On the Chemical Mechanics of Reactions of Solid Substances1

Wilhelm Bilz.

The subject of the present article is, on the one hand, the study of the mechanics of spatial changes in a solid substance and, on the other hand, the study of the question whether these changes are the cause or the consequence of chemical reactions.

The investigation was begun with the best-known example: ammines.

1. If a crystalline salt is acted upon by gaseous ammonia, then, upon formation of the ammine, \(Q\) calories of heat are liberated, according to the equation

\[ [\text{salt}] + (\mathrm{NH}_3) = [\text{ammine}] + Q \text{ cal.} \]

In order to investigate the process of liberation of this quantity of heat, the entire process may be represented as consisting of two stages.

The first stage consists in increasing the distance between the ions in the original crystal lattice to the distance at which the ions are situated in the ammine; in this, a certain amount of work \(E\) cal. is expended, necessary for overcoming the lattice energy.

The second stage of the process consists in the addition of \(m\) molecules of ammonia to the cations of the expanded lattice; in this, \(A'\) cal. are liberated for each gram-molecule of salt. The difference between the two quantities constitutes the observed heat of reaction:

\[ Q = A' - E . \tag{1} \]

In this relation \(E\) depends only on the physical nature of the salt taken; as for \(A'\), it gives the value of the specific work, little or even almost entirely independent of the physical influences determined by the structure of the salt crystal.

The exact value of this specific affinity of ammonia could be determined only with the aid of an isolated cation, entirely

separated from the crystal lattice; in what follows, however, we shall have to confine ourselves to that value of the affinity which is given by measurement of the quantity \(A'\).

By the work of expansion of the crystal lattice is meant the difference between the energy of the lattice of the initially taken salt (\(U_o\) cal.) and the energy of the expanded lattice (\(U_g\) cal.) obtained upon formation of the new salt. Here, according to Born’s definition, by the lattice energy one should understand the energy which must be expended in order to expand the lattice to an infinite distance between the ions. Thus

\[ E = U_o - U_g . \tag{2} \]

The relation (1), established as early as 1923, was used by Grimm and by the author of the present work to determine the quantities \(E\) and \(A'\) separately from the available experimental data, as will be reported in detail elsewhere [2]. In the present article, for the most part, only certain applications and conclusions will be touched upon.

The theory of the crystal lattice of Born and Landé gives for the unexpanded lattice the following expression:

\[ U_o = \frac{a}{r_o}\left(1-\frac{1}{n}\right), \tag{3} \]

from which Grimm derived for the expanded lattice

\[ U_g = \frac{a}{r}\left[1-\frac{1}{n}\left(\frac{r_o}{r}\right)^{n-1}\right]. \tag{4} \]

In these expressions \(r_o\) is the initial, and \(r\) the increased, distance between oppositely charged ions; \(a\) is the constant of mutual attraction according to Coulomb’s law, and \(n\) is the constant corresponding to the repulsive force according to Born. For those cases in which the value of \(a\) and the absolute values of the distances between ions are unknown, but where \(U_o\) can be calculated from experimental data and a definite assumption can be made for \(n\), I propose the following equation for approximate calculations:

\[ E \simeq U_o\left[1-\frac{1}{\sqrt[3]{D}\left(1-\frac{1}{n}\right)}\right], \tag{5} \]

where \(D\) is the magnitude of the expansion, i.e. the ratio of the molecular volumes of the ammoniate and of the original salt1. In such approximate calcula—

...one has to neglect, for the expanded lattice, the repulsive force, which, however, is all the more permissible the more strongly the lattice is expanded. For smaller stretching of the lattice one should use more exact calculations; in approximate estimates, however, the shortened formula is sometimes useful, since it requires only knowledge of the densities, the lattice energy of the initial salt, and a rational choice of the constant \(n\).

Concerning the energy of the crystalline lattice of many substances, one can form at least an approximate idea by making use, for this purpose, of data concerning their mechanical and thermal properties, which allows us to make a comparative estimate of their reactivity.

Fig. 1. System: calcium halide salts/ammonia. Works of lattice expansion and works of addition, as functions of the number of ammonia molecules.

