The black silver sulfide discoloration of silverware can easily be removed by heating the silver article in a sodium carbonate solution in an aluminum pan. The reaction is

\[3 \mathrm{Ag}_{2} \mathrm{~S}(s)+2 \mathrm{Al}(s) ightleftharpoons 6 \mathrm{Ag}(s)+3 \mathrm{~S}^{2-}(a q)+2 \mathrm{Al}^{3+}(a q)\]

a. Using data in Appendix 4, calculate \(\Delta G^{\circ}, K\), and \(\mathscr{E}^{\circ}\) for the above reaction. [For \(\mathrm{Al}^{3+}(a q), \Delta G_{\mathrm{f}}^{\circ}=\) \(-480 . \mathrm{kJ} / \mathrm{mol}\).]

b. Calculate the value of the standard reduction potential for the following half-reaction:

\[2 \mathrm{e}^{-}+\mathrm{Ag}_{2} \mathrm{~S}(s) \longrightarrow 2 \mathrm{Ag}(s)+\mathrm{S}^{2-}(a q)\]