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.

Which one of the following statements is correct?

Copper reduces $NO_{3}^{-}$ into $NO$ and $NO_{2}$ depending upon the concentration of $HNO_{3}$ in solution. Assuming fixed $[Cu^{2+}]$ and $P_{NO} = P_{NO_{2}} = 1 \ bar$,the $HNO_{3}$ concentration at which the thermodynamic tendency for reduction of $NO_{3}^{-}$ into $NO$ and $NO_{2}$ by copper is the same is $10^{x} \ M$. The value of $2x$ is ...... .
$[Given: E_{Cu^{2+} / Cu}^{\circ} = 0.34 \ V, E_{NO_{3}^{-} / NO}^{\circ} = 0.96 \ V, E_{NO_{3}^{-} / NO_{2}}^{\circ} = 0.79 \ V$ and at $298 \ K, \frac{RT}{F}(2.303) = 0.059]$

$Cu^{+}$ 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 equilibrium constant for the reaction: $Cl_{2(g)} + 2I^{-}_{(aq)} \to 2Cl^{-}_{(aq)} + I_{2(s)}$
Given: $E^o_{(Cl_2|2Cl^{-})} = 1.36 \ V$ and $E^o_{(I_2|2I^{-})} = 0.536 \ V$.

$A$ battery is made from $Cr$ and $Na_2Cr_2O_7$. When this battery discharges according to the reaction $Na_2Cr_2O_7 + Cr + H^{+} \rightarrow Cr^{3+} + H_2O + Na^{+}$,the chemical equation is unbalanced. If $1 \ F$ (Faraday) of electricity is passed during the charging of the battery,what is the number of moles of $Cr^{3+}$ removed from the solution (in $/3$)?