(a) (i) State Kohlrausch's law of independent migration of ions. Write an expression for the limiting molar conductivity of acetic acid according to Kohlrausch's law. (ii) Calculate the maximum work and $\log K_c$ for the given reaction at $298 \text{ K}$: $\text{Ni (s)} + 2\text{Ag}^+ \text{(aq)} \rightleftharpoons \text{Ni}^{2+} \text{(aq)} + 2\text{Ag (s)}$ Given: $E^\circ_{\text{Ni}^{2+}/\text{Ni}} = -0.25 \text{ V}$, $E^\circ_{\text{Ag}^+/\text{Ag}} = +0.80 \text{ V}$, $1 \text{ F} = 96500 \text{ C mol}^{-1}$. OR (b) (i) State Faraday's first law of electrolysis. How much charge, in terms of Faraday, is required for the reduction of $1 \text{ mol Cu}^{2+}$ to $\text{Cu}$? (ii) Calculate emf of the following cell at $298 \text{ K}$ for $\text{Mg (s)} \mid \text{Mg}^{2+} (0.1 \text{ M}) \parallel \text{Cu}^{2+} (0.01 \text{ M}) \mid \text{Cu (s)}$ $[E^\circ_{\text{cell}} = +2.71 \text{ V}, 1 \text{ F} = 96500 \text{ C mol}^{-1}, \log 10 = 1]$