Ammonia (NH_3) is produced from hydrogen and nitrogen according to the following
ID: 490388 • Letter: A
Question
Ammonia (NH_3) is produced from hydrogen and nitrogen according to the following reaction: 3H_2 + N_2 - 2NH_3 The fresh feed to the process contains hydrogen, nitrogen, and argon. The reactor effluent contains 200 mol H_2/S, 150 mol N_2/S, 1 mol Ar/s, and 75 mol NH_3/s. After the reactor, all of the ammonia is condensed and all of the gases (H_2, N_2, and Ar) leave the top stream from the condenser. Five percent of this stream is purged from the process and the rest is recycled and mixed with the fresh feed. Determine the composition of the purge stream. Determine the molar flow rate of each component in the reactor feed. Calculate the single-pass conversion of the limiting reactant. Determine the molar flow rate of each component in the process fresh feed. Calculate the overall conversions of both hydrogen and nitrogen. Suppose that the process is scaled up until the mass flow rate of ammonia production is 100 000 kg/h. What would the required fresh freed of H_2 be in kg/h?Explanation / Answer
According to the equation
Step 1: Preliminary calculation
3H2 + N2 2NH3
3moles 1 mole 2moles
If
? ? 75moles
(3x 75)/2 (1x 75)/2 75moles
112.5moles 37.5 moles 75moles
From the above it is clear that to get 75 moles of ammonia, 112.5 moles of hydrogen and 37.5 moles of nitrogen must have reacted.
The unreacted gases must have come out as effluent along with 75moles of ammonia
Step 2: Calculation of feed composition
Therefore the feed must have been (effluent + reacted moles)
Hydrogen=200 moles (effluent)+112.5moles(reacted)=312.5moles
Nitrogen=150 moles (effluent)+37.5moles(reacted)=187.5moles
Argon= 1mole
Step 3: Calculation of purged stream ( 5% of the top stream)
Top stream has 200 moles of hydrogen+150 moles of nitrogen and 1 mole of argon
Total number of moles =351moles
Out of 100 moles = 5moles is purged
Therefore out of 200 moles=10moles of hydrogen
Therefore out of 150 moles=7.5moles of nitrogen
Therefore out of 1mole=0.05mole of argon
Step 4: finding out the limiting agent
According to the equation
3H2 + N2 2NH3
3moles 1 mole 2moles
If
312.5moles ?=104.7mole
?=562.5 mole 187.5moles
We donot have 562.5 moles of hydrogen. Hence hydrogen is the limiting agent
Out of 312.5 moles of hydrogen =112.5moles of hydrogen are converted into ammonia
Therefore if 100moles are there= 112.5x 100/ 312.5=36
Step 5: overall conversion of hydrogen and nitrogen
3H2 + N2 2NH3
3moles 1 mole 2moles
Out of 4(total) moles= 2moles of ammonia are formed
Therefore out of 100 moles=50moles of ammonia will be formed
Step 6: Calculation of required fresh feed of hydrogen in kg/h
3H2 + N2 2NH3
3moles 2moles
( 3x2)=6kg 2(14+3)=34kg
312.5moles 75 moles
3moles of hydrogen= 6Kg
312.5 moles= 6x 312.5/3=625kg
2moles of ammonia= 34Kg
75 moles= 34x 75/2=1275kg
For the production of 1275kg of ammonia=625kg of hydrogen is required
Therefore for the production of 100000kg=625x100000/1275= 49019.61kg of hydrogen is required
Answers
10moles of hydrogen +7.5moles of nitrogen+ 0.05mole of argon
Therefore the feed must have been (effluent + reacted moles)
Hydrogen=200moles/h
Nitrogen=150moles/h
Argon= 1mole/h
Ammonia= 75/h
c)Single pass conversion of limiting agent Hydrogen)= 36%
d) Molar flow rate of the components in the fresh feed
Hydrogen=312.5moles/h
Nitrogen=187.5moles/h
Argon= 1mole/h
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