LINEAR FREE ENERGY RELATIONSHIPS CONCERNING EQUILIBRIA IN MODERATELY CONCENTRATED MINERAL ACIDS: A SIMPLE METHOD FOR ESTIMATING pK's OF WEAK BASES

Linear relationships exist between the logarithms of equilibrium quotients, [SH+]/[S][H+], of diverse bases as they vary with acid concentration in moderately concentrated mineral acids. For purposes of formulating these linear free energy relationships in standard form, the equilibrium quotient for protonation of a hypothetical aromatic primary amine of pKa zero has been chosen as horizontal coordinate; this is given by (−H0 − log [H+]). Log ([SH+]/[S]) + H0 is plotted against (H0 + log [H+]). The slope, [Formula: see text] of the linear plot is a parameter which characterizes the response of the equilibrium quotient to changing acid concentration. The intercept represents the thermodynamic pKa of the base. This constitutes a general method for estimating the pKa of any base which undergoes protonation in moderately concentrated mineral acid, with reference to the single acidity function, H0. For bases of diverse type, pK's estimated by this method are in good agreement with those estimated by the acidity function method. Use of the new correlation procedure as a check on the validity of several acidity functions and its application to equilibria not involving proton gain or loss are also discussed.