Stability Constants of Complexes - Thermodynamics

Thermodynamics

The thermodynamics of metal ion complex formation provides much significant information. In particular it is useful in distinguishing between enthalpic and entropic effects. Enthalpic effects depend on bond strengths and entropic effects have to do with changes in the order/disorder of the solution as a whole. The chelate effect, below, is best explained in terms of thermodynamics.

An equilibrium constant is related to the standard Gibbs free energy change for the reaction

ΔG⊖ = -2.303 RT log₁₀ β.

R is the gas constant and T is the absolute temperature. At 25 °C, ΔG⊖ = (−5.708 kJ mol−1) ⋅ log β. Free energy is made up of an enthalpy term and an entropy term.

ΔG⊖ = ΔH⊖ − TΔS⊖

The standard enthalpy change can be determined by calorimetry or by using the van 't Hoff equation, though the calorimetric method is preferable. When both the standard enthalpy change and stability constant have been determined, the standard entropy change is easily calculated from the equation above.

The fact that stepwise formation constants of complexes of the type ML_n decrease in magnitude as n increases may be partly explained in terms of the entropy factor. Take the case of the formation of octahedral complexes.

+L

For the first step m = 6, n = 1 and the ligand can go into one of 6 sites. For the second step m = 5 and the second ligand can go into one of only 5 sites. This means that there is more randomness in the first step than the second one; ΔS⊖ is more positive, so ΔG⊖ is more negative and log K₁ > log K₂ . The ratio of the stepwise stability constants can be calculated on this basis, but experimental ratios are not exactly the same because ΔH⊖ is not necessarily the same for each step. The entropy factor is also important in the chelate effect, below.