In the famous Haber process to manufacture ammonia, the reaction $3H_2+N_{2}N{H}_3$ is carried out at pressures of $800$ to $1000$atm and at $500C$ to $600C$ using a suitable catalyst. The fresh feed of gas composed of $75\mathrm{.}16$mol$\%H2,24\mathrm{.}57$mol$\%N2,$ and $0\mathrm{.}27$mol$\%Ar$ is mixed with the recycled gas and enters the reactor with a composition of $79\mathrm{.}52$ mol$\%H2.$ The stream leaving the reactor is separated. The gas stream leaving the separator contains $80\mathrm{.}01$mol$\%H2$ and no ammonia. The product ammonia contains no dissolved gases. Per $100$ moles of fresh feed:

a$.$ How many moles are recycled and purged?

b$.$ What is the single$-$pass conversion of the limiting reactant?

Please show how you got Purge stream $!!!!!!$