6001
J. Phys. Chem. 1992,96, 6001-6004
Numerical Solutions for Liquid-Junction Potentials Oscar J. Riveros Departamento de Fhico- Quimica, Pontificia Universidad Catblica de Chile, Casilla 104, Santiago 22, Chile (Received: September 5, 1991; In Final Form: March 12, 1992)
Numerical solutions of the Nernst-Planck and Poisson system of equations for a liquid junction under conditions of zero total current have been obtained to estimate junction potentials. These solutions assumed fixed values of ion concentration at the planar boundaries of an interfacial region of thickness L. The standard Planck and Goldman formulas usually employed to calculate liquid and membrane potentials are valid in the limits KL m or KL 0, respectively. However, we have shown in a previous work on a 1:1 electrolyte system that, for intermediate values of KL,they are no longer valid. We present here an extension of those calculations for the case of a three-component electrolyte solution. The numerical method used to solve these equations has been improved to yield a faster and more precise solution. The results indicate that the Planck approximation is valid only for values of K ~>L20, where ~ d - ’is the Debye length in the more dilute solution. The Goldman approximation is valid for K ~ 1. Hence, K in Figures 1 and 2 is actually K ~the , inverse Debye length in the more concentrated solution. We found that Goldman's approximation is valid for values of K ~ L0.1. If these data were plotted as a function of 4 = p1I2b the inverse Debye length in the more dilute solution, we conclude that Planck's electroneutralityapproximation is valid for K ~>L20. Moreover, we see that for 6 1 < 62 ( D 2