If the change both of \(E\) and of \(A'\) is known as a function of the magnitude of the lattice stretching, i.e. of the number of attached ammonia molecules or, more generally, of the number \(m\) of molecules that have entered into the reaction, then for any value of \(m\) one can determine the difference

\[ A' - E, \]

and thereby the heat of reaction and, by the Nernst theorem, the magnitude of the chemical affinity are determined.

In this case one can determine: whether the given substances enter into reaction at all (\(A' > E\); \(Q\) positive), what thermochemically stable compounds they are capable of forming, and what the magnitude of the affinity of the individual reactions is.

1. Let us now proceed to the description of some typical cases of the course of the curves \(E/m\) and \(A'/m\).

I. \(A'\) greater than \(E\). In Fig. 1 the curves \(E/m\) are given first of all for calcium chloride, bromide, and iodide.

The calculation of these curves is favored by the circumstance that, as I recently found, Kopp’s volume rule often, and in the case of normal ammoniates and analogous compounds even always, can be applied with great accuracy if, for ammonia and components similar to it, one uses the value of the molecular volume occupied by them at absolute zero [3]. In this way one can obtain curves even in the case where the volumes of the addition products are unknown. As is seen from the drawing, all the curves \(E\) have

ON THE QUESTION OF CHEMICAL MECHANICS

point of inflection near the axis of ordinates. Hence it follows that the work of stretching corresponding at first to one mole, while the new position of the ions is still quite close to the old one, is still comparatively small, since stretching is favored by the forces of mutual repulsion of the ions; further, as the stretching increases, the work increases and then, finally, falls, and in this region it is determined, in general, already only by Coulomb’s law.

Born [4] succeeded in finding the course of the function stretching/potential; as for the function considered here, (magnitude of the work)/(concentration), it, of course, adds nothing essentially new to what Born has done, but its use is more convenient for chemical purposes.

The course of the curves \(A'\) is determined both by the measured heats of formation \(Q\) and by the magnitude \(E\) [cf. equation (1)]. The curves, as far as can be judged from the drawing, are almost always concave with respect to the concentration axis; this means that, with increasing saturation of the cation, the energy liberated by the addition of one mole of ammonia decreases.

Further, it is evident from the drawing that all the curves \(A'\) almost coincide with one another; this is explained by the fact that the process occurring here is governed almost exclusively by the specific features of the calcium ion. In the stretched lattice the influence of the anion is considerably weakened; at infinite separation of the ions from one another it disappears altogether. The magnitude of the work of addition of one mole of ammonia to the calcium ion of the stretched lattice lies between 28 and 32 cal.; for strontium and barium it will be, in accordance with the increase in the ionic radius, somewhat smaller. From lithium to potassium the magnitude \(A'\) falls, per one mole of ammonia, approximately from 21 to 15 cal.

The characteristic differences from one another of these complex calcium-ammonia salts in the sense of their stability are as follows: iodides are more thermostable than bromides, and these in turn more than chlorides. This feature, as has already been said above, depends almost exclusively on the difference between the magnitudes of the work of expansion of the lattice of the ammonia-free salts. However, this is by no means always so. For the halide compounds of silver, the differences in the course of the curves \(E\) are considerably smaller, but they are very strong for the curves \(A'\). Here the affinity of ammonia for the silver ion is strongly dependent on the nature of the anions, which, according to modern views, is a consequence of their considerable polarization.

II. \(A'\) is less than \(E\). The upper curve \(E\) for \(\mathrm{CaF_2}\) in Fig. 1 represents the work of expansion of the lattice of calcium fluoride. As is evident from the drawing, the curve lies above the curves \(A'\) and will lie higher even in the case of making the rather improbable assumption that \(A'\) increases from chloride to fluoride in the same ratio as from bromide.

WILHELM BILTZ

to chloride. The curve corresponding to this supposition is drawn in the diagram with a dashed line. Thus \(Q\) is everywhere negative. In other words, it proves impossible to synthesize calcium fluoride ammoniate with the aid of gaseous ammonia, and indeed the experiments carried out in this direction yielded absolutely no results. Evidently, the specific affinity of ammonia for the calcium ion is not sufficiently strong to break the bond of the ions of fluorspar.

