Topic 9 · page 14 of 15

Yield, rate and the industrial compromise

For an exothermic reaction, a low temperature gives a high yield but a slow reaction, and a high temperature gives a fast reaction but a low yield. Industry settles on a compromise, and adds a catalyst, a pressure and recycling to make the best of it.

14 min read9.119.10

Read first: Temperature, catalysts and writing the justification

Two aims that pull against each other 9.11

A manufacturer wants two things from a reactor: a good yield (how much product at equilibrium) and a good rate (how fast it arrives). Equilibrium and kinetics are different ideas, and for many processes they ask for opposite conditions.

Take an exothermic reaction that is reversible.

A higher temperature does the reverse of both. Neither extreme is any use: a high yield that takes a year to appear is worthless, and so is a fast reaction that gives almost no product.

Schematic graph against temperature for an exothermic reaction. The equilibrium yield falls from high to low as temperature rises, shown as a falling teal curve. The rate rises steeply with temperature, shown as a rising orange curve. The curves cross in the middle, and a shaded band around the crossing is labelled compromise temperature. At low temperature the yield is high but the reaction is too slow, and at high temperature it is fast but the yield is low.
Schematic: yield falls and rate rises as the temperature rises. The best choice is in between.

The compromise is chosen from the conditions of the whole process, not only from the chemistry: the cost of energy, the cost of the catalyst and the plant, safety, and how much unreacted material can be recovered.

The Haber process 9.119.10

NX2(g)+3 HX2(g)⇌2 NHX3(g)ΔH=−92 kJ mol−1 \ce{N2(g) + 3H2(g) <=> 2NH3(g)} \qquad \Delta H = -92\ \text{kJ mol}^{-1}
Condition Effect on yield Effect on rate What is used
Temperature low is best (exothermic) high is best about 450 °C: a compromise
Pressure high is best (4 mol gas to 2 mol) high is best about 200 atm: a compromise with cost and safety
Catalyst none much faster iron
Removing ammonia more product none ammonia liquefied and removed

The catalyst is what makes 450 °C fast enough. The pressure is high, but not higher, because pumping gas to very high pressures needs very strong, expensive equipment and uses a lot of energy, and it becomes more dangerous. The yield per pass is modest, so the unreacted nitrogen and hydrogen are recycled back to the reactor.

Block diagram of the Haber process. Nitrogen and hydrogen in a ratio of one to three pass through a compressor at about 200 atmospheres, then a reactor containing an iron catalyst at about 450 degrees Celsius, then a cooler where ammonia condenses and is removed as a liquid. A dashed arrow carries the unreacted nitrogen and hydrogen back to the compressor.
The Haber process. The recycle loop means that little reactant is wasted even though the yield per pass is low.

Other processes 9.119.10

Process Equation ΔH (kJ mol⁻¹) Conditions
Contact (SO₃) 2SO₂ + O₂ ⇌ 2SO₃ −196 about 450 °C, 1–2 atm, V₂O₅ catalyst
Hydration of ethene C₂H₄ + H₂O ⇌ C₂H₅OH about −45 about 300 °C, 60–70 atm, H₃PO₄ catalyst

In the Contact process the yield is already high at a low pressure, so a high pressure is not worth its cost. The temperature compromise is still needed, and the catalyst works at about 450 °C. In the hydration of ethene, the mixture is recycled because the yield per pass is low, and the conditions are again a compromise between yield, rate and cost.

Worked exampleIs it worth going colder?

For the Haber reaction at 200 atm, the data table (illustrative values) gives the equilibrium yield and the relative rate, with the rate at 200 °C taken as 1.

Temperature (°C) Yield (%) Relative rate
200 89 1
400 39 200
500 18 1000
600 8 3500
  1. 200 to 600 °C: the yield falls by a factor of 89 ÷ 8 = 11, but the rate rises by a factor of 3500 ÷ 1 = 3500. At 200 °C the reaction is far too slow to use.
  2. 400 to 500 °C: the yield falls from 39% to 18%, which is a factor of 18 ÷ 39 = 0.46 (it roughly halves). The rate rises by 1000 ÷ 200 = 5.
  3. So going from 400 to 500 °C gives five times the rate for half the yield. Whether that is worthwhile depends on the cost of the lost yield against the cost of waiting. With the unreacted gases recycled, and the iron catalyst already speeding up the reaction, industry chooses a point in this range, about 450 °C.

Check yourself

  1. For an exothermic reversible reaction, state the effect of a lower temperature on (a) the equilibrium yield and (b) the rate.
  2. Explain why the Haber process uses a temperature of about 450 °C and not 200 °C or 600 °C.
  3. Explain why the pressure used in the Haber process is about 200 atm and not 1000 atm.
  4. State the role of the iron catalyst and say what it does not change.
  5. Why is unreacted gas recycled in the Haber process?
  6. In the Contact process, why is a pressure of only 1–2 atm used even though a higher pressure would increase the yield?

Answers cover these until you have tried the questions

  1. (a) The yield is higher: the position shifts in the exothermic direction, towards the products. (b) The rate is lower: fewer molecules have energy of at least EaE_\text{a}, so fewer collisions are successful.
  2. At 200 °C the yield is high (89%) but the rate is far too low. At 600 °C the rate is high but the yield is only 8%, because the reaction is exothermic. About 450 °C gives a reasonable rate, with the catalyst, and an acceptable yield.
  3. A higher pressure gives a higher yield (4 mol of gas becomes 2 mol), but the plant needs thicker, stronger and more expensive equipment, more energy for compression, and it is less safe. About 200 atm balances yield and rate against cost and safety.
  4. It provides an alternative route with a lower activation energy, so the reaction is fast enough at 450 °C. It does not change the position of equilibrium, the equilibrium yield or ΔH.
  5. The yield per pass is low, so the unreacted nitrogen and hydrogen are returned to the reactor. This reduces waste, so the overall conversion of reactants to ammonia is high and fewer raw materials are lost.
  6. The yield of SO₃ is already high at a low pressure, so the extra cost of compression and strong equipment is not worth the small increase in yield.