(a) A junior engineer consultant is hired to design a prototype portable fuel cell based on steam reforming of methanol to produce hydrogen, based in the following chemical reaction, \mathrm{H}_{2}

\mathrm{O}(\mathrm{g})+\mathrm{CH}_{3} \mathrm{OH}(\mathrm{g}) \longleftrightarrow \mathrm{CO}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) The initial gaseous reaction takes place in an adiabatic reactor of 0.5 m3, and the products are driven to a tank for further separation. Thus, for the design of the reactor, the conversion can happen at either 25°C, 45°C or 60°C. Which temperature will yield the best conversion? Justify your answer by calculating the equilibrium constants.[7 marks] where AG 298.15K and AH 298.15K are the standard state Gibbs energy and enthalpy of formation, respectively (b) Calculate the compressibility factor of 1 I mol-1 of cyclopentane at 480 K using the Soave-Redlich-Kwong equation of state. Given:[7 marks] Molar mass: 16.0430 g mol-1; Critical pressure: 45.02 bar; Critical temperature: 511.8 K; Accentric factor: 0.1960 ) For a binary system in VLE at low pressure, composition of the vapour phase yıwith equimolar liquid composition in equilibrium, i.e., [y1, X1 (= X2)] is y_{1}=\frac{P_{1}^{\text {sat }}}{P_{1}^{\text {sat }}+P_{\Omega}^{\text {sat }}} This expression is valid if the Raoult's law stands. Prove that this expression is also valid for the modified Raoult's law y_{i} P=x_{i} \gamma_{i} P_{i}^{\text {sat }} with \ln \gamma_{1}=A x_{2}^{2} \quad \text { and } \quad \ln \gamma_{2}=A x_{1}^{2} where A is a positive constant.