For a standard Ag-Zn button cell used in watches, the net reaction is . Given the standard Gibbs fre — Electrochemistry Chemistry Question
Question
For a standard Ag-Zn button cell used in watches, the net reaction is $Zn(s) + Ag_2O(s) \rightarrow ZnO(s) + 2Ag(s)$. Given the standard Gibbs free energies of formation $\Delta G_f^\circ(Ag_2O) = -11.21\text{ kJ mol}^{-1}$ and $\Delta G_f^\circ(ZnO) = -318.3\text{ kJ mol}^{-1}$, calculate the standard cell potential ($E^\circ_{cell}$) in Volts. (Use $1\text{ F} = 96500\text{ C mol}^{-1}$)
💡 Solution & Explanation
First, find the standard free energy change of the reaction: $\Delta G^\circ_{rxn} = \Sigma \Delta G_f^\circ(\text{products}) - \Sigma \Delta G_f^\circ(\text{reactants})$. Because standard free energies of elements ($Zn, Ag$) are zero, $\Delta G^\circ_{rxn} = \Delta G_f^\circ(ZnO) - \Delta G_f^\circ(Ag_2O) = -318.3 - (-11.21) = -307.09\text{ kJ mol}^{-1} = -307090\text{ J mol}^{-1}$. For the reaction, $Zn$ goes to $Zn^{2+}$ transferring 2 electrons ($n=2$). Using $\Delta G^\circ_{rxn} = -nFE^\circ_{cell}$, $-307090 = -2 \times 96500 \times E^\circ_{cell} \implies E^\circ_{cell} = \frac{307090}{193000} \approx 1.591\text{ V}$.