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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:
 Actual yield is the mass of ammonia that is actually produced during the chemical reaction.
Actual yield of ammonia (NH_{3}) = 40.8 g (given in the question)
 Theoretical yield of ammonia (NH_{3}) is the mass of product predicted by the balanced chemical equation for the reaction.
From the balanced chemical equation the mole ratio (stoichiometric ratio) N_{2}:NH_{3} is 1:2
therefore: moles NH_{3} = 2 × moles N_{2}
Assuming ALL the available N_{2} reacts completely, then the maximum amount of NH_{3} that can be produced is:
moles NH_{3} = 2 × (mass N_{2} ÷ molar mass N_{2}) = 2 × (112 ÷ [2 × 14]) = 2 × (112 ÷ 28) = 8 mol
Theoretical yield NH_{3} = predicted mass NH_{3}
Predicted mass NH_{3} = maximum mass of NH_{3} that can be produced assuming that ALL the N_{2} reacts completely:
mass(NH_{3}) = moles(NH_{3}) × molar mass(NH_{3})
predicted mass NH_{3} = 8 × (14 + 3 × 1) = 8 × 17 = 136 g
Theoretical yield = predicted mass = 136 g
 Percentage yield = (actual yield ÷ theoretical yield) × 100
Substituting the vales for actual yield and theoretical yield into the equation:
percentage yield NH_{3} = (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:
 percentage yield = (actual yield ÷ theoretical yield) × 100
Percentage yield = 45% (given in question)
percentage yield = (actual yield ÷ theoretical yield) × 100 = 45%
 Calculate the theoretical yield of NH_{3} (the mass of NH_{3} produced as predicted by the balanced chemical equation for the reaction)
From the balanced chemical equation the mole ratio (stoichiometric ratio) N_{2}:NH_{3} is 1:2
therefore moles NH_{3} = 2 × moles N_{2}
Assuming ALL the available N_{2} reacts completely, then the maximum amount of NH_{3} that can be produced is:
moles NH_{3} = 2 × (mass N_{2} ÷ molar mass N_{2}) = 2 × (168 ÷ [2 × 14]) = 2 × (168 ÷ 28) = 12 moles
theoretical yield NH_{3} = predicted mass NH_{3}
Predicted mass NH_{3} = maximum mass of NH_{3} that can be produced assuming that ALL the N_{2} reacts completely:
mass(NH_{3}) = moles(NH_{3}) × molar mass(NH_{3})
predicted mass NH_{3} = moles NH_{3} × molar mass NH_{3} = 12 × (14 + 3 × 1) = 12 × 17 = 204 g
theoretical yield NH_{3} = predicted mass NH_{3} = 204 g
 Calculate the actual yield:
percentage yield = (actual yield ÷ theoretical yield) × 100
Rearranging 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 NH_{3} = 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:
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.