In the spontaneous redox reaction X(s) + Y2+(aq) ⇌ X2+(aq) + Y(s), when [X2+] and [Y2+] are equal, the cell potential is positive. If [X2+] = 10 × [Y2+], how will Ecell change?

• A. The voltage decreases
• B. The voltage increases
• C. The voltage remains the same
• D. The voltage becomes negative

Answer: (A)

The factor being tested is how the cell potential changes with nonstandard concentrations via the Nernst equation. For this reaction, Ecell = E°cell − (0.05916/n) log Q at 25°C, where Q = [X2+]/[Y2+] because the solids are omitted.

If [X2+] = [Y2+], then Q = 1 and log Q = 0, so Ecell = E°cell (positive under standard conditions).

Now [X2+] = 10 × [Y2+], so Q = 10. With n = 2 electrons transferred in the balanced reaction (X goes to X2+ releasing 2 e− and Y2+ gains 2 e− to become Y), the equation gives Ecell = E°cell − (0.05916/2) × log(10) = E°cell − 0.05916/2 × 1 ≈ E°cell − 0.0296 V. This is a decrease in the cell potential, though it remains positive as long as E°cell > about 0.03 V.

Intuitively, increasing the product concentration X2+ relative to Y2+ makes the forward spontaneous reaction less favorable, lowering the emf.