General Case Equilibrium Potential of a Solution Containing Two Redox Couples

3 General Case Equilibrium Potential of a Solution Containing Two Redox Couples 

An initial mixture composed of the sole forms Redi and 0x2 induces the redox reaction (16.1)  

To have pure thermodynamic rigor, it is always equilibrated, even if it must be strongly displaced toward the right in order to achieve a satisfactory titration. The calculation of the solution equilibrium s potential is performed as a function of the analytical concentrations of species 1 and 2, C i and C2, with the help of the following system of equations, which are always satisfied  

At equilibrium, the solution potential may be indifferently expressed by Eq. (16.2) or (16.3). (The case of a mixture of two weak acids is analogous. The solution s pH may be expressed as a function of the pKa of either of the acids.) Equations (16.4) and (16.5) are the mass balances in couples (16.1) and (16.2). Note that Ci and C2 are the total concentrations in the forms Redi and 0x2 once the mixture is achieved but before reaction (16.1) has begun. Equation (16.6) expresses the electron balance The electrons lost by the species that is oxidized are captured by the oxidant. This relation is perhaps difficult to understand in a first approach. Some examples with tii values different from 2 values will permit us to understand them better (see Chap. 17). The electron balance relation must always be written for the calculation of solution potentials. It is necessary to solve the appropriate systems of equations. Finally, it is interesting to remark that in the above system of equations, the last three are expressed in terms of concentrations, and the first two in terms of activities. 

The five simultaneous Eqs. (16.2)-(16.6) constitute a system in five unknowns. It can be solved from a mathematical standpoint. When activities are assumed to be equal to the corresponding concentrations, we find Eq. (16.7) after reducing the system by substitution and elimination  

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