The standard reduction potential for ${\text{Zn}}^{2+}/\mathrm{Zn},{\mathrm{Ni}}^{2+}/\mathrm{Ni} \mathrm{and} {\mathrm{Fe}}^{2+}/\mathrm{Fe} \mathrm{are} -0.76,-0.23$and -0.44 V respectively. The reaction $\mathrm{X}+{\mathrm{Y}}^{2+}⟶{\mathrm{X}}^{2+}+\mathrm{Y}$ will be spontaneous if

A cell reaction is spontaneous, if ${\mathrm{\Delta G}}^{\circ }<0$
Since,     ${\mathrm{\Delta G}}^{\circ }=-{\mathrm{nF}}_{\text{cell }}^{\circ }$
Thus,    ${\mathrm{E}}_{\mathrm{cell}}^{\circ }>0$
           ${\mathrm{E}}_{\text{cell }}^{\circ }={\mathrm{E}}_{\text{oxi }}^{\circ }+{\mathrm{E}}_{\mathrm{Red}}^{\circ }$                

(a) X = Ni,  Y = Fe
       $\mathrm{Ni}+{\mathrm{Fe}}^{2+}⟶{\mathrm{Ni}}^{2+}+\mathrm{Fe}$
      $\begin{array}{r}{\mathrm{E}}_{\mathrm{Ni}/{\mathrm{Ni}}^{2+}}^{\mathrm{o}}=0.23 \mathrm{V}\\ {{\mathrm{E}}^{\circ }}_{{\mathrm{Fe}}^{2+}/\mathrm{Fe}}=-0.44 \mathrm{V}\end{array}$
   Thus,  ${\mathrm{E}}_{\text{cell }}^{\circ }={\mathrm{E}}_{\mathrm{Ni}/{\mathrm{Ni}}^{2+}}^{\circ }+{\mathrm{E}}_{{\mathrm{Fe}}^{2+}/\mathrm{Fe}}^{\circ }$
                     =-0.21 V ${\mathrm{E}}_{\text{cell }}^{\circ }<0,$reaction is non-spontaneous.
(b) X = Ni, Y = Zn,
     $\mathrm{Ni}+{\mathrm{Zn}}^{2+}⟶{\mathrm{Ni}}^{2+}+\mathrm{Zn}$
    ${\mathrm{E}}_{\mathrm{Ni}/{\mathrm{Ni}}^{2+}}=0.23\mathrm{V},{\mathrm{E}}_{{\mathrm{Zn}}^{2+}/\mathrm{Zn}}^{\circ }=-0.76\mathrm{V}$
         ${\mathrm{E}}_{\text{cell }}^{\circ }=-0.53\mathrm{V}$
    ${\mathrm{E}}_{\text{cell }}^{\mathrm{\alpha }}<0$ reaction is non- spontaneous.
(c ) $\mathrm{X}=\mathrm{Fe},\mathrm{Y}=\mathrm{Zn},\mathrm{Fe}+{\mathrm{Zn}}^{2+}⟶{\mathrm{Fe}}^{2+}+\mathrm{Zn}$
      ${\mathrm{E}}_{\text{cell }}^{\circ }={\mathrm{E}}_{\mathrm{Fe}/{\mathrm{Fe}}^{2+}}^{\circ }+{\mathrm{E}}_{{\mathrm{Zn}}^{2+}/\mathrm{Zn}}^{\circ }=0.44-0.76=-0.32\mathrm{V}$
     ${\mathrm{E}}_{\text{cell }}^{\circ }<0$, reaction is non- spontaneous.
(d) $\mathrm{X}=\mathrm{Zn},\mathrm{Y}=\mathrm{Ni}$
     $\mathrm{Zn}+{\mathrm{Ni}}^{2+}⟶{\mathrm{Zn}}^{2+}+\mathrm{Ni}$
      ${\mathrm{E}}_{\text{cell }}^{\circ }={\mathrm{E}}_{\mathrm{Zn}/{\mathrm{Zn}}^{2+}}^{\circ }+{\mathrm{E}}_{{\mathrm{Ni}}^{2+}/\mathrm{Ni}}^{\circ }=0.76-0.23=0.53\mathrm{V}$
    The reaction is spontaneous.