The $E^o$ for the cell $Zn|Zn^{2+}_{(aq)}||Cu^{2+}_{(aq)}|Cu$ is $1.10 \ V$ at $25 \ ^oC$. The equilibrium constant for the reaction $Zn + Cu^{2+}_{(aq)} \rightleftharpoons Cu + Zn^{2+}_{(aq)}$ is of the order of:

Which of the following relations represents the correct relation between standard electrode potential and equilibrium constant?
$I$. $\log K = \frac{nF E^o}{2.303 RT}$
$II$. $K = e^{\frac{nF E^o}{RT}}$
$III$. $\log K = -\frac{nF E^o}{2.303 RT}$
$IV$. $\log K = 0.4342 \frac{nF E^o}{RT}$
Choose the correct statement$(s)$.

For the reaction $Cr_{2}O_{7}^{2-} + 14H^{+} + 6e^{-} \rightarrow 2Cr^{3+} + 7H_{2}O$,the standard electrode potential is $E^{\circ} = 1.33 \ V$. Given the concentrations $[Cr_{2}O_{7}^{2-}] = 4.5 \ mmol$,$[Cr^{3+}] = 15 \ mmol$,and the cell potential $E = 1.067 \ V$,the $pH$ of the solution is nearly equal to:

For the cell,$Mn_{(s)}|Mn_{(aq)}^{2+}(0.4\,M)||Sn_{(aq)}^{2+}(0.04\,M)|Sn_{(s)}$,calculate the free energy change $(\Delta G)$ at $298\,K$ in $kJ$.
Given: $E_{Mn^{2+}|Mn}^o = -1.18\,V$; $E_{Sn^{2+}|Sn}^o = -0.14\,V$; $\frac{2.303\,RT}{F} = 0.06$

The standard e.m.f. of a cell,involving one electron change,is found to be $0.591 \ V$ at $25 \ ^oC$. The equilibrium constant of the reaction is: $(F = 96,500 \ C \ mol^{-1}; R = 8.314 \ J \ K^{-1} \ mol^{-1})$

At a temperature of $298 \ K$, the $emf$ of the following electrochemical cell: $Ag_{(s)} | Ag^{+}(0.1 \ M) || Zn^{2+}(0.1 \ M) | Zn_{(s)}$ will be (Given, $E^{\circ}_{cell} = -1.562 \ V$) (in $V$)