Consider the change in oxidation state of Bromine corresponding to different $emf$ values as shown in the diagram below:
$BrO_4^{-}$ $\xrightarrow{1.82 \ V} BrO_3^{-}$ $\xrightarrow{1.5 \ V} HBrO$ $\xrightarrow{1.0652 \ V} Br_2$ $\xrightarrow{1.595 \ V} Br^{-}$
Then the species undergoing disproportionation is:

Match the following columns:

Column-$I$	Column-$II$
$A$. Leclanche cell (Dry cell)	$P$. Converts energy of combustion into electrical energy
$B$. Lead storage battery	$Q$. Reaction at cathode: $O_{2(g)} + 4H^+_{(aq)} + 4e^- \rightarrow 2H_2O_{(\ell)}$
$C$. Fuel cell	$R$. Reaction at cathode: $MnO_2 + NH_4^+ + e^- \rightarrow MnO(OH) + NH_3$
$D$. Rusting	$S$. Reaction at anode: $Pb_{\text{(s)}} + SO_4^{2-}{_{\text{(aq)}}} \rightarrow PbSO_{4\text{(s)}} + 2e^{-}$

The number of incorrect statements from the following is:
$A.$ The electrical work that a reaction can perform at constant pressure and temperature is equal to the reaction Gibbs energy.
$B.$ $E_{cell}^0$ is dependent on the pressure.
$C.$ $\frac{dE_{cell}^0}{dT} = \frac{\Delta_{r}S^0}{nF}$.
$D.$ $A$ cell is operating reversibly if the cell potential is exactly balanced by an opposing source of potential difference.

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 $390.5 \, S \, cm^2 \, mol^{-1}$.

The values of the limiting molar conductivity $(\lambda^0)$ for $NaCl$,$HCl$ and $NaOAc$ are $126.4$,$425.9$ and $91.0 \, S \, cm^2 \, mol^{-1}$,respectively. For $HOAc$,$\Lambda^0$ in $S \, cm^2 \, mol^{-1}$ is

Given ${E^o}_{Ag^{+}/Ag} = 0.80 \ V$,${E^o}_{Mg^{2+}/Mg} = -2.37 \ V$,${E^o}_{Cu^{2+}/Cu} = 0.34 \ V$,${E^o}_{Hg^{2+}/Hg} = 0.79 \ V$.
Which of the following statements is correct?