatus for determining the freezing point, I observed each time the appearance on the walls of the tube of an insignificant quantity of colorless transparent grains, very similar to those which occur in nonhomogeneous, poorly annealed glass. Such grains, moistened with paraldehyde, disappeared after some time when this tube was left in the air. I did not investigate them, chiefly because of their insignificant quantity.)

2) A portion of paraldehyde, which had stood in a laboratory cupboard at room temperature for about 2 months (it seems 2 months 5 days) in a vial with a ground stopper, but without a cap, and which at first melted at \(+11.5^\circ\), at the end of this period gave a melting point of \(+1.5^\circ\)¹.

This second observation clearly contradicts the first, incomparably better conducted one: since the rates of chemical reactions increase strongly with temperature, and since the time in the second observation was three times less than in the first, one should, on the basis of the first experiment, have expected a completely negligible formation of aldehyde in the second experiment. The result was precisely the opposite: an almost 20-fold greater lowering of the freezing point and, corresponding to this, an abundant formation of aldehyde, approximately \(10\%\), if one assumes proportionality between the aldehyde concentration and the lowering of the freezing point. I ascribe this incorrect result, first, to the considerably lower purity of the paraldehyde in the second experiment, whose freezing point was \(1.08^\circ\) lower than that in the first experiment, which may indicate its contamination with some catalyst; secondly, I ascribe it to the circumstance that in the same cupboard, almost next to the vial containing paraldehyde, which had no cap but only a ground stopper and, moreover, perhaps a poor one, there stood two poorly closed vials with benzene saturated at \(0^\circ\) with the gases HCl and SO\(_2\); these gases—catalysts—could have diffused into the vial containing paraldehyde and caused accelerated formation of aldehyde.

Troeger (loco citato), whose observation is cited by Beilstein, says that, on standing at ordinary temperature for the course of a year, paraldehyde is almost entirely converted into aldehyde. “Bis auf eine geringe Menge unveränderten Paraldehydes ging nämlich bei der fractionirten Destillation Acetaldehyd von Siedepunkte 22–25° über.”

Troeger gives no data for judging the purity of this single sample of paraldehyde on which he made this observation, nor about how it was kept in the laboratory atmosphere, except

only indication that paraldehyde was kept not in darkness, but also not standing in direct sunlight. It may be that this specimen of paraldehyde from Troeger either already contained an admixture of some catalyst at the moment the experiment began, or, as I suspected in my second experiment, had attracted some laboratory vapors—catalysts, since it was kept not in a hermetically sealed bottle. Indeed, precisely such a relation during distillation—almost complete conversion into aldehyde—shows paraldehyde containing an admixture of catalysts; on the other hand, at ordinary temperature, at equilibrium, paraldehyde strongly predominates, as has long been known and as follows from the data of my present work. In view of all the foregoing, I am inclined much more to regard Troeger’s conclusion as poorly grounded than to see in it examples of those “false equilibria,” the theory of which has recently been developed especially by Duhem, while Pelabon and Hélier have supplied experimental material (see van’t Hoff, Vorlesungen, I Heft, 207).

A portion of paraldehyde, prepared for the 3rd time (February 21, 1900) by the method described earlier, with a boiling point of 12.40°, gave the following specific gravities:

\[ S \frac{18.07^\circ}{4^\circ} = 0.9948 \quad \text{and} \quad S \frac{18.07^\circ}{4^\circ} = 0.9953 \quad \text{(another pycnometer);} \]

\[ S \frac{50.5^\circ}{4^\circ} = 0.9586 \quad \text{and} \quad S \frac{50.5^\circ}{4^\circ} = 0.9554 \quad \text{〃 〃;} \]

I calculate

\[ S \frac{15.0^\circ}{4^\circ} = 0.9984 \quad \text{and} \quad S \frac{15.0^\circ}{4^\circ} = 0.9989 \]

Apparently, the difference among specimens of paraldehyde (as also affects the freezing point), prepared at different times, depended chiefly on the water content, for an admixture, in small doses of the latter, having a specific gravity very close to that of paraldehyde, should imperceptibly affect the specific gravity of the latter.

On the method.

The method employed was the dilatometric method. The glass apparatus in which the measurements were made had the form of an ordinary dilatometer; only, instead of a capillary, I soldered an ordinary thin tube to the reservoir. These tubes, before being soldered to the reservoir, were carefully calibrated with a short mercury column. To such a tube was soldered a reservoir made of a tube of much wider bore, and not far from the place where the reservoir was sealed a line was made with a diamond (a mark). The capacity of these ...

the reservoir up to the lower mark, measured at a definite temperature, usually with water, and sometimes also with mercury.

Dimensions of the dilatometers:

Nos. of dilatometers	Volume of the reservoir up to the lower mark, in cubic cm	Capacity of a one-millimeter segment of the thin tube, in cubic cm	How many one-millimeter segments of the thin tube are contained in the reservoir up to the lower mark
No. 2.	3.560 at \(T = 14^\circ\)	0.00706	504.3
No. 4.	3.6953 \(T = 14^\circ\)	0.00735	502.7
No. 5.	4.296 \(T = 14^\circ\)	0.00813	528.5
No. 6.	5.0465 \(T = 14^\circ\)	0.00728	693.2
No. 8.	7.981 \(T = 14^\circ\)	0.00815	979.6
No. 9.	6.5396 \(T = 25^\circ\)	0.00844	774.4
No. 10.	5.6133 \(T = 25^\circ\)	0.00832	674.8
No. 11.	10.731 \(T = 18^\circ\)	0.00984	1090.4
No. 12.	7.3165 \(T = 18.5^\circ\)	0.00408	1791.7

For calculating the capacity at higher temperatures (not above \(50.5^\circ\)), the coefficient of expansion of glass was taken as \(0.000025\). The position of the level of the contents of such dilatometers was read on a millimeter scale, which in the first experiments was fastened directly by a layer to the thin tube, so that the zero division of the scale coincided with the lower mark. In such a

The method of attachment proved unsuitable, for the paraffin oil poured onto the water of the thermostat rose, owing to capillarity between the scale and the thin tube of the dilatometer, dissolved (softened) the cement, and the position of the scale changed. This was soon noticed, and such attachment of the scale was replaced by fastening with ordinary screw clamps with leather pads. These clamps held excellently. As the thermostat I used the ordinary Ostwald thermostat (see Lehrbuch d. allg. Chemie II, Band 633, 1893) at a temperature of \(50.5^\circ\), of such a height that the whole dilatometer was under water. At the very beginning of the work I used several thermostats; the top of the thin tube of the dilatometer was in the air; a little liquid condensed in it, which previously often had to be removed by heating.

The empty, dry dilatometer was weighed; solid, powdery catalysts were introduced through the thin tube into the reservoir, after which the thin tube was wiped with filter paper tied to a copper wire; liquid catalysts and paraldehyde were poured in through a funnel with a drawn-out long tube of suitable thickness.

Having weighed the catalyst into the apparatus, I again weighed the dilatometer, which gave the weight of the catalyst taken for the experiment; sometimes, however, as with \(SO_2\) and some other catalysts, the weight of the latter was determined by ordinary analytical methods after the end of the experiment, after opening the dilatometer. After the apparatus was filled with paraldehyde (the thin tube of the dilatometer was again wiped with filter paper), the apparatus was sealed and weighed, which gave the weight of the paraldehyde taken for the experiment.

(Of course, a certain volume of air was also sealed into the apparatus; with time, as the paraldehyde was converted into aldehyde, this air greatly increased its volume, was subjected to considerable compression, and, moreover, naturally, to somewhat different degrees in different dilatometers. But these fluctuations in the various experiments were not great, at most 0.5 atmosphere, for the pressure of this air increased from 1 atmosphere to 1.5–2.0 atmospheres in different experiments, as is easy to determine by knowing the length of the column of air initially sealed in and its length at the end of the catalysis. In the apparatuses a pressure far higher than the vapor pressure of the aldehyde was established, so that I regard these changes of volume due to the somewhat different pressure in the dilatometers as far below other errors; and the experiments fully confirmed this. As should be expected from theory, an increase of pressure will lead to a smaller amount of aldehyde at equilibrium, while I sometimes obtained even a larger volume of air remaining in the dilatometers at the greater pressure—evidently because of larger observational errors.

Once, namely, when absolutely anhydrous cupric sulfate was used as the catalyst, the thin tube ended at the top in a bulb whose dimensions were considerably larger than the whole thin tube; therefore the air trapped in the apparatus, from thermal expansion and, chiefly, from the catalysis it caused, increased very little in its elasticity. Consequently, here, in comparison with the previous experiments, where the elasticity of this air sometimes increased to 2 atmospheres, theory led one to expect a larger expansion; yet somewhat less was obtained, for the reasons set forth below (see the detailed description of the experiment with $\mathrm{CuSO_4}$), and also because, evidently, only high pressures clearly reveal the limiting state in this catalysis.

Then the dilatometer, with the scale attached to it, was lowered into the thermostat, the time was noted, and after 3–4 minutes the first reading of the level was taken; this latter interval, 3–4 minutes, had proved in many preliminary experiments to be quite sufficient for the contents of the dilatometer to assume the temperature of the thermostat. The level remained unchanged thereafter, for the reservoir was a long and thin cylinder, and the thin tube, not being a fine capillary, did not show small differences of temperature.

In calculating the data of the experiment it was assumed that the catalyst, even when it dissolved completely at once or over the course of some time in the paraldehyde, did not change either its own volume or the volume of the paraldehyde. This change of volume cannot be determined directly, for it is completely masked by the catalysis. It can be done only where, for example with monochloroacetic and trichloroacetic acids, dissolution is very rapid and catalysis very slow. But in the latter case the expansion due to catalysis is quite independent of this aforementioned change of volume, for, knowing the whole of the paraldehyde, I also know its volume; and, in view of the very slow catalysis, I know the initial volume of the system, when the decomposition of the paraldehyde is still equal to zero, i.e. I have all the elements for the calculation.

Some notion of this change of volume on dissolving the catalyst may be derived by knowing these changes for other solvents similar to paraldehyde.

For example, $\mathrm{HgCl_2}$, dissolving in alcohol, if it changes its volume at all, does so quite imperceptibly within the accuracy characteristic of my measurements. Taking the determinations of I. F. Schröder (Mendeleev, Investigation of Solutions by Specific Gravity, p. 418), I find that 100 grams of a solution made from 2.4 grams $\mathrm{HgCl_2}$ + 97.6 g alcohol have, at $30^\circ$, a volume equal to 121.56 cubic cm. $\left(=\dfrac{100}{0.8227}\right)$; while before dissolution the sum of the volumes of these components is 121.54, or 121.543, or 121.545, or 121.55 cubic cm., depending on which of $(5.548—5.420—$

5.402—5.32) of the specific gravities given by Dammer (Handb. d. anorgan. Chemie), be taken for $\mathrm{HgCl_2}$; consequently, for 4–5 grams (which is what is usually present in my determinations), the difference in the volumes of such a system before and after dissolution will be, in the very worst case,

\[ \frac{121.56 - 121.54}{20} = 0.001 \]

cubic centimeters, i.e., a magnitude that may freely be neglected in determinations like mine. I deliberately chose a solution containing $2.4\%$ $\mathrm{HgCl_2}$ as the one most suitable for the concentrations with which I worked.

Further, from the work of Noyes and Abbot on the one hand, and of Goodwin and Burgers (Zeitschrift für physikalisch Chemie XXIII, 56 and XXVII, 99) on the other, the following table over ether solutions is easily computed: (the solvent is ordinary sulfuric ether, $(\mathrm{C_2H_5})_2\mathrm{O}$; volumes are in cubic centimeters).

Composition of the solution	Volumes before dissolution	Volumes after dissolution
1 gram naphthalene + 100 g ether	139.64	139.66
5 grams naphthalene + 100 g ether	143.11	143.25
1 gram azobenzene + 100 g ether	139.60	139.61
5 grams azobenzene + 100 g ether	142.93	142.93
1 gram diphenylamine + 100 g ether	139.56	139.54
5 grams diphenylamine + 100 g ether	143.01	142.72

For the computation of this table the specific gravities 1.151 (naphthalene), 1.203 (azobenzene), and 1.159 (diphenylamine) were taken from Beilstein and from Landolt (Physikalisch-Chemischen Tabellen), and the remaining data from the above-mentioned articles in the Zeitschrift f. ph. Chemie. Thus, in the formation of these solutions there occurs sometimes expansion, sometimes contraction; for weak solutions (1 : 100) changes in volume may be entirely neglected at the accuracy of my experiments; for stronger solutions (5 : 100), such an expansion as $143.25 - 143.11 = 0.14$ cubic centimeters, or such a contraction as $143.01 - 142.72 = 0.29$ cubic centimeters, referred to the amounts with which I worked (from 3.5 to 10.7 cubic centimeters, on average 7 cubic centimeters), give changes in volumes of $0.14/20 = 0.007$ and $0.29/20 = 0.014$ cubic centimeters, which are perceptible in my experiments, for they are equal to a millimeter or more of the thin tube.

Of the most commonly used solvents, alcohol and ordinary ether, by their chemical character, are most suited to paraldehyde;*) and the data given above confirm the correctness of the assumption I made regarding the invariability of the volumes upon dissolution of the catalysts, when the latter are taken in small quantities, which is what I tried to do in most of my experiments. To those experiments in which more than the usual quantity of catalyst was taken (e.g. monochloroacetic acid—6.7%, oxalic acid—3.3%, trichloroacetic acid—3.0%) I attach the least importance; it was chiefly these experiments that also gave a large percentage for the aldehyde content at the moment of equilibrium (see the chapter “Analysis of the experimental data”).

The volume occupied by the catalyst is calculated from its weight and from those specific gravities which I was able to find in the literature; moreover, if I could not find the specific gravities of these catalysts for 50.5° or for nearby temperatures, I took data for ordinary temperature, again in view of the fact that the error from this is negligible when I use these catalysts in small quantities in comparison with the paraldehyde.

Further, if the catalysis proceeded so slowly that at its beginning the level remained unchanged for a long time, it was possible, from this level (and from the dilatometer measured in advance), to pass to the initial—before catalysis—volume of the paraldehyde and catalyst, even without knowing the weight of the paraldehyde and, consequently, also the volume occupied by it; and, subtracting the volume of the catalyst, I know the volume of the paraldehyde alone before the start of catalysis. Taking this latter volume as 100 and observing the level at equilibrium, and therefore knowing the expansion due to the catalysis, I compute this expansion for 100 volumes of the initial amount of pure paraldehyde.

For rapidly proceeding catalyses, however, when during the period of setting up the experiment and heating the dilatometer in the thermostat at 50.5° the catalysis already begins, it is necessary also to know the weight of the paraldehyde used, in order to calculate, from its specific gravity for 50.5° (adopted once and for all as 0.9583), its volume before the beginning of catalysis.

The catalysis of paraldehyde is accompanied by another reaction, which I shall simply call resinification; it proceeds incomparably more slowly than the first and is manifested in a diminution of volume. The very different rates of these two processes make it possible to observe the catalysis in almost complete purity, as is shown by an examination of the following details when various catalysts are used. If paraldehyde is kept for a long time at 50.5° with strong catalysts, for example SO₂, the contents of the dilatometer shrink very considerably, by far more than 8%, and turn into a black, viscous, resinous product having the characteristic odor of aldehyde resin, insoluble in water but soluble in alcohol.

*) Acetone would be still more suitable, but I have not found the corresponding data.

Detailed Description of the Experiments.

Phosphoric acid.

As catalyst, I used a syrupy solution of phosphoric acid containing 70.4% \( \mathrm{H_3PO_4} \). This catalyst gives, with paraldehyde, two non-mixing layers. This separation into 2 layers disappears when enough aldehyde has formed.

1) Dilatometer No. 5 contains 4.1818 grams of paraldehyde; the initial volume, from observations at \(50.5^\circ\), is of course equal to

\[ \frac{4.1818}{0.9583} = 4.364 \]

cubic centimeters.

0.116 gram of catalyst was taken (3 drops); its quantity was determined after the experiment by titration with KOH—phenolphthalein as indicator—of the entire contents of the dilatometer. Consequently, assigning the catalytic action to the \( \mathrm{H_3PO_4} \) molecule, in this experiment I have 1.9% catalyst (\( \mathrm{H_3PO_4} \)) relative to the quantity of paraldehyde taken.

The height (in millimeters) of the level above the lower mark changed with time as follows:

Time. . . .	1 h. 0 min.	1 min.	3 min.	10 min.	22½ min.	40 min.\(^{1}\)	54 min.
Level. . .	19.4	20	20.2	22.1	25.3	30	33.7
Time. . . .	3 h. 40 min.\(^{2}\)	4 h. 54 min.	5 h. 9 min.	30 min.	51 min.\(^{3}\)	9 h. 12 min. in.	9 h. 12 min. in.
Level. . .	53.0	57.0	58.6	59.3	60.0	62.5	62.5

On the following day

Time. . . . . . . .	9 h. 25 min.	11 h. 27 min.	12 h. 2 min.	52 min.	2 h. 0 min.	4 h. 28 min.
Level. . . . . . .	62.5	63.0	63.0	62.8	62.8	62.5

Here the experiment was stopped.

\(^{1}\) Two non-mixing layers are still visible, but there is no turbidity.

\(^{2}\) The separation into 2 layers has disappeared; the contents of the dilatometer are colorless.

\(^{3}\) The contents are still colorless.

The contents of this dilatometer, on the following day, even before 5 o’clock, were uniform and colorless. The volume, at equilibrium, of paraldehyde and catalyst \(= 4.300 + 63 \times 0.00813 = 4.8126\) cu. cm. The volume of the aqueous lower layer—the catalyst \(= 0.116/1.5155\) (where \(1.5155\) is the specific gravity of a \(70.4\%\) solution of phosphoric acid; see Mendeleev, Investigation of Aqueous Solutions by Specific Gravity, p. 362, 1887), i.e. \(0.0773\) cu. cm.; consequently, the initial total volume \(= 4.364 + 0.0773 = 4.4413\) cu. cm.; and therefore, upon attainment of equilibrium, the expansion \(= 4.8126 - 4.4413 = 0.3713\) cu. cm., or \(8.51\%\) of the initial volume of paraldehyde before catalysis.

For the specific gravity of a \(70.4\%\) solution of phosphoric acid I took the number \(1.5155\), given by Kohlrausch for a \(70.0\%\) solution at \(15^\circ\) Cels. In fact, one should have taken a somewhat smaller number; namely, first one should have increased \(1.5155\) in accordance with the content of \(\mathrm{H_3PO_4}\), greater by \(0.4\%\) than in Kohlrausch (but this correction is small; it changes the 3rd decimal), and then decreased it in accordance with the expansion from \(15^\circ\) to \(50.5^\circ\). I have not found data for the expansion of \(\mathrm{H_3PO_4}\) solutions; but if this expansion is taken as very close to the expansion of a sulfuric-acid solution of \(80.7\%\) \(\mathrm{H_2SO_4}\) (see the above-cited work of Mendeleev, p. 116), then for the specific gravity of the phosphoric acid one should take the number \(1.47\)—greater accuracy is, of course, not required. Then the initial volume \(= 4.364 + 0.079 = 4.443\); the expansion \(= 4.8126 - 4.443 = 0.3696\) cu. cm., or \(8.47\%\); the correction, as was to be expected, is negligible; it is quite possible that a greater error is introduced by omitting the unknown correction for the change of volume upon the complete merging of the 2 layers in the course of the reaction.

2) In the diary it is noted: “the most carefully arranged experiment.” Dilatometer No. 10 contained 1 drop of catalyst, or \(0.0302\) grams \(\mathrm{H_3PO_4}\) (determined by titration), i.e. \(0.043\) grams of a \(70.4\%\) solution of phosphoric acid, of volume \(0.029\) cu. cm. \((= 0.043/1.5)\). Paraldehyde was taken, \(5.580\) grams; consequently, its initial volume at \(50.5^\circ\) equals

\[ \frac{5.580}{0.9583}=5.822^{2}); \]

therefore the initial volume of the system at \(50.5^\circ = 5.822 + 0.029 = 5.851\) cu. cm. The height (in millimeters) of the level above the lower mark changed with time as follows:

\({}^{1})\) Dilatometer No. 5, upon reaching the limit, when the level at \(50.5^\circ\) was \(=63\) millimeters above the lower mark, was lowered for 20 minutes into a bath at \(17^\circ\); then it was again transferred into the thermostat at \(50.5^\circ\), and after 3–4 minutes showed a level of only 60 millimeters, i.e. weak conversion of aldehyde into paraldehyde also occurs at the ordinary (\(17^\circ\)) temperature.

\({}^{2})\) Consequently, the amount of catalyst \((\mathrm{H_3PO_4})\) in % is equal to

\[ \frac{0.302}{5.822}\times 100 = 0.52\%. \]

February 21.

Time . . . . .	1 h. 0 m.	1 min.	10 min.	22 min.	54 min.
Level . . . .	29.6	30.0	31.4	33.3	38.0
Time . . . . .	3 h. 42 m.	4 h. 40 m.	5 h. 30 m.	51 min.	9 h. 12 m.
Level . . . .	44.3	47.3	50.2	51.0	60.6

February 22.

Time . . . . .	9 h. 25 m.	11 h. 27 m.	12 h. 52 m.	4 h. 28 m.	5 h. 40 m.
Level . . . .	78.0	79.3	80.3	82.0	82.2

The contents of the dilatometer are colorless and homogeneous.

February 23.

Time . . . . .	9 h. 34 m.	10 h. 10 m.	1 h. 27 m.	4 h. 33 m.	5 h. 40 m.
Level . . . .	84.7	85.2	85.2	85.3	85.2

February 24, the level did not change (85.2).
26 ” ” = 85.0.

The position of the level at equilibrium is taken, of course, as 85.2 millimeters; the final volume of the system is

\[ 5.6164 + 85.2 \times 0.00832 = 6.3251 \]

cubic cent.; the expansion is

\[ 6.325 - 5.851 = 0.474 \]

cubic cent., or 8.10% of the initial volume of paraldehyde.

3) The two preceding experiments were calculated according to the weight of the paraldehyde initially taken; it is impossible here to calculate according to the initial volume, for the reaction proceeds sufficiently rapidly. The third experiment with the same catalyst could not be calculated in the same way as the 2 preceding ones: during the last operation, weighing, the dilatometer was broken; therefore, not knowing the weight of the paraldehyde, I could not calculate its initial volume before catalysis; but, relying on the first determination (dilat. No. 5), it is possible to assign this initial volume, thereby making, in all probability, the most negligible error. In this third experiment the largest amount of catalyst was taken, namely 0.123 gram of H₃PO₄ (determined by titration), or 0.175 gram of a 70.4% solution of phos-

phoric acid. The dilatometer was placed in a thermostat at \(50.5^\circ\) at 12 h. 55½ m. The levels above the lower mark (in millimeters) are as follows (dilat. No. 4):

21 February.

Time . . .	12 h. 58 m.	1 h. 0 m.	1 h. 1 m.	3 m.	10 m.	22½ m.	40 m.
Level . . .	20	20.7	21.0	21.6	23.2	26.5	31.0¹)
Time . . .	54 m.	3 h. 42 m.	4 h. 40 m.	5 h. 9 m.	30 m.	5 h. 51 m.	9 h. 12 m.
Level . . .	35.0	51.3²)	55.0	56.0	56.8	57.0	59.4
Time . . .	22 Feb. 9 h. 25 m.	22 Feb. 9 h. 25 m.	11 h. 27 m.	12 h. 2 m.	52 m.	2 h.	4 h. 28 m.
Level . . .	59.1³)	59.1³)	59.9	59.7	59.7	59.7	59.4

As the position of the level corresponding to the state of equilibrium I take 59.7 millimeters above the lower mark.

Dilatometer No. 5 (see experiment 1), which had stood in the thermostat for 4½ minutes (a time, according to preliminary experiments, quite sufficient for it to assume fully the temperature \(50.5^\circ\)), had a level of 19.4 millimeters above the lower mark; the volume of the system before the start of the reaction was 4.441 cubic centimeters. Discarding 4.300 cubic centimeters, i.e. the volume of the reservoir up to the lower mark, I obtain \(4.441 - 4.300 = 0.141\) cubic centimeters, or \(0.141 : 0.00813 = 17.35\) millimeters above the lower mark for the initial volume, if there had been no conversion into aldehyde at all (\(0.00813\) is, in cubic centimeters, the volume of 1 millimeter of the tube of dilatometer No. 5). Thus, by \((19.4 - 17.35) = 2.05\) millimeters the level rose during the time before the first reading, owing to the conversion of a certain amount of paraldehyde into aldehyde. Considering that at 12 hours 59 minutes dilatometer No. 4 (the reservoir consists of a thinner tube than in the other dilatometers) had already fully assumed the temperature of the thermostat, I take for the level the number

\[ \frac{20.0 + 20.7}{2} = 20.35, \]

and, introducing the correction, i.e. subtracting 2.05, I have 18.3 millimeters above the lower mark as the level before the start of the catalysis reaction. Then, since the reservoir up to the lower mark contains 502.7 millimeter

¹) All 2 non-mixing layers are still noticeable, but there is no browning or resinification.

²) The phosphoric-acid layer is weakly colored; the paraldehyde is colorless.

