Examine the above diagram. It is one method of production of methanol $($CH$3$OH$)$ using carbon

monoxide and hydrogen. The feed is contaminated with nitrogen.

CO$+2$ H$2$CH$3$ OH

The reaction products out of the reactor $($stream $3)$ are at equilibrium such that the equilibrium constant

Keq $=3\mathrm{.}25\backslash$times $106$ mol$-2($based on moles$)$ is expressed as:

The single pass conversion for hydrogen to methanol is $5\%$ on one$-$pass through the reactor. All the

unreacted hydrogen and carbon dioxide is separated from the reactor effluent and recycled. None of the

methanol formed is recycled. The outlet gases from the separator are at $95$ oC and $1$ atm immediately

on exit from the separator. In order to avoid a built$-$up of inert N$2,$ the recycled stream is purged. The

Keq$=[$CH $3$ OH $]$

$[$CO $][$ H$2]2$

composition of the fresh feed and amount of purged hydrogen are given. Using the information

provided, compute the following:

$($a$)$ Total moles purged $($stream $6)(5$ points$)$

$($b$)$ Extent of the reaction $(5$ points$)$

$($c$)$ Composition of the recycled stream $($Stream $7)(15$ points$)$

$($d$)$ Overall conversion of CO $(10$ points$)$

$($e$)$ Single pass conversion of CO $(10$ points$)$

$($f$)$ ratio of the recycled stream to the fresh feed $($recycle ratio$)(15$ points$)$

$($g$)$ Overall conversion of Hydrogen $(10$ points$)$