KINETICS OF HOMOGENEOUS REACTIONS1

S. H. Hinshelwood, Oxford.

The Fundamental Question

Various chemical processes ultimately lead to states of equilibrium. Generally speaking, the study of these states of equilibrium is the subject of thermodynamics. But the rate at which equilibrium is reached varies within very wide limits.

The subject of chemical kinetics is the question of why molecules undergo chemical changes, and how one may predict the rate at which a given chemical reaction will proceed under definite conditions. In order to understand the importance of the question of the rates of chemical reactions, it is sufficient, on the one hand, to consider large-scale industrial processes based on catalytic gas reactions and, on the other hand, to dwell on the instability of living matter, which reduces whole branches of biochemistry to the question of reaction rates.

However, before it becomes possible to predict reaction rates, which is necessary for the applied sciences, and before it will be possible to answer the question of whether the problems they pose are soluble, it is necessary to consider, in a purely theoretical way, what occurs in the act of chemical transformation.

The greatest success may be expected from the study of simple reactions in the gas phase, since all the resources of the kinetic theory of gases can be brought to bear on this investigation.

All experimentally studied simple gas reactions can be divided into two fundamentally different classes: homogeneous and heterogeneous reactions. In homogeneous reactions, chemical changes occur with molecules freely flying in the gas phase; in heterogeneous reactions, chemical changes take place on the wall of the vessel containing the gas, or on the surface of some solid substance added to the system. The criterion of a homogeneous reaction

is the independence of its rate from the size of the solid surface in contact with the gas, whereas for a heterogeneous reaction the rate is directly proportional to this surface.

Homogeneous reactions are divided into classes depending on their “order,” i.e., according to the number of molecules taking part in each individual act of chemical transformation. The order of a reaction is easily found by considering the effect of a change in pressure on the rate. Thus, for example, the rate of decomposition of ozone is proportional to the square of the partial pressure of ozone; from elementary probability considerations it follows that, for the process to occur, a collision of two molecules is required. Thus the reaction proceeds according to the equation: \(2\mathrm{O}_3 = 3\mathrm{O}_2\), and not \(\mathrm{O}_3 = \mathrm{O}_2 + \mathrm{O}\), with a subsequent rapid combination of individual oxygen atoms into molecules. Monomolecular, bimolecular, and trimolecular gas reactions are known; examples of reactions of higher order are unknown.

The same classification could also be applied to heterogeneous reactions. When, for example, nitrous oxide decomposes on the surface of platinum or gold, the reaction proceeds according to the equation \(\mathrm{N}_2\mathrm{O} = \mathrm{N}_2 - \mathrm{O}\), and not according to the equation \(2\mathrm{N}_2\mathrm{O} = 2\mathrm{N}_2 + \mathrm{O}_2\), as occurs in the gaseous medium. However, the true order of a heterogeneous reaction cannot be determined from the influence of pressure on the rate unless quite definite conditions are observed, the consideration of which we cannot dwell on here1.

Activation.

The act of chemical transformation of molecules depends on a process called “activation,” which consists in the fact that a molecule or molecules acquire an excess of energy considerably exceeding the average energy reserve of the molecule. There is no need to determine exactly the character of this excess—whether this molecular energy is kinetic or potential. For the time being we shall not touch upon the question of the manner in which this energy is acquired. Under different circumstances and in different types of reactions, the energy of activation may have different origins: in some cases it may be imparted to the molecule by collision with another molecule, in others it may be obtained as a result of the absorption of some kind of radiant energy. Activation is a process quite general and necessary both for homogeneous and for heterogeneous reactions. It is the basis of the entire kinetic theory of the rates of reactions. A necessary condition for a chemical transformation is that the molecule or molecules taking part in this transformation,

possessed an amount of energy exceeding a certain minimum, called the activation energy. The following considerations and facts serve as evidence of this.

1. In a chemical reaction proceeding at a measurable rate, only certain exceptional molecules are, at any given moment, in such a state that they can undergo transformation. This applies to reactions of the most varied character. For a homogeneous monomolecular reaction, such as, for example, the decomposition of nitric acid anhydride, this is obvious, since otherwise all the molecules would react simultaneously. For a bimolecular reaction, for example, for the combination of hydrogen with iodine, it is easy to calculate the number of collisions between hydrogen and iodine molecules occurring at a given temperature and pressure, and to show that only one out of many millions of collisions leads to chemical interaction. When oxygen at low pressure acts on a tungsten filament, only a very small fraction of the \(O_2\) molecules striking the filament is capable of reacting with it1.

2. Further, the attainment of this exceptionally active state is noticeably facilitated by an increase in temperature. The reaction-rate constant changes with temperature according to the Arrhenius equation2:

\[ \frac{d\log k}{dT}=\frac{E}{RT^2}. \]

This gives a significantly more rapid increase in rate than could be explained, for example, by an increase in the frequency of collisions. Arrhenius himself assumed the existence, in a state of equilibrium, of “inactive” (nonreactive, passive) and “active” molecules, the latter being formed from the inactive ones by an endothermic process. He ascribed the increase of reaction rate with temperature to the normal shift of equilibrium between active and passive molecules, following from the second law of thermodynamics. Thus \(E\) in the Arrhenius equation should express the heat of formation of the active molecules. The essential points of this theory are now generally accepted, but they are expressed in a somewhat different form. We do not regard active molecules as something like a tautomeric form of normal molecules, but consider them as normal molecules possessing an exceptionally large store of energy. From the standpoint of Bohr’s theory, they may in some cases be regarded as molecules situated in one of the higher quantum states. Against the acceptance of definite tautomeric forms one may object as follows: it is difficult to imagine what they should represent in the case of such

“simple reactions, such as the decomposition of ozone or hydrogen iodide. The fact that tautomeric modifications are sometimes encountered as one of the stages in more complex reactions, for example in organic chemistry, is not at all essential. There they are quite natural. But they are not the principal characteristic of a chemical reaction in general. The active molecule of hydrogen iodide does not differ in structure from the ordinary one1.

The characteristic form of the dependence between the reaction rate and temperature follows directly from the equations of kinetic theory, which express the distribution of energy among gas molecules. At a given temperature the molecules have a certain mean kinetic energy, a certain mean rotational energy, etc. Some molecules possess a reserve of energy of some kind considerably exceeding the mean value, while others possess much less. The form of the “law of distribution” changes depending on the kind of energy under consideration, but the following law, with some approximation, is applicable to all kinds of energy. If \(N\) is the total number of molecules, then the number \(N'\) of molecules for which the energy of some definite kind—for example, rotational—exceeds the value \(\varepsilon\), is given by the equation

\[ N' = Ne^{-\frac{\varepsilon}{kT}}, \]

where \(k\) is the gas constant \(R\), divided by Avogadro’s number (Boltzmann’s constant). If instead of \(\varepsilon\), the energy per molecule, we write \(E\), the energy per gram-molecule, the equation takes the form:

\[ N' = Ne^{-\frac{E}{RT}}; \]

the term \(e^{-\frac{E}{RT}}\) represents the probability that a molecule possesses a reserve of energy of some kind exceeding \(E\) (referred to a gram-mole). Since the reaction rate is proportional to the number of active molecules, we obtain for the reaction-rate constant:

\[ k = \chi e^{-\frac{E}{RT}}. \]

The coefficient \(\chi\) varies depending on the nature of the reaction. Thus, for example, in a bimolecular reaction it depends on the number of collisions between molecules of a definite kind; in monomolecular reactions it does not depend on the number of collisions and is perhaps connected with the rate of transfer of radiant energy. In the first approximation it does not depend on temperature—or, in any case, its

changes are negligible in comparison with the very rapid change of the exponential term \(e^{-\frac{E}{RT}}\). Therefore, regarding it as constant, taking the logarithm and differentiating with respect to \(T\), we obtain the Arrhenius equation. Analogous considerations, though somewhat more complex, also apply to heterogeneous reactions1.

