The standard $e.m.f.$ of a cell,involving one electron change is found to be $0.591 \ V$ at $25^{\circ} C$. The equilibrium constant of the reaction is :
$(F=96500 \ C \ mol^{-1} ; R=8.314 \ JK^{-1} \ mol^{-1})$

At $298 \ K$, the $emf$ of the cell is ............ $V$.
$Pt | H_{2(2 \ atm)} | H_{(0.02 \ M)}^{+} || H_{(0.1 \ M)}^{+} | H_{2(1 \ atm)} | Pt$

For the electrochemical cell shown below:
$Pt \mid H_{2}(p=1 \, atm) \mid H^{+}(aq., x \, M) \mid\mid Cu^{2+}(aq., 1.0 \, M) \mid Cu_{(s)}$
The potential is $0.49 \, V$ at $298 \, K$. The $pH$ of the solution is closest to:
[Given: Standard reduction potential,$E^{\circ}$ for $Cu^{2+}/Cu$ is $0.34 \, V$; Gas constant,$R = 8.31 \, J \, K^{-1} \, mol^{-1}$; Faraday constant,$F = 9.65 \times 10^{4} \, J \, V^{-1} \, mol^{-1}$]

The cell potential for the following reaction is $0.03305 \ V$ at $298 \ K$. Find the value of $x$ for the reaction: $Zn | Zn^{2+} (0.1 \ M) || Cd^{2+} (x \ M) | Cd$. (Given: $E^{\circ}_{Zn^{2+}/Zn} = -0.76 \ V$,$E^{\circ}_{Cd^{2+}/Cd} = -0.40 \ V$) (in $M$)

At $298 \, K$,find out the $emf$ for the cell: $Al_{(s)} | Al^{+3} (0.1 \, M) || Fe^{+2} (0.001 \, M) | Fe_{(s)}$. Given $E^o_{Al^{+3}/Al} = -1.66 \, V$ and $E^o_{Fe^{+2}/Fe} = -0.44 \, V$. (in $, V$)

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$(s)$.