If standard reduction potential $\left(\mathrm{E}^{\circ}\right)$ of $\left(\mathrm{Mg}_{(\mathrm{aq})}^{+2} \mid \mathrm{Mg}_{(\mathrm{s})}\right)$, $\left(\mathrm{Ag}^{+}{ }_{(\mathrm{aq})} \mid \mathrm{Ag}_{(\mathrm{s})}\right),\left(\mathrm{Zn}^{+2}{ }_{(\mathrm{aq})} \mid \mathrm{Zn}_{(\mathrm{s})}\right)$ and $\left(\mathrm{Cu}^{+2}{ }_{(\mathrm{aq})} \mid \mathrm{Cu}_{(\mathrm{s})}\right)$ are -2.37 V , $+0.79 \mathrm{~V},-0.76 \mathrm{~V}$ and +0.34 V respectively. Which of the following reaction is spontaneous?

A reaction is spontaneous if its standard cell potential $E^{\circ}_{\text{cell}} > 0$, where $E^{\circ}_{\text{cell}} = E^{\circ}_{\text{reduction}}(\text{cathode}) - E^{\circ}_{\text{reduction}}(\text{anode})$.

Using the standard reduction potentials: $E^{\circ}(\mathrm{Mg}^{+2} \mid \mathrm{Mg}) = -2.37\ \mathrm{V}$, $E^{\circ}(\mathrm{Ag}^{+} \mid \mathrm{Ag}) = +0.79\ \mathrm{V}$, $E^{\circ}(\mathrm{Zn}^{+2} \mid \mathrm{Zn}) = -0.76\ \mathrm{V}$, and $E^{\circ}(\mathrm{Cu}^{+2} \mid \mathrm{Cu}) = +0.34\ \mathrm{V}$:

For reaction A: $\mathrm{Zn}_{(\mathrm{s})}+\mathrm{Mg}_{(\mathrm{aq})}^{+2} \longrightarrow \mathrm{Zn}_{(\mathrm{aq})}^{+2}+\mathrm{Mg}_{(\mathrm{s})}$
$E^{\circ}_{\text{cell}} = E^{\circ}(\mathrm{Mg}^{+2}) - E^{\circ}(\mathrm{Zn}^{+2}) = -2.37 - (-0.76) = -1.61\ \mathrm{V}$
Spontaneous? No

For reaction B: $2\mathrm{Ag}_{(\mathrm{s})}+\mathrm{Zn}_{(\mathrm{aq})}^{+2} \longrightarrow 2\mathrm{Ag}_{(\mathrm{aq})}^{+}+\mathrm{Zn}_{(\mathrm{s})}$
$E^{\circ}_{\text{cell}} = E^{\circ}(\mathrm{Zn}^{+2}) - E^{\circ}(\mathrm{Ag}^{+}) = -0.76 - 0.79 = -1.55\ \mathrm{V}$
Spontaneous? No

For reaction C: $\mathrm{Zn}_{(\mathrm{s})}+\mathrm{Cu}_{(\mathrm{aq})}^{+2} \longrightarrow \mathrm{Zn}_{(\mathrm{aq})}^{+2}+\mathrm{Cu}_{(\mathrm{s})}$
$E^{\circ}_{\text{cell}} = E^{\circ}(\mathrm{Cu}^{+2}) - E^{\circ}(\mathrm{Zn}^{+2}) = 0.34 - (-0.76) = 1.10\ \mathrm{V}$
Spontaneous? Yes

For reaction D: $\mathrm{Cu}_{(\mathrm{s})}+\mathrm{Mg}_{(\mathrm{aq})}^{+2} \longrightarrow \mathrm{Cu}_{(\mathrm{aq})}^{+2}+\mathrm{Mg}_{(\mathrm{s})}$
$E^{\circ}_{\text{cell}} = E^{\circ}(\mathrm{Mg}^{+2}) - E^{\circ}(\mathrm{Cu}^{+2}) = -2.37 - 0.34 = -2.71\ \mathrm{V}$
Spontaneous? No

The only spontaneous reaction is C.