To determine which ion is most likely to be reduced, we need to compare their standard reduction potentials. The standard reduction potential gives an indication of how readily a species gains electrons and is reduced to its elemental form. The more positive the reduction potential, the more likely the species is to be reduced.
Here is a list of standard reduction potentials for the given ions:
1. [tex]\( Zn^{2+} + 2e^- \rightarrow Zn \)[/tex]
[tex]\[ E^\circ = -0.76 \text{ V} \][/tex]
2. [tex]\( Ni^{2+} + 2e^- \rightarrow Ni \)[/tex]
[tex]\[ E^\circ = -0.25 \text{ V} \][/tex]
3. [tex]\( Fe^{2+} + 2e^- \rightarrow Fe \)[/tex]
[tex]\[ E^\circ = -0.44 \text{ V} \][/tex]
4. [tex]\( Mg^{2+} + 2e^- \rightarrow Mg \)[/tex]
[tex]\[ E^\circ = -2.37 \text{ V} \][/tex]
By comparing these potentials:
- [tex]\( Zn^{2+} \)[/tex]: [tex]\( -0.76 \text{ V} \)[/tex]
- [tex]\( Ni^{2+} \)[/tex]: [tex]\( -0.25 \text{ V} \)[/tex]
- [tex]\( Fe^{2+} \)[/tex]: [tex]\( -0.44 \text{ V} \)[/tex]
- [tex]\( Mg^{2+} \)[/tex]: [tex]\( -2.37 \text{ V} \)[/tex]
We see that [tex]\( Ni^{2+} \)[/tex] has the most positive reduction potential at [tex]\( -0.25 \text{ V} \)[/tex]. This implies that [tex]\( Ni^{2+} \)[/tex] is the most likely to be reduced among the given ions because a higher (or less negative) standard reduction potential indicates a greater tendency to gain electrons.
Therefore, the answer is:
B. [tex]\( Ni^{2+} \)[/tex]
