Ammonia is produced in the gas phase reaction:

N$2+3$h$2$ forms $2$NH$3$

With the stream table shown below:

$\backslash$table$[[$Stream$,\backslash$table$[[$N$\_(2)],[($molN$\_(2)/$s$)]],\backslash$table$[[$H$\_(2)],[(($molH$)$H$\_(2)/$s$)]],\backslash$table$[[$NH$\_(3)],[($moll$^(\text{'})$NH$\_(3)/$s$)]]],[1,250,750,0],[2,$n$^()\_(2$N$\_(2)),$n$^()\_(2$H$\_(2)),$n$^()\_(2$NH$\_(3))],[3,$n$^()\_(3$N$\_(2)),$n$^()\_(3$H$\_(2)),$n$^()\_(3$NH$\_(3))],[4,0,0,360],[5,$n$^()\_(5$N$\_(2)),$n$^()\_(5$H$\_(2)),$n$^()\_(5$NH$\_(3))],[6,$n$^()\_(6$N$\_(2)),$n$^()\_(6$H$\_(2)),$n$^()\_(6$NH$\_(3))],[7,$n$^()\_(7$N$\_(2)),$n$^()\_(7$H$\_(3)),$n$^()\_(7$H$\_(3))]]$

Additionally, you know:

The process and $80\%$ overall conversion of nitrogen.

For every $100$ moles recycled, $12$ moles are purged

a$)$ Perform a degree of freedom analysis on the following system boundaries: Overall system, recycle mix point, and the purge split point. Then specify the order these system boundaries must be solved. Hint: Your analysis should identify that the only solvable system boundary is the Overall system, and this should be your starting point for the rest of the question.

b$)$ Calculate the component flowrates $($mols component$/$s$)$ and composition $($mole fraction$)$ of Stream $6.$

c$)$ Calculate the total flowrate of the recycle stream $($mol$/$s$).$

d$)$ Calculate the component flowrates $($mols component$/$s$)$ in Stream $2.$"Identify the core concepts each section is evaluating. For example, problem $1$ has

sections a$,$ b$,$ and c so you will write a core concept for each part.

b$.$ Discuss why an understanding of the core concepts is important.