Answer:
To determine the identity of metal X, we need to compare the standard reduction potentials of the possible metals with the standard reduction potential of the Mg half-reaction.
From Table 18.1, we can find the standard reduction potentials for each of the metals listed:
Pb: -0.13 V
Zn: -0.76 V
Ni: -0.25 V
Fe: -0.44 V
Mn: -1.18 V
The reduction half-reaction for the Mg electrode is:
Mg2+ + 2e- → Mg E° = -2.37 V
The overall reaction for the galvanic cell is:
Mg(s) + X2+(aq) → Mg2+(aq) + X(s)
The standard cell potential is given by:
E°cell = E°(cathode) - E°(anode)
where the cathode is the reduction half-reaction and the anode is the oxidation half-reaction.
Substituting the given values, we get:
1.61 V = E°(X2+/X) - (-2.37 V)
Simplifying, we get:
E°(X2+/X) = 1.61 V + 2.37 V = 3.98 V
Comparing E°(X2+/X) with the standard reduction potentials in Table 18.1, we see that only zinc (Zn) has a reduction potential that is more negative than 3.98 V. Therefore, the metal X is zinc (Zn).
Therefore, the answer is (b) Zn.