³) The lower layer is very weakly colored. If the contents of the dilatometer are stirred, this weak coloration disappears.

a segment of the thin tube, the volume of paraldehyde and of the aqueous lower layer—phosphoric acid—up to the start of catalysis is \(502.7 + 18.3 = 527.0\) millimeter segments; and subtracting the volume occupied by the phosphoric acid—

\[ 16.2 \text{ in the same units } \left(\frac{0.175}{1.47 \times 0.00735} = 16.2\right) \]

—I have \(504.8\) for the volume of paraldehyde before the start of the reaction; the expansion upon reaching the limit is equal to \(59.7 - 18.3 = 41.4\) millimeter segments, or

\[ \frac{41.4}{504.2} \times 100 = 8.21\% \]

of the initial volume of paraldehyde.

Since the whole amount of paraldehyde taken is \(504.2 \times 0.00735 \times 0.9583\) (\(0.9583\) is the weight in grams of \(1\) cu. cm of paraldehyde at \(50.5^\circ\)) \(= 3.548\) grams, the catalyst, in the form of \(\mathrm{H_3PO_4}\), was taken in the amount

\[ \frac{0.123}{3.548} \times 100 = 3.5\% \]

of the amount of paraldehyde taken.

Without introducing such a correction for determining the initial volume, assuming that at 12 h. 58 m. catalysis had not yet begun, I would have obtained that \((502.7 + 20 - 16.2)\) volume units of paraldehyde, by the end of catalysis, expanded by \((59.7 - 20)\) volume units, which in percent is equal to \(7.84\)—a number clearly too small. The correction of the initial volume in the third experiment by \(2.05\) volume units, made under the assumption of equality of the reaction rates both in the first and in the third experiment, is therefore already close to the truth, since the initial volumes of paraldehyde in these two experiments are very close to one another: in the first, \(538\), and in the third, \(507\); the amount of catalyst, although different, cannot, given the heterogeneity of the system and the insolubility of the catalyst in paraldehyde, have a strong influence on the small magnitude of this initial expansion.

Oxalic acid.

1) Crystals of dihydrate oxalic acid were taken in an amount of \(3.3\%\) relative to the weight of the paraldehyde, namely \(3.440\) grams of paraldehyde, and \(0.120\) gram of oxalic acid \((\mathrm{C_2O_4H_2} + 2\,\mathrm{H_2O})\) by titration. Catalysis, even with this comparatively large amount of catalyst, proceeds slowly; namely, the height of the level above the lower mark (in millimeters) changed as follows:

Time . . . .	12 h. 20 m.	37 m.	1 h. 40 m.	4 h. 50 m.
Level . . . .	15	15.5	15.8	15.8

	13 December	13 December	14 December	14 December
Time . . . .	9 h. 25 m.	12 h. 10 m.	9 h. 40 m.	2 h. 15 m.
Level. . . .	19.0	20.0	31.3	36.0
	14 December	14 December	15 December	15 December
Time . . . .	5 h. 30 m.	9 h. 37 m.	3 h. 10 m.	5 h. 20 m.
Level. . . .	40.0	55.0	56.8	57.3
	16 December	16 December	17 December	18 December
Time . . . .	9 h. 28 m.	2 h. 20 m.
Level . . . .	59.4	59.4	—	59.4

The limit is evidently reached after 4 days.

The rate of catalysis clearly increases as the oxalic-acid crystals dissolve; only on 15 December did complete dissolution of these crystals occur, and the rate of the reaction on that day, despite its proximity to the limit, considerably exceeds the rate at the beginning of the reaction, i.e. on the 12th.

A similar phenomenon, also observed with sudan (see below), may perhaps represent an example of “chemical induction”*); but since in both cases we are dealing with heterogeneous systems, would it not be more correct to ascribe this slowness of expansion at the beginning of catalysis to the so familiar difference in the rate of action of the masses of the dissolved substance and of the solid phase, especially since, in the absence of motion, the catalysts, dissolving, diffuse upward from the bottom of the dilatometer only very slowly?

The maximum expansion is \(44.4\) millimeters, or \(44.4 \times 0.00704\) cubic cm. (\(0.00704\) is the volume, in cubic cm., of 1 millimeter of the narrow tube of dilatometer No. 2; see above for the dimensions of the dilatometers). Taking, at \(50.5^\circ\), the specific gravity of the oxalic acid used \((\mathrm{C}_2\mathrm{O}_4\mathrm{H}_2 + 2\mathrm{H}_2\mathrm{O})\) as 1.60 (see Chem. Handw. Fehling), I find that 100 volumes of paraldehyde expanded by 8.66 volumes, if the calculation is made according to the initial volume (level at 15.0 mm), subtracting the volume occupied by the oxalic acid. By the weight of the paraldehyde (3.44 g), converting into volumes, I have for the same expansion 8.73; or, on average, 8.70.

If the dilatometer used in this experiment, after the limit has been reached (level 59.4), is placed in ice water for 5 minutes and then again in a thermostat at \(50.5^\circ\), then after \(2^{1}/_{2}\) minutes the former level is reached: 59.5.

*) See Cohen, Studien z. Chem. Dynamik 95, 1896.

When, however, it had stood in room-temperature water for 21 minutes and was then transferred again into the thermostat at \(50.5^\circ\), the height of the level was

after 2 minutes from immersion			. . . .	59.0
after 3 minutes from immersion			. . . .	59.0
after \(6\frac{1}{4}\) minutes from immersion			. . . .	59.0

i.e. the conversion of the aldehyde into paraldehyde over these 21 min. is negligible. But after this solution had stood for 4 days at room temperature, paraldehyde is, of course, already formed in appreciable quantities: after transferring this dilatometer into the thermostat and warming it sufficiently, it at once gave a level of only 35 millimeters, and only after several days—again 59.5 millimeters, as a maximum unchanged over several days. No browning (resinification) of the contents was observed.

2) Of crystalline dihydrate of oxalic acid, \(0.58\%\) of paraldehyde was taken (in the following, 3.470 grams were taken). The heights of the levels (in millimeters) above the lower line are as follows:

Time . .	Jan. 19	20	22	23	24	25	26	29
Level .	12	20	28	31	32.5	35	36.5	40.5
Time . .	Jan. 31	Feb. 1	2	6	7	8	9	10
Level .	42	43	44.2	46.3	47.0	47.1	47.8	48
Time . .	Feb. 12	14	15	16	17	19	21	24
Level .	49.0	49	49.5	50	50	50.8	50.4	50.8

Throughout the entire time there was complete colorlessness of the dilatometer contents; the volume of the system at the beginning was

\[ \frac{3.47}{0.9583} + \text{the volume of the oxalic acid;} \]

for the final volume one should take

\[ 3.563 + 0.00706 \times 50.8 \]

(dilatometer No. 2); whence the expansion is calculated as equal to \(7.90\%\) of the initial volume of paraldehyde. Calculation from the initial level is impossible here, for the dilatometer prepared for the experiment had stood before immersion in the thermostat on January 19 for 3–4 days at room temperature, and during this period a certain amount of aldehyde, though small, had formed. (Indeed, taking 12 millimeters as the initial level, we have for the expansion only \(7.60\%\).) In view of the very slow rate of catalysis toward the end, the experiment ought to have been continued somewhat longer.

3) Oxalic acid was taken, dehydrated by heating on a water bath and by prolonged standing in a desiccator over \(H_2SO_4\). Its amount is equal to 0.52% of paraldehyde (diagram No. 9). The levels (in millimeters) above the lower mark are as follows:

	22 February	22 February	22 February	23 February
Time	11 h. 8 min.	12 h. 2 min.	5 h. 40 min.	from morning to 5 h. 40 min.
Level	26	26.1	26.1	31–34.5
Time	1 March	6 March	12 March	14 March
Level	76.8–77.7	86.6	91.0	91.8
Time	15 March	16 March	17 March	28 March
Level	92	92	92	92

The catalysis reached its limit on the 21st day, and then, for 14 days, the level remained unchanged; the contents of the dilatometer remained constantly colorless. The expansion can here quite possibly be calculated from the initial volume and gave 8.27%, for the reservoir up to the lower mark contains 774.4 millimeter divisions of the thin tube; therefore the initial volume of paraldehyde is \(774.4 + 26 - 2.6 = 797.8\), where 2.6 is the number of divisions (segments) occupied by the weighed amount (0.0335 gram) of oxalic acid

\[ \left(2.6=\frac{0.0335}{1.5 \times 0.00844}\right), \]

since the specific gravity of anhydrous oxalic acid at \(50.5^\circ\) was taken as 1.5, and the volume of 1 millimeter segment is \(0.00844\) cubic centimeters. The expansion is therefore

\[ =92-26=66\ \text{segments, which amounts to}\ \frac{66}{797.8}\times 100=8.27\%. \]

On 28 March this dilatometer was transferred to a thermostat at \(35.2^\circ\). The level was not observed immediately; approximately after 10 min. the level was \(72.8\) mm above the lower mark; this was in the morning, and also at 5 h. 40 min.; then the level fell as follows:

	28 Mar.	29	30	31	2 Apr.	4 Apr.
Time	28 Mar.	29	30	31	2 Apr.	4 Apr.
Level	72.8	68.5	65.5	63	58.5	55.1

Time . . . . . . . .	Apr. 24	May 1	May 9	May 16	May 22	June 1
Level . . . . . . .	42.5	41.3	41.0	40.6	40.7	40.8

Probably, on June 1 the dilatometer was taken out of the thermostat. The calculation of how much, at \(35.2^\circ\), upon reaching the limit of catalysis, 100 volumes of paraldehyde expand was carried out as follows. At \(25^\circ\), the reservoir up to the lower mark of dilatometer No. 9 has, when measured with water, a volume \(= 6.5396\) cubic cm, and 1 millimeter of the narrow tube has a capacity of \(0.00844\) cubic cm. Taking the coefficient of expansion of glass as \(0.000025\), we have:

The final volume at \(35.2^\circ\) of paraldehyde and oxalic acid is equal to
\[ [40.7 \times 0.00844 + 6.5396][1 + 0.000025(35.2 - 25)] = 6.885 \text{ cubic cm.} \]

The initial volume of paraldehyde + oxalic acid before catalysis at \(50.5^\circ\) is equal to
\[ [26 \times 0.00844 + 6.5396][1 + 0.000025(50.5 - 25)] = 6.764 \text{ cubic cm.} \]

Consequently, at \(35.2^\circ\) the same initial volume will be
\[ 6.684 = \frac{6.764 \times 0.9583}{0.9699}, \]
where \(0.9583\) and \(0.9699\) are the values of the specific gravities of pure paraldehyde at \(50.5^\circ\) and \(35.2^\circ\). Of course, one ought to take the specific gravities allowing in the calculation for the small amount \((0.52\%)\) of dissolved oxalic acid, but the influence of this small impurity affects almost equally, and very little, both the numerator \(0.9583\) and the denominator, and it can therefore be neglected. Consequently, the expansion due to catalysis at \(35.2^\circ\) is
\[ 6.885 - 6.684 = 0.201 \text{ cubic cm.} \]

The initial volume of pure paraldehyde, after subtracting the volume of the oxalic acid, is expressed as
\[ 6.684 - \frac{0.0335}{1.5} = 6.662 \text{ cubic cm.}; \]
therefore the sought expansion due to catalysis at \(35.2^\circ\) is equal to
\[ \frac{0.201}{6.662} \times 100 = \]
\[ = 3.02\%. \]

This expansion leads to the following composition of the liquid phase at the moment of equilibrium, if only it is assumed that the volumes of mixtures of aldehyde and paraldehyde may be calculated from the specific volumes of the components according to the rule of mixing. The ratio of the latter to one another, being equal to the inverse ratio of their specific gravities, is \(1 : 1.276\) (see the chapters on aldehyde and paraldehyde). Therefore the conversion of \(1\%\) of paraldehyde into aldehyde entails an increase of 100 volume units by 0.276 volume unit; whence it follows that the expansion found \((3.02\%)\) corresponds to the conversion of \(10.94\%\) of paraldehyde into aldehyde. A somewhat different, though quite close, result is obtained from the assumption of proportionality between the expansion and the amount of aldehyde formed from paraldehyde; namely, since an expansion equal to \(8.20\%\) of the initial volume of paraldehyde,

corresponds to an aldehyde content of 33.9% in the mixture (see below), then the dilution found (3.02%) indicates a 12.48% conversion of paraldehyde at \(35.2^\circ\) at the moment equilibrium was attained, for

\[ 8.2 : 3.02 = 33.9 : 12.47 \]

The last number (12.47) is more accurate than the first (10.94), for it was obtained under an identical assumption—true only approximately—of the applicability of the rule of mixtures, but over a considerably narrower interval.

Boric anhydride.

To characterize the action of paraldehyde on \(B_2O_3\) at ordinary temperature, paraldehyde was taken which melted at \(12.2^\circ\) and had the specific gravity

\[ S\frac{15^\circ}{4^\circ} = 0.99833, \]

and it was left at room temperature over pieces of \(B_2O_3\) for 2 days. After filtering it from the pieces of \(B_2O_3\), I obtained a filtrate which at once became turbid in air, and after some time gave a white crystalline precipitate. The specific gravity of this turbid paraldehyde was

\[ S\frac{15^\circ}{4^\circ} = 0.99887; \]

if, however, it was filtered from the white crystalline precipitate, then the specific gravity was

\[ S\frac{15^\circ}{4^\circ} = 0.99846, \]

i.e. almost the same as that of the original paraldehyde.

When paraldehyde melting at \(12.50^\circ\) was taken and allowed to stand for 4 days over \(B_2O_3\), it gave a turbid solution of specific gravity

\[ S\frac{25^\circ}{4^\circ} = 0.99888. \]

It is clear that the interaction between these 2 substances over the course of 2 and even 4 days is very weak.

This turbid solution of paraldehyde, upon addition of a solution of KOH and evaporation to dryness, gave with HCl a clear reaction of \(B(OH)_3\) on turmeric.

In order to test whether aldehyde had formed within 4 days, even if in small quantities, I mixed such a filtered turbid solution with KOH (solid), added a little water, and even on heating did not obtain any noticeable yellow-brown coloration.\(^{1}\) Aldehyde added to the same test tube in small quantities immediately produced, at ordinary temperature, abundant formation of aldehyde, brown resin, and heating of the liquid. Consequently, at room temperature the formation in 4 days of aldehyde from paraldehyde + \(B_2O_3\), if it occurs at all, is in very negligible quantities. Likewise the action at

\(^{1}\) One of the reactions for aldehydes; see Beilstein, Vol. I.

ordinary temperature, $B_2O_3$ gave, with aldehyde boiling at $22^\circ$, if it gave anything at all, only small quantities of paraldehyde; for such an aldehyde, after standing for 4 days in a sealed tube over pieces of $B_2O_3$, poured off from the $B_2O_3$, very quickly and almost completely volatilized in the air, leaving a film of a boron compound, evidently dissolved in this mixture of aldehyde (and paraldehyde), and had the clearest odor of aldehyde.

Thus $B_2O_3$ is capable either of dissolving without change in a mixture of paraldehyde with aldehyde, or, on dissolving, of forming some compound. I did not investigate this question further.

1) The powder of $B_2O_3$, not sufficiently fine, was taken in a considerable quantity, much more than 3% of the weight of the paraldehyde.

The levels (in millimeters) are as follows (the scale is reversed):

	13 December	13 December	14 December	14 December	14 December	15 December
Time . .	12 h. 22 m.	5 h. 50 m.	9 h. 40 m.	2 h. 15 m.	5 h. 30 m.	9 h. 37 m.
Level . .	98	93	71	65	65	55
Time . .	15 December	15 December	15 December	16 December	16 December	18 December
Time . .	3 h. 10 m.	5 h. 20 m.	9 h. 28 m.	2 h. 20 m.	2 h. 20 m.	9 h. 20 m.
Level . .	51	48	43	39	39	46

The volume before the beginning of catalysis (level 98) is not reliable: a certain quantity of aldehyde may have formed, and therefore the volume may be larger than the true one, for before immersing the dilatometer in the thermostat I slightly heated its reservoir in order to drive out the air bubbles lodged between the pieces of $B_2O_3$. Further, on the 17th of December no reading was taken, and on the 18th a considerable contraction was already observed, accompanied by vigorous bubbling of the contents at the bottom of the reservoir, where the pieces of $B_2O_3$ lay; consequently, the maximum volume, if it is taken as 39, has been established unreliably; it is possible that the level at equilibrium is higher. These two causes, acting in one and the same direction, lead only to the conclusion that the expansion must in any case be not less than 6.72 vol. per 100 vol. of the original paraldehyde. For such a calculation I, after cooling the dilatometer, poured off the liquid and, leaving the pieces of $B_2O_3$, washed several times with ether, dried, and measured with mercury the volume of the dilatometer free from the pieces of $B_2O_3$. With such a method an error is very probable; in view of the previously proven dissolution of $B_2O_3$ in paraldehyde, the volume of the remaining space not occupied by it, which I take in the calculation as the volume of pure paraldehyde, comes out somewhat too large, i.e., this error (if

only it is significant) acts in the same direction as the first two, giving a small number for the limiting expansion.

2) In the second experiment (dilatometer No. 5) the height (in millimeters) of the level of the liquid phase above the lower mark changed as follows:

	16 January	16 January	16 January	16 January
Time . .	12 h. 40 m.	43 min.	57 min.	1 h. 14 m.
Level . .	7.5¹)	8.2	9.2	10
	16 January	16 January	17 January	18 January
Time . .	3 h. 51 m.	5 h. 38 m.	2 h. 46 m.	from 10 h. to 5 h.
Level . .	13.2	15.8	30.5	38—40

19 January from 9½ h. to 5 h. (42—44.7)
20 ” ” 9½ h. to 12½ h. (46.5—46.0)
22 ” 49.0
23 ” 49.0
24 ” from 10 h. to 3½ h. (48.8—48.9); there is no resinification.
25 ” at 9 h. 37 min.—47.0; clear resinification at the bottom of the reservoir, where pieces of \(\mathrm{B_2O_3}\) lie; for this reason the experiment was ended.

The true weight (corrected for buoyancy) of the paraldehyde taken is \(4.084\) grams; its volume at \(50.5^\circ\) is

\[ \frac{4.084}{0.9583}=4.262\ \text{c. c.} \]

Having forgotten to determine the weight of \(\mathrm{B_2O_3}\) directly, by weighing, I can calculate it on the basis of the following data. Before immersion in the \(50.5^\circ\) thermostat, this dilatometer was kept for five minutes in a \(35.2^\circ\) thermostat, at which temperature I found the initial volume of the whole system to be \(4.276\) cubic centimeters (it should be assumed that at \(35.2^\circ\) in five minutes no appreciable formation of aldehyde occurred). For the volume of one paraldehyde at \(35.2^\circ\) I calculate \(4.211\) cubic centimeters

\[ \left(=\frac{4.084}{0.9699}\right), \]

according to the specific gravity of paraldehyde at this temperature. Consequently, at \(35.2^\circ\) the volume occupied by \(\mathrm{B_2O_3}\) was \(4.276-4.211 = 0.065\) cubic centimeters. Assuming, with an error that can perhaps be neglected, that at \(50.5^\circ\) the volume of \(\mathrm{B_2O_3}\) is the same—\(0.065\) cubic centimeters—I have for the initial volume of the system at \(50.5^\circ\)

\[ 4.262+0.065=4.327 \]

cubic centimeters; and for the final volume—

\[ 4.300+49\times0.00813=4.6982 \]

(the volume of the reservoir up to the lower mark + the volume in the thin tube upon reaching—

¹) The initial level—some readings not given here—showed small fluctuations.

or equilibrium). Consequently, the expansion \(=4.6983-4.327=0.3713\) cubic centimeters, which amounts to \(8.71\%\) of the initial volume of paraldehyde (4.262).

Another method of calculation, assuming the level before catalysis to be 7.5 millimeters above the lower mark, gives a considerably smaller number for the limiting expansion.

Namely, since the reservoir up to the lower mark contains 528.5 millimeter sections of the thin tube, and the volume of one such section \(=0.00813\) cubic centimeters, the initial volume of one paraldehyde in these units is

\[ 528.5+7.5-\frac{0.065}{0.00813}=528, \]

and the expansion \(=49-7.5=41.5\), which in percent gives 7.86. Small numbers, as in other cases, are obtained when, during the heating of the dilatometer, catalysis has already managed to begin, which may be suspected in this case; moreover, this latter calculation, by initial volume, is also unreliable because, as was said in the note on the preceding page, the initial level (7.5) gave small fluctuations. But the first method of calculation, by the weight of the paraldehyde, which gave a undoubtedly larger number (8.71%) for the desired expansion, in view of the weighing of the catalyst not being determined directly, has no special advantages over the second method; therefore, for the desired expansion I take the mean, 8.28, without assigning this experiment to the category of exact ones.

Taking for the specific gravity of \(\mathrm{B_2O_3}\) the number 1.75 (see Dammer, Handbuch. d. anorgan. Ch.), I have its weight equal to \(0.065\times1.75=0.114\) gram, i.e. \(2.7\%\) of the weight of the paraldehyde.

3) \(\mathrm{B_2O_3}\) was taken in the amount of \(0.59\%\) of the weight of the paraldehyde. The levels (in millimeters) above the lower mark were as follows:

Time . . .	16 January. 12 h. 26 m.	16 January. 29 min.	16 January. 43 min.	16 January. 5 h. 37 m.	17 Jan.
Level . . .	23.8	23.9	23.8	26	32.5
Time . . .	18 Jan.	19	20	22	23
Level . . .	40.5	47	51	59	61
Time . . .	24 Jan.	25	26	27	29
Level . . .	63.3	65	67	68	70

Time . . .	31 Jan.	1 Feb.	2	6	7
Level . . .	71.8	72.8	73.8	76.2	76.9
Time . . .	8 Feb.	9	12	14	17
Level . . .	77.1	77.5	78.9	79.2	80
Time . . .	22 Feb.	24	14 March	19	28
Level . . .	82	82	83.3	83.1	82
Time . . .	24 April	24 April	25	31 July	31 July
Level . . .	78.5	78.5	78.5	71.7	71.7

During the whole time, from January 16 to July 31, this dilatometer stood in a thermostat at \(50.5^\circ\); the solution was not colored. \(B_2O_3\) passed entirely into the solution; from this I conclude that at \(50.5^\circ\) 100 grams of paraldehyde are capable of dissolving at least 0.59 grams of \(B_2O_3\).

Calculating from the initial volume (level at 23.8) and taking for the maximum expansion the volume corresponding to the level 83.3, I find for the expansion at equilibrium only 6.02, which is considerably lower than the other numbers obtained; I postpone the explanation of this to the end of this chapter.

Sulfurous acid.

At the same time three experiments with \(SO_2\) were set up. Weighed dilatometers were filled with paraldehyde, through which several bubbles of sulfurous gas were then passed, the gas being obtained by heating sulfuric acid with copper turnings. After the catalysis was finished, the filled dilatometers were weighed, which gave the weight of one paraldehyde, for the calculation of its volume, since I neglect the small amount of \(SO_2\) (see below).

Catalysis begins already at ordinary temperature: these three dilatometers, placed in a thermostat at \(16.8^\circ\), gave the following levels in millimeters above the lower mark:

Time	Dilatometer No. 6	No. 4	No. 10
	Level	Level	Level
2 h. 0 m.	1	3	1.0
2 h. 13 m.	2	5	1.5
3 h. 45 m.	7	8	6.5

Then these dilatometers (their contents having remained colorless) were transferred at 3 h. 47 1/2 min. to a thermostat at 50.5°. The heights of the levels were as follows:

Time	No. 6	No. 4	No. 10
3 h. 50 1/2 min.	53	44	38.5
3 h. 53 min.	67	56.2	45.2
3 h. 56 min.	77	62.1	53.9
3 h. 59 min.	80.8	63.3	62.1
4 h. 1 1/2 min.	82.0	63.3	68.3
4 h. 4 min.	83.0	63.5	73
4 h. 7 1/2 min.	83.5	”	78
4 h. 10 1/2 min.	”	”	80.8
4 h. 14 1/2 min.	”	”	82.3
4 h. 19 1/2 min.	”	62.8	83.8
4 h. 24 1/2 min.	”	63.1	84.1
4 h. 29 1/2 min.	”	63.3	84.3
4 h. 34 1/2 min.	”	63.3	84.3
4 h. 44 1/2 min.	83.0	62.8	84.3
5 h. 0 min.	”	”	83.8
5 h. 26 min.	”	”	84.3

On the following day (the dilatometers having been left in the thermostat) the levels fell, owing to resinification,

to | 72 | 54 | 78 millimeters.

In this case the resinification catalyst appears in the form of separate brown droplets, not coalescing into one and accumulating, evidently because of their weight, in the lower part of the dilatometer reservoir.

The amount of sulfur dioxide was determined by discharging the contents of the dilatometer into a titrated iodine solution \((1/100\) molecule of \(I_2\) per liter) and titrating with \(Na_2S_2O_3\); in this way it was found that in the dilatometers there had been sulfur dioxide gas:

No. 6	No. 4	No. 10
0.068	0.079	0.002,

taking as 100 the amount of paraldehyde in the same dilatometers¹. The aldehyde formed during catalysis does not react with iodine, eliminating its action on \(Na_2S_2O_3\), for I found the least iodine in dilat. No. 10, and the greatest amount of iodine in dilat. No. 4, whereas the amounts of aldehyde in these dilatometers were, precisely, in the inverse ratio.

