Provide an example of a redox couple that can serve as a pH sensor electrode and describe its measured relationship to pH.

• A. The Cu2+/Cu couple; E = E° − 0.023 pH
• B. The H+/H2 couple; E = E° − 0.05916 pH at 25°C
• C. The O2/H2O couple; E = E° − 0.05916 pH
• D. The Fe2+/Fe3+ couple; E = E° − 0.05916 pH

Answer: (B)

The key idea is that a redox couple whose reaction directly involves protons will have an electrode potential that shifts with pH. For the H+/H2 couple, the half-reaction is 2H+ + 2e− ⇌ H2. Using the Nernst equation, the potential depends on the proton activity: E = E° − (RT/2F) ln(1/[H+]^2), which simplifies to E = E° − (RT ln 10 / F) pH. At 25°C, this gives E = E° − 0.05916 pH. So the potential changes by about 59 mV per unit change in pH, making this pair a direct pH sensor electrode.

Other options don’t provide that straightforward pH response. The Cu2+/Cu couple involves no protons in the reaction, so pH has little to no systematic effect on its potential. The O2/H2O and Fe2+/Fe3+ couples either rely on factors other than pH (like oxygen partial pressure) or involve no proton transfer in the primary step, so their pH dependence is not as clean or directly useful for sensing pH. Hence, the H+/H2 couple with E = E° − 0.05916 pH is the best example.