Methanol may be produced by the reaction of carbon dioxide and hydrogen:

$C{O}_2+3H_{2}C{H}_{3}OH+H_{2}O$

In the process depicted below, the fresh feed $(1)$ contains hydrogen, carbon dioxide and inerts in the composition listed in the table below. The reactor effluent $(3)$ passes through a condenser, which removes essentially all of the methanol and water formed. These products exit through stream $(7)$ with no reactants or inerts. The reactants and inerts are recycled to the reactor $(6).$ To avoid buildup of the inerts inn the system, $17\mathrm{.}2\%$ of stream $(4)$ is withdrawn from the recycle as a purge stream $(5).$ The global conversion is $90\%.$ Answer the questions below for a production of $1000$ lbmo$\frac{l}{h}$ of methanol.

a$)$ Which is the limiting reactant? $(5$pts$)$

b$)$ Fill the table below with the molar compositions and flow rates of all the streams $(25pts)$

c$)$ What is the per pass conversion? $(5$pts$)$

$\backslash$table$[[lbmo\frac{l}{h},,C{O}_2,H_2,C{H}_{3}OH,H_{2}O,$Inerts,Total$],[1,y,0\mathrm{.}2488,0\mathrm{.}7464,,,,],[F,,,,,,],[3,y,,,,,,],[F,,,,,,],[4,F,,,,,,],[y,,,,,,],[,F,,,,,,],[6,y,,,,,,],[,,,,,,],[,F,,,,,,],[,y,,,,,,],[,F,,,,,,]]$