Knowing the weight and volume of the liquid phase, I could easily determine also its specific gravity at the moment equilibrium, preceding catalysis, set in. It turned out that

in dilatometer No. 10 the liquid phase had sp. gr. $S\frac{50.5^\circ}{4^\circ}=0.8858$

"	No. 4	" $=0.8856$
"	No. 6	" $=0.8845$

The volume increases were calculated from the following data, of course by the weight of paraldehyde, since catalysis proceeds rapidly.

All the paraldehyde samples, corrected for vacuum, were

	in dilatometer No. 6	No. 4	No. 10
	5.005	3.6862	5.5966 grams
The following initial volumes, before catalysis, (dividing by 0.9583)	5.223	3.8465	5.8403 cc
and the final ones, at maximum levels 83.5—63.3—84.3 mm,	5.6585	4.1619	6.3183 cc
The expansions are equal to	0.4355	0.3154	0.4780 cc
or, as percentages of the original volume of paraldehyde	8.34	8.20	8.19

The volumes of air remaining during sealing in the thin tubes of these dilatometers, because of the thermal and catalytic expansion of the liquid phase, decreased so much that the pressures from atmospheric rose in the dilatometers

No. 6	to 2.00	atmospheres.
No. 4	" 1.53	"
No. 10	" 1.66	"

Such differences in pressures do not affect the results of my experiments, as I mentioned in the article on the method; otherwise, in the experiment with dilatometer No. 6 I ought to have obtained the smallest expansion, according to the Le Chatelier rule (see Bancroft, the phase rule, p. 4), instead of obtaining the greatest.

The considerable expansion experienced by paraldehyde under the influence of $SO_2$ and at the ordinary temperature ($16.8^\circ$) confirms once more the fact that at this temperature as well, equilibrium between these substances is established at a definite aldehyde content, the concept of which is given by the following calculation. Since the sp. gr. of paraldehyde is $S\frac{16.8^\circ}{4^\circ}=0.9963$, then the correspondingly taken quantities of paraldehyde

	in dilatometers	No. 6	No. 4	No. 10
in grams		5.005	3.6862	5.5966
and before the beginning of catalysis the volumes (dividing by 0.9963)	in cu. cm	5.024	3.700	5.617;

and, upon reaching at 3 h. 45 min., the levels (above the lower mark), in millimeters,

	7	8	6.5,
the final volumes are expressed in cubic centimeters
through	5.097	3.7541	5.667;
whence the expansions will be
in cubic centimeters	0.073	0.054	0.050,
or as percentages of the initial volumes of paraldehyde
	1.45	1.46	0.89

Since the ratio of the specific volumes of paraldehyde and aldehyde at 16.8° is \(1 : 1.270\) (I took the specific gravity at 18°, which of course introduces no appreciable error), then, calculating by the rule of mixtures (as above, with oxalic acid), I find that each 1% of paraldehyde converted into aldehyde causes an increase in volume of 0.27%; consequently, the above-mentioned percentage increases in volume indicate the following aldehyde contents (in percent by weight)

5.4	5.4	3.3

Numbers very close to these are obtained by calculation from the proportions

\[ 8.2 : 1.45\ (\text{or } 1.46,\ \text{or } 0.89) = 33.9 : X, \]

where \(X\) is the percentage, by weight, of aldehyde corresponding to the above-written expansions (see above, with oxalic acid); namely

6.0	6.0	3.7.

Thus, the equilibrium system of aldehyde and paraldehyde at 16.8° contains at least 6% aldehyde (by weight); it is unknown whether the limit of catalysis was reached in dilatometers No. 6 and No. 4; in dilatometer No. 10, however, because of the very small quantity of catalyst and the consequent very low rate of catalysis, equilibrium had evidently not yet been reached.

Zinc sulfate.

As catalyst I took zinc sulfate, dehydrated by heating the heptahydrate at as low a temperature as possible; the catalyst contained no chlorine whatsoever. Its quantity was \(0.1145\) g, which corresponds to 2.7% of the weight of the paraldehyde. Upon reaching equilibrium, after opening the dilatometer, I filtered the liquid phase from \(ZnSO_4\); \(3 \tfrac{1}{4}\) cubic centimeters of this were collected. Having diluted it with 10 cubic centimeters of water, shaken it, and filtered it from the paraldehyde, I obtained in the filtrate no trace of zinc [test: \((NH_4)_2S + NH_4Cl\)]. Consequently, catalysis takes place only on the surface of the solid phase.

The rate of the reaction was as follows: after immersion of the dilatometer in the thermostat at 50.5°, at 11 h. 12½ min. the height of the level above the lower mark (in millimeters) changed as follows:

			March 8	March 8	March 8	March 8
Time . .	\(15\frac{1}{4}\) min.	21 min.	52 min.	12 h. 20 min.	1 h. 36 min.	5 h. 30 min.
Level . .	8.7	10	12.5	15	20.5	35
Time . .	March 9, 10 h. 23 min.	March 9, 5 h. 30 min.	Mar. 12	Mar. 14	Mar. 15	Mar. 16
Level . .	48.5	48.5	49	49	48.2	47.8

Catalysis, apparently, ended within twenty-four hours.

The true weight of one paraldehyde \(=4.1337\) grams; consequently, the volume before catalysis

\[ = \frac{4.1337}{0.9583} = 4.3137. \]

Taking the specific gravity of \(ZnSO_4 = 3.4\) (see Dammer, Handbuch d. anorgan. Chemie), I have for the volume of the whole system before catalysis

\[ 4.3137 + \frac{0.1145}{3.4} = 4.3477 \]

cubic centimeters. The final volume, corresponding to a level of 49 millimeters, is equal to 4.6983 cubic centimeters (dilatometer No. 5); whence the expansion is equal to 0.3506 cubic centimeters, which, as a percentage of the initial volume of paraldehyde, amounts to 8.13.

Since \(ZnSO_4\) is completely insoluble in the liquid phase, its specific gravity is easily calculated from the above data. It turned out that the specific gravity

\[ S\frac{50.5^\circ}{4^\circ} = 0.8862. \]

Calculating the expansion from the initial level (8.7) is inapplicable here: a small number is obtained (7.60), evidently owing to catalysis having already begun while the dilatometer was being heated.

This dilatometer was transferred on March 9 for 24 minutes into a bath at room temperature and then again into a thermostat at \(50.5^\circ\); then, after 3 minutes, the level rose to 46 millimeters, and soon to 46.4; consequently, the weak conversion of aldehyde into paraldehyde (corresponding to the difference of levels \(48.5—46.4\)) took place in 24 minutes.

Copper sulfate.

The catalyst was prepared by dehydrating the ordinary pentahydrate by careful heating with frequent stirring. Of the resulting dirty-white powder, 0.085 g was taken, i.e. 1.2% of the weight of paraldehyde (dilatometer No. 12).

When catalysis was finished, the dilatometer was opened, the liquid phase was filtered off from the solid; the resulting 6 cubic centimeters of liquid, on mixing with ordinary

with dilute (10%) ammonia spirit gave no trace of a blue coloration, but did give warming, accompanied by a distinct smell of aldehyde-ammonia. Although I did not test here more exact reactions for detecting traces of copper in the solution, nevertheless, by analogy with \(\mathrm{ZnSO_4}\), it is very probable here too to allow for the insolubility of \(\mathrm{CuSO_4}\) in the liquid phase and catalysis only on the surface of \(\mathrm{CuSO_4}\). The color of \(\mathrm{CuSO_4}\) did not change. In the course of 6 days the catalysis was almost completed (judging by the rate of the reaction—here not given—i.e. by the change in height of the level with time); but the liquid reached the little ball with which the narrow tube of this dilatometer ended; therefore the dilatometer had to be opened, part of the liquid removed, and the dilatometer sealed and weighed again. Then the height of the level (in millimeters) above the lower mark changed as follows:

Time . .	28 Feb.	1 Mar.	2 Mar.	3 Mar.	6 Mar.	7 Mar.
Level . .	87.0	87	87.8–89	89	90	90

On the 7th of March this dilatometer too was opened. It is very probable that the catalysis was not yet quite finished, and the expansion would have turned out to be somewhat greater (though, of course, very little) if the experiment had been continued.

The true weight of one paraldehyde \(= 6.805\) grams; consequently, its volume before the beginning of catalysis

\[ \frac{6.805}{0.9588} = 7.101, \]

and the volume of the whole system

\[ 7.101 + \frac{0.085}{3.5} = 7.125 \]

(according to Dammer, Handbuch, for the specific gravity of \(\mathrm{CuSO_4}\) I took 3.5). The final volume, corresponding to level 90, is calculated as 7.690 cubic cm; consequently, the expansion \(= 0.565\) cubic cm, or \(7.96\%\) of the initial volume of the paraldehyde.

The specific gravity of the liquid phase is calculated from the above data:

\[ S^{50.5^\circ}_{4^\circ} = \frac{6.805}{7.690-\frac{0.085}{3.5}} = 0.8877. \]

Sulfurous cadmium.

The catalyst was obtained from the aqueous salt by heating in a porcelain crucible at a fairly high temperature, close to dark-red heat. It was taken in the amount of \(2.3\%\) of the weight of paraldehyde. The height of the liquid level above the lower mark changed (in millimeters) as follows:

Time . .	March 8	9	12	14	19	22
Level . .	161	20	23	23	24.8	24
Time . .	March 23	28	Apr. 24	25	July 31	July 31
Level . .	23.3	23.5	24.5	25	27.2	27.2

The dilatometer stood the whole time (until July 31) in a thermostat at 50.5°; no coloration of the liquid phase, characterizing resinification, was observed. Calculation by the initial volume, corresponding to a level of 16 millimeters, gives, for the initial volume in millimeter sections of the thin tube,

\[ 674{,}8 + 16 - \frac{0{,}128}{4{,}72 \times 0{,}00832} = 687{,}6 \]

[674.8—the volume of the reservoir in the above-named units up to the lower mark; 0.00832—the volume, in cubic centimeters, of one millimeter section of the tube; 0.128 and 4.72—the quantity of CdSO₄ taken in grams and its specific gravity according to Danner].

The expansion, up to April 25, is equal to 9 (=25−16) in the same units, or \(9/687{,}6 \times 100 = 1.31\%\) of the initial volume of paraldehyde. Calculation by the weight of the paraldehyde leads to almost the same result (1.38).

The weight of one paraldehyde is 5.480 grams; the volume is

\[ \frac{5{,}480}{0{,}9583} = 5{,}719 \]

cu. cm. The volume before catalysis of the whole system is

\[ 5{,}719 + \frac{0{,}128}{4{,}72} = 5{,}746 \]

cu. cm.

Taking the expansion corresponding to a level of 25 millimeters above the lower mark, I have for the final volume 5.825 cu. cm.; for the expansion, therefore, 0.079, or

\[ \frac{0{,}079}{5{,}719} = 1.38\% \]

of the initial volume of paraldehyde.

Sublimate.

Franchimont (Recueil de trav. chimiques de Pays—Bas 1, 248) showed that HgBr₂ at 90° is capable of converting paraldehyde into aldehyde; the same was to be expected also for HgCl₂.² Indeed, distilling paraldehyde over HgCl₂ at ordinary pressure, we obtain aldehyde with the formation of only a small amount of resinous pro-

products; moreover, no gaseous products insoluble in water are obtained in this reaction, for, on passing the gas bubbles evolved in the above-mentioned distillation through an aqueous bath into a eudiometer filled with water, I did not observe any gas bubbles in the latter. On heating, $\mathrm{HgCl_2}$ dissolves in paraldehyde far better than at low temperature.

1) Dilat. No. 10 contained 0.159 grams of $\mathrm{HgCl_2}$ and 5.488 g of paraldehyde, i.e. 3% catalyst. The initial volume of paraldehyde (at $50.5^\circ$) was

\[ \frac{5.488}{0.9583}=5.727, \]

and the final volume, subtracting the volume occupied by $\mathrm{HgCl_2}$ (I take the specific gravity of $\mathrm{HgCl_2}=5.4$), was $6.2375-0.030$; consequently, the expansion in % is equal to 8.41. The height of the liquid level (in millimeters) above the lower mark changed as follows:

	25 January	25 January	25 January	25 January	25 January	25 January	25 January
Time	1 h 41 m	49 m	2 h 10 m	33 m	4 h 9 m	5 h 0 m	6 h 0 m
Level	17	17	17	17	17.3	18	19
	26 January	26 January	26 January	26 January	26 January	27 Jan.	29 Jan.
Time	9 h 55 m	12 h	50 m	3 h 49 m	5 h 30 m	12 h 49 m	9 h 45 m
Level	74.8	75	75	74.7	74.5	74.1	73.3

On 29 January traces of resinification were noticed; only an insignificant amount of $\mathrm{HgCl_2}$ had not dissolved.

2) Dilat. No. 9 contained 0.160 grams of $\mathrm{HgCl_2}$ and 6.341 grams of paraldehyde, i.e. 2.54% catalyst. The initial volume of paraldehyde (at $50.5^\circ$) was

\[ \frac{6.341}{0.9583}=6.617; \]

and the final volume was $7.194-0.030$ (subtracting, as above, the volume occupied by $\mathrm{HgCl_2}$); consequently, the expansion $=0.547$ c.c., or in % $=8.27$. The height of the level (in millimeters) above the lower mark changed during the experiment as follows:

	25 January	25 January	25 January	25 January	25 January	25 January	25 January
Time	1 h 41 m	49 m	2 h 10 m	2 h 33 m	4 h 7 m	5 h 0 m	6 h 0 m
Level	12.1	12.1	12.2	12.7	14.0	12	50.0¹)

¹) Evidently, between 4 h 7 m and 6 h there occurred a certain perturbation, probably rapid dissolution, formation of gas bubbles, etc.

	26 January	26 January	26 January	26 January	26 January	27 Jan.	29 Jan.
Time . .	9 h. 55 m.	12 h.	50 m.	3 h. 49 m.	5 h. 30 m.	12 h. 40 m.
Level . .	77.5	77	76.8	76.5	76.5	76.5	75.5

On January 29 almost all the sublimate dissolved; the tarring (coloration) left negligible traces.

3) Dilatometer No. 10 (the scale was covered with resin) contained 0.261 gram of $\mathrm{HgCl}_2$ and 5.500 grams of paraldehyde, i.e. 4.75% catalyst. The height of the level above the lower mark (in millimeters) changed as follows: (January 11)

Time . . .	10 h. 32 m.	36 min.	48 min.	11 h.	12 h. 8 m.
Level . . .	32.0	32	32	32	32
Time . . .	39 min.	59 min.	1 h. 27 m.	53 min.	3 h. 25 m.
Level . . .	32	32.1	32.1	32.2	33.7
Time . . .	4 h. 20 m.	4 h. 46 m.	5 h. 42 m.	12 January, 9 h. 53 m.	12 January, 11 h. 21 m.
Level . . .	34.5	35.0	36.0	90.2	89.5
Time . . .	12 January, 2 h. 19 m.	12 January, 3 h. 56 m.	12 January, 5 h. 41 m.	13 Jan.	15 Jan.
Level . . .	89.5	90.0	90	89.0	88.2

On this day, January 15, traces of tarring were already observed—a brownish coloration.

Since the reservoir, up to the lower mark of the narrow tube, contains 674.8 millimeters of sections of the latter, the volume at the beginning of the experiment, excluding the volume of the sublimate, was

\[ =674.8+32-\frac{0.261}{5.4\times 0.00832}=700.8 \]

(see the dimensions of the dilatometers above), and the expansion was $58.2=90.2-32.0$ of the same units; hence the expansion in % $=8.31$. Apparently, at the beginning the reaction seems to lie dormant for some time, since during (10 h. 32 m.—1 h. 27 m.), almost 3 hours, a negligible change in the level, within the limits of observational error, is observed.

4) From this experiment, in view of the fact that the entire catalyst was not determined, but only its trace, and its volume, it could only be concluded that the expansion was greater than 7.71%.

Using selenium as the catalyst, I made observations also at two temperatures below 50.5°. Namely, at 35.2° I observed that 100 volumes of the initially taken quantity of paraldehyde expand, on reaching the limit of catalysis, by 3.42 volumes, while at 25.3° the same expansion is only 2.62 volumes. I do not give the details of these last two experiments, since I do not consider them sufficiently accurate (with such a small percentage of expansion, more precise dilatometers should have been used); I give these numbers only as a guide for future investigations—on the temperature coefficient of the reversible reaction studied here.

Zinc chloride.

1) Dilat. No. 4. The scale is covered with mica. Paraldehyde taken: 3.617 grams; its initial volume at 50.5° was

\[ \frac{3.617}{0.9583}=3.7745 \]

cubic cent. Catalyst—powdered, anhydrous zinc chloride—taken: 0.0175 g, or 0.48% of the weight of the paraldehyde. The greatest height of the level is observed after approximately 3 hours, namely (divisions arbitrary, lower mark at zero):

	16 January	16 January	16 January	16 January	16 January
Time . . .	1 h. 11 m.	14 min.	21½ min.	48 min.	2 h. 3 m.
Level . . .	28	39	56	80	83.5
Time . . .	3 h. 51 m.	4 h. 42 m.	5 h. 37 m.	17 January: 2 h. 46 m.	17 January: 2 h. 46 m.
Level . . .	86.0	87.0	86.9	86.9¹)	86.9¹)

Since 150 such arbitrary divisions occupy 95 millimeters, 87 divisions = 55 millimeters; whence the final volume is

\[ 3.6953+55\times0.00635=4.1005 \]

cubic cent. Taking the specific gravity of \(ZnCl_2\) as 2.75 (see Dammer, Handbuch d. anorgan. Chemie), I find for its volume 0.006 cubic cent.; whence the expansion at equilibrium will be

\[ 4.1005-0.006-3.7745=0.320 \]

cubic cent., which amounts to 8.48 percent of the initial volume of paraldehyde, before catalysis.

2) Dilat. No. 4. The scale is covered with a screw clamp. Catalyst taken: 0.080 g, i.e. 2.22% of the weight of the paraldehyde; paraldehyde, 3.602 grams;

¹) No settling is visible; complete dissolution of \(ZnCl_2\).

therefore, its initial volume is \(\dfrac{3.602}{0.9583}=3.759\) cubic cm. The final volume of the paraldehyde, excluding the volume of \(ZnCl_2\) \((=0.029\) cubic cm), is \(4.095-0.029=4.066\); therefore the expansion is \(4.066-3.759=0.307\) cubic cm, or \(8.17\%\). The height of the level (in millimeters) above the lower line varied as follows:

Time . . .	1 h. 37 m.	39 min.	43 min.	49 min.	2 h. 10 m.
Level . . .	39.9	43.0	46.2	50.4	54.4
Time . . .	33 min.	4 h. 7 m.	5 h. 0 m.	6 h. 0 m.	6 h. 0 m.
Level . . .	54.2	54.4	54.4	54.4	54.4

On the following day, from 10 o’clock to 5½ o’clock, the level remained unchanged at 54.1, and from the third day it already began slowly to fall.

3) The dilatometer, No. 6 (the scale was coated with resin), contained 0.061 grams of catalyst, i.e. \(1.23\%\) of the weight of paraldehyde; \(4.947\) grams of the latter were taken, i.e., in volume at \(50.5^\circ\),

\[ \frac{4.947}{0.9583}=5.162 \]

cubic cm. For the volume at the moment of equilibrium, subtracting the volume occupied by \(ZnCl_2\) (which had completely dissolved), I have \(5.633-0.022=5.611\) cubic cm; whence the expansion is \(0.449\) cubic cm, or \(8.70\%\). The height of the level varied as follows (in millimeters, above the lower line):

Time . . .	12 h. 53 m.	54 m.	57 m.	1 h. 11 m.	14 m.	21½ m.
Level . . .	31.2	35.5	47	71.8	74.3	77.0
Time . . .	48 min.	2 h. 3 m.	3 h. 51 m.	4 h. 42 m.	5 h. 37 m.	5 h. 37 m.
Level . . .	79.8	78.9	80.0	80.0	80.0	80.0

Although on the following day the level stood at 81 millim., I take (as a maximum) 80.0 at equilibrium, for with a reaction proceeding so rapidly, only as a result of the poor coating of the scale did I obtain a higher level on the following day. In fact, on the third day in the morning the level was \(83.3\), and when I set the scale correctly (at noon), \(78.0\).

4) Dilatometer No. 6. The scale is covered with a screw-type grease. Paraldehyde taken by weight: 4.917 grams; by volume at 50.5°:

\[ \frac{4.917}{0.9583}=5.131. \]

Catalyst—0.062 gram, i.e. 1.26%. The levels (in millimeters) above the lower mark were as follows:

Time . . .	1 h. 37 m.	39 min.	43 min.	49 min.	2 h. 10 m.
Level . . .	63	66	69	71.5	74.0
Time . . .	33 min.	4 h. 7 m.	5 h. 0 m.	6 h. 0 m.	6 h. 0 m.
Level . . .	74.4	74.3	74.2	74	74

On the following day, from 10 o’clock to 5½ o’clock, the level fluctuated within the limits 73.6–73.0 millimeters; on the third day it fell from 73 to 71 millimeters, and a distinctly clear browning of the paraldehyde was observed.

The final volume of paraldehyde at equilibrium is \(5.591-0.023=5.568\) cubic centimeters; the expansion is \(5.568-5.131=0.437\) cubic centimeters, or 8.56%.

The last experiments (the 3rd and 4th), in view of the difference obtained when dilatometer No. 6 was washed twice with water, I consider less reliable than experiment No. 2.

Cadmium chloride.

Dilatometer No. 11. Paraldehyde taken: 10.390 grams, i.e.

\[ \frac{10.39}{0.9583}=10.842 \]

cc at 50.5°. The catalyst used was commercial cadmium chloride (from Kahlbaum) in an amount of 3% (namely 0.304 gram) relative to the paraldehyde. The catalyst contained water, but I did not determine the quantity of the latter; for the specific gravity of the catalyst I took the number 3.625, given by Danner for anhydrous cadmium chloride. Neither in Danner nor elsewhere could I find the specific gravity of the dihydrate salt—\(\mathrm{CdCl_2+2H_2O}\).

The catalyst, even if it dissolves in the liquid phase, does so only slightly. During catalysis the levels (in millimeters) above the lower mark were as follows:

Time . . .	1 h. 37 m.	39 m.	43 m.	49 m.	2 h. 10 m.
Level . . .	93	102	107.0	110.9	111.9

Time . . .	33 min.	4 h. 7 min.	5 h. 0 min.	6 hours. ^1)
Level . . .	112	112	112	111

Having enlarged the scale of dependence.—The final volume, at equilibrium, is equal to 11.841−0.084 = 11.757 cubic cent. (where 0.084 cubic cent. is the volume occupied by CdCl₂); consequently, the expansion is equal to 11.757−10.842=0.915 cubic cent., or 8.44%. This latter number (8.44) for the sought expansion is, of course, higher than the true one, owing to the error made in calculating the volume occupied by the catalyst: for the specific gravity of the latter, as representing not anhydrous cadmium chloride but cadmium chloride containing water, one ought to take a number smaller than 3.625. The true number for the sought expansion will be either very close, or, in any case, not below 8.11, and for the following reasons. The commercial cadmium chloride taken by me here is, in all probability, the ordinary dihydrate—CdCl₂·2H₂O. Such a hydrate, according to Cohen’s determinations (Zeits. f. ph. Chemie 14, 71), has a transition temperature (Umwandlungstemperatur) at (approximately) 34°, above which, by the rule of indifference (Unverträglichkeit) of condensed systems, only CdCl₂H₂O and H₂O exist.

Assuming that the second molecule of water is also completely split off from CdCl₂ at the temperature of the experiment (50.5°), especially under the action of the large mass of the liquid phase (paraldehyde and aldehyde), or assuming that the hydrate CdCl₂·H₂O is formed without the appreciable change of volumes in my experiments from the anhydrous salt (specific gravity 3.625) and liquid water (all the more since, under the given conditions, such a hydrate may be strongly dissociated); further, that the water, having separated from the dihydrate, dissolves in the liquid phase without a change of volumes (which assumptions must be made for the minimum expansion, for, by the way, here the most probable has not been taken into account), I arrive at the following data: in this experiment 0.254 g of anhydrous CdCl₂ was taken, water was given off by it into the liquid phase 0.050 g; consequently, the volume of the catalyst is equal to

\[ \frac{0.254}{3.625}+0.050=0.120\ \text{cubic cent.}, \]

whence the expansion in this experiment amounts to only

\[ (11.841-0.120)-10.842=0.879\ \text{cubic cent.}, \]

which, as a percentage of the initial volume of paraldehyde, gives

\[ \frac{0.879}{10.842}\times 100=8.11. \]

^1) On the following day the level fell to 108.4 millimeters, and the CdCl₂ lying at the bottom turned brown.

Hydrochloric acid.

1) Dilatometer No. 5; as catalyst 1 drop of hydrochloric acid of specific gravity 1.12 was taken. Titrating, after the end of the experiment, the contents of the dilatometer, I found a content of HCl = 0.0056 grams HCl, or 0.0224 grams of hydrochloric acid of the indicated strength (assuming that hydrochloric acid of specific gravity 1.12 contains 25% by weight HCl, see Landolt–Börnstein tables), and by volume to have, consequently,

\[ \frac{0.0224}{1.12}=0.020 \]

cubic cm of HCl solution. Paraldehyde was taken in parallel: 4.174 grams, or 4.356 cubic cm \(\left(\frac{4.174}{0.9583}\right)\) at 50.5°. The dissolution of the added drop of catalyst, it appears, occurred immediately and completely. The levels (in millimeters) above the lower mark are as follows: (March 19).

