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 $E^o_{Fe^{+2}/Fe} = -0.44 \ V$.

The electrode potential of a chlorine electrode is maximum when the concentration of chloride ion in the solution (in $mol \ L^{-1}$) is $X$. What is the value of $X$?

Calculate the equilibrium constant of the following reaction:
$\text{Cu(s)} + 2\text{Ag}^+_{\text{(aq)}} \rightarrow \text{Cu}^{2+}_{\text{(aq)}} + 2\text{Ag(s)}$,given $E^\circ_{\text{cell}} = 0.46 \text{ V}$.

Write the Nernst equation for the $E_{cell}$ reaction in the Daniell cell. How will the $E_{cell}$ be affected when the concentration of $Zn^{2+}$ ions is increased?

Calculate the cell potential for the reaction $Mg_{(s)} \mid Mg^{2+}(0.18 \ M) \parallel Ag^{+}(0.01 \ M) \mid Ag_{(s)}$. Given standard electrode potentials are $E^{\circ}_{Mg^{2+}/Mg} = -2.37 \ V$ and $E^{\circ}_{Ag^{+}/Ag} = 0.80 \ V$. (in $V$)

Calculate the potential of a hydrogen electrode in contact with a solution whose $pH$ is $10$. (in $V$)