Moreover, as is seen from the approximate formula, the resistance of the fluorspar molecule is promoted, besides, of course, by the great energy of its lattice, also by its small molecular volume (24.6), owing to which the addition, for example, of six molecules of \(\mathrm{NH_3}\)¹) would cause an expansion by approximately six times, which greatly increases the value of \(E\) in formula (5).

Fig. 2. System: sodium chloride/ammonia. Works of expansion and addition as functions of the number of ammonia molecules.

In the same way we could, since the curve \(A'\) for normal ammoniates remains approximately the same, speak of the possibility or impossibility of obtaining ammoniates of other calcium salts; for this we need only know the energy of formation of their lattice. This problem could be solved without carrying out special chemical experiments at all, if, in determining the values \(A'\), it were possible to get by exclusively with data of atomic physics, which is to some extent possible in certain special cases.

The relation of calcium salts to water is completely analogous to their relation to ammonia. The bundle of curves for calcium halide salts that readily pass into hydrates and are readily soluble in water is separated by the curves \(A'\) from the curve \(E\) of insoluble fluorspar. At this point, as in many others, the content of the present work comes into contact with certain views of Fajans on the question of solubility, expressed by him earlier [6].

Ia. Stable are complex salts only with the highest ammonia content.

Fig. 2 presents a special case of item I. Sodium chloride forms only one ammoniate with a large amount of ammonia, namely: pentammine, \(\mathrm{NaCl \cdot 5NH_3}\). One point of the curve \(A'\) is established by measuring the heat of reaction; the further course of the curve down to the zero point can, with a high degree of probability—

¹) If the molecular volume of ammonia at zero is equal to 20, then the volume of these six moles will be 120.

…is represented as a straight line. The distance from this straight line to the expansion curve gives, provided that \(m < 5\), values for \(\frac{Q}{m}\) that are less than \(\frac{Q}{5}\). Thus the heats of formation of ammines containing less than 5 moles of \(NH_3\), when referred to one molecule of ammonia, are less than the heat of formation of the pentammine; therefore such salts cannot be obtained upon its decomposition.

The situation is exactly the same with barium chloride octammine.

Ib. Only one complex salt with a low ammonia content is stable.

The possibility is not excluded of such a course of the curve \(A'\), in which, subsequently, it would become more concave than the curve \(E\), and thus would intersect the latter. In this case the heats of formation of the higher complex compounds would become negative. However, it has not yet been possible to find an example of such a case.

It should be noted that complex salts with an exceptionally low ammonia content are also formed in the case when the curve \(A'\), in its further course, comes so close to the curve \(E\) that the molecular heats of formation of the higher ammines become less than the heat of evaporation of liquid ammonia.

Fig. 3. Work of expansion and of addition for the case when \(\frac{Q}{m}\) has a minimum between values of \(m\) equal to 3 and 7.

Ic. Stable complex salts are those with only low and high ammonia contents.

If the distance

\[ \frac{A' - E}{m} \]

for intermediate values of \(m\) has a minimum, or remains practically unchanged for them, then only the higher and lower complex salts will be thermally stable.

This case is represented schematically in Fig. 3, and it should be borne in mind that measurements of the quantity \(Q\) are considerably more accurate than the initial numerical data necessary for the theoretical calculation of the lattice energy, and that in this case one has to deal with small differences between large values. In this drawing, besides the curves \(A'\) and \(E\) themselves, the ratios of the distances between them to the quantity \(m\) are given on an enlarged scale. It is evident that the thermal decomposition of the octammine can yield only the diamine and monoammine, since the elasticities of the intermediate compounds will lie

as a result of the smallness of their heats of formation, respectively higher than the elasticity in compounds with the highest ammonia content. Thus it is not hard to see how compounds, quite possible from the standpoint of stereochemistry—for example, tetrammines—may, for energetic reasons, be absent among the products of decomposition. Similar cases are often observed; thus, for example, in the system calcium chloride–ammonia there are no compounds with 3, 4, 5, and 7 molecules of \(\mathrm{NH_3}\).

But since the difference between the heats of formation \(\dfrac{Q}{m}\) for salts with the highest and with the lowest ammonia content generally does not exceed 6 cal., and, consequently, in the question of the existence of salts with an intermediate ammonia content only fractions of calories can be involved, Fig. 1 cannot illustrate this phenomenon with sufficient accuracy. Below we shall have still more striking examples, since type Ic is also not infrequently encountered in the chemistry of other classes of substances.