Time . . .	11 h. 51 m.	53½ m.	55½ m.	58 m.	12 h. 4 m.
Level . . .	10.0	11	11.3	12	12.4
Time . . .	27 m.	41 m.	2 h. 1 m.	4 h.	5 h. 12 m.
Level . . .	13	13.8	16.0	20.0	22.3
Time . . .	47 m.	March 20.	10 h. 45 m.	12 h. 42 m.	4 h. 5 m.
Level . . .	23.8	45	46.5	48.2	48.2
Time . . .	5 h. 5 m.	March 21.	March 22.	March 23.	March 24.
Level . . .	48.5	52.8¹)	52.9²)	53.0	53.0

On March 24 the experiment was ended; the dilatometer was opened. Taking, finally, the equilibrium level to be 53 millimeters, for the volume of the entire solution I have 4.7308 cubic cm, and for the expansion \(4.7308 - (4.356 + 0.0202) = 0.3546\) cubic cm, or 8.15%. The limit was reached within 2 days. The quantity of catalyst, hydrochloric acid 25%, was 0.54%, or 0.13% HCl gas relative to the weight of paraldehyde.

2) As catalyst hydrochloric acid of specific gravity 1.19 was taken. Titrating, after the end of the experiment, the entire contents of the dilatometer, I found the quantity of HCl =

¹) No resinification; no coloration visible.
²) Resinification also not visible.

= 0.0052 grams of HCl gas, or 0.0138 grams of hydrochloric acid of the strength indicated above (assuming that such an acid contains 37.5% HCl gas); its volume is 0.0118 cubic centimeters. Paraldehyde was taken in the amount of 3.934 grams, or 4.1052 cubic centimeters at 50.5°; therefore the volume of the entire solution before catalysis = 4.1052 + 0.0118 = 4.117 cubic centimeters. The levels (in millimeters) above the lower mark were as follows:

Time . . .	March 23, 10 h 50 m	March 23, 10 h 50 m	55 m	11 h 2½ m	12½ m
Level . . .		−2.0	+0.3	2.4	3.4
Time . . .	30 m	41 m	12 h 10 m	26½ m	33½ m
Level . . .	6	7	11	13	14
Time . . .	56 m	1 h 20 m	40½ m	2 h 9 m	3 h 52 m
Level . . .	17	19.5	22	25	33.3
Time . . .	4 h 31 m	5 h 1 m	5 h 25 m	5 h 40 m	5 h 48 m
Level . . .	36	38	39	39.6	40
Time . . .	March 24, 9 h 15 m	March 24, 9 h 15 m	10 h 54 m	11 h 50 m	12 h 59 m
Level . . .	67.2	67.2	69	69.5	70.8

On March 28 the height of the level during the whole day was 75.8 millimeters; the contents of the dilatometer were transparent and colorless.

On March 29 the level was at 75.9 millimeters; then the experiment was ended.

Taking the height of the level when the limit was reached as 75.9 millimeters, I have for the final volume 4.4499 cubic centimeters; consequently, the expansion is equal to 4.4499 − 4.1170 = 0.3329 cubic centimeters, whence I conclude that 100 volumes of paraldehyde, as a result of catalysis, expanded by 8.11 volumes. In this experiment the amount of catalyst—HCl gas—was equal to 0.13% of the weight of the paraldehyde, or 0.35% of hydrochloric acid of specific gravity 1.19.

Sulfuric acid.

1) As the catalyst there was taken ordinary strong sulfuric acid, Kahlbaum, specific gravity 1.84. Of it there was taken (determined by titration) 0.0105 gram, i.e. 0.0057 cubic cm. Of paraldehyde there was taken 4.012 grams, or 4.1866 cubic cm. I take the volume of the whole system, as always before, as the sum, i.e. equal to \(4.1866+0.0057=4.1923\) cubic cm. The levels (in millimeters) above the lower mark are as follows:

Time . . .	12 h. 20 m.	21 m.	22 m.	24 m.	26 m.
Level . . .	80	86.4	90.7	94.5	96.2
Time . . .	28 m.	31 m.	35 m.	40 m.	50 m.
Level . . .	96.5	97	96.5	97	96
Time . . .	1 h. 3 m.	1 h. 35½ m.	45½ m.	57 min.
Level . . .	94.8	93.0	92.5	92

The catalysis proceeds very rapidly; toward the end of the indicated time, darkening is observed in the form of a brownish layer below. The volume upon reaching the limit proved to be \(4.544\) cubic cm; consequently, the expansion is \(4.544-4.1923=0.3517\) cubic cm, or, in percent, 8.40. Sulfuric acid (\(\mathrm{H_2SO_4}\)) was taken at 0.25% relative to the paraldehyde.

In the last experiment with \(\mathrm{HCl}\) and the first with \(\mathrm{H_2SO_4}\), a new dilatometer No. 20 was used, not included in the table where the dimensions of the other dilatometers are given. With it I carried out only these two determinations. In calculating the results, considerable discrepancies were found for the final expansion in comparison with that found for the same catalysts when measured in other dilatometers—No. 5 and No. 12. It turned out that the tube of this dilatometer (which was not the case with the others) had a very variable bore. Having measured this dilatometer with both mercury and water, filling both liquids almost exactly to those levels where the level of the liquid phase had been during the study of equilibrium, I found that at 17.3°, for this dilatometer, the capacity up to the divisions above the lower mark was:

	by mercury	by water	Mean
97.3 millimeters	4.5425 cubic cm	4.5410	4.5418
and up to 75.0 millim.	4.4415 » »	4.4420	4.4418;

therefore for 50.5° we have 4.5454 and 4.4454 cubic centimeters.

2) As catalyst, the same H₂SO₄ was taken in the amount of 0.0169 g, or 0.0092 cubic centimeters \(\left(=\frac{0.0164}{1.84}\right)\); but the dilatometer was another one—No. 12. Para-aldehyde was taken in the amount of 6.800 grams, or 7.096 cubic centimeters at 50.5°. The volume of the whole system is equal to the sum: \(7.096+0.009=7.105\) cubic centimeters. The levels in millimeters above the lower mark are as follows:

Time . . .	1 h. 34½ min.	36 min.	40 min.	45 min.
Level . . .	73	82	88	91
Time . . .	57 min.	2 h. 2 min.	7 min.	4 h. 0 min.
Level . . .	90.6	89	88.3	77.0

At 4 hours “no turbidity is visible,” as recorded in the diary, although undoubtedly one must assume the existence of some reaction following the catalysis and expressed in contraction. Taking the equilibrium level as 91 millimeters, we have for the volume 7.6936 cubic centimeters; hence for the expansion \(7.6936-7.105=0.5886\) cubic centimeters, or 8.30%. The catalyst—H₂SO₄—was taken in this experiment also as 0.25% of the weight of the para-aldehyde, and the maximum level is then reached at the same time, i.e. after 10 minutes, as in the first experiment.

Trichloroacetic acid.

Trichloroacetic acid was prepared by me from chloral hydrate and nitric acid. The product obtained was distilled repeatedly; it contained neither HCl nor HNO₃ (test with AgNO₃ and diphenylamine).

Dilat. No. 5 contained 0.1203 g of catalyst \((\mathrm{CCl}_3\mathrm{CO}_2\mathrm{H})\)¹). Taking its specific gravity at 50.5° as 1.6 (see Beilstein), we have for the volume 0.075 cubic centimeters. Para-aldehyde was taken in the amount of 4.101 grams, or 4.280 cubic centimeters at 50.5° \(\left(\frac{4.101}{0.9583}=4.280\right)\); the catalyst—CCl₃CO₂H—was taken, in comparison with the para-aldehyde, as 3%. The level heights (in millimeters, above the lower mark) are as follows:

¹) Determined by titration of the entire contents of the dilatometer after the experiment.

27 February.

Time . . .	10 h. 58½ m.	11 h. 1½ m.	11½ min.	37 min.	12 h. 26 m.
Level . . .	7.2	7.2	8.0	9.0	10.5
Time . . .	1 h. 54 m.	5 h. 20 m.	28 February 9 h. 40 m.	12 h. 42 m.	4 h. 15 m.
Level . . .	13.3	23.0	50	50.8	51.5
Time . . .	5 h. 33 m.	1 March	10 h. 33 m.	2 h. 10 m.	5 h. 44 m.
Level . . .	51.5		51.0	51.0	51.0

Such an amount (3%) of $\mathrm{CCl_3CO_2H}$ dissolves completely in paraldehyde. No resinification (clouding) was observed, at least not on the second day. The volume of the entire solution at equilibrium is 4.7186; trace, of paraldehyde alone—4.6436 cubic cm, and the expansion is $4.6436 - 4.280 = 0.3636$ cubic cm, or 8.50% of the initial volume of paraldehyde.

In view of the slowness of the catalysis, I can use another method of calculation as well. Taking as the level before catalysis 7.2, I have for the expansion $51.5 - 7.2 = 44.3$ millimeter sections of the tube; and for the initial volume in the same units—millimeter sections of the thin tube—

\[ 528.5\ \text{(volume up to the lower mark)} + 7.2 - 9.2 = 526.5 \quad \left[9.2 = \frac{0.075}{0.00813}\ \text{is} \right. \]

the volume of $\mathrm{CCl_3CO_2H}$ in the same units], or, in % of the initial volume of paraldehyde, 8.41.

Monochloroacetic acid.

1) Commercial monochloroacetic acid was repeatedly distilled; in the final product the absence of HCl was established. The catalyst $\mathrm{CH_2ClCO_2H}$ was taken (the contents of the entire dilatometer were titrated after completion of the experiment), 0.220 gram, or 0.152 cubic cm at 50.5° (its specific gravity was taken as 1.45, see Beilstein). Paraldehyde was taken, 3.272 grams, or 3.414 cubic cm (at 50.5°); consequently, the amount of catalyst was 6.7% of the amount of paraldehyde. The levels in millimeters above the lower mark are as follows:

Time . . .	28 Feb. 5 h. 9 m.	33 min.	6 h. 3 m.	1 March 10 h. 30 m.
Level . . .	5.6	5.8	6.1	20.6

Time . . .	March 1	2 h. 10 m.	5 h. 44 m.	March 2	March 3
Level . . .		22.5	24.0	29.5	32
Time . . .	March 6	March 7	March 8	March 9	12
Level . . .	38	41.0	41.5	42.0	42.8
Time . . .	March 14	15	19	20	22
Level . . .	43.0	44.0	42.0	41.5	41.5
Time . . .	March 23	28	Apr. 24	Apr. 28
Level . . .	41.8	42.0	39.5	38.0

Despite the fact that more catalyst was taken in this experiment than in any other, the rate of catalysis is very small. The initial level (5.6) cannot be used for calculating the initial volume, for the dilatometer was set up earlier, on February 28, with a smaller content by 6.7%; the volume changed very insignificantly, for which reason the dilatometer was opened and the amount of \(\mathrm{CH_2Cl.CO_2H}\) increased. I take the level height at equilibrium to be 41.9 (in the readings of March 14 and 15, some error evidently crept in, although the experiment was conducted in a deep thermostat), as the mean of the level heights counted on March 9, 12, 19, 20, 22, 23, and 28; hence the volume at equilibrium is equal to 3.859 cubic cm (dilat. No. 2), and the expansion is equal to \(3.859-(3.414+0.152)=0.297\) cubic cm, which amounts to 8.58 per 100 volumes of the paraldehyde taken for the experiment.

Analysis of the experimental data.

For the reader’s convenience I compare the above data in three tables. In the first I have collected those experiments which I consider the most reliable. Elements of such reliability, given the sharpness of the maximum of expansion, will undoubtedly be either a small amount of catalyst, or its insolubility in the liquid phase. Under the latter two conditions there falls away that principal error which must be introduced in calculating the data of an experiment, namely that the catalyst dissolves in the liquid phase without changing the volume. Such experiments are the three with sulfuric acid, where the maximum of expansion is sharp and the amount of catalyst is negligible; the experiment with

$\mathrm{ZnSO_4}$, with the complete insolubility of $\mathrm{ZnSO_4}$ in the liquid phase, has only that, albeit quite negligible, uncertainty that the specific gravity at $50.5^\circ$ of the $\mathrm{ZnSO_4}$ prepared by me is not known exactly.

To this same category I assign the 2 experiments with HCl: they were carried out, first, later, when the technique of the method had been fully worked out and the observance of all necessary details had become mechanical; secondly, they are distinguished, with a small quantity of catalyst as compared with the other experiments, by the sharpness of the limit of the reaction, not obscured by the resinification reaction; finally, the dilatometers were measured especially accurately and repeatedly.

The last 2 experiments in this table, with anhydrous oxalic and phosphoric acids, are likewise distinguished by comparatively small quantities of catalyst. Of the three experiments with oxalic acid, the most reliable is precisely this one: equilibrium set in after 21 days and for 14 days exactly one and the same volume was maintained.

Both the first and the second tables contain four columns, of which in the first I give the chemical formula of the catalyst; in the second—its weight quantity as a percentage of the initial weighed quantity of paraldehyde; in the third—the percentage increase in the initial volume of paraldehyde when the reaction reached its limit; finally, in the fourth column (the third table does not contain this column) I give the weight content of aldehyde (counting as 100 parts by weight the paraldehyde initially taken for the experiment) corresponding to the maximum expansion given in the third column, which characterizes the attainment of equilibrium; I calculated the numbers of this last column by assuming that an expansion of 8.19 corresponds at the moment of equilibrium to a weight content in the liquid phase of 33.92% aldehyde (see the chapter “Analysis of the Liquid Phase”), and by allowing, within narrow limits, proportionality between the expansions and the weight contents of aldehyde in the liquid phase of the equilibrium system.

Table One.

I	II	III	IV
1) $\mathrm{SO_2}$	0.079	8.20	33.99
2) $\mathrm{SO_2}$	0.068	8.34	34.56
3) $\mathrm{SO_2}$	0.002	8.19	33.92
4) $\mathrm{ZnSO_4}$	2.7	8.13	33.78
5) HCl	0.13	8.11	33.60
6) HCl	0.13	8.15	33.75
7) $\mathrm{C_2O_4H_2}$ (oxalic)	0.52	8.27	34.25
8) $\mathrm{H_3PO_4}$	0.54	8.10	33.55
average		8.19	33.92

In the following, second table, I collect all the remaining experiments except those two which gave clearly small numbers, although quite reliable ones for the above-mentioned expansion; them, and also 2 experiments with HgCl₂ and B₂O₃, which gave only a lower limit for the magnitude of the sought expansion, I place in the third table.

Table Two.

I	II	III	IV
9) H₃PO₄	1,9	8,51	35,24
10) H₃PO₄	3,5	8,21	34,00
11) CCl₃CO₂H	3,0	8,50	35,20
12) H₂SO₄	0,25	8,40	34,80
13) H₂SO₄	0,25	8,30	34,38
14) (COOH)₂ + 2H₂O	3,3	8,70	36,03
15) (COOH)₂ + 2H₂O	0,58	7,90	32,72
16) B₂O₃	2,70	8,28	34,28
17) CH₂ClCO₂H	6,7	8,58	35,50
18) CdCl₂	3,0	8,44	34,95
19) HgCl₂	3,0	8,41	34,83
20) HgCl₂	2,54	8,27	34,25
21) HgCl₂	4,75	8,31	34,41
22) ZnCl₂	1,26	8,48	35,12
23) ZnCl₂	2,22	8,17	33,84
24) ZnCl₂	1,23	8,70	36,03
25) ZnCl₂	0,48	8,57	35,49
26) CuSO₄	1,25	7,96	33,28

Table Three.

I	II	III
27) B₂O₃	0,59	6,07
28) CdSO₄	2,3	1,35
29) HgCl₂	not determined	expansion > 7,71
30) B₂O₃	"	" > 6,72

Turning to the data of the second table, I must make the following remarks:

I attach much less weight to experiments No. 9 and No. 10 than to No. 8: in No. 9 a sufficient (more than 2%) amount of catalyst was taken—an aqueous solution of phosphoric acid, whereas in No. 10, although the expansion obtained for the limit is very close to the mean derived from the first table,

besides the error introduced in general by a large quantity of catalyst, an error could also have occurred from the fact that the initial volume was not determined by direct weighing of paraffin, but indirectly.

No. 11 I assign to this category because of the large quantity of catalyst (3%), which dissolved completely.

No. 12 and No. 13 with a cover of $H_2SO_4$ are entered in the second table, since catalysis proceeds violently and soon a certain side reaction sets in, expressed in contraction.

No. 14 with dibasic oxalic acid gave a large number for the expansion: it was carried out first in the order of the work; the scale was attached to the thin tube with resin (which I cannot be quite certain did not, on changing, preserve its position), and the quantity of catalyst (3.3%), which dissolved completely, was large.

In experiment No. 15 (again with dibasic oxalic acid), with a small quantity of catalyst, catalysis proceeded so slowly that, for a possibly exact determination of the maximum expansion, it would have been necessary to keep the dilatometer in the thermostat longer.

Experiment No. 16 with $B_2O_3$, in view, first, of the fact that the weight, and consequently the volume, of the amount of $B_2O_3$ taken was not determined directly, but only indirectly; and second, in view of the dissolution of $B_2O_3$ in the liquid phase to the extent of at least 0.6%, also has a weight considerably smaller in comparison with those of the first table (see the detailed description of the experiments).

Experiment No. 17 suffers from the following shortcomings: first (and this, apparently, is the principal one), more catalyst was taken than in any other experiment; moreover, this catalyst dissolves completely in the liquid phase; second, the height of the level fluctuated more strongly in this experiment than in the others.

Why I placed experiment No. 18 in the second table is clear from the detailed description of the experiments. Here it is better to take 8.27 for the desired expansion (the mean of 8.44 and 8.11; see the details of the experiments), and it may, moreover, be correct to give double weight to the number 8.11, which for the desired expansion would give $8.22 = \frac{1}{3}(8.44 + 8.11 + 8.11)$ and would place this experiment in the first table.

Experiments No. 19, No. 20, and No. 21 have again been placed in this table (although they gave numbers very consistent with one another and only slightly exceeding the most reliable numbers of the first table), since the catalyst was taken in considerable excess and dissolves appreciably in the liquid phase. The subseq-

...the motive, of course, disappears if the dissolution of selenium in a mixture parallel with aldehyde is carried out with the same negligible change of volumes as its dissolution in alcohol (see the chapter on the method).

The experiments with \(\mathrm{ZnCl_2}\) (Nos. 22–25) belong to this category: they are the earliest in the course of the work; the most impeccable of them is the one that gave the number closest to the mean (8.19) obtained from the numbers of the first table; with regard to the other three I refer the reader to the detailed description of the experiments.

Finally, in experiment No. 26, given the slowness of the catalysis, the dilatometer ought to have been kept longer in the thermostat: the volume, greater by only 1 millimeter than the largest found, would have placed it fully in the first table.

In the chapter “Instead of a Preface” I said that the present work of mine made it possible for the first time to confirm experimentally, on a broad scale, the requirement of the theory: for reactions limited by an equilibrium, this equilibrium does not change with a change in the nature of the catalyst. In the preceding works one can find individual experiments confirming this theoretical conclusion. Thus (see van’t Hoff, Vorlesungen I Heft, 211), Lemoine found at \(350^\circ\) the percentage decomposition of hydrogen iodide equal to 18.6 in the absence of platinum sponge, and Hautefeuille, for the same decomposition, found 19.0% in the presence of the same catalyst; further, Ditte, observing the formation of hydrogen selenide from the elements at \(440^\circ\), found, in parallel experiments without a catalyst—pumice—and in its presence, respectively 45.2 and 46.82 percent of the hydrogen selenide formed.

K. Köllichen, studying the transformation of acetone into diacetone alcohol in aqueous solution under the influence only of basic catalysts (Zeits. f. ph. Chemie XXXIII, 129, 1900), finds, at a concentration of 40% acetone, with the catalysts

\[ \mathrm{NaOH}\qquad \mathrm{N(C_2H_5)_4OH}\qquad \text{piperidine}\qquad \mathrm{N(C_2H_5)_3}\qquad \mathrm{NH_3} \]

respectively the following percentages of unchanged acetone at the attainment of equilibrium:

\[ 90.9\%\qquad 90.9\%\qquad 90.75\%\qquad 90.4\%\qquad (90.1\%-90.3\%). \]

Summarizing the results of his experiments, K. Köllichen especially emphasizes the proposition concerning the independence of the equilibrium of reversible reactions from the different mass of the catalyst, but does not at all put forward the proposition concerning the independence of that same equilibrium from the nature of the catalyst.

Turning to my own investigations, I find that the experiments with 5 catalysts, placed in the first table, splendidly confirm the theoretical conclusion concerning the independence of the equilibrium of reversible reactions from the nat-

types of catalyst; the individual determinations differ from one another less than in Ditte’s, and also than in Kölichen’s.

The second table provides 8 new catalysts, but its numbers fluctuate considerably more strongly than in the first table. It is clear that the cause lies in the errors of the experiment inherent in determinations of this category, and not in the fact that different catalysts give rise to different, though very close, limits in reversible reactions.

The circumstances that were the cause of the fluctuations in the numbers of the second table are, it seems, of three kinds, apart from accidental ones.

1) In the initial experiments the scale was attached to the thin tube of the dilatometer with resin, and, because of the unreliability of such an attachment, could sometimes change its position during the experiment (see the chapter on the method and experiment No. 3 with $\mathrm{ZnCl}_2$ in the detailed description of the experiments); such are experiments Nos. 14, 25, 24, 21. It is clear that the numbers for the desired expansion must have turned out greater than the true ones, for when the scale is lowered the level points to the next higher divisions, i.e., the level as if rises; and indeed, in all four of the above-mentioned experiments the numbers obtained for the expansions are greater than 8.19—the most probable value for the expansion supplied by the first table.

2) The catalyst could dissolve in the liquid phase with a noticeable change in volumes, which may especially be suspected in those experiments where an appreciable amount of catalyst was taken; such are experiments Nos. 17, 11, 14. I do not include experiment No. 10 with $\mathrm{H}_3\mathrm{PO}_4$ in this category, since the separation into 2 layers does not disappear, i.e., there is no complete dissolution of the catalyst, while in experiment No. 21, although much catalyst was taken, which dissolved considerably in the liquid phase, it is very probable, by analogy with alcohol (see the chapter on the method), that dissolution of this catalyst occurs without a noticeable change in volumes.

Such a change in volumes could be equal to (approximately) one millimeter of the thin tube (see the chapter on the method), and then in experiments carried out in dilatometer No. 2 it gives a deviation from the true value of the expansion by 2 per mille, i.e., it will give for the expansion not 8.19%, but 8.38% or 7.99%.

3) In the earlier experiments (thus, for example, with zinc chloride, dihydrate of oxalic acid, boric anhydride, and sublimate) I had not yet ordered such a deep thermostat as later, into which my instruments could be immersed entirely; because of this the end of the thin tube of the dilatometer protruded from the bath, was in the air, and a drop of liquid accumulated in it, which before reading the height of the level in the dilatometers I drove down by gentle heating.

(What sort of error could arise from this (from the fact that liquid adhered to the walls of the thin tube) may be understood from the following experiments. I poured into my dilatometers mixtures of paraldehyde and aldehyde containing 34.56% and 30.70% aldehyde*). Placed in the thermostat, they had the following levels:

Time . . . . . . .	11 h. 30 m.	11 h. 38 m.	11 h. 45 m.
Level in the 1st dilatometer.	62.3	62.5	62.3
Level in the 2nd dilatometer.	35.0	35.0	35.0

These dilatometers were taken out of the thermostat, turned over so that the whole thin tube filled with liquid, and again placed in the thermostat. When they had fully assumed its temperature, the first reading gave 62.7 and 34.5, and the second (after another 5–10 minutes) 62.5 and 34.5, i.e., an error of 0.5 millimeters).

The rate of catalysis depends very strongly both on the mass and on the nature of the catalyst, and on the latter to a much greater degree than on the former, as is clearly seen from a detailed examination of the experiments; from the latter it is also clear that the magnitude of the limit is independent of the mass of the catalyst, which was previously proved by K. Kölichen (Zeitsch. f. ph. Chemie XXXIII, 129, 1900).

A study of the rate of this catalysis with different catalysts (and with different quantities of one and the same catalyst) would require a separate investigation, which is why I do not present curves of such rates, although I have data for determining them**). As regards the explanation of the clearly small expansion (which supposedly refutes the preceding conclusion), which was undoubtedly observed by me in experiment No. 27, the following seems very probable.

The catalysis of paraldehyde is produced by boric anhydride (perhaps by its whole surface, as with ZnSO₄), but not by that compound of it which is formed when it dissolves in paraldehyde (+ aldehyde). If so, then large amounts of B₂O₃ catalyze paraldehyde, giving the same limit of catalysis as other catalysts (see experiments Nos. 16 and 30); whereas small amounts of B₂O₃ will produce catalysis only up to the moment of complete dissolution of B₂O₃, after which we shall for a long time observe the state

* To precisely such a composition the liquid phase is close at equilibrium in the reaction under study.

