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:

N_2(g) + 3H_2(g) ⇋ 2NH_3(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%

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:

N_2(g) + 3H_2(g) ⇋ 2NH_3(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

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:

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.