Statistical Independence of the System

It appears relevant in view of the present knowledge of inter-molecular forces to deal with two causes of deviation from the statistical independence of the system of elementary reaction. It is generally accepted that a species occupies a site on a catalyst s surface exclusively, hence competes for the sites to cause a sort of deviation from the statistical independence in question, which will be referred to as that due to the impenetrability in what follows. Consider now two species each accommodated in different sites the impenetrability is then irrelevant, whereas they may exert force upon each other to cause deviation of another sort, which will be termed that due to the interaction. 

The current treatments of elementary reactions in terms of the mass action law are now reviewed in this section as based on the generalized theory of elementary reactions developed in the previous sections. It will be seen that the current treatment is applicable under the condition where the impenetrability alone is significant, as exemplified in this section, but is hardly reasonable in the case of the interaction operative. 

The rate law is deduced in accordance with the current procedure on the basis of the above premise and model as follows. We have from Eqs. (11.11) and (11.17) according to (iii) above 

The rate V of the reaction is now expressed by the current treatment, in terms of the mass action law, as proportional to 0(H2)0(CO2) for the Langmuir-Hinshelwood mechanism and similarly to (7 0(CO2) or C ° 0(H2) for the Rideal-Eley mechanism, depending on the premised adsorption state of the initial system. The rate law is thus obtained according to Eqs. (11.24) as 

Now let X be the number of ct s, which compose a congregated together. Since the probability of each a being unoccupied is independent of the occupied or unoccupied state of other t s according to the premised absence of interaction, we have 

---

It must be admitted that the mass action law has been successfully applied to homogeneous elementary reactions, while the statistical independence of the system underlying it is premised in the absolute reaction rate theory of Eyring et al. (1) and in the transition state method of Evans and Polanyi 2). The statistical independence is not however insured in the treatment, especially of heterogeneous elementary reactions constituting heterogeneous catalyses as exemplified below this constitutes the second limitation of the kinetics. 

Equation (11.21) exemplifies that the premised statistical independence of the system of elementary reaction leads necessarily to the mass action law. 

---