What are the units that measure free energy?

Is it $\pu{kJ/mol}$? I have done problems and I always end up with these units, but is this correct?





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> What are the units that measure free energy?
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There are several different *free* energies, but I'll tackle Gibbs and Helmholtz only here:


1. **[Gibbs free energy](http://goldbook.iupac.org/html/G/G02629.html)**: $G=H-TS$, for $H=U+PV$. Hence, by dimensional analysis, Gibbs free energy has the SI units of Joule.
2. **[Helmholtz free energy](http://goldbook.iupac.org/html/H/H02772.html)**: $A=U-TS$. 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.


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In thermodynamics the change in free energy $\Delta G$ is given by,


$$\Delta G = \Delta H - T \Delta S$$


Hence by dimensional analysis, its units must be that of $\Delta$H, which is $\pu{kJ/mol}$.


It is logical because energy is usually measured in multiples of joules (SI Unit).


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