Q.(i) In button cell, widely used in watches, the following reaction takes place: Zn(s) + Ag2O(s) + H2O(l) → Zn2+(aq) + 2Ag(s) + 2OH⁻(aq). Determine E°cell and ΔG° for the cell. (Given E°(Ag+/Ag) = +0.80 V and E°(Zn2+/Zn) = -0.76 V.) [2]

$E^{\circ}_{cell}=E^{\circ}_{cathode}-E^{\circ}_{anode}=1.56\ V$; $\Delta G^{\circ}=-nFE^{\circ}_{cell}\approx-301.1\ kJ/mol$.

(i) In the button cell reaction $Zn(s) + Ag_2O(s) + H_2O(l) \rightarrow Zn^{2+}(aq) + 2Ag(s) + 2OH^-(aq)$, zinc is oxidised (anode: $Zn \rightarrow Zn^{2+}+2e^-$) and silver(I) is reduced to metallic silver (cathode). This is a 2-electron transfer reaction ($n=2$).

$E^{\circ}_{cell} = E^{\circ}_{cathode} - E^{\circ}_{anode} = E^{\circ}(Ag^+/Ag) - E^{\circ}(Zn^{2+}/Zn) = 0.80\ V - (-0.76\ V) = 1.56\ V$

Using $\Delta G^{\circ} = -nFE^{\circ}_{cell}$ with $F = 96500\ C\,mol^{-1}$:

$\Delta G^{\circ} = -2 \times 96500 \times 1.56 \approx -301{,}080\ J/mol \approx -301.1\ kJ/mol$

The large negative $\Delta G^{\circ}$ confirms the cell reaction is strongly spontaneous, consistent with the button cell working reliably as a power source.

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