If the ion concentrations in the half-cell that is coupled to the SHE are not equal to the standard value of 1 M, the EMF can be determined by generalizing electrode reactions such as (10.19). This reaction is of the type:
reduced form = oxidized form + ze (10.31)
The terms "reduced form" and "oxidized form" refer to the element that changes its valence (or oxidation state) in the half-cell reaction. For example, in reaction 2 in Table 10.1, the element that changes valence is oxygen; the reduced form is OH- and the oxidized form is O2. The concentrations of the reduced form and the oxidized form need not be the standard values of 1 M for ions and 1 atm for gases. The EMF of a nonstandard half-cell relative to the SHE is:
sN _ so - —lni coxMlzed 1 _ e° -°^logicoHdlzed 1 (10.29)
zF V creduced ) z V creduced )
where the last form employs the numerical value of RT/F for T = 298 K multiplied by 2.3 to convert from the natural logarithm to the base-ten logarithm. The concentrations in the argument of the logarithmic term are those of the oxidized and reduced forms of the element that changes valence. If the half-cell reaction contains H+ or OH-, the concentrations of these species must also be included in the numerator and/or denominator of the logarithmic term. Solid species in pure form (such as metals or solid oxides or hydroxides) are not included in the logarithmic term because their activities are unity, as is that of water. Equation (10.29) is known as the Nernst equation and sN is the Nernst potential.
Example Calculate the Nernst potential half-cell 10 in Table 10.1 for the following concentrations: c + =0.01 M, c 2+ = 1.0 M, c 4+ = 0.1 M.
H UO2 U
The specific form of Eq (10.29) for this half-cell is:
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