What does the solution of the fundamental problem of chemical kinetics consist in?

Taking the foregoing into account, let us return for a moment to the question of the possibility of calculating absolute values of the reaction rate. We have seen that the number of active molecules is equal to the fraction of the total number of molecules, approximately expressed by \(e^{-\frac{E}{RT}}\). \(E\) can be found from the temperature coefficient of the reaction rate by the Arrhenius equation. The question arises: can we hope to calculate \(E\) a priori? The answer: this attempt lies beyond the limits of the possibilities of chemical kinetics. Since \(E\) represents the energy that must be imparted to a molecule in order to make its parts capable of rearrangement, an absolute calculation is evidently a problem of the theory of molecular structure. In this sense an analogy from the field of thermodynamics may help. The laws of thermodynamics make it possible to predict precisely the displacement of chemical equilibria with temperature, and even the absolute position of these equilibria, if we know the heat of reaction and certain other thermal properties of the system under study. But under no circumstances do they relieve us of the necessity of finding, by independent methods, the heat of reaction in each individual case. The calculation of the heat of reaction constitutes a very difficult problem of molecular mechanics, which one can hardly hope to solve at the present time. In the study of kinetics the heat of activation \(E\) plays a role analogous to that of the heat of reaction in the study of equilibrium. It is a specific molecular property which must be determined for each reaction under study before proceeding further. The next question of investigation is the following: what is the absolute reaction rate for a given heat of activation? We may hope to answer this question, and indeed considerable successes have been achieved in this direction. In the equation:

\[ \text{reaction rate} = \chi e^{-\frac{E}{RT}}. \]

\(E\) is the fundamental given quantity, determined from the temperature coefficient, but its theoretical calculation belongs to the broader field of the doctrine of the relations between structure and physical

properties. Our task is to investigate the nature of \(\chi\) in reactions of various types.

For this purpose we shall examine different kinds of homogeneous reactions in order.

Bimolecular Reactions.

It is most convenient to begin with the consideration of bimolecular reactions, since their theory is more developed than that for monomolecular and trimolecular reactions. The following bimolecular reactions are known: decomposition of hydrogen iodide \(^{1}\), \(2\mathrm{HI}=\mathrm{H}_2+\mathrm{I}_2\); combination of hydrogen with iodine \(^{2}\), \(\mathrm{H}_2+\mathrm{I}_2=2\mathrm{HI}\); decomposition of nitrous oxide \(^{3}\), \(2\mathrm{N}_2\mathrm{O}=2\mathrm{N}_2+\mathrm{O}_2\); ozone \(^{4}\), \(2\mathrm{O}_3=3\mathrm{O}_2\); acetaldehyde in the gaseous state \(^{5}\), \(2\mathrm{CH}_3\mathrm{CHO}=2\mathrm{CO}+2\mathrm{CH}_4\).

The decomposition of hypochlorous acid anhydride \(^{6}\), \(2\mathrm{ClO}=2\mathrm{Cl}_2+\mathrm{O}_2\) (the final products of the reaction), although complicated by certain side reactions, also essentially represents a bimolecular reaction. All the reactions listed have been studied rather thoroughly.

A bimolecular character was also ascribed to the combination of nitrogen with oxygen to form nitric acid \(^{7}\) and to the decomposition of nitric acid \(^{8}\); however, the experimental results, obtained by an unsatisfactory method of flow of the reacting gases, admit various interpretations and are unsuitable for calculations, since they leave doubts as to the homogeneous or heterogeneous character of the reactions under the conditions of the investigation.

Bimolecular reactions depend on collisions between molecules. The number of collisions occurring in a volume of \(1\ \mathrm{cm}^3\) per unit time can be calculated from the kinetic theory by the equation:

\[ \text{Number of collisions} = z = \sqrt{2}\pi\sigma^2 n^2 \bar{u}, \]

where \(\sigma\) is the diameter of the molecule, \(u\) is the mean square velocity of the molecules, \(n\) is the number of molecules in \(1\ \mathrm{cm}^3\) at the given temperature and pressure; \(\sigma\) is ex-

\(^{1}\) Bodenstein, ZS. f. phys. Chem., 29 (1899) 295. In connection with the critical remarks of N. A. Taylor, J. Am. Chem. Soc. 28 (1924) 984, see ref. 1, p. 49.

\(^{2}\) Bodenstein, l. c., 6.

\(^{3}\) Hunter, ZS. f. phys. Chem. 53 (1905) 441; Hinshelwood and Burk, Proc. Roy. Soc., A, 106 (1924) 284.

\(^{4}\) Chapman and Jones, J. Chem. Soc. 97 (1910) 2463.

\(^{5}\) Hinshelwood and Hutchison, Proc. Roy. Soc., A, 111 (1926) 380.

\(^{6}\) Hinshelwood and Prichard, J. Chem. Soc., 123 (1923) 2730; Hinshelwood and Hughes, J. Chem. Soc., 125 (1924) 1841; the results were confirmed in Bodenstein’s laboratory: ZS. f. phys. Chem., 116 (1925) 372.

\(^{7}\) Nernst, ZS. anorg. Chem. 49 (1906) 215.

\(^{8}\) Jellinek, ZS. anorg. Chem. 49 (1906) 229.

is calculated from the viscosity, and since viscosity is a property directly connected with the mean free path and, consequently, with the number of collisions, any arbitrariness in our definition of the molecular diameter is in no way reflected in the correctness of the formula. Thus, we can calculate the number of collisions with great confidence, at least as to the order of magnitude being determined, though not with very great accuracy. It should be noted that all molecular diameters are of the order of \(10^{-8}\) cm.

As we have already said, the number of collisions turns out to be many millions of times greater than the number of reacting molecules. This was one of the grounds that led to the assumption of the necessity of activation. Suppose that one of the colliding molecules requires (in order to react) an energy exceeding \(E_1\), and the other—exceeding \(E_2\).^1 The fractions of the total number of molecules corresponding to energy reserves exceeding \(E_1\) and \(E_2\) are \(e^{-\frac{E_1}{RT}}\) and \(e^{-\frac{E_2}{RT}}\) (approximately).

