# Thermodynamic evaluation of chelate and cooperativity effects

- Authors
- Journal
- Inorganica Chimica Acta 0020-1693
- Publisher
- Elsevier
- Publication Date
- Volume
- 79
- Identifiers
- DOI: 10.1016/s0020-1693(00)95124-7
- Disciplines

## Abstract

Abstract The chelate effect occurs in the binding of a ligand, containing two or more donor atoms, with a metal ion [1] or a macromolecule [2]. The chelate effect causes an increase in the stability of the complexes with respect to those formed with the same number of donor atoms belonging to separate liganding molecules. The evaluation of the chelate effect has been done up to now calculating the constant K chel = K M L /β MA 2 , where M = metal or macromolecule, A = monodentate ligand, L = bidentate chelating ligand, K M L = formation constant of the chelate M L, β MA 2 = cumulative formation constant of the complex MA 2. L (homotropic chelate) has two donor atoms equal to that of A. By an analysis of the binding polynomial [3] on the Bjerrum plane (n̄, −log L), it can shown how the correct equilibrium constant to evaluate the chelate effect is for bidentate chelating ligands and for n-dentate ligands. These adimensional constants are obtained as the ratio of two operational equilibrium constants, namely K M L and each of which is expressed in homogeneous reciprocal concentration units (conc. −1). If the donor atoms of the chelating ligand are different (heterotropic chelate), then the thermodynamic stability can be evaluated by , where MAB is a mixed ligand complex, and similar constants hold for higher complexes. Again the ratio is between two operational constants , each expressed in conc −1. With the same arguments it can be shown that the cooperativity effect, i.e the mutual repulsion or attraction between ligands, can be evaluated by and by for homotropic and heterotropic cooperativity, respectively. The chelate effect comprehends in itself the cooperativity effect and this can be taken into account in the constants K η = K ϵ· K γ and K η′ = K ϵ′· K γ′. The constants K ϵ, K γ K ϵ′, and K γ′ must be corrected for statistical effects. All these constants are expressed in the same units as the activity coefficients. From these constants, the corresponding changes in chemical potentials, Δμ° = − RTln K can be calculated. These values expressed in kJ mol −1 allow the evaluation on the same scale of chelate and cooperativity effects, together with changes in the activity coefficients. The correctness of the choice of scale is shown by examining the chelate effect values obtained for copper(II) complexes of dicarboxylic acids at 25 °C [4]. Cu(II)/succinate 1 1 chelate would have been unstable according to K chel. = 0.32 mol dm −3, whereas it comes out to be stable according to K η = 11.4 mol −1 dm 3 (Δμ° η = −6.03 kJ mol −1, in agreement with the experimental evidence [5]. The net chelate effect, Δμ° η, is linearly related both to the number of donor atoms and to the number of chelate rings. The enthalpy and entropy contributions to the chelate effect can also be calculated and critically analysed.

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