The use of the temperature variation of the dissociation constant for evaluating changes in AC', is reviewed with a view to establishing the degree of reliability of such values.
AC", 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 'I most appropriate " form of pK(T), viz a five-constants equation is used with the accurate data of Ives for the dissociation of cyan-acetic acid, according to the method of Clarke and Glew, the results still retain large uncertainties on AC",.
Model exact pK data can be calculated from known assumed AG", AH", AC",, first and second temperature derivatives of ACO, 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 (0"~50°C or 60°C) even very small errors (ca 04lOO25 pK units) can lead to very large uncertainties on AC", (especially at the two extremes of the temperature range) exceeding in some cases 20 cal. The identification of the true AC",(T) becomes impossible.
It is concluded that the dissociation constant method is not capable as yet of furnishing reliable AC', values; the extension of the temperature range to the neighborhood of 100°C and an increase in the degrees of freedom (es by measurements at 5" intervals) could combine to furnish fairly reliable AC', values. ';'~I -lO[lO] -10.7 1.3 -11.4 * AC, values are in cal/deg/mole. ' The same data of Harned and coworkers[l+] are analysed in each case. c This work. d The data were analysed using a procedure somewhat similar to that of Ives and Marsden[24].
5 A cubic polynomial was used, with a standard deviation of &0.0004 pK units. 'A quartic polynomial had to be employed and even then the fitting of the pK data was not very satisfactory. A difference of 0*0025 pK unit between the calculated and the experimental value was retained at one temperature.
s The two sets of AC", values under equations ( 2) and (4) refer each to an independent set of pK values of references 23 and 27 respectively. The difference between the two sets of pK values is within f0.002 pK units.
' The pK data of Bates et al.[8,91 and of Datta et aZ.[lO, 1 II were analysed according to equation ( 4). The difference between the two sets of data for each acid is within &O-O03 pK units except at one temperature where, for each acid, the difference is about 10-0055 pK units.