Yield and rate often need different conditions
Definition
Position of equilibrium
The relative amounts of reactants and products in a reaction mixture at equilibrium.
Definition
Compromise conditions
Reaction conditions chosen to give an acceptable yield at an acceptable rate and cost, rather than the best possible value of any one of them.
- In a reversible reaction, the position of equilibrium decides how much product is present once equilibrium is reached.
- The rate of reaction decides how quickly the product forms and how soon equilibrium is reached.
- A change in conditions can improve one while making the other worse, so industry chooses compromise conditions.
- A company wants the most product per hour at the lowest cost, rather than the highest possible yield.
- A high yield reached very slowly gives less product each day than a lower yield reached quickly.
- The same trade-off applies to making ethanol from ethene and steam, an exothermic reversible reaction run at about 300 ∘C300\ ^{\circ}\text{C}300 ∘C and 60 to 70 atmospheres with a phosphoric acid catalyst.
Common Mistake
Do not explain a higher yield by saying there are more collisions, because collisions explain rate, while yield depends on the position of equilibrium.
Low temperature favours ammonia but slows the reaction
Definition
Catalyst
A substance that increases the rate of a reaction by providing an alternative pathway with a lower activation energy without being used up.
- The forward reaction is exothermic: N2(g)+3H2(g)⇌2NH3(g)\text{N}_2\text{(g)} + 3\text{H}_2\text{(g)} \rightleftharpoons 2\text{NH}_3\text{(g)}N2(g)+3H2(g)⇌2NH3(g)
- Lowering the temperature shifts the position of equilibrium to the right, towards the exothermic direction, so the yield of ammonia increases.
- At 200 atmospheres, the equilibrium yield is about 36% at 400 ∘C400\ ^{\circ}\text{C}400 ∘C but only about 18% at 500 ∘C500\ ^{\circ}\text{C}500 ∘C.
- At a low temperature, fewer particles have energy greater than the activation energy, so the rate is too slow to be economical.
- About 450 ∘C450\ ^{\circ}\text{C}450 ∘C is used as a compromise, giving a lower yield but a much faster rate.
- The iron catalyst also works well only at a high temperature, which is another reason the temperature cannot be low.
Key Idea
The catalyst speeds up the forward and reverse reactions equally, so equilibrium is reached sooner but the yield does not change.
High pressure raises Haber yield, rate and costs
- There are four moles of gas on the left of the equation and two on the right, so a higher pressure shifts the position of equilibrium towards ammonia.
- At 400 ∘C400\ ^{\circ}\text{C}400 ∘C, the equilibrium yield rises from about 25% at 100 atmospheres to about 47% at 300 atmospheres.
- A higher pressure also increases the rate, because the gas particles are closer together and collide more often.
- Very high pressures need thick-walled equipment and a lot of energy to compress the gases, which is expensive and increases the risk of leaks.
- About 200 atmospheres is used as a compromise between a good yield and the cost of equipment and energy.
Note
Raising the pressure improves both the yield and the rate, so its limit is set by cost and safety rather than by the chemistry.
Graphs show how conditions affect the rate
- On a graph of rate against temperature, the rate rises more and more steeply as the temperature increases.
- On a graph of rate against pressure for a reaction of gases, the rate rises as the pressure increases, because the gases become more concentrated.
- Read values from the graph at the conditions being compared, and describe the change using numbers from the axes.
- A rate graph shows only how fast the reaction goes, so it must be read alongside yield data before conditions are chosen.
- The best temperature is where the rate is high enough while the yield has not fallen too far.
Example
Choosing a temperature for making ammonia
- A graph shows a rate of ammonia production of 222 units at 350 ∘C350\ ^{\circ}\text{C}350 ∘C and 101010 units at 450 ∘C450\ ^{\circ}\text{C}450 ∘C, while the equilibrium yield falls from about 50% to about 28%; explain why 450 ∘C450\ ^{\circ}\text{C}450 ∘C is chosen.
- The rate increases by a factor of 102=5\dfrac{10}{2} = 5210=5 between 350 ∘C350\ ^{\circ}\text{C}350 ∘C and 450 ∘C450\ ^{\circ}\text{C}450 ∘C.
- The yield falls from about 50% to about 28%, so it is a little over half as large.
- Five times the rate more than makes up for a yield about half as large, so more ammonia is made each hour at 450 ∘C450\ ^{\circ}\text{C}450 ∘C.
Raw material and energy costs affect commercial conditions
- Nitrogen comes cheaply from the air, but hydrogen is made from natural gas, so the price of gas has a large effect on the cost of ammonia.
- Only about 15% of the gases react on each pass through the reactor, so the unreacted nitrogen and hydrogen are recycled and no raw material is wasted.
- Ammonia is removed by cooling the mixture, because ammonia condenses at a much higher temperature than nitrogen and hydrogen.
- Heating and compressing the gases uses a lot of energy, so a lower temperature and pressure save fuel and electricity.
- The heat released by the exothermic reaction is used to preheat the incoming gases, which cuts energy costs.
- The catalyst gives an acceptable rate at a lower temperature than would otherwise be needed, which saves energy.
Exam technique
When a question asks you to explain the conditions used in an industrial process, deal with each condition in turn and say what it does to the rate, to the yield and to the cost.
Self review
- Why does a low temperature increase the equilibrium yield of ammonia?
- Why is a low temperature not used in the Haber process?
- Why does a higher pressure increase the yield of ammonia?
- Why is a pressure much higher than 200 atmospheres not used?
- How does recycling the unreacted gases reduce the cost of making ammonia?
