Ammonia is produced by reading nitrogen and hydrogen according to the reaction b

Question

Ammonia is produced by reading nitrogen and hydrogen according to the reaction below. N_2 + 3H_2 rightarrow 2NH_3. A feed stream consisting of 2.400% argon (by mole) and stoichiometric proportion of the reactants is fed into the system at the rate of 100 mol/min. The components enter a reactor, and then all ammonia is separated from the other components and leaves the process. The other components are recycled bade to the feed stream, with a portion being purged from the system. The mote percentage of argon in the purge stream to 4.600%, and the conversion per pass in the reactor is 14.50% What is the production rate of ammonia? What is the overall process fractional conversions of nitrogen and hydrogen? What is the flow rate of the recycle stream?

Explanation / Answer

Flow rate of argon in purge stream = (Mole % of argon in the purge stream x Flow rate of purge stream) / 100 = (4.6 mol % x 52 mol/min) / 100 = 2.4 mol/min

Flow rate of nitrogen & hydrogen in purge stream = Flow rate of purge stream - Flow rate of argon in purge stream = 52 mol/min - 2.4 mol/min = 49.6 mol/min

Flow rate of nitrogen in purge stream = Flow rate of nitrogen & hydrogen in purge stream / 4 (Dividing by 4 as the mole ratio of nitrogen & hydrogen is 1:3) = 49.6 mol/min / 4 = 12.4 mol/min

Flow rate of nitrogen & hydrogen in fresh stream = Flow rate of fresh stream - Flow rate of argon in fresh stream = 100 mol/min - 2.4 mol/min = 97.6 mol/min

Flow rate of nitrogen in fresh stream = Flow rate of nitrogen & hydrogen in fresh stream / 4 = 97.6 mol/min / 4 = 24.4 mol/min

Production rate of ammonia = (Flow rate of nitrogen in fresh stream - Flow rate of nitrogen in purge stream) x 2 (Multiplying by 2 as moles of ammonia is produced from 1 mole of nitrogen)

Production rate of ammonia = (24.4 mol/min - 12.4 mol/min) X 2 = 24 mol/min

Production rate of ammonia = 24 mol/min

Overall process fractional conversions of nitrogen = Flow rate of nitrogen in fresh stream/ Flow rate of fresh stream = 24.4 mol/min / 100 mol/min = 0.244

Overall process fractional conversions of hydrogen = Flow rate of hydrogen in fresh stream/ Flow rate of fresh stream = 73.2 mol/min / 100 mol/min = 0.732

Mole % argon in the feed stream = 2.4 mol %

Mole % of argon in the purge stream = 4.6 mol %

Therefore, the flow rate of purge stream = (Feed rate of fresh stream x Mole % argon in the feed stream) / (Mole % of argon in the purge stream) = (100 mol/min x 2.4 mol %) / (4.6 mol %) = 52 mol/min

The flow rate of purge stream = 52 mol/min

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