If we write \(E = E_1 + E_2\), this means that the fraction of all collisions

\[ e^{-\frac{E}{RT}} \]

is due to collisions of active molecules. The reaction rate must be proportional to the total number of collisions multiplied by this coefficient. Thus, the number of reacting molecules is

\[ A \cdot z \cdot e^{-\frac{E}{RT}}. \]

We know nothing about \(A\), except that it does not depend on temperature. On the contrary, everything we know about the internal economy of molecules does not contradict the assumption that only one out of many millions of collisions can be effective, even if the condition of a sufficient reserve of energy is satisfied. If we compare the activation energy with the effort that must be expended in order to hold open a heavy door of cash office, then the coefficient \(A\) represents the probability of finding the correct combination of letters that permits one to open the secret lock. This process requires no expenditure of energy, but without it no expenditure of energy will give the desired result. We shall see, however, that in bimolecular reactions the combination of molecular locks is extremely primitive, and the condition of a sufficient reserve of energy is the only essential factor.

Knowing nothing about \(A\), we can nevertheless find \(E\), since \(Z\) is proportional to \(\sqrt{T}\), and we have:

\[ k = \mathrm{const}\,\sqrt{T}\cdot e^{-\frac{E}{RT}}, \]

^1 \(E_1\) and \(E_2\) are calculated per gram-molecule.

whence, by taking logarithms and differentiating, we obtain:

\[ \frac{d\log k}{dt}=\frac{E}{RT^2}+\frac{T}{2}. \]

Thus, \(E\) can be found from the ratio of the rates at two different temperatures, and substituted into the preceding equation. This will give us the value of \(A\). Experiments show that in all known cases of bimolecular reactions the expression—the number of collisions \(\times e^{-\frac{E}{RT}}\)—comes out almost equal to the number of reacting molecules1. Thus the sole essential condition for reaction is the presence of a sufficient store of energy.

The consequences of this remarkable result are clearly reflected in the comparison of various bimolecular reactions. Since all molecular diameters have one and the same order of magnitude, the number of collisions changes only slightly in passing from one gas to another. Moreover, if there are no other essential conditions besides a sufficient store of energy, the rate of a bimolecular reaction must be determined chiefly by the value of the exponential factor \(e^{-\frac{E}{RT}}\). Different bimolecular reactions have very different values of \(E\). The greater \(E\) is, the smaller \(e^{-\frac{E}{RT}}\) is and, consequently, the lower the reaction rate. In other words, the higher the temperature at which the rate of the reaction reaches a given value. These expectations are confirmed with astonishing accuracy2.

Thus, for example, the activation energy of chlorous acid anhydride is \(21\,000\) cal.; for the decomposition of hydrogen iodide it is \(44\,000\) cal. The latter reaction must proceed considerably more slowly than the former; this is in fact observed. The two rates should approximately become equal at such temperatures that the values of \(\frac{E}{RT}\) become equal. And indeed it has been found that the decomposition of hydrogen iodide proceeds at \(760^\circ\) abs. with the same rate as the decomposition of chlorous acid anhydride at \(384^\circ\) abs., i.e. the absolute temperatures corresponding to equal rates are in the ratio of the heats of activation. Hydrogen iodide and acetaldehyde decompose at approximately the same rate at the same temperature. In accordance with this we find that

and their heats of activation are almost equal: for acetaldehyde \(E = 45500\) cal. If the specific factors indicated in the analogy with a secret lock played a noticeable role, these reactions might have equal heats of activation, but at the same temperature they could proceed at rates differing by thousands of times. Thus there is no doubt that the acquisition of activation energy is the most important, if not the only, factor determining the rate of bimolecular reactions.

The theory of the influence of temperature on the rate of reactions shows that the possession of a certain excess of energy is a necessary condition for a reaction; the calculation we have given indicates that it may also be a sufficient condition for the occurrence of a reaction.

Trying to penetrate more deeply into the mechanism of the reaction, we can move forward with considerably less certainty. From the expression: number of colliding molecules \(\times e^{-\frac{E}{RT}}\), we can compute the absolute rate of reaction, which differs from the true one by no more than a factor of 2–3. This is all the more remarkable because the calculation gives absolute values; an incorrect theory could give numbers differing from the true ones by hundreds, thousands of times or more. Therefore we must consider that the coefficient \(\chi\) is sufficiently well explained from the point of view of the number of collisions between molecules. However, in order to answer the question whether every collision is actually effective, experimental material of considerably greater accuracy than that which we have at present, or which can ever be obtained in the future, would be required. Some of the active molecules may rebound without undergoing chemical changes. We know only that their number is not so large as to affect the overall agreement of experimental results with theory. The factors limiting the accuracy of our knowledge are the following: a) the approximate character of the distribution law determining the exponential term in the equation for the reaction rate; b) the approximate value of \(\sigma\); c) the experimental difficulties of determining \(E\) with great accuracy. \(E\) can usually be determined with an accuracy of \(3\text{–}5\%\); this may give a fluctuation in the values of \(Z \cdot e^{-\frac{E}{RT}}\) by a factor of 2 or 3, whereas the number of reacting molecules is of the order of \(10^{16}\). In this connection a discussion has arisen, one not promising any particular success—whether every activated molecule reacts. We shall probably never know this.

We can say, however, that the nature of the coefficient \(\chi\) in the case of bimolecular reactions is comprehensible to us.

Trimolecular Reactions

Four trimolecular gas reactions are known, in each of which two molecules of nitric oxide take part:

\[ \begin{aligned} 2\,\mathrm{NO}+\mathrm{O}_2 &= 2\,\mathrm{NO}_2 \;{}^{1})\\ 2\,\mathrm{NO}+\mathrm{Cl}_2 &= 2\,\mathrm{NOCl} \;{}^{2})\\ 2\,\mathrm{NO}+\mathrm{Br}_2 &= 2\,\mathrm{NOBr} \;{}^{3})\\ 2\,\mathrm{NO}+2\mathrm{H}_2 &= \mathrm{N}_2+2\mathrm{H}_2\mathrm{O} \;{}^{4}). \end{aligned} \]

The last reaction proceeds in two stages:

First stage:

\[ 2\,\mathrm{NO}+\mathrm{H}_2=\mathrm{N}_2\mathrm{O}+\mathrm{H}_2\mathrm{O} \quad\text{or}\quad \mathrm{N}_2+\mathrm{H}_2\mathrm{O}_2. \]

In the second stage there occurs the rapid decomposition of the nitrous oxide or hydrogen peroxide obtained in the first stage of the reaction. Thus it is kinetically trimolecular.