Complex compounds of intermediate composition can sometimes be obtained by indirect routes; in this case such compounds prove to be metastable and decompose readily into adjacent compositions; thus, for example, sodium sulfate heptahydrate itself passes into the decahydrate and the anhydride.

As a final, though admittedly only qualitative, example of ammoniates, let us also mention the ammoniates of free metals. The first condition for their formation is the specific affinity of ammonia for the metal ion, i.e. easy ionization of the metal atom. The second necessary condition is the small lattice energy of the metal. Thus we might expect that the base, soft, and low-boiling metals would most readily add ammonia or dissolve in liquid ammonia; such metals are the alkali metals and the alkaline-earth metals. For the alkaline-earth metals the hexammines have been obtained and measured [7].

It was found here that

\[ A'_{\mathrm{Ca}} > A'_{\mathrm{Sr}} > A'_{\mathrm{Ba}}, \]

and since, in observing phenomena connected with evaporation, it was possible to establish that the lattice energies of these metals do not differ too greatly from one another, the observed, though small, decrease in the stability of the metal hexammines from calcium to barium becomes understandable.

1. Just as before, in studying the question of the dependence between valence and the magnitude of the energy\(^1\), complex

\(^1\) The literature on this question is collected in Z. f. anorg. u. allgem. Chem. 130, 93 (1923).

ammoniates proved, here as well, in the analytical decomposition of the magnitude of the energy into mechanical and chemical components, to be, so to speak, merely “guinea pigs,” and moreover very convenient ones, since in no other case can experimental material be accumulated with such ease. The data obtained, however, could claim only a conditional interest if they could not be generalized.

Further examples of the connection between the work of expansion of the lattice and reactivity are provided by polyhalide compounds. In the following table are given the lattice energies of halide salts of the alkali metals, in cal. per 1 mole, according to data compiled by Grimm [8]. The numbers enclosed in parentheses denote the corresponding molecular volumes in cubic centimeters.

Lattice energies and molecular volumes.

The stability of polyhalide compounds increases, as experience shows, together with the atomic weight of the alkali metal and of the halide; depending on these same factors, as is evident from the table, the lattice energies decrease. Thus the work of expansion for lithium chloride must have the greatest value, and for cesium iodide the smallest. And indeed: for the first salt polyhalide compounds are unknown (we have in mind here only crystalline compounds), whereas cesium iodide gives, to the highest degree, stable derivatives of this kind. The approximate formula shows that \(E\) increases with increasing \(D\), or, ceteris paribus—with decreasing molecular volume of the initial substance; we have already noted above the influence of the small molecular volume of fluorspar on its ability to resist the addition of ammonia. From the same table it is evident that, as a result of this influence, the work of expansion and the impossibility connected with it of forming crystalline polyhalides reach their greatest magnitude for lithium chloride. The general connection existing between the degree of filling of space and the possibility of forming a complex compound had already been noted earlier by various authors, though, it is true, purely empirically.

1. Similar to the polyhalides are the polysulfides. When Wilke-Dörfurt (Wilke-Dörfurt [9]), together with the author of the present work, undertook a study of the molten polysulfides of the alkali metals by means of thermal analysis, they turned to the compounds of rubidium and cesium.

A deep analogy is also presented by the polyoxides of the alkali metals, studied from the thermochemical side by French authors. True, at the present moment it is still impossible to give such a treatment of this question as would resolve it quantitatively from the standpoint of crystal-lattice theory; nevertheless, it will hardly be erroneous to conclude that the generally known fall in the stability of the peroxides of the alkaline-earth metals from \(BaO_2\) to \(CaO_2\) is explained analogously to the examples given above. In complete agreement with this is also the explanation of the formation of carbonates, as addition of \(CO_2\) to the anion of the oxides of the alkaline-earth metals.

\[ Ca^{\bullet\bullet} + O'' + CO_2 = Ca^{\bullet\bullet} + CO_3'' \]

