When one or more of the constitutents in the half-cells are not in their standard states (i.e., are nonstandard), Eq (10.5a) relates AG, the free-energy change of the overall reaction, to the cell EMF. The first step in making the connection between the cell voltage and the component concentrations is to relate AG to the chemical potentials of the constituents in the half-cells. Generalizing the analysis in Sect. 9.4, the version of Eq (9.16) for a nonequilibrium reaction is:
products where p is the chemical potential of constituent i and the sums are over the constituents in the product and reactant sides of the overall reaction, respectively. vi is the balancing number of constituent i in the overall reaction.
When a cell is short-circuited, current flows until the compositions in the two electrodes reduce AG to zero. In this limit, Eq (10.6) reduces to the chemical equilibrium condition given by Eq (9.16).
The constituents in the nonstandard half-cells are no longer restricted to pure liquids or solids, as they were in Sects. 10.1 - 10.3. If the components are solid or liquid solutions, the chemical potentials are given by p i = g° + RTlnai = g° + RTln(y ixi) (10.7)
where ai is the activity of species i in solution, or the product of the activity coefficient and the mole fraction of species i. For the special case of pure constituents (i.e., unit activity), Eq (10.7) reduces to pi = g°.
If the constituent is a gas, the chemical potential is given by:
Substitution of Eq (10.7) and/or Eq (10.8) into Eq (10.6) gives AG in terms of activities and partial pressures of the constituents in the half-cells. The cell EMF follows from Eq (10.5a). Several nonstandard-state electrochemical cells are described below.
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