These reactions proceed according to equations similar to the following:

\[ -\frac{d[\mathrm{NO}]}{dt}=k[\mathrm{NO}]^2[\mathrm{O}_2] \quad\text{or}\quad -\frac{d[\mathrm{NO}]}{dt}=k[\mathrm{NO}]^2[\mathrm{H}_2]. \]

The most natural assumption is that they depend on the simultaneous collision of three molecules. However, it may be supposed that first two molecules of nitric oxide combine to form \(\mathrm{N}_2\mathrm{O}_2\), and then a bimolecular reaction occurs between \(\mathrm{N}_2\mathrm{O}_2\) and chlorine, bromine, oxygen, or hydrogen. If the equilibrium between \(\mathrm{N}_2\mathrm{O}_2\) and \(2\mathrm{NO}\) is established rapidly, the concentration of \(\mathrm{N}_2\mathrm{O}_2\) is always proportional to \([\mathrm{NO}]^2\), and since the rate of the bimolecular reaction is proportional, for example, to \([\mathrm{N}_2\mathrm{O}_2][\mathrm{O}_2]\), it will be proportional to \([\mathrm{NO}]^2[\mathrm{O}_2]\), and, consequently, the reaction will proceed kinetically trimolecularly. This assumption seems rather artificial: indeed, it is not necessary if one considers the special nature of a triple collision. In a double collision, during a finite interval of time the colliding molecules are at such a small distance from one another that if during this time a third molecule approaches, a triple collision will occur. This interval of time may be called the “duration of the collision.” From the kinetic point of view there is no great difference between two \(\mathrm{NO}\) molecules that have collided for a finite interval of time—

\({}^{1})\) Bodenstein u. Fr. Lindner, ZS. f. phys. Chem., 100 (1922) 68.
\({}^{2})\) Trautz, ZS. anorg. Chem., 88 (1914) 285.
\({}^{3})\) Trautz u. Dalal, ZS. anorg. Chem., 102 (1918) 149.
\({}^{4})\) Hinshelwood and Green, J. Chem. Soc. 123 (1926) 730.

between and the molecule \(\mathrm{N_2O_2}\), or the so-called “complex” of two \(\mathrm{NO}\) molecules. However, there are objective objections to the supposition of the formation of \(\mathrm{N_2O_2}\), which we shall be able to understand by considering the question of the temperature coefficient of trimolecular reactions.

Bodenstein1 made the interesting observation that the reaction \(2\mathrm{NO}+\mathrm{O_2}=2\mathrm{NO_2}\) has a very small, but quite definite, negative temperature coefficient. Expressed, as usual, as the ratio of the reaction rate at \((t+10)^\circ\) to the rate at \(t^\circ\), the coefficient changes from a value of 0.912 near \(0^\circ\) to 0.997 near \(350^\circ\). One might have predicted that the temperature coefficient of a trimolecular reaction would be much smaller than for a bimolecular reaction: a collision among three molecules is a much rarer event than one between two molecules. Therefore, if the same heat of activation were required for both reactions, the trimolecular reaction would proceed considerably more slowly than the bimolecular one. Conversely, if both reactions proceed at the same temperature with the same rate, this means that the trimolecular reaction requires a considerably smaller heat of activation. Consequently, other conditions being equal, it will have a considerably smaller temperature coefficient. We can easily estimate the expected difference. Bodenstein takes the ratio of the number of triple collisions to the number of double collisions to be approximately equal to the ratio of the molecular diameter to the mean free path. Hence triple impacts are approximately \(10^3\) times rarer than double ones at atmospheric pressure. The exact geometrical arrangement of the molecules at the moment of collision is probably more important in the case of a reaction of the type \(2\mathrm{NO}+\mathrm{O_2}=2\mathrm{NO_2}\) than in the case of a simple bimolecular reaction of the type \(2\mathrm{HI}=\mathrm{H_2}+\mathrm{I_2}\), so that the probability of a productive trimolecular collision is approximately \(10^4\) times smaller than that of an effective bimolecular collision. Therefore, if the trimolecular reaction is to attain the same rate as the bimolecular reaction at the same temperature, its activation energy must be smaller by \(\Delta E\), determined from the relation

\[ \frac{e^{-\frac{E}{RT}}}{e^{-\frac{E-\Delta E}{RT}}}=10^4 . \]

This means that at ordinary temperatures the heat of activation of the trimolecular reaction is less by 6,000 cal.; at \(1000^\circ\) abs.—approximately by 15–20,000 cal. In the preceding paragraph it was indicated that, for bimolecular reactions, the ratio

between the heat of activation and the absolute rate is sufficiently well known. A bimolecular reaction proceeding at ordinary temperature with a measurable rate must have a heat of activation approximately equal to 14,000 cal. Therefore, the heat of activation of a trimolecular reaction proceeding at ordinary temperature with a measurable rate should not differ much from 8,000 cal. The corresponding temperature coefficient is very small. The rate constant of reactions is equal to the product of two factors: \(\chi \cdot e^{-\frac{E}{RT}}\). In bimolecular reactions \(\chi\) depends on the frequency of collisions and therefore increases in proportion to the square root of the temperature. In trimolecular reactions the value of \(e^{-\frac{E}{RT}}\) is such that a small positive temperature coefficient may be expected. The term \(\chi\), which depends on the frequency of triple collisions, must decrease with increasing temperature, so that the rate may in some cases have a negative temperature coefficient, as, for example, in the reaction under consideration. Bodenstein assumes that this decrease is explained by a reduction in the “duration of collision” at high temperatures. The higher the temperature, the faster the molecules move, and the smaller the probability that two molecules will remain together long enough for a third to have time to join them. A reversal of the sign of the temperature coefficient of the reaction rate will occur only if the heat of activation is small, as a result of which the “normal” effect of raising the temperature, represented by the exponential term, is easily masked. In the combination of nitric oxide with chlorine and bromine the temperature coefficient has a small positive value, only slightly exceeding unity. In a reaction that proceeds at a noticeable rate only at very high temperatures, the influence of the decrease in collision frequency ceases to be noticeable, since the heat of activation is very large. The reaction between nitric oxide and hydrogen1 proceeds near \(1100^\circ\) abs. at a rate comparable with that of the reaction between nitric oxide and oxygen at ordinary temperature. The heat of activation is 44,000 cal. If in the same temperature region a bimolecular reaction proceeded at the same rate, it would require a heat of activation of 60,000 cal. Hence it is clear that the relation between the heats of activation is approximately what might have been expected from the relative probability of triple and double collisions. More exact calculations of trimolecular collision present great difficulties.

The analysis of these reactions takes on, formally, a somewhat different form if they are regarded as bimolecular reactions between \(N_2O_2\) and mo-

current one of the gases. The hypothetical bimolecular reaction must have a normal temperature coefficient, which decreases or changes sign as a consequence of the dissociation of \(N_2O_2\), increasing with increasing temperature. It is easy to show that the apparent heat of activation of the entire reaction is equal to the difference between the heat of activation of the bimolecular reaction and the heat of dissociation of the double molecules of nitrogen oxide into simple ones. Although formally this theory is quite satisfactory, Bodenstein indicates that it requires the assumption of a very high heat of formation of double molecules of nitrogen oxide, which therefore, in accordance with Nernst’s theorem, ought to be fairly stable at low temperatures. This objection is serious, since the formation of even traces of \(N_2O_2\) has never been observed.

We see that a general understanding of the mechanism of trimolecular reactions is possible, although in calculations we must for the present be content with orders of magnitude rather than exact values. Within these limits, however, the question is clear. We see something quite different when we turn to the consideration of monomolecular reactions.

Monomolecular Reactions.

The thermal decomposition of nitrogen anhydride\(^{1}\) and gaseous acetone\(^{2}\) are homogeneous monomolecular reactions. The decomposition of sulfuryl chloride,\(^{3}\) which takes place chiefly on the walls of vessels made of soda glass, evidently depends considerably less on the vessel walls if they are made of Pyrex glass (Pyrexglass). The decomposition of phosphine,\(^{4}\) which at one time was considered a homogeneous reaction, is chiefly heterogeneous under those conditions under which it can be measured. The assertion that the conversion of cyclopropane into propylene\(^{5}\) becomes homogeneous at high temperatures is based on insufficient data.