Thus the course of this process is also dependent on the energy of the lattice of the oxides and on the work of its stretching. In series of oxides one often has to encounter types Ic, i.e. spontaneous decomposition of intermediate oxides into adjacent stages of oxidation. For example, as is known, ions of chlorous acid are capable, as a result of self-oxidation, of passing into ions of chloric and hydrochloric acids; moreover, transformations of manganese oxides were already known to the alchemists, in which \(Mn_2O_6\) spontaneously passes into \(Mn_2O_4\) and \(Mn_2O_7\). But since here we are dealing with noncrystalline substances, the question of how far the observed analogy goes beyond a purely external similarity of the phenomena must for the time being be left open. In any case, Lothar Wöhler \([^{10}]\), to whom we are greatly indebted for clarification of the question of the stability of oxides, succeeded in showing that many crystalline oxides are unstable intermediate stages: thus, for example, \(2PtO\) passes, with evolution of heat, into \(PtO_2 + Pt\).

1. As an example of a constituent with a small value of \(A\) we tried taking hydrogen sulfide. The dipole moment of hydrogen sulfide is small; therefore its specific affinity, since it is due to this dipole, is also insignificant, at least in comparison with water or ammonia. Thus, for a true salt which, owing to the electrostatic attraction of oppositely charged ions, possesses a large lattice energy, one could hardly have expected the formation of thiohydrates.

However, Friedrich Wöhler was already able to observe a product of the addition of hydrogen sulfide to aluminum chloride. Aluminum chloride is a very poor conductor; and indeed, the investigation undertaken jointly with Keunecke showed that true salts are incapable of adding hydrogen sulfide, whereas halide salts with a molecular lattice, i.e. low-boiling insulating substances from the fourth and fifth groups of the periodic system, either give definite thiohydrates, for example, \(SnCl_4 \cdot 2H_2S\), or, at least,

measure, dissolve in liquid hydrogen sulfide. Consequently, in this sense hydrogen sulfide may be regarded as a reagent for the ionic and molecular lattice, which is expressed by the inequality:

\[ A'_{\mathrm{H_2S}} > E_{\text{molec. lattice}} < E_{\text{ion. lattice}}. \]

1. Now the question involuntarily arises whether it would also be possible to artificially expand the lattice, so as thereby to bring about a reaction that does not proceed; in other words, whether it is possible to convert type II, where \(A' < E\), into type I, where \(A' > E\). For this purpose we can make use of the transformation of a lattice with a higher energy into a lattice with a lower energy, for which it will first be necessary to introduce a substance with a high specific affinity in such a way that the lattice, expanded in this manner, becomes capable of subsequently adding components with a lower affinity. In this case one often has to overcome a slight resistance of the forces of the lattice only in the immediate vicinity of its normal state. Thus, for example, from the curve for calcium fluoride (see Fig. 1) it is evident that the curve \(E\), already after an extension corresponding to the first mole, becomes concave with respect to the concentration axis: further expansion therefore corresponds to ever smaller resistances of the lattice. And consequently, in order to expand and activate the crystal, only 1 mole of a substance possessing a strong affinity is required, which is, to a certain extent, a “pioneer” for the subsequent ones. The best substance in this sense, possessing a whole series of valuable qualities, is, thanks to its high dipole moment, water.

In numerous experiments with other true salts, for example with nickel fluoride, just as in the case of fluorspar, it proved impossible to add ammonia directly. However, after the preliminary introduction of a water molecule, the expanded crystal added, with an energy of approximately 11 cal. per 1 mole, 5 molecules of ammonia. In this way nickel fluoride pentammine with one particle of water was obtained. Experimentally, Rahlfs carried this out in a special apparatus resembling a Soxhlet apparatus, into which the hydrates of the fluoride salt were placed and extracted with liquid ammonia. In this process the ammonia removed the water and replaced it, leaving only one molecule, apparently necessary for breaking up the salt lattice.

In addition to these ad hoc examples with fluorides, there exist many older observations of a similar kind, according to which certain compounds are able to exist “only in the presence in them of water of crystallization”; at the slightest attempt to remove this water, they undergo fundamental changes. Thus, the monohydrate of hexammine chromic chloride, on dehydration, passes into chloropentammine chromic chloride; the anhydride of hexammine can be obtained only for the bromide and iodide. Until quite recently fairly

...were satisfied with such explanations of this phenomenon: for example, for the hydrates of tetrachloro derivatives of iodic metals it was said that complex formation in the anion cannot occur if the same formation does not at the same time occur in the cation; thus a certain symmetry of the spatial arrangement was assumed to underlie the phenomenon [11].

