Question

The cell potential for the following cell
\(\mathrm{Pt\,|\,H_2(g)\,|\,H^+(aq)\,||\,Cu^{2+}(0.01\ M)\,|\,Cu(s)}\)
is 0.576 V at 298 K. The pH of the solution is __________. (Nearest integer)
(Given : \(E^o_{\mathrm{Cu^{2+}/Cu}} = 0.34\) V and \(\dfrac{2.303\,RT}{F} = 0.06\) V)

Hint:

Write the cell reaction \(\mathrm{H_2 + Cu^{2+} \rightarrow 2H^+ + Cu}\) (n = 2) and apply the Nernst equation, assuming \(\mathrm{H_2}\) at 1 bar.

Answer 1

Correct Answer: 5

Cell reaction: \(\mathrm{H_2(g) + Cu^{2+} \rightarrow 2H^+ + Cu(s)}\), n = 2, \(E^o_{cell} = 0.34 - 0 = 0.34\) V.
Nernst: \(E = E^o - \dfrac{0.06}{2}\log\dfrac{[H^+]^2}{[Cu^{2+}]}\) (\(p_{H_2}\) = 1 bar).
\(\log\dfrac{[H^+]^2}{0.01} = -2\,pH + 2\).
\(0.576 = 0.34 - 0.03(2 - 2\,pH) = 0.34 - 0.06 + 0.06\,pH = 0.28 + 0.06\,pH\).
\(pH = \dfrac{0.576 - 0.28}{0.06} = \dfrac{0.296}{0.06} = 4.93 \approx 5\).
Answer: 5