We shall therefore confine ourselves to considering the decomposition of nitrogen anhydride and acetone. In the first of these reactions, nitrogen anhydride decomposes into oxygen, nitrogen dioxide, and nitrogen tetroxide; in the second, acetone gives carbon oxide and ethane, which undergoes further transformations. Nitrogen anhydride decomposes at ordinary temperature, acetone at a dull red heat.

1) Daniels and Johnston, J. Amer. Chem. Soc., 43 (1921) 53.
2) Hinshelwood and Hutchinson, Proc. Roy. Soc., A. 111 (1926) 245.
3) D. F. Smith, J. Amer. Chem. Soc. 47 (1925) 1862.
4) Trautz u. Bhandarkar, ZS. anorg. Chem., 106 (1919) 95; Hinshelwood and Topley, J. Chem. Soc., 125 (1924) 393.
5) Trautz u. Winkler, J. pr. Chem., 104 (1922) 53.

The present state of the theory of monomolecular reactions may be characterized as follows:

1. Perrin1 proposed that, since the rate of a monomolecular reaction does not depend on the pressure of the gas, and the latter can be expanded to an infinitely large volume without changing the probability of transformation of a molecule, the process of chemical change can in no way be determined by molecular collisions. This consideration was the chief basis of the “radiation theory,” developed by McLewis (W. C. Mc. C. Lewis) and by Perrin himself.

2. From this proposition two different ways out were proposed. Lindemann2 pointed out that the usual experimental data concerning monomolecular reactions prove only that these reactions do not depend on pressure within known limits, and do not justify extrapolation to infinite dilution of the gas. Independence of pressure over a wide, but not infinite, range can be explained without rejecting the hypothesis of collisions as the cause of activation. It is only necessary to assume that molecules acquire and lose activation energy considerably faster than they react. This could occur in the event that molecules, in order to react, must not only receive the necessary store of energy but also be in the appropriate phase.

Moreover, it is necessary to assume that they enter this phase so rarely that, before entering into reaction, the activation energy imparted to them by a collision may be taken away from them by a new collision. According to the distribution law, a constant fraction of the total number of molecules will at any given moment possess activation energy, whatever the pressure may be; of these, some fraction will react, but this fraction is so small that it will not cause a noticeable change in the overall concentration of active molecules. Therefore, over wide limits of pressure variation, the reaction will be monomolecular. However, at very low pressures the time between two collisions will become so long that the loss of “active” molecules as a result of the chemical process can no longer be considered small in comparison with the rate of activation and deactivation. The number of active molecules cannot be kept constant, and the rate constant of the monomolecular reaction will begin to decrease. The reaction will gradually begin to acquire the character of a bimolecular one.

Christiansen and Kramers3 proposed the so-called “chain mechanism,” according to which the reaction products, carrying with them the initial heat of activation plus the heat of reaction, are capa-

able to activate, by collision, the next molecule of the reacting substance that they encounter. This process continues indefinitely. The normal fraction of molecules that have received the energy of activation by collision is thus kept constant, independently of the pressure and in spite of the fact that the fast active molecules are removed as a result of the chemical reaction, since every such loss is immediately compensated by the activation of a new molecule by the “hot” products of the reaction. Therefore a chemical transformation may proceed according to the law of a monomolecular reaction, while being in essence bimolecular. According to this theory, inert gases, including the accumulating reaction products, should exert a noticeable retarding effect, since they should take away the energy from the newly formed molecules of the reaction products before this energy can be transferred to the molecules of the reacting substances.

Christiansen and Kramers are compelled to make the arbitrary assumption that the reaction products are capable of giving up their energy only to molecules of the reacting substances. Such an assumption must be confirmed experimentally.

Thus, the following possibilities remain:

\[ \begin{array}{rcl} \text{Activation by collision} & \left\{ \begin{array}{l} \text{Lindemann mechanism}\\ \text{Christiansen--Kramers mechanism} \end{array}\right.\\[1em] \text{Activation by absorption} & \left\{ \begin{array}{l} \text{Simple radiation theory }{}^{1)}\\ \text{Extended radiation theory }{}^{2)} \end{array}\right.\\ \text{of radiation} && \end{array} \]

The simple radiation theory assumes that a molecule is activated by a quantum of monochromatic radiation whose frequency is equal to \(\dfrac{E}{Nh}\), where \(E\) is the heat of activation, \(N\) is Avogadro’s number, and \(h\) is Planck’s constant. The modification of the simple radiation theory amounts to the fact that several quanta may be absorbed simultaneously or successively, whereas the extended radiation theory assumes that the activation energy may be supplied by a continuous series of frequencies.

We shall consider these different possibilities in connection with the experimental data relating to the decomposition of nitrogen pentoxide and acetone.

The simple radiation theory fails at once. It predicts that the decomposition of nitrogen pentoxide should depend on absorption of radiation in the short infra-red region. At present it is known that radiation of the calculated frequency does not exert

\(^{1)}\) Perrin (see 25); W. C. Mc. C. Lewis, J. Chem. Soc., 109 (1916) 796; 111 (1917) 457; 113 (1918) 471.
\(^{2)}\) Cf. Tolman, J. Amer. Chem. Soc., 47 (1925) 1524.

influence on the rate of this reaction. For acetone the calculated frequency lies in the visible region of the spectrum, where acetone does not absorb light.

There is no direct experimental verification for the extended radiation theory. We shall, however, return to it after considering the collision mechanism.

The chain mechanism is highly improbable. Hunt and Daniels1 showed that the presence of a large excess of nitrogen did not affect the rate of decomposition of nitrogen pentoxide, even when the latter’s elasticity was very small. Hirst2 showed that argon likewise does not affect the reaction rate. The rate of decomposition of acetone is not appreciably changed by the presence of nitrogen or carbon oxide; experiments at very low acetone pressures have not been carried out.

Moreover, it is not obvious whether a chain mechanism can operate at all in the case of an endothermic reaction, such as the monomolecular decomposition of \(N_2O_5\) into \(N_2O_4\) and \(O\). Nevertheless, this theory should not yet be definitively rejected.

Lindemann’s hypothesis encounters still greater difficulties. Hunt and Daniels found that the monomolecular character of the decomposition of nitrogen pentoxide is preserved when the pressure is lowered at least to \(0.01\) mm of mercury. Hirst and Rideal3 confirmed this and showed that at very low pressures the reaction-rate constant tends rather toward some increase than toward a decrease. This last observation is important in the sense that it rejects a possible objection—that the experiments were carried out at an elasticity which was not sufficiently small for the expected decrease of the constant to be observed. The increase of the constant may be explained by the fact that at high pressures there occurs some deactivation of molecules by collisions with other molecules, diminishing at low pressures.

Still more important is the fact that, in the decomposition of nitrogen pentoxide and acetone, the number of reacting molecules is in any case far greater than the number that can be activated by collisions. The mechanism under consideration requires that the number of collisions be not only sufficient, but considerably exceed what is sufficient, in order to maintain a supply of molecules endowed with the necessary energy. In the case of acetone decomposition the number of reacting molecules is approximately \(10.5\) times greater than the number of molecules that can be activated by collisions.

