For the decomposition of $Al_2O_3$ at $500\,^{\circ}C$,the Gibbs energy change is given by $\frac{2}{3} Al_2O_3 \rightarrow \frac{4}{3} Al + O_2$,$\Delta G = 966 \, kJ \, mol^{-1}$. What is the potential difference (in $V$) required for the electrolytic reduction of $Al_2O_3$ at $500\,^{\circ}C$?

The extent of charge of a lead accumulator is determined by

Calculate $\Delta G^{\circ}$ for the following cell reaction.
$Zn_{(s)} + Ag_2O_{(s)} + H_2O_{(l)} \longrightarrow Zn^{2+}_{(aq)} + 2Ag_{(s)} + 2OH^{-}_{(aq)}$
Given: $E^{\circ}_{Ag^{+}/Ag} = +0.80 \ V$ and $E^{\circ}_{Zn^{2+}/Zn} = -0.76 \ V$

Calculate $\Delta G^{\circ}$ for the reaction $Mg_{(s)} + Sn_{(aq)}^{2+} \longrightarrow Mg_{(aq)}^{2+} + Sn_{(s)}$ if $E_{cell}^{\circ}$ is $2.23 \ V$. (in $kJ$)

The equilibrium constant for the reaction $Zn_{(s)} + Sn^{2+}_{(aq)} \rightleftharpoons Zn^{2+}_{(aq)} + Sn_{(s)}$ is $1 \times 10^{20}$ at $298 \ K$. The magnitude of standard electrode potential of $Sn/Sn^{2+}$ if $E_{Zn^{2+}/Zn}^0 = -0.76 \ V$ is $............ \times 10^{-2} \ V$. (Nearest integer)
Given : $\frac{2.303 \ RT}{F} = 0.059 \ V$

$Zn_{(s)} | Zn^{2+}_{(aq)} || Cu^{2+}_{(aq)} | Cu_{(s)}$ is