# Yield Calculations Chemistry Tutorial

## Key Concepts

• Yield is the mass of product formed in a chemical reaction.
• Actual yield is the mass of product formed in an experiment or industrial process.
• Theoretical yield is the mass of product predicted by the balanced chemical equation for the reaction.
• Percentage yield = (actual yield ÷ theoretical yield) × 100
• Optimum yield is the best possible yield achieved for a set of given reaction conditions.
• For a chemical reaction which goes to completion(1):

actual yield = theoretical yield

so, percentage yield = 100%

• For a chemical reaction at equilibrium(2):

actual yield < theoretical yield

so, percentage yield < 100%

• For a chemical reaction at equilibrium, actual yield can be affected by factors such as:

⚛ temperature

⚛ concentration

⚛ pressure and volume (gaseous systems)

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## Worked Example of Percentage Yield Calculations: Calculating Percentage Yield

Question: 112 g of nitrogen gas reacts with hydrogen gas to produce 40.8 g of ammonia gas according to the equation given below:

N2(g) + 3H2(g) ⇋ 2NH3(g)

Calculate the percentage yield of ammonia.

Solution:

1. Actual yield is the mass of ammonia that is actually produced during the chemical reaction.

Actual yield of ammonia (NH3) = 40.8 g (given in the question)

2. Theoretical yield of ammonia (NH3) is the mass of product predicted by the balanced chemical equation for the reaction.

From the balanced chemical equation the mole ratio (stoichiometric ratio) N2:NH3 is 1:2
therefore: moles NH3 = 2 × moles N2

Assuming ALL the available N2 reacts completely, then the maximum amount of NH3 that can be produced is:
moles NH3 = 2 × (mass N2 ÷ molar mass N2) = 2 × (112 ÷ [2 × 14]) = 2 × (112 ÷ 28) = 8 mol

Theoretical yield NH3 = predicted mass NH3
Predicted mass NH3 = maximum mass of NH3 that can be produced assuming that ALL the N2 reacts completely:
mass(NH3) = moles(NH3) × molar mass(NH3)
predicted mass NH3 = 8 × (14 + 3 × 1) = 8 × 17 = 136 g

Theoretical yield = predicted mass = 136 g

3. Percentage yield = (actual yield ÷ theoretical yield) × 100

Substituting the vales for actual yield and theoretical yield into the equation:

percentage yield NH3 = (40.8 ÷ 136) × 100 = 30%

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## Worked Example of Percentage Yield Calculations: Calculating Mass of Product from Yield

Question: Ammonia can be produced from hydrogen gas and nitrogen gas according to the equation below:

N2(g) + 3H2(g) ⇋ 2NH3(g)

Calculate the mass of ammonia produced if 168 g of nitrogen gas produces a yield of 45%.

Solution:

1. percentage yield = (actual yield ÷ theoretical yield) × 100

Percentage yield = 45% (given in question)
percentage yield = (actual yield ÷ theoretical yield) × 100 = 45%

2. Calculate the theoretical yield of NH3 (the mass of NH3 produced as predicted by the balanced chemical equation for the reaction)

From the balanced chemical equation the mole ratio (stoichiometric ratio) N2:NH3 is 1:2
therefore moles NH3 = 2 × moles N2

Assuming ALL the available N2 reacts completely, then the maximum amount of NH3 that can be produced is:
moles NH3 = 2 × (mass N2 ÷ molar mass N2) = 2 × (168 ÷ [2 × 14]) = 2 × (168 ÷ 28) = 12 moles

theoretical yield NH3 = predicted mass NH3
Predicted mass NH3 = maximum mass of NH3 that can be produced assuming that ALL the N2 reacts completely:
mass(NH3) = moles(NH3) × molar mass(NH3)
predicted mass NH3 = moles NH3 × molar mass NH3 = 12 × (14 + 3 × 1) = 12 × 17 = 204 g
theoretical yield NH3 = predicted mass NH3 = 204 g

3. Calculate the actual yield:

percentage yield = (actual yield ÷ theoretical yield) × 100

Re-arranging this equation gives:

actual yield = theoretical yield × (percentage yield ÷ 100)

Substituting the values for percentage yield and theoretical yield into this equation:

actual yield of NH3 = 204 × (45 ÷ 100) = 91.8 g

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## Factors Affecting Actual Yield

Le Chatelier's Principle can be used to predict the affect of changes in temperature, concentration, gas pressure and volume on actual yield as summarised in the table below:

Factor Conditions Actual Yield % Yield
reactant concentration increase   increases increases

reactant concentration decrease   decreases decreases

temperature increase exothermic reaction decreases decreases
endothermic reaction increases increases

temperature decrease exothermic reaction increases increases
endothermic reaction decreases decreases

gas pressure increase mol reactant(gas) > mol product(gas) increases increases
mol reactant(gas) < mol product(gas) decreases decreases

gas pressure decrease mol reactant(gas) > mol product(gas) decreases decreases
mol reactant(gas) < mol product(gas) increases increases

Note that if a change to the equilibrium system results in an increase in the actual yield of product then the percentage yield of that product must also increase.

Likewise, if a change to the equilibrium system results in an decrease in the actual yield of product then the percentage yield of that product must also decrease.

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Footnotes:

(1) A reaction that goes to completion is a spontaneous, irreversible reaction.
The arrow used to indicate this in a chemical equation is →

(2) A reaction at equilibrium is a reversible reaction.
The arrow used to indicate this in a chemical equation is ⇋