Derivation of thermodynamic functions of ionisation from acidic dissociation constants. The sigma plot method vis-à-vis polynomial regression procedures

Abstract

For ΔG°(T) data at equally spaced T, classical difference tables are invaluable for assessing the quality of the measurements and in setting limits to their exploitation by currently used statistical methods. A return to the principles of the Everett and Wynne-Jones calculation is advocate; first differences are used to proceed directly to a best estimate of an average ΔC^°_P. This allows the original data to be treated by the Σ-plot method, based on a chosen definition of ideal acidic dissociation behaviour, which gives idealised values of the required thermodynamic functions. If experimental accuracy permits, systematically distributed residuals from the Σ-plot will be available to study deviations from the defined ideal behaviour and to secure closer approximations to the themodynamic functions, including dΔG^°_P/dT.

In so far as the interpolations used are rectilinear, the method minimises distortions due to the “smoothing-in” of incoherent errors, and is preferred to methods based on initial curvilinear data-fitting, the hazards of which are demonstrated in detail. Comparisons with, and correction of, some previously published data require the use throughout of cal units (1 cal = 4.184 J).