Chemical Potential of Idea gas?

Question

Let's say we have a mixture of different ideal gases. I found that the chemical potential of a single component of the mixture is $$\mu_{i}=g_{i}^{0}+Ln(\frac{f_{i}}{P_{ref}})$$

where $f_{i}$ is the fugacity of the component. I also found somewhere else that the chemical potential of pure substances is the molar gibbs property. Would it be safe to then say..

$$\mu_{i}(T,P)=g_{i}(T,P)$$

Answer 1

Yes, by definition chemical potential is related to Gibbs potential in the following way:

$\mu_i = \left(\frac{\partial G}{\partial n_i}\right)_{p,T,n_{j\neq i}} = g_i$

Those two notation are synonyms. You will find very detailed and precise explanation of this in: Atkins, Physical Chemistry.