680. Methods for computing successive stability constants from experimental formation curves

Abstract

Attention is drawn to the approximations implicit in existing methods for computing, from experimental data, the successive stability constants governing the formation of complexes in step-equilibria. A new " correction term " method is described. This makes use of the symmetry properties of the formation curve for the particular case N = 2.best" set of stability constants from inconsistent experimental data is shown to be soluble by a least-squares treatment after an algebraic transformation. This procedure is applicable to systems of higher complexity. The effects of improved methods of computation are illustrated by examples taken from the literature. The problem of computing the Note onSymbolism.-Following Bjerrum most authors have used k n to represent the stability constant of a complex MLn relative to MLn -1. Schwarzenbach uses KML. Now K is customarily used for equilibrium constants, and k for velocity constants, and to avoid confusion we shall use Kn for the above stability constant. The overall constant [ML,]/[M] [L]" (see p. 3399) has been variously designated EL&&, (Schwarzenbach), K , (Bjenum), and fin (Fronaeus and other Scandinavian authors). We prefer the last, so that the expression fin = K1K2K3 . . . K, in our terminology corresponds to Kn = klk,k, . . . kn in Bjerrum's.THE formation of a complex species ML, from a central atom or ion M, and molecules or ions of a Zigad L, is assumed to be governed by a series of thermodynamic equilibrium constants defined by where K , is the classical (concentration) equilibrium constant, F , = fnn;,-, .fL/'f-, and charges are omitted for the sake of generality. If L is uncharged, ML, and MLncarry the same ionic charge, so that, provided measurements are made in solutions of constant, and not too high, ionic strength, F, may be set equal to unity, and the convenient approximation Kn Bjerrum (KgZ. Danske Videnskab. SeZsk., 1946, 22, Nr. 18) used a single average value of Fn in his studies of complexes formed by cupric and chloride ions. The same author (" Metal Ammine Formation in Aqueous Solution," P. Haase, Copenhagen, 1941) introduced the concept of the degree of formation, or ligand number, E, which he defined as the average number of ligand molecules or ions per molecule of M, and showed that for all systems in which only mononuclear complexes occur, values of Z, and of [L], the concentration of free ligand, are related by the equation where Pn = K1K2 . . . K,, and Po = 1, by definition. Experimental methods for the determination of stability constants, developed by Leden, Bjerrum, and Fronaeus, have recently been discussed by Sullivan and Hindman KnT = (MLn)/(MLn-1)(L) = KnIFn KnT is valid.

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“…The weight is calculated by 16 was applied for determination of the initial estimates of the formation constants for the complex at the studied conditions.…”

“…The pKa 2 value of the studied buffer was determined from the overall protonation constant calculated by the linearization method of Irving and Rossotti. 16 Initial estimates of pKa 2 value was refined with the ESAB2M computer program 17 by minimizing the error squares sum.…”