Metal equilibrium constant value of complex formation is relatively simple and the degree of stability of hydrated metal ions in solution and ligand binding molecules or ions of a measure. The strength of the chemical bond between the metal and the ligand acts to determine the stability of the complex, but other factors also have an effect.
The equilibrium constant is related to the standard free energy change ΔG å应 of the reaction:
△G Θ =-RTlnK
The change of standard free energy is determined by the changes of standard 焓 and standard entropy △H Θ and △S Θ
△G Θ =△H Θ -T△S Θ
Standard enthalpy is a measure of the degree of heat of the reactants and products at the time of formation of the complex, and is determined by the type of chemical bond formed between the metal ion and the ligand. In the case of single-charged monodentate ligand, each stage of △ H Θ value typically between + 20kJ / mol and -20kJ / mol, and when a strong covalent bond, △ H [Theta] values it possible high -80kJ ∕mol.
The standard enthalpy of complex formation is different from the enthalpy change, which is closely related to the structure of the complex environment. The standard entropy change ΔS Θ in the aqueous electrolyte solution is usually positive. This unexpected fact is due to the structural damage of the water around the complex. The positive entropy change caused by such structural failure is much larger than the negative entropy caused by the vibration and rotational entropy of the single metal and the translational entropy of the ligand. If the ligand is negatively charged, the neutralization of the charge during formation of the complex reduces the number of ions in the system and affects the entropy change. This causes a large positive entropy change, resulting in a more stable complex.
The association of metal ions with uncharged monodentate ligands does not reduce the number of ions present in the system, and there is no relocation of water molecules. In this case, only a small positive entropy change or even a negative entropy change occurs when the complex is formed. The value of ΔS 通常 is usually the single most important factor in controlling the stability of the complex. The higher the temperature, the more normal the standard entropy change in the solution will be, and the standard entropy of anion generation will be more negative. Therefore, in general, the higher the temperature, the more positive the entropy generated by the complex, and the more stable the complex.
The standard enthalpy change ΔH T å应 of the reaction when the temperature is not 25 ° C can be written as
(1)
Similarly, the standard entropy change can be written as
(2)
In the formula, ΔC p Θ is the standard heat capacity when the pressure is constant. thus
(3)
Introducing a Gibbs free energy function, which can be written as
(4)
Substituting this formula into equation (4)
(5)
and
(6)
As long as the free energy function of the reaction is known, that is, the standard change ΔC p Θ of the enthalpy under constant pressure is known, the equilibrium constant K T of the reaction at any temperature can be obtained from the formula (6).
Although the free energy function of many reactions can be found, the equilibrium reaction in most aqueous solutions is not known. Therefore, some assumptions need to be made in order to estimate the lgK T value of such a reaction in a system involved in hydrometallurgy.
If there is not enough heat capacity data, it is generally assumed that ΔC p Θ is a constant, and then equation (4) becomes
(7)
Points are sorted out
(8)
Substitute (6)
(9)
This also corresponds to a linear change in the ΔH å应 of the reaction with temperature.
The values ​​of ΔC p Θ , ΔH p Θ and ΔS p Θ for the complex reaction are now poorly known, and only a few cases know the equilibrium constant value in a small temperature range. Therefore, it can only be assumed that ΔH Θ varies with temperature to calculate ΔC p Θ . However, the values ​​thus obtained are very sensitive to errors with small equilibrium constants.
The equilibrium constant value is also related to the pressure, but the effect of the pressure below the critical pressure on the equilibrium constant in the aqueous solution is relatively small.
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