Consider the cell reaction at $300 \ K$: $A_{(s)} + B^{2+}_{(aq)} \rightleftharpoons A^{2+}_{(aq)} + B_{(s)}$. Its $E^{\circ}$ is $1.0 \ V$. The $\Delta_{r}H^{\circ}$ of the reaction is $-163 \ kJ \ mol^{-1}$. What is $\Delta_{r}S^{\circ}$ (in $J \ K^{-1} \ mol^{-1}$) of the reaction? $(F = 96500 \ C \ mol^{-1})$

During the discharging of a lead storage cell,the concentration of $H_2SO_4$ reduces from $40\% \ w/w$ to $30\% \ w/w$. Find the total charge produced in $faraday$. Given the volume of the solution $= 4.9 \ L$ and density $= 1.2 \ g/mL$. (Assume volume and density remain constant)

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 $\lambda_{HCOO^{-}}^{\circ} = 54.6 \ S \ cm^2 \ mol^{-1}$)

Given below are two statements:
Statement $I$: For $KI$,molar conductivity increases steeply with dilution.
Statement $II$: For carbonic acid,molar conductivity increases slowly with dilution.
In the light of the above statements,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 a $70 \%$ efficient hydrogen-oxygen fuel cell working under standard conditions at $1 \ bar$ and $298 \ K$. Its cell reaction is
$H_{2(g)} + \frac{1}{2} O_{2(g)} \rightarrow H_2O(\ell)$
The work derived from the cell on the consumption of $1.0 \times 10^{-3} \ mol$ of $H_{2(g)}$ is used to compress $1.00 \ mol$ of a monoatomic ideal gas in a thermally insulated container. What is the change in the temperature (in $K$) of the ideal gas?
The standard reduction potentials for the two half-cells are given below.
$O_{2(g)} + 4H^{+}(aq.) + 4e^- \rightarrow 2H_2O(\ell), E^{\circ} = 1.23 \ V$
$2H^{+}(aq.) + 2e^- \rightarrow H_{2(g)}, E^{\circ} = 0.00 \ V$
Use $F = 96500 \ C \ mol^{-1}, R = 8.314 \ J \ mol^{-1} \ K^{-1}$