Problem $3$:

Ammonia is an important starting product for fertilizers but also pharmaceuticals. In the famous Haber

process ammonia is produces from Nitrogen and Hydrogen according to:

$H_2+N_{2}N{H}_3$

Only a small fraction of the material entering the reactor reacts in one pass, so a recycle reactor is

needed. The reactor consists of a mixer, a reactor and a separator, which is able to remove all of the

produced ammonia from the mixture leaving the reactor. Since the reacting nitrogen is obtained from

the air it contains a small amount of rare gases $($mostly Argon, Ar$)$ that do not react. The rare gases

would continue to build up in the reactor until their effect on the reaction equilibrium becomes adverse,

so a splitter is introduced between the separator and the mixer allowing the purge $($release$)$ of a small

amount of gas.

The fresh feed of case is composed of $75\mathrm{.}16\%H_2,24\mathrm{.}57\%N_2$ and $0\mathrm{.}27\%$ Ar$.$ It is mixed with the recycled

gas and enters the reactor with a composition of $79\mathrm{.}52\%$ of $H2.$ The purge stream leaving the reactor

contains $80\mathrm{.}01\%H_2,$ argon and nitrogen but no ammonia. The product ammonia contains no dissolved

gases.

For a basis of $100\mathrm{.}00$mol of fresh feed:

How many moles are recycled and purged?

What is the single pass and the overall conversion?