For a spontaneous reaction,determine the values of $\Delta G^o$,equilibrium constant $K$,and $E^o_{cell}$ respectively.

For the reaction $4B_{(s)} + 3O_{2(g)} \rightarrow 2B_2O_{3(g)}$,the standard cell potential is $E^o_{cell} = 1.433 \ V$. Calculate the molar entropy $(S_m^o)$ of oxygen gas in $J/K \ mol$.
Given:
$(\Delta_fH^o)_{B_2O_3(g)} = -840 \ kJ/mol$
$(S_m^o)_{B_2O_3(g)} = 280 \ J/K \ mol$
$(S_m^o)_{B(s)} = 10 \ J/K \ mol$
Assume $\Delta_rG^o = -nFE^o_{cell}$ and $\Delta_rG^o = \Delta_rH^o - T\Delta_rS^o$ at $T = 298 \ K$.

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.

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: $F = 96500 \text{ C mol}^{-1}$

The molar conductivity of $0.027 \ M$ methanoic acid is $40.42 \ S \ cm^2 \ mol^{-1}$. The value of dissociation constant of this acid is
(Given $\lambda_{H^{+}}^{\circ} = 349.6 \ S \ cm^2 \ mol^{-1}$ and $\lambda_{HCOO^{-}}^{\circ} = 54.6 \ S \ cm^2 \ mol^{-1}$)

The conductivity of $0.001028 \, mol \, L^{-1}$ acetic acid is $4.95 \times 10^{-5} \, S \, cm^{-1}$. Calculate its dissociation constant if $\Lambda_m^\circ$ for acetic acid is $390.5 \, S \, cm^2 \, mol^{-1}$.