YIELD

The amount of product obtained from a chemical reaction is referred to as the yield.

THEORETICAL YIELD

The maximum amount of the product that can be obtained during calculations of a chemical equation is called the theoretical yield.

ACTUAL YIELD

The maximum amount of the product that can be obtained during an actual chemical reaction in a laboratory is called the theoretical yield.

PERCENT YIELD

The ratio of the actual yield to the theoretical yield expressed as a percentage is called the percentage yield. It is expressed as:

Percent yield = actual yield/theoretical yield x 100

The percentage yield of a multi-step reaction is calculated by the following formula.

Percentage yield of multi-step reaction = (multiply all percent yield steps in fractions) x 100

IMPORTANT NUMERICALS  

Q: A reaction involves the combustion of 25 g of methane (CH₄) with excess oxygen. Calculate the theoretical yield of carbon dioxide (CO₂) and water (H₂O). If the actual yield of CO₂ is 60 g, calculate the percent yield.

Sol: CH₄ + 2O₂ → CO₂ +2H₂O

In this equation, firstly, the number of moles of CH₄ is calculated (because some information about CH₄ is provided). By using the mass-mole relationship moles of CH₄ are calculated.

No. of moles = mass/molar mass ⇒ No. of moles = 25/16 = 1.56

In the second step, the number of moles of CO₂ is to be calculated. As from the balanced equation it is indicated that the mole ratio between CH₄ and CO₂ is 1:1. So, CO₂ also contains 1.56 calculated number of moles.

In the third step theoretical yield of CO₂ (in g)is calculated by using the mass-mole relationship as: No. of moles = mass/molar mass ⇒ mass = no. of moles x molar mass ⇒ 1.56 x 44 = 68.75 g.

In last step percentage yield is calculated as: Percent yield = actual yield/theoretical yieldx100 ⇒ 60/68.75 x100 = 87.27%.

Q: A synthesis reaction produces 50 g of product, but the theoretical yield is 62.5 g. Calculate the percent yield. If the reaction is repeated with a different catalyst, the percentage yield increases to 90%. Calculate the new actual yield.

Sol: Thepercentage yield is calculated as: Percent yield = actual yield/theoretical yield x 100 ⇒ (50/62.5) x 100 = 80%. In the new percentage yield, the actual yield is calculated as: Percent yield = actual yield/theoretical yield x 100 ⇒ 90 = (actual yield/62.5)  x 100 ⇒ actual yield =90 x 62.5/100 = 56.25 g.

Q: A multi-step reaction involves the conversion of reactant A to product D through intermediates B and C. Calculate the overall percent yield if the percent yields of each step are 80%, 90%, and 85%, respectively.

Sol: Percentage yield of multi-steps reaction = (multiply all percent yield steps in fractions) x 100 ⇒ (0.8 x 0.9 x 0.85) x 100 = 61.2 %.

Q: 10.0 g of impure CaCO₃ (80% pure) is heated. Calculate the theoretical and percent yield of CO₂ gas if 2.0 g of CO₂ is collected. CaCO₃→CaO+CO₂

Sol: In this problem, first of all, the mass of pure CaCO₃ is calculated by a simple expression. Amount of pure sample = amount of impure sample x purity percentage/100 ⇒ Amount of pure sample = 10 x 80/100 = 10 × 0.80 = 8.0 g.

For the calculation of the theoretical yield of CO₂, firstly, the number of moles of CO₂ is calculated, which is obtained by comparing with a pure sample of CaCO₃ (because some information about CaCO₃ is provided). No. of moles of  CaCO₃ = mass/ molar mass   ⇒ 8/100 = 0.08 mol. From the balanced equation, it is indicated that the mole ratio between CaCO₃  and CO₂ is 1:1. So, CO₂ also contains 0.08 calculated number of moles. So, the mass (theoretical yield) is calculated by using the mole-mass relationship.

No.of moles = mass/molar mass ⇒ mass = 0.08 × 44 = 3.52 g.

Percent yield = actual yield/theoretical yield x 100 ⇒ (2/3.52) x 100 =56.82%.