Group $8$

In the process of methanol production, a gas stream containing $40$mol$\%C{O}_2,$

$60$mol$\%H_2$ is fed to the reactor. The product from the reactor is condensed

where liquid methanol is separated using distillation column. Unreacted gases

are recycle in a ratio of $3$:$2$mol of recycle to moles of fresh feed. Parts of the

recycled gases are purged from the process. $90\%$ of the purified methanol can

be achieved from this process with the overall conversion of $85\%$ from the fed

gas. Recycling the unreacted gases can improve the methanol conversion to

$80\%-100\%$ although one pass of reactant gas has about $25\%$ conversion.

How much methanol is produced and what is the amount of recycle and purge

gases from this process? The reaction equation is $C{O}_2+3H_{2}C{H}_{3}OH+H_{2}O.$help