One might suppose that the calculations of the rate of activation by collisions are based on false assumptions and quantitatively

are completely incorrect. But the fact that analogous calculations give such a coincident and satisfactory interpretation of bimolecular reactions deprives this assumption of probability. A particularly striking contrast is presented by the decompositions of gaseous acetone and acetaldehyde1. Although these two reactions are chemically similar and proceed in the same temperature regions, the first is monomolecular, while the second is bimolecular, as is evident from the vapor-density [[unclear: measurements?]]. This means that the second definitely depends on collisions between molecules. If the calculation of the maximum rate of activation is wrong when applied to acetone, then there is no reason to suppose that it will prove correct when applied to the bimolecular reaction of aldehyde decomposition. However, in this case the maximum number of molecules that can be activated by collisions proves, as usual, to be almost equal to the number of reacting molecules.

Therefore, in general, at the present time it is difficult to deny that monomolecular reactions really are what they appear to be, namely changes of individual molecules independent of collisions with other molecules. It must be admitted that views on this question have changed rapidly over the last several years and are still far from being finally established.

So far as can be judged at present, some generalized form of the radiation theory is not definitively excluded. Perhaps the view that molecules exchange energy through some kind of thermal radiation, which they are capable of absorbing or emitting, is the most satisfactory. For this purpose one may invoke the entire gamut of isothermal radiation with which any gas can be in equilibrium at a constant temperature. This could have been accepted without particular discussion as a reasonable and harmless assumption, had the controversy over the obviously unsatisfactory special radiation theory never arisen. The special radiation theory is refuted by the objection that illumination of a gas by a source of intense radiation of suitable wavelength ought to have enormously accelerated the reaction, which in fact is not observed. The view which we here regard as possible, though unproved, is at least not affected by this objection. Radiation is not considered necessary in itself; it only provides the means by which the Maxwellian distribution of internal energy among molecules is maintained, despite the loss of active molecules in the reaction and despite the insufficiency of collisions to maintain this distribution. For this purpose isothermal radiation is invoked, which, being in equilibrium with the gas, may be pre—

converted into all the other forms of molecular energy. We cannot increase the reaction rate by illuminating it with an external source, since in doing so we would have to increase simultaneously all the other kinds of molecular energy and thus raise the temperature of the whole mass of gas. The acceleration of the reaction as a result of a rise in temperature, of course, should not trouble us. Since radiation must be regarded as nothing other than an internal carrier of energy, the law of distribution that must be used in the equation for the reaction rate will have the form that pertains to the internal energy of the molecules and will not be determined by the character of the radiation.

Another question is whether the exchange of energy between molecules can take place by means of radiation with sufficient speed. This has been discussed by several authors, but the question cannot be considered to have received a definitive solution.

The whole problem must at present be regarded as open.

In the case of bimolecular reactions, \(\frac{E}{RT}\) has, approximately, the same value for different systems at temperatures corresponding to the same reaction rates. There are also serious indications of a similar proportionality of \(E\) and \(T\) for trimolecular reactions. It is interesting that the same rule holds also for monomolecular reactions. The heat of activation in the decomposition of nitrous anhydride is equal to 24,700 cal. The rate constant at \(55^\circ\) is 0.00150. The rate constant for the decomposition of acetone reaches this value only at \(562^\circ\), i.e. at an absolute temperature 2.55 times higher. In agreement with this, the heat of activation of acetone is considerably higher, namely 68,500 cal. The corresponding values of \(\frac{E}{RT}\) are 38.0 for nitrous anhydride and 41.4 for acetone. It is clear that in this case as well the heat of activation plays the principal role in determining the absolute rate of the reaction; other factors play a relatively subordinate role.

General rule.

On the basis of the foregoing, one may attempt to formulate a general rule, which until now has never been stated in explicit form. It seems to us that it has fundamental significance, although it is only approximate in character. The rate constant of a reaction may be expressed in the form \(z e^{-\frac{E}{RT}}\). The rule consists in the fact that, for reactions of a given type, changes in \(z\) are small in comparison with changes in the exponential factor, and that therefore the acquisition of the activation energy is the chief factor deter—

affecting the reaction. An analogy to this may be found in the process of evaporation, where the probability that a molecule will acquire energy sufficient for evaporation is determined by the expression \(e^{-\frac{\lambda}{RT}}\) (\(\lambda\) is the latent heat of evaporation). The rate of evaporation at a given temperature is equal to \(A \cdot e^{-\frac{\lambda}{RT}}\). Trouton’s rule, which is approximately justified by experiment, shows that, for a given rate of evaporation, \(\frac{\lambda}{T}\) is the same for the majority of substances. Thus, the changes in \(A\) from one substance to another are small in comparison with the changes in the exponential term. This also indicates that the acquisition of energy by a molecule is not only a necessary, but also a sufficient, condition for evaporation to occur.

The rule that we have established for chemical reactions is an approximation to the proposition that the acquisition of the activation energy is not only a necessary, but also a sufficient, condition for the reaction to proceed. This may not be justified with complete accuracy, but it is evidently valid with some approximation.

CHARACTER OF THE ACTIVATION ENERGY.

We have already discussed the question of whether molecules in monomolecular reactions are activated by collisions or by radiation. Experimental data seem to show that they cannot be activated sufficiently rapidly by collisions. In polymolecular reactions, collisions are in any case necessary, whether or not they participate directly in the activation process. Since for all forms of energy the distribution law can be expressed approximately in the form \(e^{-\frac{E}{RT}}\), it is easy to see that the number of collisions between molecules already possessing a reserve of some kind of energy exceeding \(E\) is almost equal to the number of collisions between molecules possessing the same excess of kinetic energy of translation. Therefore it is quite possible, and even probable, that in polymolecular reactions the activation energy is chiefly ordinary energy of translation, which is converted into the required form of internal energy at the moment of collision. However, there is no reason why all forms of energy could not act simultaneously, since a constant exchange takes place among all forms of thermal energy. This question is discussed in more detail in Tolman’s article1.

The Influence of Inert Gases and Moisture on the Rate of Gaseous Reactions.

Usually it is so small that it may be neglected. Foreign gases, such as, for example, nitrogen, carbon dioxide, or oxygen, neither accelerate nor retard a simple bimolecular reaction, for example, the decomposition of nitrogen pentoxide. The decomposition of nitrogen anhydride likewise does not depend on the presence of a large excess of foreign gases. Griffith and McKeown1 came to the conclusion that the decomposition of ozone is somewhat retarded by oxygen and slightly accelerated by argon, nitrogen, and helium.

Unfortunately, under the conditions of their experiments the reaction proceeded partly homogeneously and partly heterogeneously, which makes the result somewhat uncertain. (By using suitable vessels, a purely homogeneous reaction can be followed, as Chapman and Clark have shown.) However, from the fact that the rate constant changes less when the reaction is accelerated by an inert gas than in the absence of an inert gas, it was concluded that the acceleration must be ascribed to the homogeneous reaction. Griffith and McKeown suppose that activated ozone molecules remain associated for a finite interval of time, during which they may collide with a molecule of an inert gas. Collision with oxygen favors the resolution of the complex back into ozone molecules, whereas collision with argon favors decomposition into reaction products. The magnitude of these effects is insignificant. It is desirable that this investigation be continued.

