Derivation of an Equation for the Diffusion Potential

Abstract

AN equation for the potential across a membrane arising from the steady-state diffusion of univalent ions was derived by D. Goldman¹ under the assumptions of a constant electric field and constant ionic mobilities across the membrane. His equation may be written as²: where V is the electric potential on the right side of the membrane relative to the left side, $C_{i^{\text{+}}}$ is the concentration of the ith positive ion, $C_{i^{\text{−}}}$ is the concentration of the ith negative ion, P is the permeability of the membrane to an ion, r and l denote the right and left side of the membrane respectively, and R, T, and F have their usual meanings. It is the purpose of this communication to derive, without the use of the above two assumptions, an equation similar to equation (1) in which the permeabilities are replaced by unidirectional rate constants.