Entropy and the chelate effect

Entropy may be harnessed as a driving force in the context of helicates as well as in mononuclear complexes, as evidenced by the 24-to-5 and 3-to-5 conversions shown in Scheme 1.21. Two distinct hierarchical layers of control over subcomponent substitution may thus be employed in tandem, based upon p JC, differences and the chelate effect. 

It should be pointed out, however, that the thermodynamic explanation of the chelate effect, in particular the contribution of entropy as presented above, is actually not as straightforward as it might appear. The entropy change for a reaction depends on the standard state chosen for reference and for very concentrated solutions one might chose unit mole fraction instead of one molal and the chelate effect would disappear. However, this is not realistic and for solutions one molal (or less) there is a real chelate effect. In very dilute solutions (0.1 M or less) where complexation of metal ions is generally most important, the chelate effect is of major importance and is properly understood as entropically driven. 

On the basis of the values of AS° derived in this way it appears that the chelate effect is usually due to more favourable entropy changes associated with ring formation. However, the objection can be made that and /3l-l as just defined have different dimensions and so are not directly comparable. It has been suggested that to surmount this objection concentrations should be expressed in the dimensionless unit mole fraction instead of the more usual mol dm. Since the concentration of pure water at 25°C is approximately 55.5 moldm , the value of concentration expressed in mole fractions = cone in moldm /55.5 Thus, while is thereby increased by the factor (55.5), /3l-l is increased by the factor (55.5) so that the derived values of AG° and AS° will be quite different. The effect of this change in units is shown in Table 19.1 for the Cd complexes of L = methylamine and L-L = ethylenediamine. It appears that the entropy advantage of the chelate, and with it the chelate effect itself, virtually disappears when mole fractions replace moldm . ... 

The chelating effect of the surface appears to be the driving force for the formation of the surface cis-octahedral complex. Equation 17, which is the sum of eqs 15 and 16, is accompanied by an entropy increase with the release of water molecules and the disappearance of charged species leading to a subsequent disordering of nearby solvent molecules. This aspect is well documented in solution coordination chemistry [68, 69]. 

As a very simple case, consider the reactions, and the pertinent thermodynamic data for them, given in Table 1-1. In this case the enthalpy difference is well within experimental error the chelate effect can thus be traced entirely to the entropy difference. 

The term chelate effect was first used in 1952 by Schwarzenbach (15). To demonstrate the nature of the chelate effect he used as models a bidentate ligand and two unidentate ligands which form coordinate bonds of equivalent strength with a metal ion. He predicted increased stability for the metal chelate on the basis of statistical considerations. The model required a zero heat of reaction in the replacement of two unidentate ligands by one bidentate chelating ligand, so that the stabilizing chelate effect must be an entropy effect. 

The above explanation of the chelate effect depends on the fact that a unit molal standard state is employed for all solute species. The heat and entropy of the replacement reaction correspond to those that would result from converting the reactants to products in their standard states ... 

The importance of translational entropies was first pointed out by Adamson (7) who recalculated the formation constants of a number of mono- and poly-amine complexes for a unit mole fraction standard state. This calculation showed that the chelates are no more stable than analogous complexes with fewer chelate rings. Thus, for the pure substances (having the same properties as the dilute solute species), there would be no stabilizing entropy of translation for each mole of product formed, and reactions in which the number of moles of product is greater than the number of moles of reactant would not be favored. Thus, it is seen that the chelate effect due to translational entropy apphes only to reactions in solution, and that for pure substances (i.e., for the solid state) chelates are not favored over simple complexes. 

Many other examples of steric effects are compiled in recent equilibrium data (17) j and many of the observed effects are apparently due to enthalpies and entropies of formation of the free ligand in solution. For this reason, more reliable data on heats and entropies of chelate formation and on heats and entropies of formation of metal ions and ligands in solution should be accumulated for developing further understanding of the chelate effect. 

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