How does pH affect the potential of the H+/H2 couple at 25°C?

• A. E = E° − 0.05916 pH; increasing pH lowers the H+/H2 potential.
• B. E = E° + 0.05916 pH; increasing pH raises the potential.
• C. E = E° − 0.1 pH; every pH unit changes by 0.1 V.
• D. E = E°; pH has no effect at 25°C.

Answer: (A)

The effect of pH on the H+/H2 couple comes from the Nernst equation for a reaction that involves protons. For the reduction 2H+ + 2e− → H2, the potential depends on the proton activity. If the hydrogen gas is at unit activity, the equation simplifies to E = E° − (RT/F) ln(a_H+). Since a_H+ = 10^(-pH), ln(a_H+) = −2.303 pH, giving E = E° − (2.303 RT/F) pH. At 25°C, 2.303 RT/F ≈ 0.05916 V, so E = E° − 0.05916 pH. This means that as pH increases (fewer protons), the potential becomes more negative—the H+/H2 couple shifts to lower potential with higher pH. The given form E = E° − 0.05916 pH reflects this, and the statement about increasing pH lowering the potential is the correct interpretation. The other options either sign the slope differently, use an incorrect coefficient, or state no pH dependence, which contradicts the Nernst description for a proton-involved couple.