The equilibrium constant of a $2$ electron redox reaction at $298 \, K$ is $3.8 \times 10^{-3}$. The cell potential $E^{\circ}$ (in $V$) and the free energy change $\Delta G^{\circ}$ (in $kJ \, mol^{-1}$) for this equilibrium,respectively are

Which of the following statements is not correct $:-$

Identify the correct statements from the following:
$(A)$ At $298 \ K$,the potential of a hydrogen electrode placed in a solution of $pH = 10$ is $-0.59 \ V$.
$(B)$ The limiting molar conductivity of $Ca^{2+}$ and $Cl^{-}$ are $119$ and $76 \ S \ cm^2 \ mol^{-1}$ respectively. The limiting molar conductivity of $CaCl_2$ is $195 \ S \ cm^2 \ mol^{-1}$.
$(C)$ The correct relationship between $K_{c}$ and $E_{cell}^{0}$ is $E_{cell}^{0} = \frac{2.303 RT}{nF} \log K_{c}$.

$A$ battery is constructed of $Cr$ and $Na_2Cr_2O_7$. The unbalanced chemical equation when such a battery discharges is: $Na_2Cr_2O_7 + Cr + H^{+} \to Cr^{3+} + H_2O + Na^{+}$. If one Faraday of electricity is passed through the battery during charging,the number of moles of $Cr^{3+}$ removed from the solution is:

The process of rusting of iron occurs as follows:
$Fe \rightarrow Fe^{2+} + 2e^{-}, E^{o} = 0.44 \ V$
$2H^{+} + 2e^{-} + \frac{1}{2} O_2 \rightarrow H_2O_{(l)}, E^{o} = 1.23 \ V$
Then for this reaction,$\Delta G^{o} = .... \ kJ/mol$

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 $K_{sp} = \text{solubility product}$)