The Haber$-$Bosch process is used industrially to synthesize ammonia $($a fertilizer$)$

from the metal$-$catalyzed reaction of gaseous nitrogen and hydrogen. This process was first

developed in Germany in the early $20$th century and sustained German agriculture and food supply

during World War I. Fritz Haber and Carl Bosch later received the Nobel Prize in Chemistry in

$1918$ and $1931,$ respectively.

For this problem, consider the hypothetical $($uncatalyzed$)$ gas$-$phase reaction of nitrogen and

hydrogen:

N$2$

$+3$H$2$

$2$NH$3$

This reaction is to be carried out in an isothermal and isobaric CSTR$.$ The feed stream is $50$ mol$\%$

H$2$ and $50$ mol$\%$ N$2,$ at a pressure of $16\mathrm{.}4$ atm and $500$ K$.$

$($a$)$ Construct a complete stoichiometric table, choosing the limiting reactant as the basis $($A$),$

the other co$-$reactant as B$,$ and the product as C$.$

Species Fj$0$Fj

Fj cj $=$ Fj $/$ v

$($b$)$ Assume that the reaction, as written, is an elementary step with k $=10$ dm$9$ mol$-3$

s

$-1$

$.$

Calculate the conversion in an isobaric CSTR with a $50$ s residence time