Question

Which from following formulae is used to obtain value of E^°cell for a reaction taking place in Dry cell?

Options

• \[\frac{-\Delta G^{\circ}}{F}\]

• \[\frac{-\Delta G^{\circ}}{2F}\]

• \[\frac{-\Delta G^{\circ}}{3F}\]

• \[\frac{-\Delta G^{\circ}}{4F}\]

Answer 1

\[\frac{-\Delta G^{\circ}}{2F}\]

Explanation:

\[\Delta\mathrm{G}^{\circ}=-\mathrm{nFE}_{\mathrm{cell}}^{\circ}\]

\[\mathrm{E}_{\mathrm{cell}}^{\circ}=-\frac{\Delta\mathrm{G}^{\circ}}{\mathrm{nF}}\]

Reactions of dry cell:

\[\mathrm{Anode:~Zn_{(s)}\longrightarrow Zn_{(aq)}^{2+}+2e^{-}}\]

\[\text{Cathode:2NH}_{4(\mathrm{aq})}^++2\mathrm{MnO}_{2(\mathrm{s})}+2\mathrm{e}^-\longrightarrow\mathrm{Mn}_{2}\mathrm{O}_{3(\mathrm{s})}+2\mathrm{NH}_{3(\mathrm{aq})}+\mathrm{H}_{2}\mathrm{O}_{(\mathrm{l})}\]

From the above reactions, n = 2

∴ \[\mathrm{E}_{\mathrm{cell}}^{\circ}=-\frac{\Delta\mathrm{G}^{\circ}}{2\mathrm{F}}\]