  The Mean Spherical Approximation (MSA) is a commonly-used thermodynamic
theory for computing the energetics of ions in the primitive model (i.e.,
charged hard-sphere ions in a background dielectric). For the excess chemical
potential, however, the early MSA formulations (which were widely adopted) only
included the terms needed to compute the mean excess chemical potential (or the
mean activity coefficient). Other terms for the chemical potential $\mu_i$ of
individual species $i$ were not included because they sum to $0$ in the mean
chemical potential. Here, we derive these terms to give a complete MSA
formulation of the chemical potential. The result is a simple additive term for
$\mu_i$ that we show is a qualitative improvement over the previous MSA
version. In addition, our derivation shows that the MSA's assumption of global
charge neutrality is not strictly necessary, so that the MSA is also valid for
systems close to neutrality.
