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I know that the chemical potential is the molar Gibbs free energy and that it is an intensive variable and that the gibbs free energy is extensive. However, they have identical units: $\mathrm{J~mol^{-1}}$. I don't understand why $G$ is extensive if it has $\mathrm{mol^{-1}}$ in its units.

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    $\begingroup$ It's a matter of notation - technically, $G$ has units of $\mathrm{J}$. But we commonly speak of $\Delta G_r$ of a chemical reaction which has units of $\mathrm{J~mol^{-1}}$. The reason is because $\Delta G_r$ is by definition a difference of molar Gibbs energies: $\Delta G_r = \sum_J \nu_J G_{m,J}$ (or chemical potentials if you prefer). The stoichiometric coefficients $\nu$ are dimensionless and $G_m$ has units $\mathrm{J~mol^{-1}}$. I find it a bit irritating that this notation (same with $\Delta S$ and $\Delta H$) is used in thermochemistry, but that's just how it is. $\endgroup$ – orthocresol Oct 25 '15 at 16:48

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