Units for dissociation constant and relationship to Gibbs Free Energy
free energy change of -32 kcal/mol, which yields something on the order of 10^-24 at 298K. 


Seems the main mistake is a sign error.  Also "log" must mean "natural logarthim" the way the equation in the question is written to be correct.

If the free energy change is negative, the equillbrium constant is $&gt;1$

Should be $10^{\frac{32\frac{kcal}{mol}}{2.303\times0.00199\frac{kcal}{Kmol}\times{298K}}} = 10^{23}$