Balancing rate and yield

Definition

Yield

The amount of the desired product obtained from a reaction.

Definition

Compromise conditions

Operating conditions chosen to balance an acceptable rate, an acceptable yield, cost and safety, rather than to make any one of these as large as possible.

Industrial chemists want to make a high yield of product at a fast rate, as cheaply and as safely as possible.
For a reversible reaction, the conditions that give the highest yield at equilibrium are not always the conditions that give the fastest rate.
Each condition is judged by asking how it affects the position of equilibrium and how it affects the rate of reaction.
Cost and safety then limit how far each condition can be pushed.
The conditions actually used are therefore compromise conditions.

Haber process temperature

The forward reaction in the Haber process is exothermic: $N2(g)+3H2(g)⇌2NH3(g)\mathrm{N_{2}(g) + 3H_{2}(g) \rightleftharpoons 2NH_{3}(g)}$ , $kJ/mol\Delta H = -92\ \text{kJ/mol}$ .
A low temperature would shift the position of equilibrium to the right, in the exothermic direction, and give a higher yield of ammonia.
At a low temperature, however, the particles have less kinetic energy, so the rate would be too slow, even with a catalyst.
A high temperature would give a fast rate but would shift the equilibrium to the left and give a low yield.
A higher temperature would also need more fuel for heating, which increases the cost.
$∘C450\ ^\circ\text{C}$ is a compromise temperature that gives an acceptable yield at an acceptable rate.

Haber process pressure

There are $4$ moles of gas on the left of the equation and $2$ moles of gas on the right.
A high pressure shifts the position of equilibrium to the right, towards fewer moles of gas, so the yield of ammonia increases.
A high pressure also increases the rate, because the gas particles are closer together and collide more frequently.
Very high pressures need thick-walled reaction vessels and pipes and powerful compressors, which are expensive to build and to run.
Very high pressures also increase the risk of leaks and explosions, which is a safety hazard.
$kPa20\,000\ \text{kPa}$ ( $atm200\ \text{atm}$ ) is a compromise between a good yield and rate on one side, and cost and safety on the other.

Haber process catalyst and recycling

The iron catalyst increases the rates of the forward and reverse reactions equally.
It does not change the position of equilibrium, so it does not change the yield.
It means equilibrium is reached more quickly, so ammonia is made at an acceptable rate without raising the temperature further.
Using the catalyst therefore saves energy and money.
Although only about $15%15\%$ of the gases react on each pass, recycling the unreacted nitrogen and hydrogen means that almost all of them are eventually converted into ammonia.

Example

Linking each Haber condition to rate and yield

Temperature: the forward reaction is exothermic, so a lower temperature would give more ammonia, but $∘C450\ ^\circ\text{C}$ is used because a lower temperature would make the rate too slow.
Pressure: there are fewer moles of gas on the right, so a high pressure gives more ammonia and a faster rate, but $atm200\ \text{atm}$ is used because higher pressures cost too much and are too dangerous.
Catalyst: iron increases the rate so that equilibrium is reached quickly, but it has no effect on the yield.
Recycling: unreacted gases are returned to the reactor, so the low yield on each pass does not waste raw materials.

Contact process conditions

The forward reaction in the Contact process is also exothermic: $2SO2(g)+O2(g)⇌2SO3(g)\mathrm{2SO_{2}(g) + O_{2}(g) \rightleftharpoons 2SO_{3}(g)}$ , $kJ/mol\Delta H = -197\ \text{kJ/mol}$ .
A lower temperature would increase the yield of sulfur trioxide but make the rate too slow, so $∘C450\ ^\circ\text{C}$ is used as a compromise.
There are $3$ moles of gas on the left and $2$ moles of gas on the right, so a high pressure would shift the equilibrium to the right.
Even at $kPa200\ \text{kPa}$ ( $atm2\ \text{atm}$ ), the position of equilibrium already lies far to the right, and almost all of the sulfur dioxide is converted.
A higher pressure would only increase the yield slightly, which would not justify the extra cost of high-pressure equipment.
Keeping the pressure low also reduces the risk of toxic sulfur dioxide and corrosive sulfur trioxide leaking from the plant.
The vanadium(V) oxide catalyst increases the rate so that equilibrium is reached quickly at $∘C450\ ^\circ\text{C}$ , without affecting the yield.

