Reversible reactions and the competitive effect

In his initial treatment of reaction in a hard sphere solvent, Kapral only considered the case of irreversible reaction. Pagistas and Kapral extended 

Most of the techniques necessary have already been introduced in the previous analysis. However, it is necessary to follow the concentration and therefore the singlet and doublet densities of A, AB and also C and CB. These are ff, /f and The collision operator of eqn. (306) is no longer adequate because it describes the collision of A and B to form C and B. An equivalent term for the collision of C and B to give A and B must also be introduced into eqn. (194) for the singlet density of A. These two terms then describe the rate of loss of A by reaction of A with B and the back reaction forming A and B from C and B 

A similar equation may be written to describe the evolution of the singlet density of the reactant C. Cluster functions are introduced and, after using a super-position approximation again, the analysis follows that of Kapral [285] very closely with the complication that, instead of only singlet XA and doublet xAB correlation functions, it is necessary to consider the equation for C in tandem. This requires the use of the matrix notation for compactness. 

Now let us revert to the chemical equation (306) above. The rate for the forward and reverse processes leads to the establishment of an equilibrium where the concentration of A, B and C are n Q, nBq and. Prior to that time, the concentrations are nA, nB and nc. The usual rate equation is 

Defining the excess concentration of A and C over their equilibrium concentrations as (8nA) — nA — nAn — — 8nc) — nc — n q, this becomes 

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