The evaluation of Δ C° p for acid-base equilibria from pK measurement

Abstract

The use of the temperature variation of the dissociation constant for evaluating changes in Δ C° p is reviewed with a view to establishing the degree of reliability of such values. Δ C° p values obtained from dissociation constant measurements are compared, where possible, with the calorimetrically determined values. Significant differences are apparent, suggesting serious shortcomings in the indirect methods of evaluation used so far. The related question of the appropriate form of the pK( T) equation is also discussed. When the “most appropriate” form of pK( t), viz a five-constants equation is used with the accurate data of Ives for the dissociation of cyano-acetic acid, according to the method of Clarke and Glew, the results still retain large uncertainties on Δ C° p . Model exact pK data can be calculated from known assumed Δ G°, Δ H°, Δ C° p , first and second temperature derivatives of Δ C° p at a chosen reference temperature. By introducing variations of various magnitudes and signs on these model values, very accurate “experimental-like” pK values can be generated. When these accurate pK values are analysed on the computer, using the method of Clarke and Glew, and the results are compared, it becomes apparent that over the normal experimental range (O°−50°C or 60°C) even very small errors ( ca 0·00025 pK units) can lead to very large uncertainties on Δ C° p (especially at the two extremes of the temperature range) exceeding in some cases 20 cal. The identification of the true Δ C° p ( T) becomes impossible. It is concluded that the dissociation constant method is not capable as yet of furnishing reliable Δ C° p values; the extension of the temperature range to the neighborhood of 100°C and an increase in the degrees of freedom ( eg by measurements at 5° intervals) could combine to furnish fairly reliable Δ C° p values.