The standard cell potential $E^o$ for the reaction $aA + bB \to cC + dD$ is related to the equilibrium constant $K_c$ by the expression:

$E_{1}$,$E_{2}$ and $E_{3}$ are the emfs of the following three galvanic cells respectively.

What is the reduction potential of a hydrogen gas electrode when pure hydrogen gas is at $1 \ atm$ pressure and the platinum electrode is in contact with an $HCl$ solution of $pH$ $1$ at $298 \ K$ (in $V$)?

The $e.m.f.$ of the following galvanic cells are represented by $E_1, E_2, E_3$ and $E_4$. Which of the following statements is true?
$(i)$ $Zn|Zn^{2+} (1 \, M)||Cu^{2+} (1 \, M)|Cu$
$(ii)$ $Zn|Zn^{2+} (0.1 \, M)||Cu^{2+} (1 \, M)|Cu$
$(iii)$ $Zn|Zn^{2+} (1 \, M)||Cu^{2+} (0.1 \, M)|Cu$
$(iv)$ $Zn|Zn^{2+} (0.1 \, M)||Cu^{2+} (0.1 \, M)|Cu$

Under which of the following conditions is the $E$ value of the cell for the given reaction maximum?
$Zn_{(s)} + Cu^{2+}_{(aq)} \rightleftharpoons Cu_{(s)} + Zn^{2+}_{(aq)}$
$\left( \frac{2.303 RT}{F} \text{ at } 298 \ K = 0.059 \ V, E^{\circ}_{Zn^{2+}/Zn} = -0.76 \ V, E^{\circ}_{Cu^{2+}/Cu} = +0.34 \ V \right)$
Let $[Zn^{2+}] = C_2$ and $[Cu^{2+}] = C_1$.

The equilibrium constant for the following general reaction is $10^{30}$. Calculate $E^o$ for the cell at $298 \ K$.
$2 X_2(s)+3 Y^{2+}(a q) \rightarrow 2 X_2^{3+}(a q)+3 Y(s)$