** For those catalysts that dissolve rapidly in paraldehyde (e.g., SO₂, HCl, trichloroacetic and monochloroacetic acids).

equilibrium, the constancy of volume, or, more precisely, the very, very slow compression due to the occurrence of a side reaction (resinification). Experiment No. 27 gives precisely such a picture, and, considering the detailed description of the experiments, we see that, indeed, even at ordinary temperature \(B_2O_3\) is capable of dissolving, or of forming some compound with paraldehyde, for paraldehyde that has stood for 2 (or 4) days over large pieces of \(B_2O_3\), when filtered, gives a solution that very quickly, almost at once, becomes cloudy in air and in a short time gives a considerable quantity of white, clearly crystalline powder, in which the presence of boron was established. Since paraldehyde is only slightly volatile at ordinary temperature, one cannot suppose that this considerable quantity of white crystalline powder represents boric anhydride, as such, dissolved in paraldehyde and left from the saturated solution upon evaporation of the solvent; it is incomparably more probable to think that, under the action of the moisture of the air, some (not investigated by me) very unstable compound of paraldehyde and boric anhydride decomposes and precipitates \(B(OH)_3\) (*), or that boric anhydride, although it dissolves in paraldehyde as such, in this dissolved state combines very greedily with the moisture of the air and precipitates as a hydrate of boric anhydride. In a word, the experiments with \(B_2O_3\) in no way refute the rule concerning the independence of the reaction limit from the nature of the catalyst. The preceding explanation is not at all applicable to experiment No. 28 with mercuric cadmium: the latter catalyst, even if it dissolved in the liquid phase, did so only very little (judging by eye) and was hardly capable of giving any solid compound of paraldehyde and mercurous salt capable of producing catalysis. I do not yet have any explanation for this reliable experiment.

It remains to determine the composition of the liquid phase at the moment of equilibrium. For this it is necessary to have pure aldehyde; to the description of the method of preparing it and of its properties I devote the following lines.

On aldehyde.

For the first time the aldehyde was prepared by me in the following way. One portion—by slow distillation of paraldehyde (more precisely, of the low-boiling fractions obtained during the purification of commercial paraldehyde) with catalysts (\(B_2O_3\), or \(HgCl_2\)). It must be driven slowly; otherwise much metaldehyde forms in the cooled distillate, if sublimate is taken as the catalyst.

Another portion of aldehyde was obtained by passing through aldehyde-ammonia. The latter method is not advantageous: much aldehyde is lost and in the end

*) Or perhaps this compound decomposes not by the moisture of the air, but by its oxygen.

obviously it is not acetaldehyde that is being driven off (perhaps crotonaldehyde). These two portions, after having stood for a long time in the cold,^1) were mixed and distilled twice with a dephlegmator; the aldehyde vapors issuing from it were dried with calcium chloride. The tube containing the latter was immersed in a bath at a temperature of \(25^\circ\). An aldehyde was obtained boiling at \(21—22^\circ\) (the thermometer was not checked). Determinations of the specific gravity gave:

\[ S \frac{18.08^\circ}{4^\circ}=0.7840 \]

\[ S \frac{18.55^\circ}{4^\circ}=0.7831. \]

The analysis of this aldehyde was carried out by oxidizing it with \(K_2Cr_2O_7\) in acetic acid; the excess dichromate was destroyed with potassium iodide, and the liberated iodine was titrated with \(Na_2S_2O_3\) (Bongartz’s method, Zeitschr. f. analyt. Chemie 29, 609). 0.884 g of aldehyde was weighed into a glass bulb; this amount was dissolved in 100 cubic centimeters of water; for titration, 10 cubic centimeters of this aqueous solution of aldehyde were taken each time. Then of dichromate (1 cubic centimeter of it contained 0.00995 g of pure \(K_2Cr_2O_7\)) there was consumed for the oxidation of these 10 cubic centimeters: 1) 19.6 and 2) 19.7 cubic centimeters; these quantities of dichromate are capable of converting into acetic acid 1) 0.0876 and 2) 0.0882 g of aldehyde. Since, on preparing a one-percent solution of aldehyde in water, the volume of the former almost disappears (see below), I should have found the amount of aldehyde (in the event of its purity) equal to 0.0884 gram; on the average, however, 0.0879 gram was found, which argues for the sufficient purity of the aldehyde obtained by me.

The second time I prepared the aldehyde by slowly distilling paraldehyde with a small amount of crystalline phosphoric acid with a dephlegmator.^2) The product obtained was distilled again, 2 or 3 times in the same way with a dephlegmator, but without a catalyst, through a tube with \(CaCl_2\), heated to \(23—25^\circ\). By this method two portions were obtained: a) from the residues of paraldehyde, the remainders from various experiments with it, and b) from fairly pure paraldehyde. These portions were examined separately. Measurement of the specific gravities gave the following figures:

Portion a.	Portion b.
Pycnometer A.	Pycnometer B.
\(\displaystyle S \frac{18.00^\circ}{4^\circ}=0.7836\)	\(\displaystyle S \frac{18.00^\circ}{4^\circ}=0.7833\)

^1) In order to separate metaldehyde, if any had formed.

^2) Very little aldehyde is resinified.

\[ S\frac{25.5^\circ}{4^\circ}=0.7734 \]

and a second determination in the same pycnometer.

\[ S\frac{25.5^\circ}{4^\circ}=0.7733 \]

\[ S\frac{35.45^\circ}{4^\circ}=0.7595 \]

\[ S\frac{35.35^\circ}{4^\circ}=0.7597 \]

\[ S\frac{50.5^\circ}{4^\circ}=0.7375^{1)} \]

\[ \left. \begin{array}{c} S\frac{25.5^\circ}{4^\circ}=0.7732 \end{array} \right\} \]

\[ S\frac{35.35^\circ}{4^\circ}=0.7599 \]

Consequently, portions a and b should be considered identical in specific gravity as well²).

Analysis of these two portions was also carried out by the above-mentioned method of Bourcart. From portion a, 0.9168 gram was weighed out and dissolved in 100 cubic centimeters of water. For 10 cubic centimeters of this aqueous aldehyde solution, the titration of iodine required Na₂S₂O₃: 1) 39.9 cubic centimeters and 2) 40.1 cubic centimeters; taking the mean (40.0), I find that 10 cubic centimeters of this solution contain 0.09199 gram of pure aldehyde, and assuming that aldehyde, on dissolving, loses its volume and that my aldehyde is perfectly pure, I should have obtained 0.09168 gram.

From portion b I weighed out 1.3635 grams and dissolved it in 120 cubic centimeters of water. Assuming, as for portion a, the two latter conditions, there should have been found in 10 cubic centimeters

\[ \frac{10\times 1.3635}{120}=0.1136 \]

gram of aldehyde, whereas 0.1135 g was found. Such determinations sufficiently attest to the purity of the product.

That aldehyde, on dissolving in water in the amount of one percent, almost loses its volume is proved by the following measurement. The prepared one-percent solution of aldehyde had the specific gravity

\[ S\frac{19^\circ}{4^\circ}=0.9980, \]

whereas, according to Rosetti’s data (Wüllner, Lehrbuch d. Experim. Physik, 2 Band, 84), pure water has

\[ S\frac{19^\circ}{4^\circ}=0.99846. \]

If, in the formation of a one-percent aqueous solution of aldehyde, there occurred no change

¹) Temperatures according to a normal thermometer.
²) And almost identical in specific gravity with aldehyde prepared earlier.

volume, then 100 grams

of such a solution would have a volume

\[ \frac{1}{0.7821^{1})}+\frac{99}{0.99846}=100.4366 \ \text{cc}, \]

whence \(S \frac{19^\circ}{4^\circ}=0.9957\), which is far below the number (0.9980) obtained by me directly.

Analysis of the liquid phase at the moment of equilibrium.

The first method was the same as that which K. Kölichen had already used earlier (loco citato): namely, it consisted in preparing, by weighing, a series of mixtures of paraldehyde and aldehyde with a variable aldehyde content (the total weight quantity of paraldehyde + aldehyde always being taken as equal to 100); in the same dilatometers\(^{2}\) as before, and in a manner entirely analogous to the preceding experiments for determining the maximum expansion, I subjected these mixtures at \(50.5^\circ\) to the action of the same quantity of one and the same catalyst (only in 2 cases were other catalysts used). With different quantities of aldehyde, there was observed now a decrease, now an increase in volume, and, finally, approximate invariability of it. It is clear that the last mixtures, with known aldehyde content in advance, represent a composition very close to the one sought. The catalyst must be chosen such that, on the one hand, while the dilatometer is being set up for the experiment, it would not at room temperature change at all the composition of the prepared mixture of paraldehyde and aldehyde during the (comparatively) short time required for this; on the other hand, it is desirable, of course, to choose such a catalyst as would produce catalysis comparatively quickly and would not change the volume of the above-mentioned mixtures for reasons other than catalysis (for example, oxalic acid would be very suitable, because at ordinary temperature over a short period it has no effect at all on such mixtures; see the experimental details, but by the very act of dissolving it may change the volume of the system, and the action of small quantities of it is very prolonged).

Sublimate, used only once for such experiments, proved to be entirely unsuitable: when the dilatometer is filled, it very quickly converts the aldehyde in the given mixture into paraldehyde and must always show expansion at \(50.5^\circ\), unless there is very little aldehyde. The most suitable catalyst proved to be an aqueous solution of phosphoric acid containing \(70.4\%\ \mathrm{H_3PO_4}\); as is seen from the detailed description of the experiments, in

\(^{1}\) The specific gravity of aldehyde, calculated for \(19^\circ\) from my measurements.

\(^{2}\) The dilatometers were always filled with the prepared mixture while cooling both the liquid and the charged dilatometer, so that the aldehyde would not volatilize.

one day, even with an amount of \(0.54\%\) of catalyst relative to paraldehyde, completes catalysis and almost does not react with the aldehyde at ordinary temperature (during the short time of setting up the dilatometer); furthermore, even with a large amount of this catalyst—6 drops, or \(3.5\%\) \(H_3PO_4\), relative to the whole paraldehyde—the level does not fall on the next day from the onset of a side reaction, resinification. In those of the following experiments where I indicate neither the quantity nor the quality of the catalyst, one should understand 4–5 drops of an aqueous solution of phosphoric acid containing \(70.4\%\) \(H_3PO_4\).

Trichloroacetic acid is the same, except that I preferred phosphoric acid, for in smaller quantity it acts more vigorously.

But in view of the foregoing, such a solution of phosphoric acid satisfies the ideal requirements of this method only in part, and therefore, under the conditions of my problem, this method must be recognized as somewhat inaccurate. In accordance with what has been said above, the following experiments were carried out.

1) Aldehyde \(24.7\%\); rapid expansion is observed; namely, the level of the liquid phase rose by 18 divisions over 3 h 56 min, and on the following day stood another 7 divisions higher (the divisions are arbitrary, not millimetric).

2) Aldehyde \(43.92\%\). I obtain a considerable contraction—by 67.5 divisions over the course of a day.

3) Aldehyde \(39.65\%\). A slow contraction is observed, by 10 millimeters in a period of less than a day.

4) Aldehyde \(38.34\%\). The levels in millimeters are as follows:

Time . . . . .	1 h 41 m	49 min	57 min	5 h 45 m
Level . . . .	171	172	172.3	173

Time . . . . .	On the next day	On the third day
Level . . . .	172	171

In this experiment, after filling, the dilatometer stood for a considerable time at ordinary temperature; consequently, when introduced into the thermostat at \(50.5^\circ\), I already had less than \(33.34\%\) aldehyde in the mixture, which is why, in contrast to the following experiments, an insignificant expansion was observed. This experiment shows only that the contraction from side reactions (resinification) on the first day is insignificant, since after 2 days the level fell only from 173 to 171 millimeters.

5) Aldehyde 40.34%; catalyst—a considerable quantity of sulfo. According to the dilatometer’s indications, when I transferred it from the cooling mixture, below 0°, into a bath at room temperature, I observed boiling of the liquid phase and the separation along the walls of the reservoir of an abundant quantity of some crystals (metaldehyde?). An increase in volume by 17 divisions is observed over the course of 2 hours 16 minutes; then—upon reaching the maximum—contraction and resinification. The explanation of this experiment was given above.

6) Aldehyde 38.28%; catalyst—a considerable quantity of trichloroacetic acid, which dissolves instantly in the liquid. I observe a clear contraction—by 17 divisions over the course of 16 minutes. I give here the change in height of the level with time, since here the first reaction, the contraction from catalysis, is very clearly separated in velocity from the second—the contraction from resinification.

Time . . . . .	4 h. 7 m.	11½ min.	15½ min.	18½ min.	23 min.
Level . . . .	194	182	180	180	176
Time . . . . .	35 min.	5 h. 10 m.	5 h. 45 m.	11 h. 21 m.	5 h. 27 m.
Level . . . .	176	176	176	170	169

on the following day.

7) Aldehyde 37.21%, millimeter scale, turned downward.

Time . . . . . . . . . .	12 h. 26 m.	42 min.	1 h. 7 m.	20 min.
Level . . . . . . . . . .	11	12	13	13
Time . . . . . . . . . .	36 min.	53 min.	4 h. 1 m.	4 h. 56 m.
Level . . . . . . . . . .	14	14	15.5	16

A small but clear contraction.

8) Aldehyde 35.23%.

Time . . . . . .	1 h. 15 m.	19 min.	37 min.	4 h. 1 m.	56 min.	5 h. 33 m.
Level . . . . .	73.5	73.5	73	73	73	73.3

9) Aldehyde 33.36%.

Time . . .	4 h 53 m	55 min	57 min	5 h 3 m	10 min	17 min	5 h 33 m
Level . . .	43	43.1	43.5	43.5	43.7	43.8	44.2

I obtain, although very slight, a clear gradual expansion, and even after 60 hours the level remained at 44 millimeters: whereas the level of the dilatometer in experiment 8 over the same interval of time (60 hours) fell to 68.5 millimeters, i.e. by 5 millimeters; unfortunately, in the last experiment the level was not read on the next day, wherefore I cannot judge with complete certainty whether a mixture with 35.23% aldehyde gives contraction from catalysis or invariability of volume; and although according to the 9th experiment*) this contraction must be ascribed to catalysis, and not to resinification, I nevertheless do not consider this last conclusion strictly substantiated, and therefore acknowledge that this method gives, for the composition of the liquid phase in the reversible reaction

\[ (\mathrm{CH_3COH})_3 = 3\mathrm{CH_3COH} \]

for aldehyde more than 33.36% and less than (or equal to) 35.23%, by weight.

The second, more exact method of establishing the composition of the liquid phase at 50.5° at the moment of equilibrium consisted in measuring specific gravities. Having prepared by weighing three mixtures of aldehyde and paraldehyde (the aldehyde content is given as a percentage of the total weight of aldehyde + paraldehyde), I measured their specific gravities at 50.5°. It turned out that for mixtures containing 38.28—34.55—30.79% aldehyde, the specific gravities

\[ S\frac{50.5^\circ}{4^\circ} \]

are equal to 0.8726—0.8839—0.8951. Hence I calculate the derivative of the specific gravity with respect to percentage composition \(ds/dp\) and find:

\[ ds/dp \text{ (for } p \text{ in the limits } 38.28—34.55)=0.00304. \]

\[ \text{” ” ” ” ” } 34.55—30.79)=0.00297. \]

On the other hand, for the specific gravity of the liquid phase at equilibrium I have five numbers: 1) 0.8858, 2) 0.8856, 3) 0.8845, 4) 0.8862, 5) 0.8877.

The first three numbers are given by the experiments with \(SO_2\); so little of it was taken, less than 0.1%, that with the accuracy of such measurements one may neglect the influence of the dissolved \(SO_2\) on the specific gravity of the solvent. The last two numbers are given by the experiments with \(ZnSO_4\) and \(CuSO_4\), substances insoluble in noticeable doses in the above-mentioned liquid phase; therefore data 4) and 5) also give the specific gravity of pure paraldehyde and aldehyde. Based on the value of \(ds/dp\) and the specific gravities of the three above-mentioned mixtures of aldehyde and paraldehyde, I calculate to what aldehyde content these specific

*) Also according to the 4th experiment.

weight. I obtain: 1) 33.92, 2) 33.99, 3) 34.36, 4) 33.78 and 5) 33.28; hence (the mean of the five preceding numbers) 33.87% aldehyde and 66.13% paraldehyde, and represents the composition of the liquid phase at equilibrium at 50.5° Cels. The data of this exact method agree fully with the data of the first, approximate one.

Addendum.

I shall conclude this chapter by setting forth some data on catalysts for paraldehyde. They were tested in the same dilatometers as those described above (but the divisions are often not millimetric, but arbitrary) with the aim only of deciding qualitatively whether or not a given substance catalyzes paraldehyde at 50.5°. The amount of catalyst was usually taken to be very considerable, much greater than in the experiments cited above, in order to increase the rate of catalysis. Among substances that have no action on paraldehyde, that do not change its volume¹, are $\mathrm{As_2O_3}$—$\mathrm{Hg(CN)_2}$—$\mathrm{Na_2SO_4}$ (anhydrous)—$\mathrm{ZnSO_4 \cdot 7H_2O}$—$\mathrm{HgO}$ (prepared by the wet method)—ordinary iodine.

Formic acid—an aqueous solution of specific gravity 1.20, i.e., according to my determinations (Materials for the investigation of aqueous solutions by specific gravity, 1893) about 90% $\mathrm{HCO_2H}$—acts slowly. This catalyst, at first taken in a huge quantity—equal parts by volume of paraldehyde and such aqueous $\mathrm{HCO_2H}$—gave a maximum rise of the level within 7 minutes (expansion = 16 millim.), which then remained unchanged for 6½ hours.

In a second experiment the dilatometer contained 8 cu. cm. of paraldehyde, 0.1 cu. cm. of this formic acid, and the expansion proceeded very slowly: in 18 days the initial volume, 980 units, increased by only 3 units (approximately).

Acetic acid catalyzes still more slowly. Crystalline acid was taken, approximately 1 volume to 3½ volumes of paraldehyde. Then the levels (arbitrary) in a thermostat at 50.5° were as follows:

Date	Level
January 11	52.7
January 12	57.5
January 15	65.0
January 16 and later	65.0

Lieben (see Beilstein) indicates that aldehyde and $\mathrm{C_2H_5I}$ in a sealed tube at 100° give paraldehyde. I distilled paraldehyde—

with a small amount of \(C_2H_5J\), almost colorless, from Kahlbaum. The mixture began to boil at about \(70^\circ\), and the thermometer rose rapidly and continuously to \(120^\circ\). On distillation, KOH does not split off aldehyde.

Similar experiments carried out with other catalysts, e.g., \(B_2O_3\), \(PO_4H_3\), \(HgCl_2\), etc., always gave a complete, with negligible resinification, conversion of paraldehyde into aldehyde. Of course, here \(C_2H_5J\), owing to its volatility, acted not so strongly as the above-mentioned catalysts, but small amounts of aldehyde could have formed. It remains to be admitted that \(C_2H_5J\), even if it proves to be a catalyst, is a very weak one. The dilatometric method shows that \(C_2H_5J\) does not catalyze paraldehyde: a mixture of paraldehyde and \(C_2H_5J\) does not change its volume over the course of 28 days at \(50.5^\circ\). I explain Lieben’s experiment by the fact that, owing to the presence of water (or another reaction), \(HJ\) was formed, which, during the cooling of the contents of the sealed tube from \(100^\circ\) to ordinary temperature, converted the aldehyde into paraldehyde; heating to \(100^\circ\) in this transformation played only the role of promoting the formation of the catalyst (in all probability hydrogen iodide), for at this temperature one must expect, under the influence of catalysts, the reverse, i.e., a strong conversion of paraldehyde into aldehyde.

Franchimont (Recueil de trav. Chim de Pays-Bas, I, 239) had already shown that under the influence of \(CH_3COCl\) (acetyl chloride) paraldehyde at room temperature passes partly into aldehyde (and back). Testing this reaction dilatometrically at \(25.5^\circ\)—in a very precise dilatometer—I found a rapid and large increase in volume, followed by a slower contraction, i.e., some side reaction. There were taken \(10\) cubic centimeters of paraldehyde per \(2.3\) cubic centimeters of \(CH_3COCl\),

CHAPTER TWO.

EQUILIBRIA BETWEEN PARALDEHYDE AND ALDEHYDE IN SOLUTIONS.

A) Solutions in acetone.

Acetone, from Kahlbaum, sold as boiling at \(56^\circ\)—\(58^\circ\), was subjected to distillation with a dephlegmator over a large quantity of \(\mathrm{CaCl_2}\). All the acetone distilled over within the range \(56.2^\circ\)—\(56.5^\circ\) (calibrated thermometer) at a barometer reading of \(753^{\mathrm{mm}}\) (corrected). The aldehyde was prepared, as before, by distilling 250 cubic centimeters of paraldehyde with crystalline \(\mathrm{H_3PO_4}\) (apparently no more than 10 grams of the latter were taken) from a water bath, the temperature of which was kept between \(80^\circ\)—\(70^\circ\), while the temperature of the vapors passing into the dephlegmator fluctuated between \(26^\circ\)—\(31^\circ\). Then this aldehyde was distilled three times by itself with a dephlegmator, after which there was placed a \(\mathrm{CaCl_2}\)-tube, immersed in a bath at a temperature of \(22\)—\(25^\circ\).

Mixtures of acetone, paraldehyde, and aldehyde were prepared—in view of the volatility of the aldehyde—with constant use of a bath of crushed ice and common salt.

The composition of the mixtures investigated of these three substances I give in the following manner: the percentage content of aldehyde, always taking the amount of paraldehyde \(+\) aldehyde as 100; then the total number of grams of paraldehyde \(+\) aldehyde and the number of grams or cubic centimeters of solvent (acetone).

Such mixtures were poured through a capillary funnel into dilatometers, which, in view of their great mobility, takes place comparatively quickly, although these mixtures, when being poured in, have a temperature below \(0^\circ\). Before immersion in the thermostat, the dilatometers were sealed and a scale, with divisions in millimeters, was attached, as in the experiments of Chapter 1; only here much more sensitive dilatometers were used, and, moreover, of almost identical capacity; the reservoir up to the thin tube contained 20 (approximately) cubic centimeters, and the thin tube in almost all the dilatometers had such a small bore that a segment of it 1 millimeter long had a capacity of less than \(0.004\) cubic centimeters. In view of such great sensitivity of the instrument, with the strongly expanding contents of the dilatometer, from fluctuations of tempera-

of the thermostat temperature (usually \(\pm 0.1^\circ\) C., but sometimes more) the level sometimes fluctuated by 1 millimeter or a little more; sometimes the thermostat held the temperature still worse, which also accounts for larger fluctuations.

Heating such large dilatometers in the \(50.5^\circ\) thermostat required much more time than when using the instruments which I employed in the experiments of Chapter 1; therefore I always made the first reading of the level (the height of the meniscus) in the capillary tube of these dilatometers approximately 10 min. after lowering the instrument into the thermostat.

The method of observation consisted in preparing solutions in which, with a variable ratio between paraldehyde and aldehyde, the weight ratio of the solvent to the sum of the weights of paraldehyde \(+\) aldehyde was kept constant. Under the influence of the catalyst, either expansion or contraction of such solutions was observed (and sometimes invariability of volume) at different weight ratios of paraldehyde and aldehyde. Obviously, the solution prepared by me whose volume does not change under the influence of the catalyst will have the composition characteristic of the equilibrium system which the substances under study give under the conditions considered.

Since, in order to calculate the equilibrium constant, it is necessary to know the active masses of paraldehyde and aldehyde (i.e., the specific volumes of solutions of these substances) at the moment equilibrium is reached, for the solutions which I recognized as such equilibrium systems I determined, by special experiments, of course in the absence of catalyst, the specific weights at \(50.5^\circ\). Such specific weights, according to the notation adopted earlier, I denote in the form \(S\frac{50.5^\circ}{4^\circ}\).

I carried out catalysis in acetone solutions (and in toluene solutions) using the so-called complex catalyst, i.e. a mixture of one volume of strong sulfuric acid (specific weight 1.84) and four volumes of an aqueous solution of phosphoric acid containing 70.4% (by weight) \(H_3PO_4\). In almost all experiments the same amount of this complex catalyst was taken—10 drops.

The catalyst dissolves completely in the acetone solution and, after a certain time, resinifies the aldehyde, owing to which the mixture becomes yellow, with the color progressively intensifying over time, and contraction of the mixture begins; but the latter phenomenon becomes noticeable only when it can be said with certainty whether the cleavage of paraldehyde or the condensation of aldehyde has occurred, for the resinification reaction has a rate considerably lower than that of the catalysis of paraldehyde. In describing the individual experiments I always give the change in the height of the level (meniscus) in the capillary with time, which gives an idea of the rate of catalysis,

and on equilibrium, and on the onset of a side reaction (resinification). The concentration \(1:X\) denotes the approximate composition of the solution in such a way that \(X\) volumes of solvent correspond to 1 volume of paraldehyde; moreover, in the sum of the weights of paraldehyde and aldehyde the latter is taken as paraldehyde, and the specific gravity of paraldehyde is taken as unity. The temperature of the experiments with all solvents was the same as before—50.5° Celsius.

Concentration 1:10.

Experiment 1. Aldehyde 79.03%,

3.105 grams (paraldehyde + aldehyde) + 31 cubic centimeters of acetone.

Time in minutes	Levels
10	125.0
14	124.5
20	126.0
30	128.0
39	132
47	133
52	134.0
66	139
79	142.0 etc.

considerable and rapid expansion.

Experiment 2. Aldehyde 89.7%,

2.315 grams (paraldehyde + aldehyde) + 18.231 grams of acetone.

Time	11 h. 39 m.	54 m.	12 h. 7 m.	13 m.	23 m.	33 m.	48 m.
Level	275.0	278	277	277.0	278.0	276.0	277.0
Time	1 h. 8 m.	1 h. 32 m.	56 m.	2 h. 1 m.	12 m.	3 h. 17 m.	4 h. 45 m.
Level	278.0	278	278.0	278.0	278.0	273.0	276.0

Thus, invariability of volume was observed at this concentration. The specific gravity of this mixture \(S_{\frac{50.5^\circ}{4^\circ}}\) is equal to 0.7595.

