For the concentration cell Fe(s) | Fe3+ (0.100 M) || Fe3+ (1.00 M) | Fe(s) at 25 C, what is Ecell in millivolts?

• A. 9.87 mV
• B. 19.7 mV
• C. 29.6 mV
• D. 59.2 mV

Answer: (D)

In a concentration cell, the voltage comes from differences in the concentrations of the same redox couple; since the standard potential for a concentration cell (where the two electrodes are the same material and the same redox pair) is effectively zero, the cell potential is set entirely by the ratio of concentrations of the species that undergo change in oxidation state. Here, the Fe3+/Fe2+ couple involves one electron transfer, so the Nernst form reduces to a simple log dependence on the concentration ratio. If we take the right-hand half-cell as the cathode, Ecell = (0.0592/1) log([Fe3+]right/[Fe3+]left). With 1.00 M on the right and 0.100 M on the left, the ratio is 10, and Ecell = 0.0592 × log(10) = 0.0592 V, which is 59.2 mV. The positive sign corresponds to this orientation of the cell as written.