Safety and cost

Heating to a high temperature uses a lot of fuel, so energy costs rise with temperature.
High pressures need stronger equipment and more energy to run the compressors.
Hydrogen is flammable and ammonia is toxic, so a leak from a high-pressure Haber plant is especially dangerous.
A lower yield on each pass is acceptable when unreacted gases are recycled, because the raw materials are not wasted.
A catalyst lets a plant run at a lower temperature than would otherwise be needed for the same rate, which lowers the energy cost.

Exam technique

Explaining a chosen condition

A question about a single condition usually needs a point about the position of equilibrium and a point about the rate, so cover both.
For temperature, state that the forward reaction is exothermic, so a lower temperature gives a higher yield, but the rate would be too slow.
For pressure, state the moles of gas on each side, give the effect on the yield and the rate, then give the cost or safety reason for not going higher.
Make cost points specific, such as “high pressure needs expensive, strong vessels and pipes”, rather than writing “it is expensive”.
For the Contact process pressure, explain that the yield is already very high at $atm2\ \text{atm}$ , so a higher pressure is not worth the cost.
For a catalyst, write that it increases the rate but has no effect on the yield or the position of equilibrium.

Common Mistake

Do not write that $∘C450\ ^\circ\text{C}$ gives the highest yield, because a lower temperature would give a higher yield.
Do not write that the catalyst increases the yield of ammonia or sulfur trioxide.
Do not leave out safety when you explain why a higher pressure is not used in the Haber process.

Self review

Why would a low temperature give a high yield of ammonia?
Why is a temperature lower than $∘C450\ ^\circ\text{C}$ not used in the Haber process?
Give two effects of increasing the pressure in the Haber process.
Why is a pressure of only $atm2\ \text{atm}$ used in the Contact process?
Why is the unreacted nitrogen and hydrogen recycled?

Balancing rate and yield

Definition

Yield

The amount of the desired product obtained from a reaction.

Definition

Compromise conditions

Operating conditions chosen to balance an acceptable rate, an acceptable yield, cost and safety, rather than to make any one of these as large as possible.

Industrial chemists want to make a high yield of product at a fast rate, as cheaply and as safely as possible.
For a reversible reaction, the conditions that give the highest yield at equilibrium are not always the conditions that give the fastest rate.
Each condition is judged by asking how it affects the position of equilibrium and how it affects the rate of reaction.
Cost and safety then limit how far each condition can be pushed.
The conditions actually used are therefore compromise conditions.

Haber process temperature

The forward reaction in the Haber process is exothermic: $N2(g)+3H2(g)⇌2NH3(g)\mathrm{N_{2}(g) + 3H_{2}(g) \rightleftharpoons 2NH_{3}(g)}$ , $kJ/mol\Delta H = -92\ \text{kJ/mol}$ .
A low temperature would shift the position of equilibrium to the right, in the exothermic direction, and give a higher yield of ammonia.
At a low temperature, however, the particles have less kinetic energy, so the rate would be too slow, even with a catalyst.
A high temperature would give a fast rate but would shift the equilibrium to the left and give a low yield.
A higher temperature would also need more fuel for heating, which increases the cost.
$∘C450\ ^\circ\text{C}$ is a compromise temperature that gives an acceptable yield at an acceptable rate.

Haber process pressure

There are $4$ moles of gas on the left of the equation and $2$ moles of gas on the right.
A high pressure shifts the position of equilibrium to the right, towards fewer moles of gas, so the yield of ammonia increases.
A high pressure also increases the rate, because the gas particles are closer together and collide more frequently.
Very high pressures need thick-walled reaction vessels and pipes and powerful compressors, which are expensive to build and to run.
Very high pressures also increase the risk of leaks and explosions, which is a safety hazard.
$kPa20\,000\ \text{kPa}$ ( $atm200\ \text{atm}$ ) is a compromise between a good yield and rate on one side, and cost and safety on the other.

Haber process catalyst and recycling

The iron catalyst increases the rates of the forward and reverse reactions equally.
It does not change the position of equilibrium, so it does not change the yield.
It means equilibrium is reached more quickly, so ammonia is made at an acceptable rate without raising the temperature further.
Using the catalyst therefore saves energy and money.
Although only about $15%15\%$ of the gases react on each pass, recycling the unreacted nitrogen and hydrogen means that almost all of them are eventually converted into ammonia.

Example

Linking each Haber condition to rate and yield

Temperature: the forward reaction is exothermic, so a lower temperature would give more ammonia, but $∘C450\ ^\circ\text{C}$ is used because a lower temperature would make the rate too slow.
Pressure: there are fewer moles of gas on the right, so a high pressure gives more ammonia and a faster rate, but $atm200\ \text{atm}$ is used because higher pressures cost too much and are too dangerous.
Catalyst: iron increases the rate so that equilibrium is reached quickly, but it has no effect on the yield.
Recycling: unreacted gases are returned to the reactor, so the low yield on each pass does not waste raw materials.

