Relation between Reaction Rates and Free Energies Rate Close to Equilibrium

From Eqs. (IV.3.4) and (IV.3.7) we see that at equilibrium the ratio of the rates of forward and reverse reactions is a function only of the equilibrium constant divided into the equilibrium-constant expression in concentration units  

When the system is close to equifibrium (that is, R//Rb = 1) then AF/RT is close to zero and we can make a Taylor s series e.xpansion of the function 0(AF/RT) about the origin. We find 

If one measures the net rate of reaction near equilibrium and plots the results against AF/RTj the points should fall on a straight line whose slope is equal to sRb- If one now repeats such measurements with different starting concentrations of the reacting species, one can deduce the dependence of Rb on concentrations and hence the form of the rate laws for the system. Such measurements have been made for the catalytic hydrogenation of benzene by Prigogine et al. with confirmation of the relationships shown. 

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