Calculate the potential of the half cell containing $0.1\mathrm{M} {\mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7\left(\mathrm{aq}\right), 0.2\mathrm{M} {\mathrm{Cr}}^{3+}\left(\mathrm{aq}\right) \mathrm{and} 1.0\times {10}^{-4}\mathrm{M} {\mathrm{H}}^{+}.$ The half cell reaction is

${\mathrm{Cr}}_2{{\mathrm{O}}_7}^{2-} \left(\mathrm{aq}\right) + 14{\mathrm{H}}^{+}\left(\mathrm{aq}\right) +6{\mathrm{e}}^{-} \to 2{\mathrm{Cr}}^{3+}\left(\mathrm{aq}\right) + 7{\mathrm{H}}_2\mathrm{O}$,   ${\mathrm{E}}_{\mathrm{cell}}^{\mathrm{o}} = 1.33\mathrm{V}$.

Calculate ${\mathrm{K}}_{\mathrm{c}}$ for the reaction at 298K  $\mathrm{Zn}\left(\mathrm{s}\right) + {\mathrm{Cu}}^{2+} \left(\mathrm{aq}\right) \rightleftharpoons {\mathrm{Zn}}^{2+}\left(\mathrm{aq}\right) + \mathrm{Cu}\left(\mathrm{s}\right)$

$∆{\mathrm{G}}^{\mathrm{o}} =-212.30 \mathrm{kJ}/\mathrm{mole}, {\mathrm{E}}_{{\mathrm{Zn}}^{2+}/\mathrm{Zn}}^{\mathrm{o}} =-0.76\mathrm{V}, {\mathrm{E}}_{{\mathrm{Cu}}^{2+}/\mathrm{Cu}}^{\mathrm{o}} =0.34\mathrm{V}$

Calculate the emf of the cell at 298K  $\mathrm{Sn}\left(\mathrm{s}\right)/{\mathrm{Sn}}^{2+}\left(0.05\mathrm{M}\right)//{\mathrm{H}}^{+}\left(0.02\mathrm{M}\right)/{\mathrm{H}}_2 1\mathrm{atm}.\mathrm{pt}$

Given that ${\mathrm{E}}_{{\mathrm{sn}}^{2+}/\mathrm{sn}}^{\mathrm{o}} = -0.144\mathrm{V}$

Calculate the emf of the cell with the cell reaction

 $\mathrm{Ni} + 2{\mathrm{Ag}}^{+} \left(0.002\mathrm{M}\right) \to {\mathrm{Ni}}^{2+}\left(0.160\mathrm{M}\right) + 2\mathrm{Ag}; {\mathrm{E}}_{\mathrm{cell}}^{\mathrm{o}} = 1.05\mathrm{V}$ 

$$\begin{gathered} {\mathrm{Cu}}^{2+} + 2{\mathrm{e}}^{-} \rightleftharpoons \mathrm{Cu} ; {\mathrm{E}}^{\mathrm{o}} = +0.34\mathrm{V} \\ {\mathrm{Ag}}^{+} + {\mathrm{e}}^{-} \rightleftharpoons \mathrm{Ag} ; {\mathrm{E}}^{\mathrm{o}} = +0.80\mathrm{V} \end{gathered}$$

For what concentration of ${\mathrm{Ag}}^{+}$ ions will be the emf of the cell be zero at 25^oC. The concentration of ${\mathrm{Cu}}^{2+}$ is $0.1\mathrm{M}$. $\left(\log 3.919 =0.593 \right)$

Calculate the degree of dissociation $\left(\mathrm{\alpha }\right)$ of ${\mathrm{CH}}_3\mathrm{COOH}$ at $298\mathrm{K}$. Given that

$$\begin{gathered} {{\mathrm{\Lambda }}^{\mathrm{m}}}_{{\mathrm{CH}}_3\mathrm{COOH}} = 11.75 {\mathrm{cm}}^2 {\mathrm{mol}}^{-1} \\ {\mathrm{\Lambda }}_{{\mathrm{CH}}_3{\mathrm{COO}}^{-}}^{\mathrm{o}} = 40.95 {\mathrm{cm}}^2 {\mathrm{mol}}^{-1} \\ {\mathrm{\Lambda }}_{{\mathrm{H}}^{+}}^{\mathrm{o}} = 349.15 {\mathrm{cm}}^2 {\mathrm{mol}}^{-1} \end{gathered}$$