Sometimes it is possible, as it were, by “outwitting nature,” to obtain, without introducing water into the molecule, a compound not foreseen by the theory and completely anhydrous; for example, by precipitating isolated complex cations from solutions (for instance, hexamminecobalt ions) with fluoride ions; but the hexammine-fluoride cobalt thus obtained will in any case not be a stable compound.

1. The decrease in the magnitude \(E\) upon the addition of water, described in § 6, and the accompanying decrease—increase in reactivity, should not be confused with the catalytic influence of small quantities of water. First, because here, depending on the circumstances, large quantities of water are sometimes also necessary; second, because water takes part in the reaction; and finally, third, because the essence of the phenomenon lies not in the rate of reaction but in the conditions of equilibrium. However, under certain circumstances water may also promote an increase in the reaction rate by means of a primary expansion of the lattice, and in practice in many cases it will be necessary to take into account the possibility of both effects of water.

In conclusion we shall indicate several examples relating to analytical, mineral, and colloid chemistry.

First—the hardening of burnt gypsum [12]. Gypsum calcined to a very high temperature and thus dehydrated to anhydrite cannot directly add water; the dihydrate can be obtained from it only indirectly, through solution. On the contrary, the hemihydrate, i.e. anhydrite that has added half a molecule of water, is very easily hydrated to gypsum, since its lattice is still capable of reactions. Gypsum that has been completely dehydrated by mild heating, but not subjected to strong calcination, likewise proves reactive. X-ray measurements and density measurements made recently have shown that the lattice of calcium sulfate dehydrated in this way differs very little from the lattice of the hemihydrate; consequently, the theory fully explains the retention of reactivity in this case. The structure of the lattice of strongly calcined anhydrite, on the contrary, proves to be very greatly altered and compacted, as is shown by spatial, X-ray, and hardness measurements.

Second—the resistance of silicates to chemical action. Here the action of water may, in the full sense of the word, be compared with the action of a stone-drilling machine.

Those silicates, such as, for example, zeolites, which are loosened already by the water contained in them by nature and in which the expansion of the lattice is so considerable that the water, only weakly fixed spatially, can move rather freely in the lattice—such silicates are rapidly decomposed and gelatinized by acid, whereas typical anhydrous silicates of the primary rocks do not produce such an effect.

In this case hardness can again serve as a measure of the lattice energy, which also explains the relation between these quantities that the author of the present work had already noted earlier, namely: the hardest silicates are especially difficult to decompose. Such silicates, in general, are also the most resistant to weathering—one of the factors of their natural destruction—since weathering is connected above all, of course, with the process of hydration. We encounter a similar relation between hardness and chemical stability continually in everyday chemical practice: an ordinary example for the analyst is the almost complete stability of corundum and strongly ignited ferric oxide toward hydrochloric acid, in contrast to the easy solubility in it of the same oxides in the aqueous state.

A number of other examples are furnished by alloys (special steels). As in the cases described above, the matter reduces to the fact that the magnitude \(Q\) of reactivity is this time determined by two factors: first, by \(A'\), expressing the specifically chemical character of this ability, and by \(E\), which gives the magnitude of the physical resistance.

Thus, for substances differing only slightly from one another in the magnitude of \(A'\), the measure of their reactivity will be the magnitude \(E\), i.e. in the present case hardness; so that mechanically hard substances in this case may at the same time be recognized as “chemically hard.”

As a final example we shall cite the phenomena of swelling \([1^3]\). The curves of Fig. 1 may be applied quite fully to hydrates if the curves \(A'\) are shifted somewhat. In doing so, for true hydrates only those ordinates will have a natural meaning which correspond to the stoichiometric values \(m\); furthermore, the curves are limited by the value \(m\) by which the composition of the highest hydrate is determined. In the case where no formation of mixed crystals takes place, the appearance of a new phase upon the transition of a substance from one degree of hydration to an adjacent one may serve as the sign of a true hydrate.

