Identify the set of metals which require same amount of charge for the deposition of one mole of metals: (a) \(\mathrm{Na}, \mathrm{Ag}, \mathrm{Al}\) (b) \(\mathrm{Zn}, \mathrm{Cu}, \mathrm{Ag}\) (c) \(\mathrm{Al}, \mathrm{Cu}, \mathrm{Zn}\) (d) \(\mathrm{Mg}, \mathrm{Zn}, \mathrm{Cd}\)

Write the reduction half-reactions for each of the metals given in the options: (a) Na, Ag, Al \(\mathrm{Na}^{+} \mathrm{+} \mathrm{e}^{-} \mathrm{\rightarrow} \mathrm{Na}\) \(\mathrm{Ag}^{+} \mathrm{+} \mathrm{e}^{-} \mathrm{\rightarrow} \mathrm{Ag}\) \(\mathrm{Al}^{3+} \mathrm{+} 3\mathrm{e}^{-} \mathrm{\rightarrow} \mathrm{Al}\) (b) Zn, Cu, Ag \(\mathrm{Zn}^{2+} \mathrm{+} 2\mathrm{e}^{-} \mathrm{\rightarrow} \mathrm{Zn}\) \(\mathrm{Cu}^{2+} \mathrm{+} 2\mathrm{e}^{-} \mathrm{\rightarrow} \mathrm{Cu}\) \(\mathrm{Ag}^{+} \mathrm{+} \mathrm{e}^{-} \mathrm{\rightarrow} \mathrm{Ag}\) (c) Al, Cu, Zn \(\mathrm{Al}^{3+} \mathrm{+} 3\mathrm{e}^{-} \mathrm{\rightarrow} \mathrm{Al}\) \(\mathrm{Cu}^{2+} \mathrm{+} 2\mathrm{e}^{-} \mathrm{\rightarrow} \mathrm{Cu}\) \(\mathrm{Zn}^{2+} \mathrm{+} 2\mathrm{e}^{-} \mathrm{\rightarrow} \mathrm{Zn}\) (d) Mg, Zn, Cd \(\mathrm{Mg}^{2+} \mathrm{+} 2\mathrm{e}^{-} \mathrm{\rightarrow} \mathrm{Mg}\) \(\mathrm{Zn}^{2+} \mathrm{+} 2\mathrm{e}^{-} \mathrm{\rightarrow} \mathrm{Zn}\) \(\mathrm{Cd}^{2+} \mathrm{+} 2\mathrm{e}^{-} \mathrm{\rightarrow} \mathrm{Cd}\)

Now, let's compare the number of moles of electrons involved in each set of reduction half-reactions: (a) Na, Ag, Al 1 mole of electron for Na 1 mole of electron for Ag 3 moles of electrons for Al (b) Zn, Cu, Ag 2 moles of electrons for Zn 2 moles of electrons for Cu 1 mole of electron for Ag (c) Al, Cu, Zn 3 moles of electrons for Al 2 moles of electrons for Cu 2 moles of electrons for Zn (d) Mg, Zn, Cd 2 moles of electrons for Mg 2 moles of electrons for Zn 2 moles of electrons for Cd

From the comparison, we can see that option (d) has a set of metals that require the same amount of charge (2 moles of electrons) for the deposition of one mole of metals: \(\mathrm{Mg}^{2+} \mathrm{+} 2\mathrm{e}^{-} \mathrm{\rightarrow} \mathrm{Mg}\) \(\mathrm{Zn}^{2+} \mathrm{+} 2\mathrm{e}^{-} \mathrm{\rightarrow} \mathrm{Zn}\) \(\mathrm{Cd}^{2+} \mathrm{+} 2\mathrm{e}^{-} \mathrm{\rightarrow} \mathrm{Cd}\) So, the correct answer is (d) Mg, Zn, Cd.