Question

The cell, \[\ce{Zn | Zn^{2+} (1 M) || Cu^{2+} (1 M) | Cu}\], (\[\ce{E^{\circ}_{cell} = 1.10 V}\]), was allowed to be completely discharged at 298 K. The relative concentration of Zn²⁺ to \[\ce{Cu^{2+}\left(\frac{[Zn^{2+}]}{[Cu{2+}]}\right)}\] is:

Options

• antilog (24.08)

• 37.3

• 10^37.3

• 9.65 × 10⁴

Answer 1

10^37.3

Explanation:

When the cell is completely discharged, the cell reaction attains equilibrium and E_cell = 0.

For the given cell,

\[\ce{Zn | Zn^{2+} (1 M) || Cu^{2+} (1 M) | Cu}\]

Equilibrium constant for this reaction is

\[\ce{K_{eq} = \frac{[Zn{^{2+}_{(aq)}}]}{[Cu{^{2+}_{(aq)}}]}}\]

\[\ce{E_{cell} = E{^{\circ}_{cell}} - \frac{0.059}{n} log_10 \frac{[Zn{^{2+}_{(aq)}}]}{[Cu{^{2+}_{(aq)}}]}}\]

or, \[\ce{0 = 1.10 - \frac{0.059}{2} log_10 K_{eq}}\]

or, \[\ce{log_10 K_{eq} = \frac{1.10 × 2}{0.059}}\]

= 37.3

∴ K_eq = 10^37.3