# What is the difference between the chemical potential μ and the molar Gibbs free energy Gm?

I'm not too sure if I understand this correctly:
Is the $G_\mathrm{m}$, the Gibbs free energy of the entire system, divided by the amount of substance making up the system, while $\mu$ is the Gibbs free energy of a component of the system?

If so, what does ${\partial G_\mathrm{m}}/{\partial n}=\mu$ signify? As in, what's the difference between this and $\mathrm{d}G/\mathrm{d}n=\mu$?

• @orthocresol Any particular reason you removed the subscripted unicode m? May 27 '16 at 9:25
• @Martin i.imgur.com/0GueIzJ.png May 27 '16 at 11:20
• @orthocresol O.ô Guess you have some missing fonts then. Can you read any of the wikipedia page on unicode sub/superscript? (Also you just triggered a rollback war auto flag, lol.) May 27 '16 at 11:32
• @Martin oops, sorry! Well, about two-thirds of the symbols are fine, the others don't appear. The subscripted numbers work (so chemical formulae in titles tend to work) May 27 '16 at 14:23
• You are thinking in the right direction, but it has no mathematical sense. Now there is a misunderstanding of derivatives :-) We can fix $T$ and $p$ in a system, but $\partial G / \partial T$ (or $p$) won't be null, because they represent how $G$ would change if in infinitesimal change in $T$ (or $p$) is performed. May 27 '16 at 15:54

The chemical potential of a species is the partial derivative of the Gibbs free energy of the mixture of components with respect to the number of moles of that particular species, holding the temperature, pressure, and number of moles of all the other species constant. For a single component system, this is reduces to the total free energy divided by the number of moles.

• I request that the answer be made more clear by giving an example of the difference between molar Gibbs Free Energy and Chemical Potential. Jun 26 '16 at 12:13
• I don't know how I can say it any more clearly. The Chemical Potential is defined as the partial molar free energy. Jun 26 '16 at 12:44