Concentration 1:6.

Experiment 3. Aldehyde 67.1%,

6.519 grams (paraldehyde + aldehyde) + 39 cubic cm of acetone.

Time . . .	4 h. 35 m.	40 m.	52 m.	5 h. 0 m.	12 m.
Level . . .	85	98	117	125	135

A clearly strong increase in volume, i.e., the formation of a new (above 67.1%) amount of aldehyde from paraldehyde.

Experiment 4. Aldehyde 78.4%,

3.308 grams (paraldehyde + aldehyde) + 19.85 cubic cm of acetone.

Time . . . . . .	1 h. 20 m.	24 m.	32 m.	37 m.	43 m.	3 h. 6 m.	4 h. 4 m.	5 h. 10 m.
Level . . . . . .	69.0	72	75	77	79	92	92	89.0

At 5 h. 10 m. the level fell, probably from resinification. A clearly significant increase in volume, i.e., the formation of aldehyde.

Experiment 5. Aldehyde 81.77%,

3.077 grams (paraldehyde + aldehyde) + 18.5 cubic cm of acetone, or 14.656 grams.

Time . . . .	12 h. 48 m.	55 m.	1 h. 7 m.	14 m.	22 m.	34 m.	3 h. 7 m.	4 h. 0 m.	4 h. 40 m.
Level . . . .	−18	−16	−14.0	−11	−21	−7	−3	−6.0	−6.0

All levels are given taking the lower mark of the dilatometer as 0, i.e., all levels are below the lower mark; in all probability, at 4 h. 0 min. the action of resinification is already noticeable. Clearly there is new formation of aldehyde.

Experiment 6. Aldehyde 84.12%.

3.406 grams (paraldehyde + aldehyde) + 20.4 cubic cent., i.e.
19.278 grams of acetone.

Time . . .	4 h. 25 m.	30 m.	40 m.	53 m.	59 m.	5 h. 19 m.	33 m.	48 m.	6 h. 0 m.
Level . . .	9	7	9	10	11	12	13	14	13

On the next day there was strong compression from resinification. The specific gravity of this solution
\(S \dfrac{50.5^\circ}{4^\circ} = 0.7608\). Expansion must be acknowledged, although a very weak one.

Experiment 7. Aldehyde 85.37%.

4.411 grams (paraldehyde + aldehyde) + 26.5 cubic cent. of acetone
or 20.915 grams.

Time . . .	4 h. 35 m.	41 m.	52 m.	5 h. 5 m.	11 m.
Level . . .	2	3	6	6	6
Time . . .	19 m.	25 m.	43 m.	52 m.	5 h. 59 m.
Level . . .	6	6	4	3	1

At 7 h. 55 min. the level fell to \((-10.0\) millim.), but at 5 h. 59 m. the solution was still completely colorless.

It is difficult to decide whether I have here an increase or constancy of volume. It may be that the rise of the level from 2 to 6 millim. is due to fluctuations in the temperature of the thermostat; otherwise the volume-increase reaction proceeded very rapidly; probably, in comparison with experiment 6, constancy of level should be acknowledged.

The specific gravity \(S \dfrac{50.5^\circ}{7^\circ}\) of this solution = 0.7600.

Experiment 8. Aldehyde 86.66%,

3.395 grams (paraldehyde + aldehyde) + 20.4 cubic cent. or 16.188 grams acetone.

Time . . .	12 h. 23 m.	29 m.	37 m.	46 m.	54 m.	1 h. 2 m.	10 m.	24 m.	34 m.	48 m.
Level . .	33	35	34	36	36	34	35	34	33	32

In the diary it is recorded: “the experiment, unless compression gives a false impression, for there is a possibility of suspecting volatilization of aldehyde.” The specific gravity of this mixture was not determined*. As the percentage of aldehyde at equilibrium one should take the mean of the last two experiments, i.e. 86%.

Concentration 1:4

Experiment 9. Aldehyde 63.05%,

4.192 grams (paraldehyde + aldehyde) + 13.33 grams acetone—gives a strong expansion.

Experiment 10. Aldehyde 72.51%,

3.827 grams (paraldehyde + aldehyde) + 12.143 grams, or 15.3 cubic cent. acetone.

Time . . . . . . .	12 h. 25 m.	30 min.	37½ m.	45 min.	50 min.	1 h. 8 m.
Level . . . . . .	49	51	56	60	63.6	71
Time . . . . . . .	25 min.	40 min.	3 h. 8 m.	4 h. 5 m.	5 h. 10 m.	5 h. 10 m.
Level . . . . . .	77.0	82.0	85.0	82	78.0	78.0

At 5 h. 10 min. there is a slightly noticeable coloration. Clearly a new formation of aldehyde.

*) On the basis of experiments 6 and 7, it should be taken as = 0.760.

Experiment 11. Aldehyde 76.96%,

4.781 grams (paraldehyde + aldehyde) + 19.12 cubic centimeters of acetone, or 15.143 grams.

Time ............	11 h. 6 m.	17 min.	26½ m.	38 min.
Level ............	48	51	54	56
Time ............	48 min.	12 h. 6 m.	45 min.	1 h. 35 m.
Level ............	58	61	63	60

At 1 h. 35 m. signs of resinification are already noticeable—a yellow coloration. Clearly a new formation of aldehyde.

Experiment 12. Aldehyde 79.90%,

4.124 grams (paraldehyde + aldehyde) + 16.5 cubic centimeters, or 13.094 grams, of acetone.

Time .....	4 h. 9 m.	14 min.	24 min.	31 min.	40 min.
Level .....	103	102	106	107	108
Time .....	54 min.	5 h. 20 m.	29 min.	55 min.	55 min.
Level .....	109	110	109	109	109

Specific gravity of the solution \(S \frac{50.5^\circ}{4^\circ} = 0.7633\).

A slight expansion must be acknowledged.

Experiment 13. Aldehyde 81.62%,

4.121 grams (paraldehyde + aldehyde) + 13.07 grams of acetone. For some reason, when filling the dilatometer this solution gave an abundant, solid precipitate (metaldehyde?); therefore the experiment must be regarded as doubtful.

Time . . . . . . . .	12 h 29 m	37 min	43 min	57 min
Level . . . . . . .	49	51	50	50.5
Time . . . . . . . .	1 h 25 m	3 h 3 m	52 min	4 h 28 m
Level . . . . . . .	50.5¹)	42²)	38	35

The specific gravity of this solution

\[ S_{\frac{50.5^\circ}{4^\circ}} = 0.7633. \]

Apparently, the volume of the solution is unchanged. The first reading of the height of the meniscus was made 1 h 8 min after immersion of the dilatometer in the thermostat (at 11 h 21 min); for another whole hour the height of the meniscus does not change, and then a clear contraction already sets in.

Experiment 14. Aldehyde 81.75%,

4.553 grams (paraldehyde + aldehyde) + 18.2 cubic cent. acetone, or 14.467 grams.

Time . . . .	4 h 32 m	35 min	40 min	47 min	59 min
Level . . . .	60	59	57	56	55
Time . . . .	5 h 6 m	16 min	28 min	44 min
Level . . . .	53	52³)	51	49

Is this contraction not due to the fact that I did not mix with the solution the heavy drops of catalyst, \(H_2SO_4 + H_3PO_4\), but that they dissolved with contraction? The specific gravity of the solution

\[ S_{\frac{50.5^\circ}{4^\circ}} = 0.7630. \]

¹) The mixture in the dilatometer began to become slightly colored; the precipitate at the bottom of the dilatometer does not disappear.
²) The turbidity increased; the precipitate does not disappear.
³) No coloration.

Experiment 15. Aldehyde 81.77%,

5.548 grams (paraldehyde + aldehyde) + 22.2 cubic sant. or 17.546 grams acetone.

Time . . . . .	4 h. 35 m.	45 min.	52 min.	5 h. 5 m.	11 min.
Level . . . .	19	19	22	26	24
Time . . . . .	19 min.	25 min.	43 min.	52 min.	59 min.
Level . . . .	26	25	21.5	20.5	20

and at 7 h. 33 min. the contraction was so strong that the level was at zero divisions. Here the catalyst was thoroughly mixed, before being lowered into the thermostat, with an acetone solution. Although, apparently, at 5 h. 43 min. the level began to fall, the contents of the dilatometer are colorless.

(In dilatometer No. III, pure acetone used for these experiments was mixed with 10 drops of the complex catalyst. It was placed in the thermostat on July 13 at 5 h. 28 min.; then the levels were

Time . . . . . . . . . .	5 h. 43 m.	52 min.	59 min.	7 h. 33 m.
Level . . . . . . . . . .	10	9	9	8

and on July 18 the level had fallen by 40 millim., and the contents had become strongly brown.)

Consequently, acetone alone, under the influence of the complex catalyst, gives contraction, but the rate of this reaction is very small in comparison with the rate of resinification and, in particular, with the rate of catalysis.

Experiment 16. Aldehyde 82.85%,

4.766 grams (paraldehyde + aldehyde) + 19.1 cubic sant. or 15.210 grams acetone. Since, in some of the preceding experiments, the thermostat did not maintain the temperature well, in this experiment, together with the readings of the level, I also made temperature readings, which I present. Little catalyst was taken in this experiment (only 4 drops), which also explains the slowness of the catalysis.

Time . . . . .	12 h. 37 m.	42 min.	52 min.	1 h. 2 m.	13 min.
Level . . . .	78	78	77	77	76
Temperat. . . .	50,35	50,45	50,4	50,4	50,4
Time . . . .	26 min.	36 min.	50 min.	2 h. 5 m.	15 min.^1)
Level . . . .	75	71	71	70	70
Temperat. . . .	50,35	50,4	50,4	50,4	50,4
Time . . . .	3 h. 0 m.	3 h. 44 m.	4 h. 30 m.	32 min.	5 h. 16 m.
Level . . . .	66	63	59	59	54
Temperat. . . .	50,45	50,4	—	—	—

At 5 h. 16 min. traces of coloration are observed. The column shows a clear contraction of volume, i.e., a new formation of paraldehyde; it must therefore be acknowledged that the equilibrium at this dilution corresponds to 81,8% aldehyde.

Concentration 1 : 2.

Experiment 17. Aldehyde 65,26%,

10,301 grams (paraldehyde + aldehyde) + 20,6 cubic centimeters of acetone, or 16,343 grams.

Time . . . .	4 h. 46 m.	52 m.	5 h. 2 m.	8 m.	28 m.	45 m.	6 h. 0 m.
Level . . .	96	98	101	103	110^2)	113	116

On the next day, compression: the level fell to 89, the mixture turned brown. A clear new formation of aldehyde.

^1) The contents are colorless.
^2) The coloration is almost imperceptible.

Experiment 18. Aldehyde 72.47%,

7.153 grams (paraldehyde + aldehyde) + 14.3 cubic cent. or 11.321 grams of acetone.

Time . . . . .	3 h. 35 m.	41½ min.	50 min.	4 h. 6 m.	14 min.
Level . . . .	12	13	10	10	10
Time . . . . . . .	21 m.	27 m.}	5 h. 0 m.	5 h. 55 m.
Level . . . . . .	9	6	0.0	−4.5

It must be admitted that contraction occurs, i.e. the formation of paraldehyde. The equilibrium is about 71% aldehyde, but the data are insufficient to judge it more precisely.

B) Solutions in toluene.

Beginning work with solutions in toluene (earlier than with other solvents), I carried out a series of, so to speak, exploratory experiments. Their purpose was to determine at what approximate ratio between paraldehyde and aldehyde, at a given dilution with solvent, equilibrium between these substances sets in. The method was the same as in the subsequent exact experiments; only the solutions were prepared not by weighing three substances (paraldehyde, aldehyde, and solvent), but by measuring them with a pipette. Paraldehyde and toluene were drawn into the pipette at the ordinary temperature of these liquids and assigned the corresponding temperature-specific densities, while the aldehyde was of course cooled below zero, but as its specific gravity I used the specific gravity determined by me for room temperature. In the following table, under heading I, I give the composition of these ternary mixtures, expressing it as (I:X), meaning thereby that in mixture X volumes of toluene correspond to 1 volume of paraldehyde, counting the aldehyde also as paraldehyde; under heading II is given the percentage, approximate content by weight of aldehyde, taking the sum of the weights of paraldehyde and aldehyde as 100; the third heading shows the catalyst, and in the fourth is given the observed, more or less strong, change in the volume of the mixtures from catalysis:

I.	II.	III.	IV.
1 : 10	73%	$\mathrm{SO_2}$	Distinct contraction.
"	65%	?	Distinct expansion.
"	69%	$\mathrm{SO_2}$	No change in volume.
1 : 7	58%	"	Negligible expansion,
"	62%	"	No change in volume.
1 : 4	40.5%	$\mathrm{H_3PO_4}$—solution.	Distinct expansion.
"	50%	"	Slight expansion.
"	55%	"	Distinct contraction.
"	45%	"	Distinct expansion.
"	47.8%	"	Distinct expansion.
"	52%	"	Slight expansion.
"	55%	$\mathrm{SO_2}$	Strong contraction.
"	45%	"	Distinct expansion.
1 : 2	45%	$\mathrm{H_3PO_4}$	No change in volume.
"	46.5%	"	Slight contraction.

These approximate experiments give the same results as the more exact ones below. They indicate, in equilibrium systems, the following approximate aldehyde content:

for concentrations \(1 : 10\) . . . 69% aldehyde.
" \(1 : 7\) . . . 62% "
" \(1 : 4\) . . . 53% "
" \(1 : 2\) . . . 45% "

The following exact experiments were carried out entirely analogously to the preceding ones, with acetone.

In all the experiments the so-called composite catalyst was used, i.e. a mixture of 1 vol. $\mathrm{H_2SO_4}$ and 4 vol. of an aqueous solution of phosphoric acid containing 70.4% $\mathrm{H_3PO_4}$. In all the experiments the same quantity of this catalyst was taken, 10 drops. At the bottom of the dilatometer reservoir it forms an aqueous layer that does not mix with the toluene solution; it becomes resinified (turns brown) very quickly, sometimes during a single heating of the dilatometer, i.e. within 10 minutes, but this phenomenon does not affect the change in volume of the entire system caused by catalysis; resinification of the toluene layer begins much later, and often, even when this latter occurs, the expansion of the solution still continues.

Concentration 1 : 10.

Experiment 1. Aldehyde 66.74%,

3.960 g (paraldehyde + aldehyde) + 40 cu. cm toluene. There is a suspicion that the aldehyde has become somewhat volatilized.

Time . . . .	12 h. 38 m.	53 min.	1 h. 2 m.	17 min.	33 min.
Level . . . .	−1	+1.2	+2.5	+6	8
Time . . . .	15 min.	2 h. 15 m.	4 h. 14 m.	5 h. 15 m.	55 min.
Level . . . .	11	12	16	17	16

Clear expansion, and on the following day the level = 13 millim.; moreover, the toluene layer became resinous. In this experiment the lower aqueous layer of catalyst, even at 12 h. 38 min., already has a clear, though faint, yellow coloration.

Experiment 2. Aldehyde 66.53%,

4.268 g (paraldehyde + aldehyde) + 40 cu. cm toluene.

Time . . . .	11 h. 59 m.	12 h. 12 m.	21 m.	35 m.	51 m.	1 h. 7 m.	1 h. 25 m.
Level . . .	38¹)	38	41	40	40	40	42
Time . . . .	37 m.	51 m.	3 h. 18 m.	4 h. 20 m.	5 h. 0 m.	23 m.	55 m.
Level . . .	41	42	44	44	46²)	50	49

Clear expansion—new formation of aldehyde.

Experiment 3. Aldehyde 68.29%,

4.362 g (paraldehyde + aldehyde) + 40 cu. cm toluene.

Time . . .	1 h. 30 m.	37 m.	47 m.	51 m.	3 h. 18 m.	40 m.	5 h. 23 m.
Level . . .	27	28	31	32	36	37	33

Expansion is clear.

¹) Colored only the lower aqueous layer of catalyst—H₃PO₄ + H₂SO₄.
²) The toluene layer also colored.

Experiment 4. Aldehyde 69.2%,

4.195 grams (paraldehyde + aldehyde) + 40 cubic cent. of toluene.

Time . . . . . . .	4 h 36 m	41 m	44 m	48 m	52 m	5 h 8 m
Level . . . . . . .	112	115	114	113	114	115
Time . . . . . . .	23 m	29 m	36 m	51 m	59 m	8 h 20 m
Level . . . . . . .	115	116	116	115	115	114

On the next day, owing of course to resinification, the level fell to 91 millim. Apparently, there is an equilibrium system, in other words, constancy of volume.

Experiment 5. Aldehyde 70.04%,

3.386 grams (paraldehyde + aldehyde) + 34.6 cubic cent. of toluene.

Time . . . . . . .	10 h 57 m	1 h 5 m	9 m	22 m	45 m	12 h 1 m
Level . . . . . . .	123	123	122	122	122	123
Time . . . . . . .	55 m	1 h 27 m	3 h 15 m	4 h 25 m	5 h 48 m	5 h 48 m
Level . . . . . . .	123	124	122	120¹)	119	119

Here too the volume is unchanged, but there is a suspicion that the aldehyde in this experiment is less than 70.04%; namely, appreciable oxidation of it to CH₃CO₂H may have occurred, for little aldehyde remained in the vial where it was stored. To avoid this error, I subsequently tried, after opening the sealed tube with aldehyde, to use it all on the same day.

¹) The toluene layer is already colored.

Experiment 6. Aldehyde 68.96%,

3.321 grams (paraldehyde + aldehyde) + 32.2 cubic centimeters of toluene.
Aldehyde fresh.

Time . . . .	1 h. 9 m.	15 m.	25 m.	31 m.	43 m.	53 m.
Level . . . .	98	96	97	97	97	98
Time . . . .	2 h. 10 m.	4 h. 17 m.	41 m.	57 m.	6 h. 0 m.	6 h. 0 m.
Level . . . .	98	97	97	96	94	94

The volume is unchanged—an equilibrium system.
On the following day the level fell to 72.8.

Specific gravity \(S \frac{50.5^\circ}{4} = 0.8347\). For the percentage of aldehyde at equilibrium one should take the mean from the last three experiments, i.e. 69.4%.

Concentration 1:7.

Experiment 7. Aldehyde 59.05%,

4.033 grams (paraldehyde + aldehyde) + 28 cubic centimeters or 24.207 grams of toluene.

Time . . . .	4 h. 53 m.	58 m.	5 h. 6 m.	15 m.	22 m.	30 m.
Level . . . .	−1	−1	−1	−1	+1	+3
Time . . . .	37 m.	48 m.	55 m.	6 h. 3 m.	8 h. 10 m.	8 h. 10 m.
Level . . . .	+4	+5	+4	+4	+12	+12

Aldehyde fresh. Undoubtedly—expansion.

Experiment 8. Aldehyde 60.85%,

3.920 grams (paraldehyde + aldehyde) + 28 cubic centimeters of toluene.

Time . . .	12 h. 45 m.	53 m.	1 h. 0 m.	8 m.	16 m.	25 m.	30 m.	37 m.	45 m.	5 h. 10 m.
Level . . .	61	61	61	61	62	62	61	61¹)	62	63²)

Specific gravity of the toluene solution \(S \dfrac{50.5^\circ}{4^\circ} = 0.8355\). Apparently, one may regard the system as being in equilibrium, but there may be less aldehyde than 60.85%, owing to oxidation, for although it was corked the day before, the flask, having developed a crack, stood that way overnight.

Experiment 9. Aldehyde 62.18%,

3.956 grams (paraldehyde + aldehyde) + 21.200 grams of toluene.

Time . . .	12 h. 33 m.	38½ m.	46 m.	55 m.	1 h. 5 m.
Level . . .	103	104	104	103	103
Time . . .	14 m.	3 h. 0 m.	4 h. 0 m.	5 h. 0 m.	5 h. 45 m.
Level . . .	102	101	100	98	97

Either contraction, or constancy of volume. Specific gravity of this solution \(S \dfrac{50.5^\circ}{4^\circ} = 0.8351\). I assume that at this concentration equilibrium occurs at an aldehyde content equal to the mean of the two last experiments, \((62.18 + 60.85) : 2 = 61.5\%\) aldehyde.

¹) Toluene colorless.
²) Toluene slightly screened.

Concentration 1 : 4.

Experiment 10. Aldehyde 52.30%,

5.230 grams (paraldehyde + aldehyde) + 20 cubic centimeters of toluene, or 17.200 grams.

Time . . .	11 h. 6 m.	13	21	37	45
Level . . ,	89	93	96	103	105
Time . . .	12 h. 0 m.	15 m.	37 m.	1 h. 0 m.	2 h. 0 m.
Level . . .	108	111	113	117	121

Clear expansion.

Experiment 11. Aldehyde 53.80%,

4.226 grams (paraldehyde + aldehyde) + 16.6 cubic centimeters of toluene, or 14.334 grams.

Time . . .	1 h. 25 m.	32 m.	37 m.	43 m.	48 m.	55 m.	2 h. 4 m.
Level . . .	117	117	117	116	116	116	117
Time . . .	4 h. 3 m.	23 m.	35 m.	47 m.	5 h. 5 m.	5 h. 30 m.	40 m.
Level . . .	116*)	115	116	117	116	114	115**)

On the following day the level fell to 92 millimeters. The specific gravity of this solution
\(S \frac{50.5^\circ}{4^\circ} = 0.838\). Equilibrium system, constancy of volume.

) The toluene is slightly colored.
*) The toluene is already considerably colored.

Concentration 1:2.

Experiment 12. Aldehyde 45.21%,

10.088 grams (paraldehyde + aldehyde) + 20 cubic centimeters of toluene, or 17.334 grams.

Time	11 h. 18 m.	23½ m.	29 m.	37 m.	52 m.	12 h. 23 m.	32 m.	50 m.
Level	75	76	76	76	78	79	78	80
Time	1 h. 10 m.	25 m.	54 m.	2 h. 10 m.	4 h. 17 m.	41 m.	57 m.	6 h.
Level	82	82	82	83	86	87	87	87

By the end of the experiment the toluene was distinctly colored. Distinct expansion. Specific gravity

\[ S \frac{50.5^\circ}{4^\circ} = 0.8431. \]

Experiment 13. Aldehyde 46.31%,

10.683 grams (paraldehyde + aldehyde) + 21.4 cubic centimeters, or 17.717 grams, of toluene.

Time	11 h. 18 m.	28 m.	47 m.	12 h. 4 m.	18 m.
Level	98	98	98	98	97
Time	34 m.	46 m.	1 h. 4 m.	4 h. 0 m.	5 h. 0 m.
Level	97	97	97	97	95

Specific gravity of this solution

\[ S \frac{50.5^\circ}{4^\circ} = 0.8426. \]

I assume in this experiment the volume remains unchanged.

C) Aqueous solutions.

Concentration 1 : 10.

Experiment 1. Aldehyde 70%*);

as solvent, I took 20 cubic cm of pure water and 20 cubic cm of decinormal hydrochloric acid. A strong and rapid increase in volume is observed.

Experiment 2. Aldehyde 70%;

the solvent (and likewise the catalyst) was a mixture of 36 cubic cm of water and 4 cubic cm of decinormal hydrochloric acid. A clear expansion was observed.

Experiment 3. Aldehyde 85%;

solvent—35 cubic cm of water and 5 cubic cm of decinormal acid. A clear expansion is observed.

Experiment 4.

Composition of the mixture: 4.84 cubic cm of pure aldehyde + 35 cubic cm of water + 5 cubic cm of decinormal hydrochloric acid.
The change in level height with time is as follows:

Time . . . . .	4 h. 27 m.	57 min.	5 h. 14 m.	5 h. 31 m.	5 h. 55 m.
Level . . . .	40	40	39	43	42

Experiment 5. Aldehyde 93%;

as solvent I took 35 cubic cm of water and 5 cubic cm of decinormal hydrochloric acid.

Time . . . . . . . .	5 h. 29 m.	5 h. 32 m.	5 h. 55 m.
Level . . . . . . . .	109	107.5	108

*) As 100 was taken the sum of the weights of paraldehyde and aldehyde, as before, in the experiments with acetone, and the method of observation was exactly the same.

In experiments 4 and 5 the thermostat did not hold the temperature, and I carried out these experiments simultaneously and, out of absent-mindedness, lowered into the thermostat very cold (the preparation of the solutions, so as not to lose aldehyde, was carried out under cooling) and, moreover, large, accurate dilatometers*). On the next day, when the thermostat held the temperature perfectly, the dilatometer of the 4th experiment showed, all day long, invariably 40, i.e. a distinct expansion.

Experiment 6

is a complete repetition of experiment 5, i.e. aldehyde 93%. With the thermostat temperature unchanged, the levels were as follows:

Time . . . . .	12 h. 20 m.	1 h. 4 m.	1 h. 47 m.	4 h. 24 m.	5 h. 37 m.
Level . . . .	140	140	141	142.2	143.8

and on the next day 145 millimeters. Expansion, undoubtedly.

It must be acknowledged that at this concentration (1 : 10), in aqueous solutions, in the presence of the catalyst, there is practically**) only aldehyde, i.e. almost 100% of the paraldehyde is subjected to catalysis.

Concentration 1 : 6.

