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(A) reaction is spontaneous if the standard cell potential $E^{\circ}_{cell}$ is positive,which corresponds to a negative Gibbs free energy change $\D

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Copper-silver nitrate interface

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(A) reaction is spontaneous if the standard cell potential $E^{\circ}_{cell}$ is positive,which corresponds to a negative Gibbs free energy change $\Delta G^{\circ} = -nFE^{\circ}_{cell}$.For system $(A)$: $Cu(s) + 2Ag^{+}(aq) \rightarrow Cu^{2+}(aq) + 2Ag(s)$.$E^{\circ}_{cell} = E^{\circ}_{cathode} - E^{\circ}_{anode} = E^{\circ}_{Ag^{+}/Ag} - E^{\circ}_{Cu^{2+}/Cu} = 0.80 \ V - 0.34 \ V = 0.46 \ V$.Since $E^{\circ}_{cell} > 0$,the reaction is spontaneous.For system $(B)$: $Ag(s) + Cu^{2+}(aq) \rightarrow Ag^{+}(aq) + Cu(s)$.$E^{\circ}_{cell} = E^{\circ}_{Cu^{2+}/Cu} - E^{\circ}_{Ag^{+}/Ag} = 0.34 \ V - 0.80 \ V = -0.46 \ V$.Since $E^{\circ}_{cell} Therefore,the copper-silver nitrate interface shows a spontaneous reaction.

Consider the systems having liquid-solid interface,$(A)$ copper wire in silver nitrate solution and $(B)$ silver wire in copper sulphate solution. Predict which interface will show spontaneous reaction,if $E_{Cu^{2+}/Cu}^{\circ} = 0.34 \ V$ and $E_{Ag^{+}/Ag}^{\circ} = 0.80 \ V$?

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