Contact process conditions

The forward reaction in the Contact process is also exothermic: $2SO2(g)+O2(g)⇌2SO3(g)\mathrm{2SO_{2}(g) + O_{2}(g) \rightleftharpoons 2SO_{3}(g)}$ , $kJ/mol\Delta H = -197\ \text{kJ/mol}$ .
A lower temperature would increase the yield of sulfur trioxide but make the rate too slow, so $∘C450\ ^\circ\text{C}$ is used as a compromise.
There are $3$ moles of gas on the left and $2$ moles of gas on the right, so a high pressure would shift the equilibrium to the right.
Even at $kPa200\ \text{kPa}$ ( $atm2\ \text{atm}$ ), the position of equilibrium already lies far to the right, and almost all of the sulfur dioxide is converted.
A higher pressure would only increase the yield slightly, which would not justify the extra cost of high-pressure equipment.
Keeping the pressure low also reduces the risk of toxic sulfur dioxide and corrosive sulfur trioxide leaking from the plant.
The vanadium(V) oxide catalyst increases the rate so that equilibrium is reached quickly at $∘C450\ ^\circ\text{C}$ , without affecting the yield.

Safety and cost

Heating to a high temperature uses a lot of fuel, so energy costs rise with temperature.
High pressures need stronger equipment and more energy to run the compressors.
Hydrogen is flammable and ammonia is toxic, so a leak from a high-pressure Haber plant is especially dangerous.
A lower yield on each pass is acceptable when unreacted gases are recycled, because the raw materials are not wasted.
A catalyst lets a plant run at a lower temperature than would otherwise be needed for the same rate, which lowers the energy cost.

Exam technique

Explaining a chosen condition

A question about a single condition usually needs a point about the position of equilibrium and a point about the rate, so cover both.
For temperature, state that the forward reaction is exothermic, so a lower temperature gives a higher yield, but the rate would be too slow.
For pressure, state the moles of gas on each side, give the effect on the yield and the rate, then give the cost or safety reason for not going higher.
Make cost points specific, such as “high pressure needs expensive, strong vessels and pipes”, rather than writing “it is expensive”.
For the Contact process pressure, explain that the yield is already very high at $atm2\ \text{atm}$ , so a higher pressure is not worth the cost.
For a catalyst, write that it increases the rate but has no effect on the yield or the position of equilibrium.

Common Mistake

Do not write that $∘C450\ ^\circ\text{C}$ gives the highest yield, because a lower temperature would give a higher yield.
Do not write that the catalyst increases the yield of ammonia or sulfur trioxide.
Do not leave out safety when you explain why a higher pressure is not used in the Haber process.

Self review

Why would a low temperature give a high yield of ammonia?
Why is a temperature lower than $∘C450\ ^\circ\text{C}$ not used in the Haber process?
Give two effects of increasing the pressure in the Haber process.
Why is a pressure of only $atm2\ \text{atm}$ used in the Contact process?
Why is the unreacted nitrogen and hydrogen recycled?

6.3.4 Explaining industrial conditions

Balancing rate and yield

Haber process temperature

Haber process pressure

Haber process catalyst and recycling

Linking each Haber condition to rate and yield

Contact process conditions

Safety and cost

Explaining a chosen condition

Review 6.3.4 Explaining industrial conditions by teaching Genie

6.3.4 Explaining industrial conditions

Balancing rate and yield

Haber process temperature

Haber process pressure

Haber process catalyst and recycling

Linking each Haber condition to rate and yield

Contact process conditions

Safety and cost

Explaining a chosen condition

Review 6.3.4 Explaining industrial conditions by teaching Genie

6.3.4 Explaining industrial conditions

Balancing rate and yield

Haber process temperature

Haber process pressure

Haber process catalyst and recycling

Linking each Haber condition to rate and yield

Contact process conditions

Safety and cost

Explaining a chosen condition

Review 6.3.4 Explaining industrial conditions by teaching Genie

6.3.4 Explaining industrial conditions Revision Guide

6.3.4 Explaining industrial conditions

Balancing rate and yield

Haber process temperature

Haber process pressure

Haber process catalyst and recycling

Linking each Haber condition to rate and yield

Contact process conditions

Safety and cost

Explaining a chosen condition

Review 6.3.4 Explaining industrial conditions by teaching Genie

6.3.4 Explaining industrial conditions Revision Guide