Boltzmann ion densities in a symmetric electrolyte

For point ions of charge $\pm e$ in potential $\psi$, equilibrium electrochemical potentials give $n_{\pm }=n_0\exp [\mp e\psi /(k_{B}T)]$, with $n_0$ the reservoir density of each species. The charge density is $-2e{n}_0\sinh [e\psi /(k_{B}T)]$. A negative wall enriches positive counterions and depletes negative co-ions.