Consider the following data.

Electrolyte	$\Lambda_m^\circ$ $(S\text{ cm}^2\text{ mol}^{-1})$
$BaCl_2$	$x_1$
$H_2SO_4$	$x_2$
$HCl$	$x_3$

$BaSO_4$ is sparingly soluble in water. If the conductivity of the saturated $BaSO_4$ solution is $x\text{ S cm}^{-1}$, then the solubility product of $BaSO_4$ can be given as (Here $\Lambda_m = \Lambda_m^\circ$)

$Cu^{+}$ ion is not stable in aqueous solution because of disproportionation reaction. $E^o$ value for disproportionation of $Cu^{+}$ is .............. $V$ (Given $E^o_{Cu^{2+}/Cu^{+}} = 0.15 \ V$,$E^o_{Cu^{2+}/Cu} = 0.34 \ V$)

Calculate the standard cell potentials of galvanic cells in which the following reactions take place:
$(i)$ $2Cr_{(s)} + 3Cd^{2+}_{(aq)} \rightarrow 2Cr^{3+}_{(aq)} + 3Cd_{(s)}$
$(ii)$ $Fe^{2+}_{(aq)} + Ag^{+}_{(aq)} \rightarrow Fe^{3+}_{(aq)} + Ag_{(s)}$
Calculate the $\Delta_r G^\Theta$ and equilibrium constant of the reactions.

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:

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

Consider the following electrochemical cell at standard condition: $Au_{(s)} | QH_2, Q | NH_4X(0.01 \ M) || Ag^{+}(1 \ M) | Ag_{(s)}$. Given $E_{\text{cell}} = +0.4 \ V$. The couple $QH_2 / Q$ represents the quinhydrone electrode,and the half-cell reaction is given as: $Q + 2e^- + 2H^+ \rightarrow QH_2$ with $E^o_{Q/QH_2} = +0.7 \ V$. Given: $E^o_{Ag^+/Ag} = +0.8 \ V$ and $\frac{2.303 \ RT}{F} = 0.06 \ V$. The $pK_b$ value of the ammonium halide salt $(NH_4X)$ used here is $.........$ (nearest integer).