How to Calculate Percentage Yield?

Percentage yield is the weighted average of the product obtained divided by the theoretical yield. The quantity of product received from a chemical process is called the actual yield, whereas the quantity of product produced from the stoichiometric or balanced equation when the limiting reactant is used is called the theoretical yield. For a chemical reaction, the actual and theoretical yields are measured in the same units. The most commonly used units for these quantities are moles or grams.

Percentage yield Formula

The ratio of experimental yield to the theoretical yield multiplied by 100 gives the percentage yield of a chemical reaction. Generally, the value of percentage yield is less than 100 percent since the actual yield produced after the reaction is frequently smaller than the theoretical value. If its value is more significant than 100%, it clearly indicates that more sample was retrieved from the reaction than expected. If the actual and theoretical yields are equal, the percent yield is 100%.

P = (A / T) × 100 %

Where,

• P is the percentage yield,
• A is the actual yield,
• T is the theoretical yield.

For example,

Consider the decomposition process of calcium carbonate.

CaCO₃ → CaO + CO₂

The above reaction indicates that for every mole of reactant, CaCO₃, only one mole of the product CaO is obtained. This clearly tells us that the reactant and product have 1:1 mole ratio.

Suppose for this reaction, we have 2 moles of reactant. This means we will get 2 moles of the product too. But consider that in actual, the yield was 1.5 moles. To calculate the percentage yield, we find the ratio of actual yield and expected yield.

So, the percentage yield becomes,

P = (1.5/2) × 100 %

= 75%

Sample Problems

Problem 1: Calculate the percentage yield of a chemical reaction if 2 moles of the product were obtained against an expected yield of 4 moles.

Solution:

We have,

A = 2

T = 4

Using the formula we have,

P = (A / T) × 100 %

= (2/4) × 100 %

= (1/2) × 100 %

= 50%

Problem 2: Calculate the percentage yield of a chemical reaction if 5 moles of the product were obtained against an expected yield of 6 moles.

Solution:

We have,

A = 5

T = 6

Using the formula we have,

P = (A / T) × 100 %

= (5/6) × 100 %

= (0.833) × 100 %

= 83.3%

Problem 3: Calculate the actual yield of the product if the percentage yield of a chemical reaction is 90% and the expected yield is 5 moles.

Solution:

We have,

P = 90

T = 5

Using the formula we have,

P = (A / T) × 100 %

=> A = PT/100

=> A = 90 (5)/100

=> A = 450/100

=> A = 4.5 moles

Problem 4: Calculate the actual yield of the product if the percentage yield of a chemical reaction is 80% and the expected yield is 2 moles.

Solution:

We have,

P = 80

T = 2

Using the formula we have,

P = (A / T) × 100 %

=> A = PT/100

=> A = 80 (2)/100

=> A = 160/100

=> A = 1.6 moles

Problem 5: Calculate the expected yield of the product if the percentage yield of a chemical reaction is 98% and the actual yield is 3 moles.

Solution:

We have,

P = 98

A = 3

Using the formula we have,

P = (A / T) × 100 %

=> T = A/P × 100

=> T = (3/98) × 100

=> T = 3.06 moles

Problem 6: Calculate the expected yield of the product if the percentage yield of a chemical reaction is 92% and the actual yield is 2.5 moles.

Solution:

We have,

P = 92

A = 2.5

Using the formula we have,

P = (A / T) × 100 %

=> T = A/P × 100

=> T = (2.5/92) × 100

=> T = 2.7 moles

Problem 7: Calculate the percentage yield for the below decomposition reaction if the number of reactant moles is 6 and the actual yield is 2.8 moles.

2NO → N₂ + O₂

Solution:

The given reaction indicates that for every 2 moles of reactant, NO, only one mole of the product N₂ is obtained. This clearly tells us that the reactant and product have 2:1 mole ratio.

If the number of reactant moles is 6, then the product moles are clearly 3. So, the theoretical value is 3 moles.

Given that the actual product value is 2.8 moles.

So, the percentage yield becomes,

P = (2.8/3) × 100 %

= 93%

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