Experiment 7. Aldehyde 96.5%;

5.206 grams (paraldehyde + aldehyde) + 31.2 cubic centimeters of water. To this solution I added 7 drops of the complex catalyst***)

Time . . . . . . .	1 h. 34 m.	37 m.	40 m.	42 m.	47 m.	50 m.
Level . . . . . . .	19	19	20	20	13†)	14.5
Time . . . . . . .	56 m.	3 h. 5 m.	30 m.	4 h. 0 m.	13 m.	39 m.
Level . . . . . . .	14	13	13	14	14	12

*) Whereupon the temperature of the thermostat at once clearly fell.

**) With the accuracy of the method chosen by me.

***) The (complex) catalyst is exactly the same as in the experiments with acetone.

†) I removed a gas bubble that had formed in the capillary, which caused the level to change—to fall.

And at 5 h 14 min the level = 12.0. One should acknowledge the invariability of the volume. In this experiment, in view of the slow filling of the dilatometer, it may (?) be suspected that part of the aldehyde evaporated.

Experiment 8.

Pure aldehyde 3.696 grams + 22.2 cubic centimeters of water. This solution for some reason turned slightly opalescent. Complex catalyst—7 drops.

Time . . . .	2 h 15 m	20 m	3 h	3 h 44 m	4 h 13 m	32 m	5 h 16 m	29 m	35 m
Level . . . .	53	53	51	50.5	49	50	49	49	49

and on the following day the level fell to 45; apparently—weak compression.

Concentration 1 : 4.

Experiment 9. Aldehyde 94.4%;

3.177 g (paraldehyde + aldehyde) + 12.71 grams of water; 3 drops of complex catalyst.

Time . . . .	4 h 39 m	43 m	52 m	59 m	5 h 9 m	18 m	35 m	45 m	55 m
Level . . . .	108	106	107	106	106	106	104	104	104

At 5 h 55 m complete decolorization; on the following day the level fell to 95, but no resinification (yellowing) is visible.

Experiment 10. Aldehyde 89.7%;

4.707 g (paraldehyde + aldehyde) + 18.85 cubic centimeters of water, or 18.815 grams. 4 drops of complex catalyst.

Time . . . . . .	1 h 13 m	15 m	20 m	29 m	42 m	2 h 33 m
Level . . . . . .	95	97	99	99	100	101
Time . . . . . .	55 m	4 h 0 m	33 m	5 h 0 m	20 min.
Level . . . . . .	100	103	104	104	104

The next day the level dropped and continued to drop over the course of a week, although the solution continued to remain colorless. Consequently, the limit of the reaction at this dilution is closer to 94.4% than to 89.7%.

At equilibrium I take

\[ \frac{94.4 \times 2 + 89.7}{3} = 92.8\% \]

aldehyde.

Conclusions.

In the following table I summarize the results obtained in the separate experiments described above, on solutions in water, acetone, and toluene. In the first column are given the concentrations of the solutions, expressed by means of \(1 : X\) (see the dilution experiments with toluene); in the next three—the weight percentage of aldehyde characteristic of the equilibrium system with different solvents.

Concentrations.	Solvents — water.	Solvents — acetone.	Solvents — toluene.
\(1 : 10\)	almost 100	89.7	69.4
\(1 : 7\)	—	—	61.5
\(1 : 6\)	96.5	86	—
\(1 : 4\)	92.8	81.8	53.8
\(1 : 2\)	—	71 (?)	46.3

Thus the equilibrium in the liquid phase, other conditions being equal, depends to an extraordinary degree on the nature of the solvent, and in this result my work adjoins the recently published work of Prof. I. W. Brühl (Die Rolle d. Medien in Lösungsvorgänge, Zeitschr. f. ph. Chemie 1899 XXX, 1); only the reaction considered here, the limiting transformation of paraldehyde into aldehyde, makes it possible to investigate this equilibrium quantitatively (and, moreover, with a very large number of solvents), whereas in the above-mentioned work Brühl is limited rather to qualitative results. Studying the more or less strongly expressed transition of certain substances into their tautomers both under the influence of heat and under the influence of dissolution in certain solvents, and defining the latter as the “tautomerizing force” of the solvent, Brühl, for the latter, instead of quantitative data, uses expressions: “very weak” (for chloroform, see p. 36 loco citato) or “strong” (for ethyl alcohol), etc. Brühl says there: “A comparison of the dissociating force of solvents with any other property of theirs can never be adduced—

lead to the conclusion of their proportionality. This is also not the case with respect to the dielectric constant of solvents; there can exist only a qualitative connection between dissociating and dielectric forces, a certain general correlation (im grossen und ganzen); the same kind of relation also exists between tautomerizing and dielectric forces. Below are given, for the solvents investigated here, the dielectric constants \(E\) according to Drude’s measurements and, for comparison, according to the measurements of other observers.

Solvent	Tautomerizing force	Dielectric constants \(E\)
Chloroform	very weak	4.95; 3.95 (Thwing); 5.01 (Ratz).
Benzene	weak	2.26; 2.25 (Nernst).
Carbon disulfide	weak	2.64; 2.50 (Thwing); 2.63 (Franke).
Bromoform	weak	4.72
Ethyl alcohol	strong	21.7; 25.0 (Thwing); 25.8 (Nernst).
Methyl alcohol	strong	32.5; 34.0 (Thwing); 32.6 (Tereshin).

And further, p. 37, “ethyl ether according to Drude has almost the same \(E\) (4.36) as chloroform (4.95), whereas the former body dissociates much more strongly. Acetic acid has \(E\) (6.46) only slightly greater than chloroform, whereas the former, as is known, is much more effective as a cleaving agent of aggregates. Further, it has been proved that pure alcoholic solutions of many electrolytes conduct better than when water is added. On the contrary, both Thwing and Drude found that absolute methyl and ethyl alcohols, upon addition of water, give larger dielectric constants; whereas a diminution of electrical conductivity would lead one to expect smaller \(E\)’s.

Although it has been firmly established in every respect that there can be no question of proportionality between the dielectric and dissociating forces, nevertheless there is a very noteworthy, firmly established qualitative connection.”

And my present investigations once again emphasize very clearly this same qualitative connection, if one compares, on the one hand, the dissociating force of the solvents investigated, as it is expressed in a more or less far-reaching dissociation of paraldehyde (see above the table derived from my experiments), and, on the other hand, the dielectric constants of the same solvents (I take them from p. 47, Brühl, loco citato).

Water—81.7; acetone—20.7; toluene—2.4.

The correlation between the dielectric constant and the dissociating (into ions) force of a solvent was put forward by Nernst in 1894 (Zeitschr. f. ph.

Chemie 13, 531), and already from 1895 (Zeitschr. f. ph. Chemie 18, 515) it is interpreted by Brühl from the standpoint of the residual affinities of solvents. Calling “energy of the medium” (Medialenergie) that energy of the solvent which produces the splitting of aggregates of dissolved substances, determines the magnitude of their dielectric constant and the tautomerization and ionization connected with the latter, Brühl sees in these phenomena, as the cause, chiefly the influence of the residual or additional affinities of the solvents (p. 42).

This question still contains very much that has not been solved, and, in the sense of clarifying Brühl’s idea, I think only that the study of the dissociation of paraldehyde in various solvents (and a very large number of them can be selected) could provide much illuminating material, for this reaction is capable, like few others, of characterizing the dissociating properties of solvents by exact data.

I shall add further that, according to the cryoscopic data, in all three solvents investigated one must expect for the molecules precisely those magnitudes which paraldehyde and aldehyde also have in the vapor state, i.e. \((\mathrm{CH_3COH})_3\) and \(\mathrm{CH_3COH}\); consequently, the cause of the difference in the dissociating forces does not lie in a different aggregation of the dissolved substance in the different solvents.

The equilibrium between the substances investigated by me very much recalls the limiting reaction studied by Koelichen (Zeitsch. f. ph. Chemie 1900 XXXIII, 129), namely the splitting of diacetone alcohol into 2 molecules of acetone, likewise under the influence of catalysts (alkaline ones). Both for diacetone alcohol and for paraldehyde, the dissociation increases with increasing mass of the solvent, and in dilute solutions practically reaches 100%, while the constant in the Guldberg–Waage equation for the equilibrium state correspondingly increases, and its changes with change in concentration are expressed by similar curves (see Koelichen, p. 143, loco citato). To the reaction investigated by me the Guldberg–Waage equation must be applied in the following form:

\[ \frac{1-x}{v}=K\frac{x^3}{v^3}, \text{ whence } \frac{(1-x)v^2}{x^3}=K, \]

where \(K\) is the equilibrium constant, \(v\) is the volume of the solution in liters, in which one gram-molecule (132 grams) of paraldehyde is contained, and \(x\) denotes the degree of splitting of paraldehyde, i.e. that part of one molecule of paraldehyde which at equilibrium has passed into aldehyde.

In the following table I give the values of this constant for toluene solutions, taking for \(x\), of course, from my preceding table the values—0.463—0.538—0.615—0.694 for the corresponding

concentrations placed in column I; column II contains these quantities \(x\); column III gives \(V\), which is easily calculated from the weight composition of the solutions*) and from the specific gravity determined for the temperature \(50.5^\circ\); finally, the fourth column gives the values of the constant \((K)\).

I (concentration).	II (\(x\)).	III \(V\) (liters).	IV (\(K\)).
\(1 : 10\)	0,694	1,493	2,105
\(1 : 7\)	0,615	1,128	2,106
\(1 : 4\)	0,538	0,692	1,420
\(1 : 2\)	0,463	0,4165	0,938

As with Koelichen, there is at first a strong increase of the constant \(K\), and then its invariability.

In view of the fact that errors in determining the specific gravity of solutions, amounting, for example, to 0.003, have very little effect on the values of the constant (as is not difficult to verify from the formula), I can, taking for this constant the value 2.105, and calculating the specific gravity of the solution by the rule of mixtures, calculate also the percentage of dissociation at any given dilution from the following cubic equation \((1-x)v^2=Kx^3\).

Having also carried out, for acetone solutions, the corresponding calculations of the constant \(K\), and, by the same equation as for toluene solutions, I obtain the following table, entirely similar to the table for toluene solutions:

I (concentration).	II (\(x\)).	III \(V\) (liters).	IV (\(K\)).
\(1 : 10\)	0,897	1,544	0,340
\(1 : 6\)	0,860	1,000	0,220
\(1 : 4\)	0,818	0,720	0,172

For aqueous solutions I do not make the corresponding calculations of the constant \(K\); for such solutions, at a concentration of \(1 : 10\), I have, for the mass of aldehyde, a number very close to 100%; therefore, as is easy to see from the very formula used for calculating \(K\), a small error in deter-

*) Of course, when calculating \(V\), for the weight of paraldehyde one must take the sum of the weighed amounts of paraldehyde and aldehyde.

the determination of the mass of aldehyde will have a very strong effect on the magnitude of this constant, and to determine this mass of aldehyde accurately presents considerable difficulty. The second reason is the absence of data for the specific gravities of these solutions, although the latter, as I have already mentioned somewhat above, is not so important, and it would be possible to calculate such specific gravities for the given concentrations by the mixing rule. If for \(V\), and for aqueous solutions at a concentration of \(1:6\), one takes a value equal to 1 liter (which is, of course, very close to the truth), then for \(E\) I calculate only \(0.077 \left[= \dfrac{0.035}{0.965^3}\right]\), i.e., as should have been expected, a strong decrease of the constant.

Thus, for the dissociation of paraldehyde in the three solvents investigated, a strong decrease of the constant is observed together with an increase of the dissociation of paraldehyde in the given solvent in comparison with the others.

Let us suppose that in acetone, beginning with a concentration of \(1:10\), an invariable constant, equal to 0.34, has been reached, and let us take as a measure of the dissociating power of the solvent the reciprocal of that dilution \((v)\) at which in both solvents we have the same ratio between the active masses of paraldehyde and aldehyde; then for toluene

\[ \frac{(1-x)v_1^2}{x^3}=2.104, \]

and for acetone

\[ \frac{(1-x)v_2^2}{x^3}=0.34. \]

Hence the ratio of the dissociating powers of toluene and acetone

\[ \left[\frac{1}{v_1}:\frac{1}{v_2}\right] \]

is equal to the inverse ratio of the square roots of the corresponding constants. For bimolecular reactions, where one molecule splits only into two others, as for diacetone alcohol, the ratio of the dissociating powers will already be simply equal to the inverse ratio of the constants.

Further, for monomolecular reactions, where one molecule passes only into one molecule of another structure (for example, the transformation of the enol form into the keto form, the transformation of an ortho isomer into a para isomer, etc.), at equilibrium we have, for the first solvent,

\[ k_1=\frac{1-x_1}{x_1}, \]

and for the second,

\[ k_2=\frac{1-x_2}{x_2}; \]

where \(k_2\) and \(k_1\) are constants, and \(x_1\) and \(x_2\) are those parts of 1 gram-molecule of the substance initially taken which at equilibrium have assumed another structure. The magnitude of the dilution \((v)\) does not enter into such equations; the dissociating power of the solvents must then be determined through \(x_1\) and \(x_2\) at the same dilution; consequently, the ratio of the dissociating powers of two solvents will be

\[ \frac{x_1}{x_2}=\frac{1}{k_1+1}:\frac{1}{k_2+1}=\frac{k_2+1}{k_1+1}. \]

For reactions in which one particle splits into 4 others, we shall again have a different relation, etc.

Let us suppose that, having chosen several solvents

\[ A_1—A_2—A_3\ldots, \]

quite analogously to the study of the dissociation of paraldehyde in aqueous, toluene, and acetone solutions, I study some monomolecular reversible reaction; then I replace this latter by some bimolecular one, then by a trimolecular one, etc., taking the same solvents. Then, according to the preceding, I obtain:

	Monomolecular reaction.	Bimolecular reaction.	Trimolecular reaction.
Equilibrium constants.	\(\kappa_1—\kappa_2—\kappa_3\ldots\)	\(\gamma_1—\gamma_2—\gamma_3\ldots\)	\(\delta_1—\delta_2—\delta_3\ldots\)
Quantities proportional to the dissociating forces of the solvents . . . . . .	\(\dfrac{1}{\kappa_1+1},\ \dfrac{1}{\kappa_2+1},\ \dfrac{1}{\kappa_3+1}\ldots\)	\(\dfrac{1}{\gamma_1},\ \dfrac{1}{\gamma_2},\ \dfrac{1}{\gamma_3}\ldots\)	\(\dfrac{1}{\sqrt{\delta_1}},\ \dfrac{1}{\sqrt{\delta_2}},\ \dfrac{1}{\sqrt{\delta_3}}\ldots\)

Admitting the possibility of a numerical relation of the dissociating forces and of some function of the physical properties of the pure solvents (for example, dielectric constant, latent heat of evaporation, etc.; see Brühl loco citato), I obtain

\[ f(A_1): f(A_2): f(A_3)\ldots = \dfrac{1}{\kappa_1+1}:\dfrac{1}{\kappa_2+1}:\dfrac{1}{\kappa_3+1}\ldots \]

\[ "\quad "\quad "\ldots = \dfrac{1}{\gamma_1}:\dfrac{1}{\gamma_2}:\dfrac{1}{\gamma_3}\ldots \]

\[ "\quad "\quad "\ldots = \dfrac{1}{\sqrt{\delta_1}}:\dfrac{1}{\sqrt{\delta_2}}:\dfrac{1}{\sqrt{\delta_3}}\ldots \]

Whence

\[ \dfrac{1}{\kappa_1+1}:\dfrac{1}{\kappa_2+1}:\dfrac{1}{\kappa_3+1}\ldots = \dfrac{1}{\gamma_1}:\dfrac{1}{\gamma_2}:\dfrac{1}{\gamma_3}\ldots = \dfrac{1}{\sqrt{\delta_1}}:\dfrac{1}{\sqrt{\delta_2}}:\dfrac{1}{\sqrt{\delta_3}}\ldots \]

(Of course, all this at the same temperature and with the other physical factors the same.)

It should be noted that the last relation was derived on the supposition that the reactions being studied do not change their order, even though the solvent, the medium in which they occur, changes.

If such a relation existed, then we would also have a single numerical series of the dissociating powers of solvents, and then, having investigated the latter with respect to some monomolecular reaction, i.e. the series \(k_1 - k_2 - k_3 \ldots\), and, on the other hand, having determined, for only one solvent from the series taken, in the study of some bimolecular reaction, the equilibrium constant, one of the \(\gamma\)’s, and consequently also the dissociating power of the solvent, I could already calculate from the above relation all the other \(\gamma\)’s. The same would hold with respect to \(b\), etc. For this reason alone one cannot expect this, that different chemical compounds, which we would study in reactions of different order, would manifest themselves differently in different solvents as regards their ability to form complex molecules; and the latter entails that one and the same reaction in different solvents would also have a different order; consequently, the basic assumption from which the preceding relation was derived is violated; for this reason, too, a single numerical series of the dissociating powers of solvents has no place. (As an example I shall mention only that the dissociation of the ester \(\mathrm{CCl_3CO_2(C_5H_{11})}\) into trichloroacetic acid and amylene, studied by Nernst and Hohmann, changes its order when the solvent amylene is replaced by benzene, as a result of which the equilibrium constant also changes very greatly, contrary to the value expected in the absence of a change in the order of the reaction; see Zeitsch. f. phys. Chemie 11, 352).

Brühl, in the article cited above, comes to the same conclusion, although from different considerations (p. 35):

“The dissociating power of different solvents, both with respect to ionization and with respect to the splitting of aggregates, is not some constant property, as set forth in the introduction. It depends rather both on the nature of the given solvent and on the nature of the dissolved substance. Therefore, strictly speaking, the dissociating powers of different solvents can be compared not in general, but only with respect to one and the same dissolved substance. If, however, one wishes to compare different solvents with respect to their dissociating properties in general, i.e. without paying attention to the properties of the dissolved substance, then this can be done only from the qualitative side; there can be no question of any true quantitative relation.”

It is easy to see what the ratio of two equilibrium constants in the liquid phase will be equal to for two different solvents; one need only also take account of the gas phase. Then for solutions in toluene we obtain the following four equations:

\[ \frac{1-x_1}{v_1}=K_m\frac{x_1^3}{v_1^3}\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots (I) \]

having place for the active masses of paraldehyde and aldehyde, dissolved in toluene, and the equilibrium constant \(K_m\) (see above, p. 88).

For the equilibrium between the vapors of aldehyde and paraldehyde in the gas phase we have

\[ p_n = K_r (p_a)^3 \ldots \tag{II} \]

where \(p_n\) and \(p_a\) are the partial pressures of these vapors, and \(K_r\) is the equilibrium constant in the gas phase.

The equilibrium of the molecules of paraldehyde, dissolved in toluene and present in the gas phase, leads to the equation

\[ \frac{1-x_1}{v_1}=L_n p_n \ldots \tag{III} \]

where \(L_n\) is a quantity proportional to the solubility of the vapors of paraldehyde in the liquid phase, under the conditions existing at the moment of the equilibrium under consideration (see Nernst, Theor. Chem. 2nd Auflage, 450), and \(x—v—p_n\), of course, have the same meanings as in the first two equations.

Finally, the condition of equilibrium of the aldehyde molecules, gaseous and dissolved in the liquid phase, quite analogously to the preceding one (III), is the following equation:

\[ \frac{x_1}{v_1}=L_a p_a \ldots \tag{IV} \]

where only \(L_a\) denotes a quantity proportional to the solubility of the vapors of aldehyde in the same liquid phase.

For solutions in acetone we have four entirely analogous equations:

\[ \frac{1-x_2}{v_2}=K_m\frac{x_2^3}{v_2^3}\ldots \tag{1} \]

\[ p'_n=K_r(p'_a)^3\ldots \tag{2} \]

\[ \frac{1-x_2}{v_2}=L'_n p'_n\ldots \tag{3} \]

\[ \frac{x_2}{v_2}=L'_a p'_a\ldots \tag{4} \]

In equations (2) and (II) the constants \(K_r\) are identical, for the vapors of the solvents in the gas phase act as indifferent gases, i.e. they do not change the equilibrium constants (see Nernst, Theor. Chem. 2nd Auflage, 413), and therefore these two equations give

\[ p_n:p'_n=p_a^3:p_a'^3\ldots \tag{5} \]

The equations (I), (III), (IV) give

\[ L_n p_n=K_m L_a^3 p^3\ldots \tag{6} \]

In exactly the same way, from equations (1), (3), and (4) we obtain

\[ L'_n p'_n = K_a L'_a{}^3 p'_a{}^3 \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots (7) \]

The last three equations also yield

\[ \frac{L_n}{L'_n}\times\left[\frac{L'_a}{L_a}\right]^3 = K_m : K_a \]

that simple relation between the constants \(K_m\) and \(K_a\), from which one can calculate one of them (\(K_m\) or \(K_a\)) from the other, knowing the quantities on the left-hand side, i.e. the partial pressures of the vapors or their solubilities.

The last formula is easily transformed into the following:

\[ \frac{L_n}{L_a^3} : \frac{L'_n}{L'_a{}^3} = K_m : K_a \quad \text{or} \quad K_m : K_a = f(L_n,L_a) : f(L'_n,L'_a) \]

Repeating the same reasoning for any bimolecular reaction, we have:

\[ \frac{L_n}{L_a^2} : \frac{L'_n}{L'_a{}^2} = K_m : K_a \quad \text{or} \quad K_m : K_a = F(L_n,L_a) : F(L'_n,L'_a) \]

Thus, the equilibrium constants in a reversible reaction are determined one from the other, but only if we take into account both the form of the function \(f\) or \(F\), and hence the order and the character of the reaction, and those physical properties \(L_n\)—\(L_a\)—\(L'_n\)—\(L'_a\), which depend both on the solvent and, necessarily, on all the dissolved substances participating in the reversible reaction under study.

CHAPTER THREE.

Having established that in aqueous solutions, with a concentration of 1 volume of paraldehyde to 10 volumes of water, under the influence of catalysts there occurs practically (for the chosen dilatometric method) complete decomposition of paraldehyde into 3 particles of aldehyde (see the preceding chapter, aqueous solutions), I investigated the rate of this catalysis at 50.5° under the influence of aqueous solutions of various acids. Since in this case as well the reaction studied by me is very reminiscent*) of the catalysis of diaceton alcohol, studied by Koelichen (Zeitsch. f. ph. Chemie XXXIII, 155), it remains only for me to give a free translation of that passage from this latter work where the method is discussed (with, of course, the appropriate changes).

According to the reaction scheme

$$ (\mathrm{CH_3COH})_3 = 3\ \mathrm{CH_3COH}. $$

this catalysis of paraldehyde into 3 molecules of aldehyde must proceed according to the well-known logarithmic law for reactions of the first order. It is known that for the latter the formula holds

$$ \frac{dx}{dt} = K(a - x), $$

which after integration gives for the rate constant \(K\) the following logarithmic expression:

$$ \frac{1}{t}\log\frac{a}{a-x} = K $$

where \(a\) is the initial mass of the substance undergoing transformation, and \(x\) is the quantity of it that has reacted in time \(t\). If it is impossible to measure \(x\) analytically, one may make use of some special physical property of the system, which changes proportionally to the concentration of the disappearing or forming substance.

*) From the standpoint of the method of observation.

To measure the rate of catalysis of paraldehyde particles into 3 particles of aldehyde, I chose the very same dilatometric method as I had used in studying equilibria. When paraldehyde is split, a considerable expansion takes place; its course as a function of time, in sufficiently dilute solutions (1 volume of paraldehyde to 10, and even 20, volumes of water), is still observed very clearly.

Assuming that the above-mentioned expansions are proportional to the amounts of paraldehyde subjected to catalysis, I call, after \(x\) observations, the ever increasing expansions with time. But \(a\)—the initial mass of paraldehyde—cannot be expressed in this measure, for the volume at the very beginning of catalysis is unknown; before the first reading, when the contents of the dilatometer assume the temperature of the thermostat, a certain quantity of paraldehyde has evidently already passed into aldehyde. But for the constant of a first-order reaction one may take another equation: namely, without changing the magnitude of this constant, one begins to count time from the moment of the first observation, and not from the moment at which catalysis begins*). Then the equation is:

\[ \frac{1}{t - t_0}\log\frac{a - x_0}{a - x_t} = K, \]

in which \(t_0\) and \(x_0\) are the quantities, for the time and the level in the dilatometer, observed at the time of the first reading. The fraction \(\frac{a-x_0}{a-x_t}\) will thus give the ratio of the amounts of paraldehyde that had not yet reacted at times \(t_0\) and \(t\). With the assumption made concerning proportionality between the quantity of paraldehyde that has reacted and the expansion accompanying this catalysis, I can substitute, for the quantities \(a-x_0\) and \(a-x_t\), the expansions observed from the times \(t_0\) and \(t\) to the end of the reaction.

Assuming constancy of the capillary diameter (which was shown by careful calibration), I can, in calculating the results, substitute into the formula simply the number of divisions (millimeters) passed through during the expansion by the upper level. All these simplifications are possible, for the rate constant for reactions of the first order depends only on the unit of time**).

Moreover, the calculation was carried out, instead of with natural logarithms, using Briggsian logarithms, so that all the constants have the corresponding proportionality factor.

