At $T(K)$,the molar conductivity of $0.04 \ M$ acetic acid is $7.8 \ S \ cm^2 \ mol^{-1}$. If the limiting molar conductivities of $H^{+}$ and $CH_3COO^{-}$ at $T(K)$ are $349$ and $41 \ S \ cm^2 \ mol^{-1}$ respectively,the dissociation constant of acetic acid is

During electrolysis of aqueous $NaOH$,$4 \ g$ of $O_2$ gas is liberated at $NTP$ at the anode. The volume of $H_2$ gas liberated at the cathode in $litres$ is $..............$

Consider the following statements pertaining to fuel cells :-
$(a)$ Hydrogen-oxygen fuel cells make use of concentrated $KOH$ solution as an electrolyte and porous graphite impregnated with platinum as electrodes.
$(b)$ The efficiency of a fuel cell is less than unity due to polarization at electrodes and the resistance offered by the electrode and the electrolyte.
$(c)$ The electrical work,assuming the cell to be working reversibly,may be represented as $-\Delta G = W_{\text{electrical}} = -\Delta H + T\Delta S$.
Which of the above statements are correct?

The standard electrode potential $E^{\ominus}$ and its temperature coefficient $\left( \frac{dE^{\ominus}}{dT} \right)$ for a cell are $2 \ V$ and $-5 \times 10^{-4} \ V \ K^{-1}$ at $300 \ K$ respectively. The cell reaction is
$Zn_{(s)} + Cu^{2+}_{(aq)} \rightleftharpoons Zn^{2+}_{(aq)} + Cu_{(s)}$
Standard reaction enthalpy $\left( \Delta_r H^{\ominus} \right)$ is ....... $kJ$

At $25^\circ \text{C}$,given the following data: $Ag_{(s)} + I^-_{(aq)} \rightarrow AgI_{(s)} + e^-$,$E^o = 0.152 \ V$; $Ag_{(s)} \rightarrow Ag^+_{(aq)} + e^-$,$E^o = -0.800 \ V$. What is the value of $\log \ K_{sp}$ for $AgI$? (where $K_{sp} = \text{solubility product}$)

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

List-$I$ (Conversion)	List-$II$ (Number of Faraday required)
$A$. $1 \ mol$ of $H_2O$ to $O_2$	$I$. $3 \ F$
$B$. $1 \ mol$ of $MnO_4^{-}$ to $Mn^{2+}$	$II$. $2 \ F$
$C$. $1.5 \ mol$ of $Ca$ from molten $CaCl_2$	$III$. $1 \ F$
$D$. $1 \ mol$ of $FeO$ to $Fe_2O_3$	$IV$. $5 \ F$

Choose the correct answer from the options given below: