# Units for dissociation constant and relationship to Gibbs Free Energy

How does one "convert" between an equilibrium constant calculated from the Gibbs free energy for a dissociation reaction and experimentally determined dissociation constants?

$$\Delta G^\circ=-RT\log(K_{eq})$$

I think I understand the derivation of this equation and why the equilibrium constant should be unitless if it's defined in terms of activities.
But I have a binding reaction that has an estimated free energy change of $-32~\mathrm{kcal/mol}$, which yields a dissociation constant on the order of $10^{-24}$ at $298~\mathrm{K}$.
Is it correct to just multiply the equilibrium constant by the standard concentration (1 molar) to get a more typical dissociation constant with units? A yoctomolar dissociation constant seems kind of strange to me, but I'm not sure where I've made a mistake.

• Is it $\ce{AB<=>A + B}$, with $\Delta G^\circ_{\mathrm{diss}}(\ce{AB})=-32~\mathrm{kcal/mol}$? Multiplying with the standard concentration just adds a unit to the same value. Also your definition of $K$ is slightly incorrect: goldbook.iupac.org/S05915.html Jul 3, 2014 at 3:04

If the free energy change is negative, the equillbrium constant is $>1$
Should be $10^{\frac{32\frac{kcal}{mol}}{2.303\times0.00199\frac{kcal}{Kmol}\times{298K}}} = 10^{23}$