Reverse reaction rate from equilibrium thermodynamics ($k_r=k_f/[K(c^{\circ }{)}^{\Delta \nu }]$)

For an elementary reversible reaction with concentration-based rates obeying the law of mass action, writewhere stoichiometric coefficients ${\nu }_i$ are positive for products. At detailed balance, $r_f=r_r$, soThis $K_c$ carries a power of concentration when $\Delta \nu ={\sum }_i{\nu }_i\ne 0$.

For an ideal solution with activities $a_i=c_i/c^{\circ }$, the dimensionless thermodynamic equilibrium constant is $K={\prod }_i(c_{i,\mathrm{eq}}/c^{\circ }{)}^{{\nu }_i}$. ConsequentlyKeeping the standard concentration factor is what makes the units of both rate coefficients consistent. For $A+B\rightleftharpoons C$, $\Delta \nu =-1$ and $k_r=k_f{c}^{\circ }/K$: a second-order forward coefficient becomes a first-order reverse coefficient.

Thermodynamics fixes this ratio only under the stated elementary, reversible rate-law model. It does not determine either coefficient separately or replace a multistep reaction mechanism by one elementary step.