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 $\mathrm{d}G/\mathrm{d}n=\mu$?