Q:

Why are partial molar Gibbs energy and Gibbs energy per mol equal?

I'm not a chemist, but I need some insight into chemical thermodynamics. 
In the book that I'm reading (Nevers, 2012), equation (4.28) relates the chemical potential of a pure species to it's Gibbs energy per mol:
$\qquad\mu_a^{(1)} = \bigg( \dfrac{\partial G}{\partial n_a} \bigg)_{T,P,n_b...} = g_a^{(1)}$
where the subscript stands for the species $a$, the superscript stands for it's phase, $\mu$ is the chemical potential and $g$ is the Gibbs energy per mol.
I understand the first equal sign. Though, I don't understand the second equal sign. What am I missing?

A:

The key is that the Gibbs free energy is an extensive quantity. This means that for a single-component system it can be written as
$$ G\left(T,P,N\right) = N\cdot g\left(T,P\right) $$
where N is the number of particles and g is the Gibbs free energy per particle. In other words, if you double the number of particles and double the volume (at fixed temperature and pressure), then G will also double. 
From the above expression you can see that the chemical potential is just the Gibb's free energy per particle: 
$$\mu\left(T,P\right) = g\left(T,P\right)$$

