(a) (i) Calculate the emf of the following cell at 298 K: Al ( s )| Al^3+(0.001 M ) ∥ Ni^2+(0.1 M )| Ni ( s ); [ Given: E_Al^°^3+ / Al =-1.66 V,…

Calculate the emf of the following cell at $\displaystyle 298$ K : \[\begin{aligned} & \mathrm{Al}(\mathrm{~s})\left|\mathrm{Al}^{3+}(0.001 \mathrm{M}) \| \mathrm{Ni}^{2+}(0.1 \mathrm{M})\right| \mathrm{Ni}(\mathrm{~s}) \\ & {\left[\text { Given }: \mathrm{E}_{\mathrm{Al}^{\circ}}{ }^{3+} / \mathrm{Al}=-1.66 \mathrm{~V}, \mathrm{E}_{\mathrm{Ni}^{2+} / \mathrm{Ni}}^{\circ}=-0.25 \mathrm{~V}, \log 10=1\right]} \end{aligned} \]

With the help of a graph explain why it is not possible to determine $\displaystyle \mathbf{\Lambda}_{\mathrm{m}}^{\circ}$ for a weak electrolyte by extrapolating the molar conductivity $\displaystyle \left(\mathbf{\Lambda}_{\mathrm{m}}\right)$ versus $\displaystyle \mathrm{C}^{1 / 2}$ curve as for strong electrolyte.

The molar conductivities of $\displaystyle \mathrm{NH}_{4}^{+}$and $\displaystyle \mathrm{Cl}^{-}$ion are $\displaystyle 73.8 \mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}$ and $\displaystyle 76.2 \mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}$ respectively. The conductivity of $\displaystyle 0.1 \mathrm{M} \mathrm{NH}_{4} \mathrm{Cl}$ is $\displaystyle 1.29 \times 10^{-2} \mathrm{~S} \mathrm{~cm}^{-1}$. Calculate its molar conductivity and degree of dissociation.

Calculate the half-cell potential at $\displaystyle 298$ K for the reaction \[\mathrm{Zn}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Zn} \] if $\displaystyle \left[\mathrm{Zn}^{2+}\right]=0.1 \mathrm{M}$ and $\displaystyle \mathrm{E}_{\mathrm{Zn}^{2+} / \mathrm{Zn}}^{\circ}=-0.76 \mathrm{~V}$.