Diffusional titration errors in coulometry Part I. Analytical solutions for non-stationary diffusion through non-interacting membranes

Abstract

Analytical solutions are given for non-steady state diffusion in a membrane and a semi-infinite connecting chamber. The one-dimensional macroscopic diffusion inside the membrane is assumed to be governed by Fick's law using an empirical proportionality constant. The solutions apply to membranes without dead-end pores. The concentration distributions in the membrane and connecting chamber and the total sample amount inside these are calculated for linearly and exponentially decreasing types of titration. Analytical solutions under the simplified assumption of linear concentration distribution inside the membrane are also given.