Kinetic Theory of Reaction Rates.

(A. March. Physik. Zeitschr. XVIII, 1917, p. 53).

In a paper published in Phys. Zeitschr. in 1917, March, using the methods of statistics, attempts to give a kinetic picture for the rates of gas reactions. March’s theory is of quite general character, although he confines his attention to the special case of the dissociation of a gas—namely, when a gas suddenly passes from a state under very high pressure into a state under very low pressure. The elements that make up the gas molecule are located in phase spaces (spaces of generalized coordinates) and are connected with definite phase points; according to March they will always be associated if the values of their generalized coordinates do not exceed certain limiting values. These values determine the surface separating two phase spaces—the “space of association” and the “space of dissociation.” The process of decomposition of the molecule consists in the fact that some phase point, in which one or another element of the molecule is bound, passes from the “space of association” into the “space of dissociation”; the reverse process corresponds to the reverse transition of the phase point. Assuming further that the force function of the intramolecular forces can be expressed by the formula:

\[ V=\frac{1}{2}\left(\alpha_1\rho_1^{2}+\alpha_2\rho_2^{2}+\alpha_3\rho_3^{2}+\ldots+\alpha_\mu\rho_\mu^{2}\right) \]

where \(\rho_1,\rho_2\ldots,\rho_\mu\) are generalized momenta, and that the gas dissociation follows the scheme:

\[ A \rightleftarrows A_1 + A_2 \]

March gives the following expressions, respectively, for the coefficients of the rates of the forward and reverse reactions:

\[ \text{1)}\qquad \frac{1}{n}\cdot\frac{dn}{dt}=K= \frac{ e^{-\frac{\varepsilon}{\alpha T}}\cdot \frac{\overline{dE}}{dt} }{ 2\alpha_1\rho_1 \displaystyle\int_{-\rho_1}^{+\rho_1} e^{-\frac{\alpha_1\rho_1^{2}}{2\alpha T}}\cdot d\rho_1 } \]

2)

\[ \frac{1}{k'} \cdot \frac{dn'}{dt} = K' = \frac{dE}{dt} \]

The quantity \(\frac{dE}{dt}\) expresses the average rate of change of energy with time, per molecule; \(\varepsilon = \frac{1}{2}\alpha_1\rho_1^2\); \(\rho_1\) is the limiting value of the moment \(\rho\); \(T\) is the absolute temperature; \(\alpha\) is Boltzmann’s constant. In the concluding part of the work, March indicates that his theory, while not coming into contradiction with the formulae obtained thermodynamically by other scholars, permits convenient application to photochemical processes and to the new catalysis.

A. Predvoditelev.