Methanol $(C{H}_{3}OH)$ is produced by the reaction of carbon dioxide $(C{O}_2)$ and hydrogen $(H_2).$ The feed to the reactor is made up of $30\%$ by volume $CO2$ and $70\%$ by volume $H2$ where a fractional conversion of the hydrogen of $0\mathrm{.}60$ is achieved. The product gas consisting of methanol and water, and unreacted hydrogen and carbon dioxide is passed to a condenser which separates the products of the reaction from the unreacted gases.

a$.$ Write down a balanced stoichiometric equation for the above reaction.

$5\%$

b$.$ Prepare a neat process flow diagram and fill in all of the known$/$unknown flow rates and compositions.

$5\%$

c$.$ Conduct a Degree$-$of$-$Freedom analysis on the reactor, condenser and overall process and show that it is necessary to specify one other process variable to allow you to balance the PFD$.$

$20\%$

d$.$ Assuming a basis of $100mo\frac{l}{h}$ feed to the reactor determine the flow rates and compositions of all streams in the process.

$30\%$

e$.$ Express the composition of the exit gas stream from the reactor in mass fractions.

f$.$ The single pass mode of operation is very wasteful of the feed

$10\%$ gases. If the exit gas from the condenser is recycled and mixed with a fresh feed stream such that the reactor feed stream remains unchanged, determine the molar flow rate and composition of the fresh feed to the process.

$20\%$

g$.$ What modification to the process described in $($f$)$ would be required if the input stream contained $0\mathrm{.}004\%$ by volume of an inert gas.

$5\%$

h$.$ If it is required to design a process to produce $160$kmo$\frac{l}{h}$ of methanol what quantity of fresh feed gas would be required.

$[5\%]$