Numerical Simulation of pH Measurement in Dilute Solutions of the System H2O–KCl–HCl

Abstract

Potentiometric pH measurements on cells with liquid junctions are known to be biased with respect to the notional pH in dilute acid solutions, but detailed evaluation of the problem is obstructed by experimental difficulties. In this work, pH measurements are simulated numerically on a kind of the Harned cell with a free-diffusion junction between the saturated solution of KCl and dilute solutions of HCl + KCl with ionic strength and acid concentration varying from 0.0001 to 0.1 in terms of molarity. The pH is standardized against the solution 0.0001 M HCl + 0.05 M KCl, and the simulations are based on known solution properties (transport numbers, activity coefficients and diffusion coefficients). The bias is found to range from −0.012 to 0.056 in the composition range studied. The cell response is nearly linear in the notional pH in solutions with varying acid concentration, but no such relation is found in solutions with varying ionic strength at fixed acid concentration. It is shown that the Henderson equation underestimates the residual liquid-junction effect in very dilute solutions, largely due to failure to account for activity coefficients varying along the junction.