 Nernst equilibrium potential

The Nernst equilibrium potential is the inside-minus-outside membrane potential at which one ion species has equal electrochemical potential on both sides of a cell membrane. At uniform temperature $T$, using the same reference chemical potential on both sides, $z\ne 0$ is the signed ion charge number, $R$ the molar gas constant, $F$ the Faraday constant, and $a$ the dimensionless thermodynamic activity of that ion. For an ideal dilute chemical solution, the activity ratio becomes the concentration ratio. See Purves et al.: the forces that create membrane potentials and the Nernst equation.

The short derivation is to set the outside-to-inside electrochemical potential change from membrane transport to zero: $RT\ln (a_{\mathrm{inside}}/a_{\mathrm{outside}})+zFV=0$, and solve for $V$. An open pathway carrying only this species by passive transport then has this reversal potential. A balance of several nonzero ion electric currents does not establish this equilibrium condition for each species.