Equilibrium yield

You have seen in previous topics that reversible reactions can achieve a state of equilibrium where not all the reactants will have been converted into products. This leads to a situation where a reaction may have a yield of less than 100%. Although we can use equilibrium constants to measure the position of equilibrium, in terms of the amount of product made in a reaction, it is more useful to talk about the yield of the reaction.

The yield of a reaction is defined as the percentage of product produced. It is calculated by comparing the amount actually produced with the amount that would have been produced if reactants were completely used up in the reaction.

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Example

sulfuric acidAs part of the production of sulfuric acid, sulfur trioxide (SO3) is produced in the reaction shown below.

2 SO2(g) + O2(g) reversible arrow 2 SO3(g) + heat

In a laboratory test, 100 g of sulfur dioxide was reacted in excess oxygen and 75 g of sulfur trioxide was produced. What would be the % yield of this reaction?

n(SO2)present = *eq* n divided by M = *eq* 100 divided by 64.06 = 1.56 mol
n(SO3)expected = *eq* 2 divided by 2 × n(SO2) = 1.56 mol
m(SO3)expected = n × M = 1.56 × 80.06 = 125 g
% yield = *eq* actual amount produced divided by expected amount produced × 100
= *eq* 75 divided by 100 × 100 = 60% yield


Improving the yield

A chemical engineer is responsible for making sure that the yield of a reaction is high enough to make the process viable. Use your knowledge of Le Châtelier's principle to decide which of the following actions will increase the equilibrium yield of this reaction.

1
Which of the following changes will increase the yield of this reaction?

a)
b)
c)
d)
e)
f)

Making the following changes will increase the yield of this reaction:

  • Increase pressure. This would favour the forward reaction because there are fewer molecules of gas on the right-hand side (products) than the left hand side (reactants).
  • Increase the concentration of oxygen. This would favour the forward reaction because the system would move to reduce the oxygen concentration.
  • Remove some of the sulfur trioxide as it is formed. This will reduce the concentration of the sulfur trioxide, therefore the forward reaction will be favoured in order to oppose this change.

These changes will not increase the yield of this reaction:

  • Increase temperature. This would favour the reverse (endothermic reaction).
  • Increase the volume of the reaction container. This would have the effect of reducing the pressure. Therefore the reverse reaction would be favoured because there are more molecules of gas in the reactants than the products.
  • Use a suitable catalyst. Catalysts do not affect the position of equilibrium so they will have no effect on the yield of the reaction.
Check your answer
Yield and calculation of product

If a reaction does not go to completion, this must be taken into account when calculating the amount of a substance produced in the reaction. There are several ways of approaching these types of problems. The example below shows one possible method.

Example

The reaction below was carried out in conditions that resulted in a yield of 85%.

2 SO2(g) + O2(g) reversible arrow 2 SO3(g)

Calculate the maximum mass of sulfur trioxide that could be made from 200 g of sulfur dioxide.

n(SO2)present = *eq* n divided by M = *eq* 200 divided by 64.06 = 3.12 mol

An extra factor is added to the conversion of number of moles to allow for the fact that only 85% of the sulfur dioxide actually reacts before equilibrium is achieved.

n(SO3)expected = *eq* 2 divided by 2 × n(SO2) × *eq* 85 divided by 100 = 2.65 mol

m(SO3) expected = n × M = 2.65 × 80.06 = 210 g (answer to 2 significant figures)

Yield and calculation of reactant

If you want to produce a certain amount of product from a reaction, it is clear that more reactant will need to be used if the reaction has a yield of less than 100%. In this case the conversion factor will be 100 divided by the value of the percentage yield.

Example

Calculate how much sulfur dioxide would be required to produce 400 g of sulfur trioxide from the reaction below if the yield of the reaction is 70%.

2 SO2(g) + O2(g) reversible arrow 2 SO3(g)


n(SO3)present = *eq* m divided by M = *eq* 400 divided by 80.06 = 5.00 mol
n(SO2)required = *eq* 2 divided by 2 × n(SO3) × *eq* 100 divided by 70= 7.14 mol

m(SO2)required = n × M = 7.14 × 64.06 = 458 g

Yield consolidation

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Complete the problem sheet Opens a 289kBMicrosoft® Word document in a new browser window. which will test your knowledge of the concept of equilibrium yield.


Avoiding equilibrium

Remember that a true state of equilibrium can only be established within a closed system. In terms of maximising the amount of product, processes are often designed to avoid the system achieving equilibrium. This is because no new product is effectively being produced while the system is at equilibrium (because the rate of the reverse reaction is equal to the rate of the forward reaction). However, the theories of equilibrium can still be applied to these situations, and this is done in the following section.

reflection icon

  • When designing an industrial process, why is it important to try to maximise the yield?
  • When a piece of magnesium was added to a beaker of acid, it totally dissolved. Why is this an example of a reaction with a 100% yield?
  • Compare the concept of yield to the concept of limiting reagent, which you should have previously encountered. Explain why the idea of a limiting reagent is not related to reversible reactions.