The process of rusting of iron occurs as follows:
$Fe \rightarrow Fe^{2+} + 2e^{-}, E^{o} = 0.44 \ V$
$2H^{+} + 2e^{-} + \frac{1}{2} O_2 \rightarrow H_2O_{(l)}, E^{o} = 1.23 \ V$
Then for this reaction,$\Delta G^{o} = .... \ kJ/mol$

If $\Lambda^{0}_{NaCl} = 126 \ S \ cm^{2} \ mol^{-1}$,$\Lambda^{0}_{KBr} = 125 \ S \ cm^{2} \ mol^{-1}$,and $\Lambda^{0}_{KCl} = 150 \ S \ cm^{2} \ mol^{-1}$,then find $\Lambda^{0}_{NaBr}$ in $S \ cm^{2} \ mol^{-1}$.

Consider an electrochemical cell: $A_{(s)} | A^{n+}(aq, 2 \ M) || B^{2n+}(aq, 1 \ M) | B_{(s)}$. The value of $\Delta H^{\ominus}$ for the cell reaction is twice that of $\Delta G^{\ominus}$ at $300 \ K$. If the emf of the cell is zero,the $\Delta S^{\ominus}$ (in $J \ K^{-1} \ mol^{-1}$) of the cell reaction per mole of $B$ formed at $300 \ K$ is. . . . . . . (Given: $\ln(2) = 0.7, R = 8.3 \ J \ K^{-1} \ mol^{-1}$.)

Match List-$I$ with List-$II$.

List-$I$	List-$II$
$A$. $Cd_{(s)} + 2 Ni(OH)_{3(s)} \rightarrow CdO_{(s)} + 2 Ni(OH)_{2(s)} + H_2O_{(l)}$	$I$. Primary battery
$B$. $Zn(Hg) + HgO_{(s)} \rightarrow ZnO_{(s)} + Hg_{(l)}$	$II$. Discharging of secondary battery
$C$. $2 PbSO_{4(s)} + 2 H_2O_{(l)} \rightarrow Pb_{(s)} + PbO_{2(s)} + 2 H_2SO_{4(aq)}$	$III$. Fuel cell
$D$. $2 H_{2(g)} + O_{2(g)} \rightarrow 2 H_2O_{(l)}$	$IV$. Charging of secondary battery

Choose the correct answer from the options given below.

Match the following:

List-$I$	List-$II$
$(A)$ Potential of hydrogen electrode at $pH = 10$	$(I)$ $0.76 \ V$
$(B)$ $Cu^{2+}|Cu$	$(II)$ $0.059$
$(C)$ $Zn|Zn^{2+}$	$(III)$ $-0.591 \ V$
$(D)$ $\frac{2.303RT}{F}$	$(IV)$ $0.337 \ V$
	$(V)$ $-0.76 \ V$

$(a)$ $A-III, B-I, C-II, D-V$
$(b)$ $A-II, B-V, C-I, D-IV$
$(c)$ $A-III, B-IV, C-I, D-II$
$(d)$ $A-V, B-I, C-IV, D-II$

Consider the following two half-cell reactions:
$CO_2 + 6H^+ + 6e^- \rightarrow CH_3OH + H_2O$ $(E^{\ominus} = 0.02 \text{ V})$
$\frac{1}{2}O_2 + 2H^+ + 2e^- \rightarrow H_2O$ $(E^{\ominus} = 1.23 \text{ V})$
$A$ fuel cell was set up such that the cell operates under standard conditions. The fuel cell works with $80\%$ efficiency. If the work derived from the cell using $1 \text{ mol}$ of $CH_3OH$ is used to compress an ideal gas isothermally against a constant pressure of $1 \text{ kPa}$, then the change in the volume of the gas, $\Delta V =$ . . . . . . $\text{m}^3$. (nearest integer) Given: $F = 96500 \text{ C mol}^{-1}$