91Ó°ÊÓ

Derive a general relation for the pressure tipendence of the emf of an clectrichemical cell at constant temperature. Show that for the celi whose diagrarn is \(\mathrm{Pl}(\mathrm{s})\left|\mathrm{H}_{2}(\mathrm{~g})\right| \mathrm{HCl}(\mathrm{aq})|\mathrm{AgCl}(\mathrm{s})| \mathrm{Ag}(\mathrm{s})\) that $$ \left(\frac{\partial E}{\partial}\right)_{T}=-\frac{2\left(\bar{V}_{\mathrm{HCO}}+\bar{V}_{A B}\right)-\left(\bar{V}_{\mathrm{H}_{2}}+2 \bar{V}_{\mathrm{ABC}_{\mathrm{O}}}\right)}{F} $$ where \(\bar{V}_{\mathrm{HCt}}\) is the partial molar volume of the \(\mathrm{HCl}(\mathrm{aq})\) at molality \(m, \bar{V}_{\mathrm{H}_{2}}\) is the partial molar volume of \(\mathrm{H}_{2}(\mathrm{~g})\) at pressure \(P\), and \(\bar{V}_{\mathrm{Al}}\) and \(\bar{V}_{A \mathrm{Ag} \mathrm{l}}\) are the molar volumes of \(A \mathrm{~g}(\mathrm{~s})\) and \(\mathrm{AgCl}(\mathrm{s})\). Argue that at relatively low pressures $$ E_{2}-E_{1} \approx \frac{R T}{2 F} \operatorname{in} \frac{P_{2}}{P_{1}} $$ where \(E_{f}\) is the emf of the cell at pressure \(P_{f}\).

Given that $$ \begin{array}{ll} \mathrm{Hg}_{2}^{21}(\mathrm{aq})+2 e^{-} \longrightarrow 21 ! g(\mathrm{l}) & E^{\jmath}=+0.796 \mathrm{~V} \\ 2 \mathrm{Hg}^{2-}(\mathrm{aq})+2 e^{-} \longrightarrow \operatorname{lig}_{2}^{2+}(\mathrm{aq}) & E^{\kappa}=+0.907 \mathrm{~V} \end{array} $$ calculate the value of \(E\) for $$ \mathrm{Hg}^{21}(\mathrm{ag})+2 e \longrightarrow \mathrm{Hg}(\mathrm{l}) $$

Given that $$ \begin{array}{ll} \mathrm{Cr}^{3}(\mathrm{aq})+2 e^{-} \rightarrow \mathrm{Cr}(\mathrm{s}) & E^{n}=-0.91 \mathrm{~V} \\ \mathrm{Cr}^{3+}(\mathrm{aq})+e^{-} \longrightarrow \mathrm{Cr}^{21}(\mathrm{aq}) & E^{e}=-0.41 \mathrm{~V} \end{array} $$ calculate the value of \(E^{5}\) for $$ \mathrm{Cr}^{3+}(\mathrm{aq})+3 e^{\cdot} \rightarrow \mathrm{Cr}(\mathrm{s}) $$