Potentiometric Determination of Overlapping Dissociation Constants

Abstract

The dissociation constants of polyprotic acids can be determined potentiometrically by defining a variable, P, as the average number of protons dissociated. The proton balance equation for the titration of these acids with base led to a general expression which could be solved graphically or through the use of linear regression or nonlinear regression analysis. Experimental data for a number of acids and for a series of simulated titration curves were analyzed using the three methods. The graphical solution was found to be applicable in all instances. As the ratio of K1 to K2 for diprotic acids increased from 50 to 1000, the value of K2 estimated by the use of linear regression became progressively worse and finally could not be determined at all. In all instances, the value of K1 was determined to within a relative error of 0.5%. In all instances in which nonlinear regression analysis was used, the values for K1 were determined to within 0.3% and those for K2 were determined to within 0.02%. This technique requires an initial estimate of each constant. These initial estimates are then refined in an iterative procedure until satisfactory convergence is obtained. The digital computer program used in this work is unique in that initial estimates are obtained within the computer program itself. The program also determines the total number of dissociable protons. This latter property can be extremely useful for compounds with an unknown number of acidic sites.