The $EMF$ of a hydrogen electrode in terms of $pH$ is (at $1 \ atm$ pressure).

Find the $emf$ of the following cell reaction,given $E^0_{Cr^{3+}/Cr} = -0.74 \ V$ and $E^0_{Fe^{2+}/Fe} = -0.44 \ V$ at $25^{\circ} C$ for the cell: $Cr \ | \ Cr^{3+}(0.1 \ M) \ || \ Fe^{2+}(0.01 \ M) \ | \ Fe$. (in $V$)

Write a note on the relation between Gibbs free energy and cell potential for a cell reaction.

The standard electrode potential for $Cu^{+2}/Cu$ is $0.34 \ V$. Calculate the reduction potential at $pH = 14$ for the above couple $V$ $[K_{sp}[Cu(OH)_2] = 1 \times 10^{-19}]$

Give the Nernst equation for the following reaction: $M_{(aq)}^{n+} + ne^{-} \to M_{(s)}$

One half cell in a voltaic cell is constructed by dipping a silver rod in an $AgNO_3$ solution of unknown concentration, and the other half cell is a $Zn$ rod dipped in a $1 \text{ M}$ solution of $ZnSO_4$. $A$ voltage of $1.60 \text{ V}$ is measured at $298 \text{ K}$ for this cell. What is the concentration of $Ag^+$ ions in terms of $\log x$ (where $x = [Ag^+]$)? Given: $E^\ominus_{Zn^{2+}/Zn} = -0.76 \text{ V}$, $E^\ominus_{Ag^+/Ag} = +0.80 \text{ V}$, and $\frac{2.303RT}{F} = 0.059 \text{ V}$.