The measured voltage at 25.0°C of a cell in which the reaction described by the equation
$Zn(s) + Cu^{2+}(aq,\ 1.00\ M) ⇋ Cu(s) + Zn^{2+}(aq,\ 0.100\ M)$
occurring at the concentrations given is 1.13 V. Calculate the value of $E^{\circ}_{cell}$ for the cell.

Question

The measured voltage at 25.0°C of a cell in which the reaction described by the equation

[latex]Zn(s) + Cu^{2+}(aq,\ 1.00\ M) ⇋ Cu(s) + Zn^{2+}(aq,\ 0.100\ M)[/latex]

occurring at the concentrations given is 1.13 V. Calculate the value of [latex]E^{\circ}_{cell}[/latex] for the cell.

Accepted Answer

Using Equation 25.13 with [latex]ν_{e} = 2[/latex], we obtain

[latex]E_{cell} = E^{\circ}_{ cell} –\left(\frac{0.02570\ V}{ u_{e}} ight) ln\ Q \qquad (at\ 25.0^{\circ}C)[/latex] (25.13)

[latex]E_{cell} = E^{\circ}_{ cell} –\left(\frac{0.02570\ V}{2} ight) ln\frac{[Zn ^{2+}]/M}{[Cu ^{2+}]/M}[/latex]

([latex]Zn(s)[/latex] and [latex]Cu(s)[/latex] do not appear in the Q expression because they are both solids.) Therefore,

[latex]1.13\ V = E^{\circ}_{ cell} – \left(\frac{0.02570\ V}{2} ight) ln\left(\frac{0.100}{1.00} ight)[/latex]

from which we calculate

[latex]E^{\circ}_{ cell} = 1.13\ V + (0.01285\ V)ln(0.100) = 1.10\ V[/latex]

Note that [latex]E_{ cell} > E^{\circ}_{ cell}[/latex] because Q < 1.

Question 25.6: The measured voltage at 25.0°C of a cell in which the reacti......