(a) Define the fuel cell. Give the basic construction of the cell.

(b) In a laboratory investigation, ethanol is esterified to produce ethyl acetate and water at \(100^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) pressure according to the following equation:
\[ \mathrm{CH}_{3} \mathrm{COOH}(\mathrm{l})+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{l})=\mathrm{CH}_{3} \mathrm{COOC}_{2} \mathrm{H}_{5}(\mathrm{l})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \]
What is the equilibrium constant for the reaction at \(100^{\circ} \mathrm{C}\) ? What is the composition of the reaction mixture if initially one mol each of acetic acid and ethanol are present? The data given for the reaction are \(\Delta G_{298}^{0}=1160 \mathrm{cal}\) and \(\Delta H_{298}^{0}=1713\) cal.

(c) A system consisting of \(2 \mathrm{~mol}\) methane and \(3 \mathrm{~mol}\) water is undergoing the following reaction:
\[ \begin{align*} \mathrm{CH}_{4}+\mathrm{H}_{2} \mathrm{O} & \rightarrow \mathrm{CO}+3 \mathrm{H}_{2} \tag{A}\\ \mathrm{CH}_{4}+2 \mathrm{H}_{2} \mathrm{O} & \rightarrow \mathrm{CO}_{2}+4 \mathrm{H}_{2} \tag{B} \end{align*} \]
Derive expressions for mole fractions in terms of the extent of reaction.