Principle of microscopic reversibility and equilibrium constants

Above we discussed various types of collisions. A reverse process corresponds to each of these processes. Cross sections and rate constants of forward and reverse elementary processes are mutually related. This relationship is determined by the laws of conservation of energy and total angular moment. 

Process 3 is the most general type of an elementary process for the collision of heavy particles because it is accompanied by the simultaneous redistribution of atoms and energies of internal and translational motions. The principle of microscopic reversibility for this process has the following form  

The rate constant and cross section are related between each other duough the distribution functiony(v, T) by expression (2.18). Using this expression with the Maxwell distribution function d[v, T), we can write expressions for the rate constants of the forward k(jj — l,m) and reverse /,m — iJ) reactions. 

Using expressions (2.38), (2.39), and (2.18), we can easily obtain the expression for the ratio of the rate constants of the forward to reverse reactions 

Relationship (2.40) expresses the principle of detailed balancing for microscopic processes. 

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