The fresh feed to an ammonia production process contains nitrogen (N₂) and hydrogen (H₂) in stoichiometric proportion, along with an inert gas (I).   The feed is combined with a recycle stream containing the same three species, and the combined stream is fed to a reactor in which a low single pass conversion of nitrogen is achieved.  The reactor effluent flows to a condenser.  A liquid stream containing essentially all of the ammonia formed in the reactor and a gas stream containing all of the inerts and the unreacted nitrogen and hydrogen leave the condenser.  The gas stream is split into two fractions:  one is removed from the process as a purge stream, and the other is the recycle stream combined with the fresh feed. 

a.  Let x_I0 be the mole fraction of inerts in the fresh feed, f_sp the single pass conversion of nitrogen in the reactor and y_p the fraction of the gas leaving the condenser that is purged (mol purged/ mol total). Taking a basis of 1 mol fresh feed, draw and fully label a process flowchart, incorporating x_I0, f_sp, and y_p in the labeling.  Then, assuming that the values of these three variables are given, write a set of equations for the total moles fed to the reactor (n_A), the moles of ammonia produced (n_p), and the overall nitrogen conversion (f_ov).  Each equation should involve only one unknown variable, which should be circled.

b.  Solve the equations of part a for x_I0=0.01, f_sp=0.20, y_p=0.10. 

c.  Briefly explain in your own words the reasons for including (i) the recycle stream and (ii) the purge stream in the design process.