Ammonia plant: yield versus rate when changing conditions
An ammonia plant runs N₂(g) + 3H₂(g) ⇌ 2NH₃(g), ΔH = −92 kJ mol⁻¹, over an iron catalyst at 450 °C and 200 atm. At these conditions the gas leaving the reactor contains about 35% ammonia by volume. Management proposes lowering the temperature to 380 °C and raising the pressure to 400 atm to increase the ammonia content of the exit gas. The reactor engineer replies that at 380 °C the equilibrium percentage of ammonia does rise, but the plant produces less ammonia per day than before. A second proposal is to pass the exit gas through a condenser, liquefying the ammonia and returning the unreacted nitrogen and hydrogen to the reactor. A third is to double the amount of catalyst in the reactor. Sulfur compounds in the feedstock are known to poison the catalyst, and compression is the largest single electricity cost on the site.
1. Use Le Chatelier's principle to predict the effect of lowering the temperature and raising the pressure on the equilibrium yield. Then explain how the engineer's observation can be true at the same time.
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Temperature: the forward reaction is exothermic (ΔH = −92 kJ mol⁻¹), so lowering the temperature removes heat and the system responds by favouring the exothermic direction - to the right. The equilibrium constant increases and the equilibrium percentage of ammonia rises.
Pressure: 4 mol of gas form 2 mol, so increasing pressure favours the side with fewer gas molecules - again to the right. 400 atm gives a higher equilibrium yield than 200 atm.
Why output per day can still fall: a plant does not run at equilibrium; it runs for a fixed contact time. The rate constant depends on temperature roughly as e^(−Ea/RT), so dropping from 450 °C to 380 °C slows both forward and reverse reactions sharply. If the gas leaves the reactor before it has had time to approach the new (higher) equilibrium position, the exit composition can be further from equilibrium than it was at 450 °C, even though the target has moved up. At 450 °C the exit gas is close to equilibrium (≈35%); at 380 °C it may be far below its equilibrium value.
The judgement: yield per pass and rate of production are different quantities. The industrial temperature is a compromise chosen so that equilibrium is reached quickly enough, with a catalyst, to maximise tonnes per day - not to maximise equilibrium percentage.
2. Explain why the plant uses about 200 atm rather than 1000 atm, even though higher pressure increases the yield.
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Higher pressure helps in two ways: it shifts the equilibrium towards ammonia, and it increases the concentration of the gases so collisions are more frequent and the reaction reaches equilibrium faster.
The reason it is not taken further is economic and engineering, not chemical:
- compression is the largest electricity cost on the site, and the energy needed rises steeply with pressure;
- reactor vessels, pipework and compressors must withstand far greater stress, so thicker walls of more expensive alloy are needed, with much higher capital cost;
- safety and maintenance costs rise (leaks of hydrogen at high pressure, fatigue, inspection);
- the gain in equilibrium yield per extra atmosphere falls off, so beyond a certain point the extra ammonia does not pay for the extra compression.
200 atm is therefore an economic optimum: enough pressure to give a good yield and a fast reaction with the iron catalyst at 450 °C, without the cost of extreme high-pressure equipment.
3. Assess the condenser-with-recycle proposal and the proposal to double the catalyst. Which increases the ammonia made per day, and which changes the position of equilibrium?
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Condenser and recycle: removing ammonia lowers the concentration of the product. The reaction quotient Q is now less than K, so the system is no longer at equilibrium and shifts to the right to replace the ammonia removed. Because this is repeated continuously, conversion of nitrogen and hydrogen can approach completion even though the yield per pass is only about 35%. Recycling the unreacted gases means no feedstock is wasted. This genuinely increases the ammonia produced per day, and it works by continuously disturbing the equilibrium.
Doubling the catalyst: a catalyst provides an alternative path of lower activation energy. It speeds the forward and reverse reactions by exactly the same factor, so it does not change K or the equilibrium position, and it does not change the equilibrium yield. It does increase the ammonia made per day, because the gas reaches (or gets closer to) equilibrium within the fixed contact time - that is, it allows the plant to operate at a lower, economically better temperature. Doubling the amount again gives diminishing returns once equilibrium is already reached, and it does not protect against sulfur poisoning: the sulfur must be removed from the feedstock first, or the extra catalyst is simply poisoned faster.