In the addition of water in zeolites, the appearance of a new phase is, it is true, not observed, but the stoichiometric limitation remains in force. In swelling substances even it is absent. In what follows, when speaking of the phenomena of swelling, we shall understand by these only those to which Katz (J. R. Katz), the best expert in this field, gave the name of phenomena of swelling “without complications,” i.e. which pro-

they proceed above all without strong influences from capillarity and without hysteresis [^14].

With such a restriction of the concept, the difference between swelling and non-swelling substances can, to a certain extent, be likened to the difference between fluorspar and the other halogen compounds of calcium, assigning the swelling substances to type I and the non-swelling ones to type II. If, in a first approximation, changes in \(A'\) and \(n\) are neglected, then only the lattice energy can serve as the criterion of an identical degree of swelling. In this connection it is immediately striking that typical swelling substances are substances with a low lattice energy, namely: proteins, polysaccharides, lipoids, and tanning substances; all these are substances with molecular lattices and high molecular volume.

Ionic lattices, owing to their high energy, caused by electrostatic forces, are in general incapable of swelling; a certain analogy to such a phenomenon has to be observed in soaps, in which a high molecular volume is combined with a tendency toward strong hydrolytic decomposition. Just as many salts, by means of preliminary treatment of them with water, can be artificially made capable of adding ammonia, it is possible in practice to realize a phenomenon which might be called “preliminary swelling” and which consists in an artificial loosening of the molecular lattice by means of an auxiliary substance capable of being absorbed with particular ease. In the same way one can explain why certain inorganic oxide hydrates swell, whereas in the corresponding anhydrous oxides this ability is entirely absent; the reason is that, as was already noted above, oxide hydrates are softer than the oxides themselves.

Infinite swelling leads to the formation of reversible colloids.

Irreversible colloids are metastable formations.

Both from experience and from theory it is known that reversible colloids are formed from substances with a molecular lattice, whereas substances in whose lattices electrostatic, i.e. very considerable, forces predominate (such as: noble metals, sparingly soluble salts, sulfides) can form only stable sols, if they are not protected from the forces acting in the lattices by colloids of the first kind.

LITERATURE:

1. W. Biltz, Zeitschr. f. anorg. u. allg. Chemie. 130, 133 (1923).
2. Zeitschr. f. anorg. u. allg. Chem. 145, 63 (1925).
3. W. Biltz, Zeitschr. f. anogr. u. allg. Chemie. 103, 116 (1923); W. Billtz und E. Birk. Zeitschr. f. anorg. u. allg. Chemie. 134, 125 (1924).

1. M. Born, Der Aufbau der Materie. 2nd ed., p. 65. Berlin, Julius Springer. 1922. Cf. A. Eucken, Grundriss der phys. Chem., p. 99. Leipzig, Akadem. Verlagsges. 1922.

2. Cf. the comparison in Zeitschr. f. anorg. u. allg. Chem. 130, 98 (1923); the measurements were made by G. F. Hüttig.

3. K. Fajans, Naturwissenschaften, 1921, p. 729.

4. W. Biltz and G. F. Hüttig, Zeitschr. f. anorg. u. allg. Chem. 114, 174 (1920).

5. H. G. Grimm, Zeitschr. f. Phys. Chem. 102, 113, 141 and 504 (1922). Supplement: H. G. Grimm and K. F. Herzfeld, Zeitschr. f. phys. 19, 141 (1923).

6. Zeitschr. f. anorg. Chem. 50, 67 (1906).

7. Zeitschr. f. Elektrochemie. 15, 129 (1909) and 27, 406 (1921).

8. F. Ephraim, Lehrb. d. anorg. Chemie, 1922, see, for example, p. 184.

9. W. Biltz, Zeitschr. f. anorg. u. allgem. Chem. 143, 231 (1925).

10. A somewhat more detailed description of swelling phenomena from the theoretical side will be printed in “Kolloid. Zeitschrift”.

11. Cf. J. R. Katz, Ergebnisse der exakten Naturwissenschaften. 3, 316 (1924).

1. Substitution of the value of \(E\) from equation (5) into equation (1) gives a relation between the heat of reaction and the change in volume for the reactions under consideration. Such relations were sought, among others, by Richards; however, the empirical rules obtained so far have not led to unambiguous conclusions. ↩↩