Chapter 11, Problem 8P

Consider the simple bimolecular reaction

$A+B\underset{k-1}{\overset{k+1}{\rightleftharpoons }}C+D$ where and are the rate constants for the forward and reverse reactions. ΔG is related to the concentration of the reactants and products as well as the equilibrium constant, K, as described by Equation 3.27

$\Delta G=RT\ln \left(\frac{Q}{K}\right)$
Since the law of mass action governs reaction kinetics, the forward and reverse fluxes, J, can be defined as:

$J^{+}=K+1[A][B](forwardflux)J^{-}=K-1[C][D](reverseflux)$

ΔG can be defined in terms of the ratio of forward and reverse fluxes:

$\Delta G=-RT\ln \left(\frac{J^{+}}{J^{-}}\right)$
Derive this equation.