What are the units that measure free energy?
What are the units that measure free energy?


There are several different free energies, but I'll tackle Gibbs and Helmholtz only here:


Gibbs free energy: $G=H-TS$, for $H=U+PV$. Hence, by dimensional analysis, Gibbs free energy has the SI units of Joule.
Helmholtz free energy: $A=U-TS$. Again, by dimensional analysis, Helmholtz free energy also has the SI units of Joule.


Since both are only "free energies", it makes sense to assign them the SI unit Joule. 

That said, however, almost everywhere they are specified in terms of $\pu{kJ/mol}$ because that makes the comparison across different substances easier. Since $G$ is an extensive function, its value can vary even with the amount of substance. Your calculated $\Delta G_\mathrm f^\circ$ can differ from mine even if we take the same substance, just because we had the amounts different. Hence, to ease comparison and computations, they are "specified" in terms of $\pu{kJ/mol}$, although their correct SI unit is Joule.