The influence of inert gases is of special interest in the case of reactions in which two atoms unite into a molecule, for example \(Br + Br = Br_2\). Herzfeld2 pointed out that, in the collision of two atoms and in the exothermic formation of a molecule, the “nascent” molecule contains not only the initial energy of both atoms, but also all the heat liberated in the reaction. Therefore, according to Herzfeld, it is incapable of prolonged existence unless it gives up this excess energy by collision with some other molecule. Thus, in order for the reaction \(A + B = AB\) to occur, not only a double impact (collision) of \(A\) and \(B\) is required, but a “triple impact”—the collision of the molecules \(A\), \(B\), and \(C\). This consideration does not apply to bimolecular reactions of the type \(A + B = C + D\), since \(C\) and \(D\) fly apart after the collision in which they were formed, carrying with them the excess energy in kinetic form3. None of the reactions considered up to now belongs to that type,

KINETICS OF HOMOGENEOUS REACTIONS

to which Herzfeld’s theory is applicable. Examples of such reactions are not hard to find: reactions such as the combination of ethylene with chlorine¹) and with bromine²) proceed on surfaces. The same is true, in all probability, for the combination of ammonium chloride with ammonia³). Therefore in these reactions there is no difficulty in removing the heat of reaction from the “hot,” newly formed molecules. The combination of phosphorus trichloride with chlorine⁴), giving phosphorus pentachloride, is, to be sure, a homogeneous reaction, but its rate is so great that it cannot be measured.

The only reaction that admits a check of Herzfeld’s theory is the combination of bromine atoms into a molecule. Its rate was determined by the indirect method of Bodenstein and Lütkemeyer⁵) and of Bodenstein and Müller⁶). Inert gases did not affect it in the expected direction; the fraction of the total number of collisions between bromine atoms leading to combination was small, but did not depend on the total pressure of the gases in the system.

At the present time it is known that, since molecules possess more than one degree of freedom, they can have a store of energy considerably exceeding the energy of their decomposition into atoms. Therefore, if the heat of reaction were distributed among several degrees of freedom, a molecule, once formed, could continue to exist. However, since vibrational and rotational energy are quantized, it is unlikely that the store of energy which is to be distributed will amount to exactly an integral number of quanta. Therefore distribution will be impossible unless it is possible to get rid of the difference between the total energy and some integral number of quanta. In reactions where two or three molecules of reaction products are formed, the kinetic energy of the recoiling molecules carries off this excess. But when only one molecule is formed, the excess energy must be given off by radiation. The radiation may be infrared, of low frequency, with small quanta, difficult to distinguish in ordinary experiments. But little is known about this.

Of the chemical reactions that have been investigated, homogeneous gas reactions constitute only a small fraction. It is not always prudent to apply to them conclusions drawn from entirely different fields of investigation. The question has been raised more than once: is it possible to attempt to interpret from the standpoint of kinetic theory reactions which, perhaps, would not proceed at all if the gases were completely dried.

¹) Norrish and Jones, J. Chem. Soc., 129 (1926) 55.
²) Stewart and Edlund, J. Amer. Chem. Soc., 45 (1923) 1014.
³) According to unpublished observations by Birk (R. E. Burk) in Oxford.
⁴) H. A. Taylor, J. Physic. Chem., 28 (1924) 510.
⁵) Bodenstein und Lütkemeyer, ZS. f. phys. Chem., 114 (1924) 208.
⁶) Bodenstein u. Müller, ZS. Elektrochem., 30 (1924) 416.

This question is based on a misunderstanding. Most of the reactions studied by Baker and others, which are retarded by intensive drying, are either reactions between substances in different phases, as, for example, the action of sulfurous anhydride on barium oxide, or surface reactions—the combination of ammonia with hydrogen chloride may serve as an example of such a reaction. The photochemical reaction of the combination of hydrogen with chlorine ¹) is retarded by drying, but this is a very special case, representing an anomaly in almost every respect. For no simple homogeneous gas reaction of definite order, for which the molecular statistics has been developed, has a retarding influence of drying been demonstrated. Moreover, it would not be intelligible. A typical case of the inhibition of a reaction by drying is the combination of ammonia with ammonium chloride. If quite exceptional precautions are not taken in drying the vessels, the reaction proceeds with immeasurably great speed. If the walls are completely dry, the reaction does not occur at all. There is no proper proportionality between the moisture content and the reaction rate, as should be observed in the case of a triple interaction among \( \mathrm{NH_3} \), \( \mathrm{H_2O} \), and \( \mathrm{HCl} \). On the other hand, in a heterogeneous reaction such behavior is entirely intelligible ²): if the amount of water is sufficient to form a monomolecular layer on the walls of the vessel, the full effect is observed, and any excess above this amount (an exceedingly small one) will produce no further action.

The explosion of carbon monoxide with hydrogen is, in all probability, a homogeneous reaction, though admittedly one not very convenient for measuring the kinetics of the reaction. In this example, however, as might have been expected, a proper proportionality is observed between the water content and the velocity of the explosion wave. Here water plays a definite stoichiometric role in the series of reactions, of which the first is probably the following:

\[ \mathrm{CO} + \mathrm{H_2O} = \mathrm{CO_2} + \mathrm{H_2}. \]

In general, we must regard the negative criticism of kinetic investigations of gas reactions as poorly founded.

Photochemical Reactions in Gases

Light is absorbed and emitted by molecules in the form of quanta, the magnitude of which is determined by the relation: energy \(= h\nu\). Irradiation of molecules with monochromatic light gives us the possibility of imparting

¹ Coehn and Jung, ZS. f. phys. Chem., 110 (1924), 705.
² Bowen, J. Chem. Soc., 127 (1924), 1255. Norris, Faraday Soc., Discussion on Photochemical Reactions in Liquids and Gases (1925), p. 575. See also ZS. f. phys. Chem., 120 (1925).

molecules precisely determined quantities of energy. Therefore one might have expected that there exists a definite relation between the frequency of the photochemically active light and the heat of activation. However, all hopes of learning in this way anything more about the mechanism of chemical reactions proved vain. The reasons for this are most easily understood from a simple example. Let us consider the chlorine molecule. In it two atoms are joined by the so-called nonpolar bond, which in all probability reduces to electron orbits common to both nuclei. Each atom has, besides this, its own independent electrons. Excitation of the molecule by light in the visible region of the spectrum transfers these latter electrons to higher quantum orbits. One or the other of the atoms may thereby absorb much energy before the bond between them is weakened, and the molecule breaks apart. Indeed, the absorbed energy may considerably exceed the energy of dissociation. Photochemical excitation delivers the energy not to the place where it must be delivered in order to decompose the molecule. In accordance with this idea we find that photochemical quanta are in general much greater than the ordinary chemical energy of activation1.

