  In this work we revisit the concept of chemical potential $\mu$ in both
classical and quantum gases from a perspective of Equilibrium Statistical
Mechanics (ESM). Two new results regarding the equation of state
$\mu=\mu(n,T)$, where $n$ is the particle density and $T$ the absolute
temperature, are given for the classical interacting gas and for the
weakly-interacting quantum Bose gas. In order to make this review
self-contained and adequate for a general reader we provide all the basic
elements in an advanced-undergraduate or graduate statistical mechanics course
required to follow all the calculations. We start by presenting a calculation
of $\mu(n,T)$ for the classical ideal gas in the canonical ensemble. After
this, we consider the interactions between particles and compute the effects of
them on $\mu(n,T)$ for the van der Waals gas. For quantum gases we present an
alternative approach to calculate the Bose-Einstein (BE) and Fermi-Dirac (FD)
statistics. We show that this scheme can be straightforwardly generalized to
determine what we have called Intermediate Quantum Statistics (IQS) which deal
with ideal quantum systems where a single-particle energy can be occupied by at
most $j$ particles with $0 \leqslant j \leqslant N$ with $N$ the total number
of particles. In the final part we address general considerations that underlie
the theory of weakly interacting quantum gases. In the case of the weakly
interacting Bose gas, we focus our attention to the equation of state
$\mu=\mu(n,T)$ in the Hartree-Fock mean-field approximation (HF) and the
implications of such results in the elucidation of the order of the phase
transitions involved in the BEC phase for non-ideal Bose gases.
