Question

The cell potential for the following cell

\[\ce{Pt|H2 (g)| H+ (aq)||Cu^{2+} (0.01 M)| Cu(s)}\]

is 0.576 Vat 298 K. The pH of the solution is ____. (Nearest integer)

Options

• 5

• 10

• 6

• 2

Answer 1

The cell potential for the following cell

\[\ce{Pt|H2 (g)| H+ (aq)||Cu^{2+} (0.01 M)| Cu(s)}\]

is 0.576 Vat 298 K. The pH of the solution is 5.

Explanation:

\[\ce{Anode: H2 -> 2H+ + 2e-}\]
\[\underline{\ce{Cathode: Cu^{2+} + 2e- -> Cu}}\]

\[\phantom{.....}\ce{Cu^{2+} + H2 -> 2H+ + Cu}\]

`"E"_"cell" = "E"_"cell"^0 - 0.06/2 log  (["H"^+]^2)/(["Cu"^(2+)])`

`0.576 = 0.34 - 0.06/2 log {["H"^+]^2/[0.01]}`

⇒ 7.87 = - log [H⁺]² + log 10^-2

⇒ pH = 4.93 ≈ 5