Nevertheless, the study of photochemical processes has led to the discovery of a number of facts of fundamental importance for chemical kinetics. In most cases photochemical reactions obey, to a greater or lesser degree, Einstein’s law of photochemical equivalence. The foundations of this law may be expressed as follows: a) light is absorbed by molecules in the form of quanta having magnitude \(h\nu\); b) a quantum of light in the visible region of the spectrum is a very large quantity for a single molecule, and if a molecule that has absorbed such a quantum does not react at once, then it will almost certainly lose this energy by giving it up in a collision before it succeeds in absorbing a new quantum—processes in which molecules absorb more than one quantum of visible light are never encountered, or only very rarely; c) since a quantum of light is an amount of energy many times greater than the average store of energy of a molecule at ordinary temperature, it is unlikely that the effectiveness of light in exciting a chemical reaction will depend appreciably on small changes in the internal structure of the molecule. Therefore, if light is at all capable of exciting a reaction, then it is highly probable that each quantum will produce an effect. Einstein’s law establishes that, for each quantum of absorbed active light, one molecule is excited to reaction.

For the decomposition of hydrogen bromide and hydrogen iodide in the gaseous state, Warburg2 found that for each absorbed quantum re-

two molecules are involved. Boden1 found the very same thing for the decomposition of chloric-acid anhydride. This is explained by assuming the following mechanism:

\[ \mathrm{Cl_2O} + h\nu = \mathrm{Cl_2O}\ \text{(activated)} \]

\[ \mathrm{Cl_2O}\ \text{(activated)} + \mathrm{Cl_2O} = 2\mathrm{Cl_2} + \mathrm{O_2}, \]

or

\[ \mathrm{Cl_2O} + h\nu = \mathrm{Cl_2} + \mathrm{O} \]

\[ \mathrm{Cl_2O} + \mathrm{O} = \mathrm{Cl_2} + \mathrm{O_2} \]

The formation and decomposition of ozone approximately follow Einstein’s law, as does the combination of chlorine with sulfurous anhydride and the bromination of \(\mathrm{C_6H_{12}}\)2. In the decomposition of ammonia, it is as though only one molecule out of four reacts. However, this result may not be very accurate.

On the other hand, for one absorbed quantum many molecules of phosgene are formed (from chlorine and carbon monoxide), and for one absorbed quantum hundreds of thousands of molecules of hydrogen and chlorine combine. Reactions of this kind can be explained by the so-called “chain mechanism.” Let us explain it with the following example:

\[ \begin{aligned} \mathrm{Cl_2} &\longrightarrow 2\mathrm{Cl} \\ \mathrm{Cl} + \mathrm{H_2} &= \mathrm{HCl} + \mathrm{H} \\ \mathrm{H} + \mathrm{Cl_2} &= \mathrm{HCl} + \mathrm{Cl}\ \text{etc.} \end{aligned} \]

This is only an illustration. In the reaction of combination of hydrogen with chlorine, water also enters into the chains of reactions. Generally speaking, there is an initial photochemical reaction, followed by purely thermal processes. Weigert and Kellermann3 found direct proof of the existence of such chains by kinematographically studying the state of the gas after instantaneous illumination by a spark.

It remains an open question whether the reactive chains in the combination of hydrogen with chlorine are not subject to some influence of the vessel walls. Opinions on this question are divided, and decisive experiments have not yet been carried out.

An interesting transition region between photochemical and thermal reactions was discovered by the investigations of Cario and Franck4, who illuminated a mixture of hydrogen and mercury vapor with the light of the mercury spectral line \(2536.7\ \text{\AA}\). The mercury atoms, excited by the light, upon collisions with hydrogen molecules split them into atoms or, at least, converted them into a chemically active state.

Other experiments of the same kind were carried out by Taylor and Marshall^1), who in this way activated hydrogen and caused it to react in the cold with ethylene, carbon monoxide, oxygen, and nitrous oxide. According to Hirst and Rideal^2), these reactions proceed only in the presence of liquid mercury, the surface of which is illuminated, and consequently belong to heterogeneous reactions. In any case, one must not lose sight of the possibility of the formation of mercury hydride^3).

Mixed Reactions.

An interesting, although special, question is the role of free atoms in chemical kinetics. The rate of decomposition of carbonyl chloride^4) in the region of 700° is proportional to the square root of the concentration of the chlorine present. This makes it possible to suppose that the decomposition depends on collisions of carbonyl chloride molecules with chlorine atoms, since the concentration of atomic chlorine is proportional to the square root of the concentration of molecular chlorine: \([\mathrm{Cl}_2] = k[\mathrm{Cl}]^2\).

Norrish and Rideal^5) suppose that the interaction of hydrogen with sulfur in the gaseous state occurs between hydrogen molecules and sulfur atoms formed upon the dissociation of more complex molecules in sulfur vapor.

Bromine atoms apparently take part in the very complex mechanism of the combination of hydrogen with bromine^6). It may be supposed that the process breaks down into the following stages:

\[ \mathrm{Br}_2 \rightleftharpoons 2\mathrm{Br} \]

\[ \mathrm{Br} + \mathrm{H}_2 = \mathrm{HBr} + \mathrm{H} \]

\[ \mathrm{H} + \mathrm{Br}_2 = \mathrm{HBr} + \mathrm{Br} \]

\[ \mathrm{H} + \mathrm{HBr} = \mathrm{H}_2 + \mathrm{Br} \]

This mechanism leads to the equation:

\[ \frac{d[2\mathrm{HBr}]}{dt} = \frac{k[\mathrm{H}_2]\sqrt{[\mathrm{Br}_2]}} {m+\dfrac{[2\mathrm{HBr}]}{[\mathrm{Br}_2]}} , \]

^1) Taylor and Marshall, J. Physic. Chem., 29 (1925) 1140.
^2) Hirst and Rideal. Nature, 115 (1925) 899.
^3) On the mechanism of photochemical reactions see the article by E. V. Shpolsky, p. 433.
^4) Christiansen, ZS. f. physik. Chem., 103 (1922) 99; Bodenstein und Pleut, ibid., 110 (1924) 399.
^5) Norrish and Rideal, J. Chem. Soc., 123 (1923) 696, 1689, 3202.
^6) Bodenstein und Lind, ZS. f. physik. Chem., 57 (1906) 168.

where \(m\) is a constant. This equation was found empirically by Bodenstein and Lind before the theory of the process had been proposed.

Usually such reactions, which depend on a quite special mechanism, are too complex for it to be possible to resolve them into all the intermediate stages and to find the heat of activation for each of them1.

Trans.

1. The question of the kinetics and mechanism of homogeneous reactions was the subject of discussion at the First Conference on Physicochemical Questions, held in 1927 in Leningrad. See the proceedings of the conference in Reports on Scientific and Technical Work in the Republic, issue XXII, 1927, especially the report by Ya. K. Syrkin and the discussion. See also V. Kondrat’ev, N. Semenov, Yu. Khariton, Electron Chemistry, 1927. ↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩↩

2. Ibid. ↩↩↩↩↩↩↩

3. Weigert und Kellermann, ZS. f. physik. Chem., 10 (1923) 1. ↩↩↩↩

4. Cario und Franck, ZS. f. Physik, 21 (1922) 161. ↩