The dilatometers used for these experiments all had large reservoirs, at least 20 cubic centimeters, and fine capillaries. They were filled with the solution under study in such a way that above the capillary there rose

) Ostwald, Lehrbuch d. allg. Chemie \(2^2\), 209.
) Ostwald, Lehrbuch d. allg. Chemie* (2 Aufl.) \(2^2\), 231.

a funnel, into which the solution was poured, and through the capillary a thin capillary tube was passed into the reservoir, through which air was drawn out. Then the solution, under atmospheric pressure, was rapidly forced into the dilatometer. Having connected the capillary tube with a water pump by means of rubber tubing, producing a rarefaction to \(1/3\)—\(1/5\) atmosphere, I left this dilatometer for some time in a bath having a temperature of about \(40^\circ\) Celsius, in order to drive the air out of the solution, and then sealed the open end of the dilatometer, or closed it with a thick-walled rubber stopper (with a glass rod), tying the rubber tightly to the capillary with wire. Such stoppers held satisfactorily. A millimeter scale was attached to the capillary tube of the dilatometer by means of a screw clamp with leather pads. The dilatometer, sealed in this way, was then completely immersed in a deep thermostat, and 10–15 min. after immersion the first reading was taken. Sometimes, soon afterward, I noticed an air bubble, owing to its incomplete removal from the solution, at the mouth of the capillary, and again repeated its removal with the pump, having lowered the dilatometer into warm (\(40^\circ\)) water.

The solutions studied for the rate of transformation were always prepared from a solution of paraldehyde in water and titrated solutions of acids, by measuring both with precise pipettes (sometimes the acids and their salts were weighed), so that to 1 volume of paraldehyde (or a portion of it, the remainder being made up with water) there corresponded 10 volumes of acid containing in a liter approximately \(1/10\) gram-molecule or equivalent (exactly 0.0968 gram-molecule).

The above-mentioned solution of paraldehyde in water was always prepared by mixing the following precisely measured volumes: 15 cubic cent. of pure paraldehyde and 137.5 cubic cent. of distilled water. The dissolution of the latter mixture takes place especially rapidly if it is cooled in ice water, when the paraldehyde sinks to the bottom, and then removed from the cold bath; the paraldehyde, expanding most strongly, then rises upward and, on its way through the aqueous layer, quickly dissolves.

In describing the individual experiments I give the composition of the solution, the times of readings in minutes, the levels in millimeters*) and the rate constant (\(K\)), calculated by the formula

\[ \frac{1}{t-t_0}\log \frac{a-x_0}{a-x_t}=K \]

in whole numbers; the true magnitude of the latter will be 10000 times smaller than the one given.

*) The observed levels were finally taken as the highest, limiting position, unchanged for a long time, sometimes for several days, and corresponding to the end of catalysis; such levels correspond to the time denoted by the infinity sign (\(\infty\)).

Experiment 1.

24.8 cubic cm of a paraldehyde solution were mixed with 2 cubic cm HCl, containing 1.18 gram-molecules per liter, which gives 1 volume of paraldehyde + 10 volumes of acid (decinormal).

Time . . . .	12½	19½	24	32⅔	39⅔	45	60	72	80
Levels . . . .	−6	+7.5	15	28	37	43.5	58	67.5	72.5
K	—	84	84	84	84	85	86	88	89
Time . . . .	89½	107½	130	143	156	168	189	∞
Levels . . . .	77.5	84.5	90.5	93	95	96	97.5	99
K	89	90	93	95	98	—	—	—

The regular increase of the constant K is explained here by the fact, as is evident from the subsequent experiments, that a solution which is homogeneous at ordinary temperature becomes turbid at the beginning of expansion, since paraldehyde at 50.5° dissolves in water less readily than at ordinary temperature. In this experiment the dilatometer was closed with a rubber stopper.

Experiment 2.

The composition of the solution was exactly the same as in the preceding experiment, only the dilatometer was sealed.

Time . . . .	48½	50⅓	57⅓	67	74¾	84	95	109	120	∞
Levels . . .	18.5	21.5	34.5	49.5	61	71.5	82	93	100	123.5
K	—	70?	82	82	86	86	86	89	91	—

K does not have a constant value for the same reason as in experiment 1.

Experiment 3.

27.9 cubic cm of paraldehyde solution + 9.3 cubic cm water + 3 cubic cm HCl (containing 1.18 gram-molecules per liter); consequently,

0.75 volume of paraldehyde + 0.25 vol. of pure water + 10 volumes HCl (in a liter, 0.0968 gram-molecules).

Time . . . . . .	25⅓	30½	35½	40½	45½	52⅔	59½	70½
Levels . . . . . .	90.7	99	105.8	112	117.8	125	131	140
K	—	90	87	86	87	88	87	89
Time . . . . . .	94	105	121	153	173	186	∞
Levels . . . . . .	153.3	157	161	167	169	170	173.3
K	92	91	90	—	—	—	—

A solution of paraldehyde of such concentration remains homogeneous throughout the catalysis, and the value of K must be recognized as constant and equal on average to 0.00887.

The dilatometer is closed with a rubber stopper.

Experiment 4.

24.8 cubic centimeters of water + 24.8 cu. cm of paraldehyde solution + 4 cu. cm HCl (1.18 gram-molecules in 1 liter); consequently,

0.5 volume of paraldehyde + 0.5 vol. water + 10 volumes of decinormal hydrochloric acid.

Time . . . . . .	55	67	73¾	80½	90½	99⅓
Levels . . . . .	55	73.2	81.6	90	100	106.3
K	—	88	88	91	93	92
Time . . . . . .	109⅓	120⅓	135	146	161	∞
Levels . . . . .	113.2	117.5	125	129	133.5	139.4
K	93	90	96	95	92	—

On average K = 0.00918. In this experiment the most sensitive dilatometer was used (its reservoir had a capacity of 42 cubic centimeters); the upper—

... to seal its lower end. These four experiments with hydrochloric acid show that the constants \(K\) change negligibly with dilution and are constant for the chosen dilution and homogeneity of the mixture, which indicates that this reaction belongs to the first order.

The latter is also confirmed by other, further experiments.

It is known that strong acids, in the presence of their salts (e.g., sodium salts), act more strongly (in the sense of increasing the rate) on the inversion of cane sugar than pure acids. Therefore I carried out the following corresponding experiments.

Experiment 5.

The solution had the composition: 0.75 volume of paraldehyde \(+\) 0.25 vol. of water \(+\) 10 volumes of a solution containing, in 10 liters of water, one gram-molecule of HCl and NaCl.

Time . . . . .	37	42	47	52	57	\(62\frac{1}{3}\)	\(68\frac{1}{3}\)	74
Levels . . . . .	61	67	73.7	79	84	88.5	93.4	97.6
K	—	84	94	93	95	94	96	97
Time . . . . .	82	91	102	113	123	134	154	\(\infty\)
Levels . . . . .	102.3	107.5	111	115.2	117	119	121.3	126
K	97	101	98	102	100	100	—	—

On average the constant \(= 0.00973\), i.e. it has clearly, though only slightly, increased in comparison with the constant of experiment 3.

Experiment 6.

The solution had the composition: 0.75 vol. of paraldehyde \(+\) 0.25 vol. of water \(+\) 10 volumes of a solution containing, in 10 liters of water, 1 gram-molecule of HCl and 2 gram-molecules of NaCl. The dilatometer was sealed.

Time . . . . .	56	61	66	71	76	81
Levels . . . . .	238	244	250.7	255	260	264.1
K	—	94	106	99	102	103

Time . . . .	86	96	109	119	∞
Levels . . .	268	274	280.5	284.1	296.5
K	104	104	106	107	K

On average \(K=0.01040\), i.e., again an increase of the constant occurred under the influence of the addition of NaCl.

Experiment 7.

The solution had the composition: 0.75 vol. of paraldehyde + 0.25 vol. of water + 10 vols. of a solution containing, in 10 liters of water, one gram-molecule of HCl and 4 gram-molecules of NaCl. Under the influence of 4 NaCl, a clear decrease in the solubility of paraldehyde at \(50.5^\circ\) is observed: after being placed in the thermostat, the solution became turbid, but soon became homogeneous. The rate of the reaction was observed in the clarified, homogeneous solution. The dilatometer was sealed.

Time . . . .	32	37	42	47	52	57	62	67	72
Levels . . .	59	69	77.5	85.1	91.7	98	103.7	107.5	111
K	—	117	115	115	115	117	119	117	115
Time . . . .	78	84	90	105	125	145	167	∞
Levels . . .	115.7	120	122.8	128.5	133.6	135.8	136.8	138.5
K	118	122	121	130	—	—	—	—

On average \(K=0.01174\) (in deriving the mean, the last value—130—was discarded). Again there is a new increase of the constant.

Experiment 8.

The solution had the composition: 1 volume of paraldehyde + 10 volumes of decinormal trichloroacetic acid. The latter contained no traces of hydrochloric or nitric acid. At the beginning of the experiment at \(50.5^\circ\), the mixture was turbid (the same phenomenon as when hydrochloric acid was used at the same dilution).

Time . . . . .	36	41	46	51	61	66	71	81½
Levels . . . . .	48	56.5	65	73	87.3	93.4	99.5	110.5
K	—	64	67	68	69	69	70	70
Time . . . . .	92½	102	113	123	134	148	160	167.7
Levels . . . . .	119.5	127.5	134.5	140.7	145	151.8	154	∞
K	70	71	72	74	73	—	—	—

Again, in view of the inhomogeneous solution, K, although only slightly, increases in the course of the experiment.

Experiment 9.

Taken were 27.9 cubic centimeters of paraldehyde solution + 9.3 cubic centimeters of water + 2 cubic centimeters of trichloroacetic acid (1.18 gram-molecules per liter). Consequently, the solution had the composition: 0.75 volume of paraldehyde + 0.25 volume of water + 10 volumes of decinormal trichloroacetic acid (exactly 0.0968 gram-molecule per liter). The end of the dilatometer was closed with rubber.

Time . . . . .	30½	35½	40½	50½	60½	70½
Levels . . . .	26.3	33.8	39.3	51	60	68.3
K		81	73	75	74	75
Time . . . . .	77.2	81.5	86	91.3	108	∞
Levels . . . .	83	90½	101	113	209	110.7
K	76	77	76	77	84	—

Discarding the first and last values for K, I have on average K = 0.00754.

Experiment 10.

24.8 cubic centimeters of the paraldehyde solution and 2 cubic centimeters of sulfuric acid were taken (1.18 gram-molecules in 1 liter). Consequently, the solution contained 1 volume of paraldehyde + 10 volumes of sulfuric acid (1/5 normal).

At the beginning of the experiment, at 50.5°, the solution is turbid.

Time . . . .	29	34	47	52	62 1/2	70 1/2	82 1/2	96	107
Levels . . . .	34	40	53.5	58	65.3	70.4	76.2	81	84.3
K	—	91	95	96	96	98	99	99	101
Time . . . .	128	141	151	164	182	290	323	392	∞
Levels . . . .	88.5	90	91.3	92	93	94	94	94	94
K	105	105	—	—	—	—	—	—	—

In view of the nonuniformity of the solution, the increase in K is weak.

Experiment 11.

24.8 cubic centimeters of the paraldehyde solution + 1 cubic centimeter of water + 1 cubic centimeter of sulfuric acid, containing the same as in the preceding experiment, were taken. Consequently, the solution contained 1 volume of paraldehyde + 10 volumes of sulfuric acid, containing 1 equivalent (more precisely 0.968) in 10 liters.

Time . .	22 1/2	27	35 1/2	47	55	67.5	81
Levels . .	193	197.5	203	210.4	216	224	231.5
K	—	53	42	41	43	45	46
Time . .	91	104	121.5	230	261	302	∞
Levels . .	236.3	242	248.8	270.5	273	275.8	276.8
K	46	47	48	54	—	—	—

Here again the solution is turbid at 50.5° during the first period.

Experiment 12

18.6 cubic centimeters of paraaldehyde solution + 6.2 cubic centimeters of water + 2 cubic centimeters of sulfuric acid were taken (1.18 gram-molecules per liter). Consequently, the solution consists of 0.75 vol. paraaldehyde + 0.25 vol. water + 10 volumes of sulfuric acid containing 0.0968 gram-molecules per liter. The dilatometer was sealed. The solution did not become cloudy after immersion in the thermostat.

	31	36	41	46	51	56	61	66
Time . . .	31	36	41	46	51	56	61	66
Levels . . .	62	69.5	76	81.3	86.3	91	95.5	99
K	—	101	99	96	95	96	97	96
Time . . .	71	81 1/2	91	101	144	165	∞	∞
Levels . . .	102.3	107.5	111.7	117	125.2	127.2	130.5	130.5
K	96	94	94	100	98	—

On average, K = 0.00960.

Experiment 13

The solution consists of 0.75 vol. paraaldehyde + 0.25 vol. water + 10 vol. of a solution containing 0.0484 gram-molecules of sulfuric acid per liter (i.e., half as much sulfuric acid as in the preceding experiment). The dilatometer was sealed.

	43	46	51	59	68	79	95 1/2	111
Time . . . . .	43	46	51	59	68	79	95 1/2	111
Levels . . . . .	10.2	12.5	17	22.9	29.6	36.6	45.7	52.9
K	—	42	47	46	48	48	48	48
Time . . . . .	124	135	152	184	199	292	∞	∞
Levels . . . . .	58	61.8	67.8	73.2	77.0	87	91	91
K	48	48	50	47	49	—	—	—

On average, K = 0.00480.

Experiment 14.

The solution was composed of 0.75 vol. paraldehyde + 0.25 vol. water + 10 vol. of a solution containing, in 10 liters of water, one gram-molecule each of \(H_2SO_4\) and \(ZnSO_4\) (zinc sulfate). This solution became turbid at a temperature of \(45^\circ\) C., but very soon became transparent again.

Time	\(23 \frac{1}{3}\)	28	33	38	43	48	53	58
Levels	54.4	61.3	66.7	71.6	76.5	81	85	88.9
\(K\)	—	74	66	63	63	62	61	61
Time	63	68	\(73 \frac{1}{3}\)	78	88	172	198	\(\infty\)
Levels	92.2	96	100	102.2	108	134	138	143.7
\(K\)	60	61	62	61	62	65	—	—

On average \(K = 0.00622\).

Experiment 15.

The solution was composed of 0.75 vol. paraldehyde + 0.25 vol. water + 10 vol. of a solution containing, in one liter, 0.0968 gram-molecule of oxalic acid.

Time	2	7	14	24	33	44	56	145	151
Levels	19.2	24.5	31.2	41	49	57.5	66	104.5	105.5
\(K\)	—	44	43	44	45	45	46	47	46
Time	161	171	185	202	248	268	291	\(\infty\)
Levels	107.8	110	112.5	115	120.2	121.7	123.2	127.3
\(K\)	47	47	47	47	48	48	—	—

On average \(K = 0.00460\).

Experiment 16.

The solution was composed of 0.75 vol. paraldehyde + 0.25 vol. water + 10 volumes of a solution containing, in 1 liter, 0.0484 gram-molecule of oxalic acid. The dilatometer was sealed.

Time . . . . .	3	13	23	33	43	53	63	73
Levels . . . . .	16	21.8	26.6	30.5	35	38	43	45.8
K	—	30.5	29	27	27	26	27	27
Time . . . . .	157	170	205	229	255	285	∞
Levels . . . . .	67.5	71.6	76.2	80.2	83.6	85.9	101.5
K	26	27	26	27	27	26

On average \(K = 0.00266^*\).

The limit was reached only on the following day; in the evening, later than 5 o’clock, the levels were not observed.

Experiment 17.

The solution was composed of 0.75 vol. paraldehyde + 0.25 vol. water + 10 volumes of a solution containing, in 1 liter, 0.0968 gram-molecule of monochloroacetic acid. The dilatometer was sealed.

Commercial monochloroacetic acid was distilled twice and then fractionally melted twice. A weighed portion of it, 0.995 g, required for neutralization 44.35 cu. cm of titrated caustic potash; at absolute purity it would require KOH—44.36 cu. cm.

Time . . . . .	50	59	80	98	123	143	168	193
Levels . . . . .	22	24.2	30	32	37	42	46	50
K	—	9.4	10.6	8.4	8.5	9.1	8.8	8.6

*) In deriving the average, only the first two values of the constant were not taken.

Time . . . . . .	278	291	326	350	376	406	$\infty$
Levels . . . . .	63.2	65.5	69	72.7	76.1	79	134.8
K	8.6	8.7	8.5	8.6	8.7	8.6

On average (discarding the first two values)

$$ K = 0.000864. $$

The limiting maximum level, 134.8, was reached only on the third day; on the second day I had:

Time . . . .	9 h 25 m	11 h 3 m	12 h 20 m	1 h 46 m	3 h 48 m	4 h 40 m
Levels . . . .	127.5	128.7	128.7	129.8	131.0	131.2

Experiment 18.

The solution was exactly the same as in the preceding experiment. The dilatometer was soldered shut.

Time . .	21	97	111	145	169	196	225	1154	1253	$\infty$
Levels . .	12.3	25.7	29	33.4	37.8	42	46	103.5	105.8	112.5
K	—	8.2	8.8	8.3	8.6	8.7	8.7	9.2	—

On average $K = 0.000864$.

Experiment 19.

The solution was composed of 0.75 volume of paraldehyde + 0.25 vol. water + 10 volumes of a solution containing, in 10 liters of water, 0.968 gram-molecule of $\mathrm{CH_2ClCO_2H}$ and $\mathrm{CH_2ClCO_2Na}$. I did not calculate the rate constants here. The following data show how greatly the rate fell from the addition of the salt in comparison with that of experiment 17 (or 18).

	first day	first day	first day	first day	first day
Time . . .	1 h. 31 min.	43 min.	50 min.	3 h. 46 min.	4 h. 39 min.
Level . . .	23,0	23,1	23,0	27,8	29,8
Time . . .	5 h. 45 min.	—	—	—	—
Level . . .	33	62,8	100	114,5	136,0

The dimensions of the dilatometers in this experiment and in experiment 17 are almost identical; but there, in 241 min. \((=291-50)\), the level rose by 43,5 millimeters \((=65,5-22)\), whereas here in 248 min. (from 1 h. 45 min. to 5 h. 45 min.) it rose only by 10 millimeters. The limiting expansions, however, are the same—136 and 134,8.

(A solution of hypochlorous acid of a concentration close to that which I had in experiments 17–19, after being kept in the same thermostat at \(50,5^\circ\) for two or three days, did not show any noticeable decomposition into hydrochloric and glycolic acids.)

Conclusions.

In the following table the preceding data are summarized. In column I I give how many volumes of paraldehyde are contained in 11 volumes of the mixture (these 11 volumes are retained as the total volume in all experiments); in column II is given the chemical formula of the catalyst and its content in 10 liters (more precisely in \(10/0{,}968\)), expressed in gram-molecules; in column III are the values \(K\) of the rate constants to the fourth decimal place according to the equation on p. 97, and for inhomogeneous values at the beginning of expansion of the solutions the largest and the smallest of these observed values of \(K\) are given; finally, column IV contains the values of the same \(K\), referred to the value \(K\), taken as 100, for HCl at a paraldehyde concentration of 0,75, and HCl—one molecule in 10 liters.

I	II	III (k)	IV (k)
1	HCl . . . . . . . 1 gram-mol.	84—95	—
1	HCl . . . . . . . 1 ” ”	82—91	—
0,75	HCl . . . . . . . 1 ” ”	88,7	100
0,5	HCl . . . . . . . 1 ” ”	91,8	103
0,75	(HCl + NaCl) . . . in ” ”	97.3	110

I	II	III ($k$)	IV ($k$)
0.75	$(\mathrm{HCl}+2\,\mathrm{NaCl})$ . . . in gram-mol.	104.0	117
0.75	$(\mathrm{HCl}+4\,\mathrm{NaCl})$ . . . in gram-mol.	117.4	132
1	$(\mathrm{CCl_3CO_2H})$ . . . $1$ gram-mol.	67–74	—
0.75	$(\mathrm{CCl_3CO_2H})$ . . . $1$ gram-mol.	75.4	85.0
1	$\mathrm{H_2SO_4}$ . . . $1$ gram-mol.	95–105	—
1	$\mathrm{H_2SO_4}$ . . . $\frac{1}{2}$ gram-mol.	42–48	—
0.75	$\mathrm{H_2SO_4}$ . . . $1$ gram-mol.	96.0	108
0.75	$\mathrm{H_2SO_4}$ . . . $\frac{1}{2}$ gram-mol.	48.0	54
0.75	$(\mathrm{H_2SO_4}+\mathrm{ZnSO_4})$ . . . in gram-mol.	62.2	70.1
0.75	$(\mathrm{CO_2H})_2$ . . . $1$ gram-mol.	46.0	52
0.75	$(\mathrm{CO_2H})_2$ . . . $\frac{1}{2}$ gram-mol.	26.6	30
0.75	$\mathrm{CH_2ClCO_2H}$ . . . $1$ gram-mol.	8.64	9.7
0.75	$\mathrm{CH_2ClCO_2H}$ . . . $1$ gram-mol.	8.64	9.7
0.75	$\mathrm{CH_2ClCO_2H}+$ $+\mathrm{CH_2ClCO_2Na}$ . . . in gram-mol.	considerably less than 8.64	—

This table permits the following conclusions to be drawn.

1) The reaction (catalysis) of the decomposition of a paraldehyde molecule into 3 molecules of aldehyde is evidently expressed, with respect to the rate, by the equation

\[ -\frac{dx}{dt}=K(a-x), \]

i.e. it belongs to the so-called reactions of the first order (monomolecular), for, first, $K$ retains a clearly constant value, provided that we have a homogeneous system throughout the entire catalysis, and secondly this quantity $K$ is almost completely independent of the volume, i.e. of the concentration of paraldehyde*).

2) The catalysis of paraldehyde fully repeats, with respect to the action of the catalysts (the activity coefficients of acids), the catalyses of cane sugar and methyl acetate, namely:

a) the acids fall, both qualitatively and quantitatively, into one and the same series, almost coinciding with the series of their electrical conductivities.

In column I I give the electrical conductivities of normal (1 equivalent per liter) acid solutions, investigated by Ostwald**), referred to the conductivity of HCl, taken as $=100$. From these acids I select only those which I also investigated. In column II are given the values of the constants

* Studien z. chem. Dynamik von E. Cohen 3, 1896.
** Elektrochemie 1102,

velocities observed by Ostwald in the catalysis of methyl acetate by the same acids; in III—the corresponding values for the inversion of cane sugar (loco citato); and finally, in column IV—the constants observed by me, from column IV of the preceding table.

	I.	II.	III.	IV.
Hydrochloric	100	100	100	100
Trichloroacetic	62.3	68.2	75.4	85
Sulfuric	65.1	73.9	73.2 *)	54
Oxalic	19.7	17.6	18.6	26.6
Monochloroacetic	4.9	4.3	4.84	8.64

Taking into account Ostwald’s words (loco citato): “If one recalls that neither the temperature nor the dilution was the same in the three series of experiments being compared, then the agreement of these three series, the differences of which otherwise proceed in a perfectly regular manner, must be recognized as very satisfactory”; then—that I worked with dilutions greater than in the first three columns (and then, for weak acids, the activity coefficients increase more rapidly than for strong ones), I can recognize that the agreement of my fourth series with the first three “must be recognized as very satisfactory.”

b) In the three methods being compared, adding salts to their acids produces exactly the same changes.

c) Accepting, as do the adherents of the doctrine of ions, that catalysis is produced here also by H-ions, one should expect that, for sulfuric acid, as a strongly dissociated acid, a halving of the concentration will lower the velocity constant almost by half; whereas for oxalic acid, with a decrease in concentration, the activity falls less, owing to the relative increase in the number of ions. (See experiments 12 and 13 on the one hand, and experiments 15 and 16 on the other.)

) Nernst (Theoretische Chemie* 1898, 508) instead of this number gives one that agrees perfectly with mine—53.6.

CONTENTS

Instead of a preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–7

CHAPTER ONE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–64

On paraldehyde . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–12

On the method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–17

Detailed description of the experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18–49

Experiments with phosphoric acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18–22

” ” oxalic ” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22–26

” ” sulfuric ” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31–34

” ” hydrochloric ” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44–45

” ” acetic ” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46–47

” ” trichloroacetic acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47–48

” ” monochloroacetic ” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48–49

” ” boric anhydride . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27–31

” ” zinc sulfate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34–35

” ” copper sulfate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35–36

” ” cadmium sulfate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36–37

” ” sublimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37–40

” ” zinc chloride . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40–42

” ” cadmium chloride . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42–43

Analysis of the experimental data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49–56

On aldehyde . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56–59

Analysis of the liquid phase at the moment of equilibrium . . . . . . . . . . . . . . . . . . . . 59–63

Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63–64

CHAPTER TWO.

(equilibria in solutions of acetone, toluene, and water) . . . . . . . . . . . . . . . . . . . . . . 65–94

Solutions in acetone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65–75

” ” toluene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75–82

” ” water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83–86

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86–94

CHAPTER THREE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95–110

Rates of catalysis under the influence of hydrochloric acid . . . . . . . . . . . . . . . . . . . . 98–99

” ” hydrochloric acid and sodium chloride . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100–101

” ” ” trichloroacetic acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101–102

” ” ” sulfuric acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103–104

” ” ” ” ” and $\mathrm{ZnSO_4}$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

” ” ” oxalic acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105–106

” ” ” monochloroacetic acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106–107

” ” ” ” ” $+\mathrm{CH_2ClCO_2Na}$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107–108

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108–110

1. It might perhaps be more correct to say: acting extremely slowly, imperceptibly over the course of several days. ↩↩↩↩↩↩

2. Which was also proved by me in 1888. ↩↩