Topics in Organic Chemistry: Reaction Yield - Definitions, Formula & Examples

In this article we will learn about Reaction Yield. The yield of reaction is the amount of product formed from given starting material. Reaction yield is written in percentage and given on the reaction arrow along with reaction conditions.

Key words: Chemical reaction, Theoretical yield, Percent yield, Overall yield.

Definitions

In a chemical reaction amount of product formed is known as yield of that reaction. Theoretically we can calculate the amount of product formed as the reaction completes. The ideal amount of product formed in the reaction is known as theoretical yield. But in practical theoretical yield cannot be isolated because of various factors such reaction conditions, chromatographic purifications and formation of by products. Hence the isolated yield is always compared with theoretical yield and it is reported in percentage also known as percent yield.

For example consider a hypothetical reaction in which compound A (1 mol) and compound B (1 mol) reacts together to form compound AB. If there is no by product form in the reaction then theoretically 1 mol of compound AB should form as a result of reaction. Now consider that compound A has molecular weight 100 g/ mol and compound B has molecular weight 50 g/mol. Therefore molecular weight of compound will be 150 g/mol. In the reaction if we used 1 g of compound A (1/100 = 0.01 moles) then compound B is needed 0.01 moles. To calculate required amount of compound B we need multiply 0.01 moles x molecular weight; therefore 0.01 moles x 50 = 0.5 g. The compound AB formed in the reaction should be 0.01 moles. (Table 1)

Reaction
Compound	A	B	AB
Molecular Wt.	100 g /mol	50 g/mol	150 g/mol
Amount	1g	0.01 x 50 = 0.5 g	------
Moles	1g / 100 g = 0.01 moles	0.01 moles	0.01 moles

Table: 1

Calculation of theoretical yield

Case 1

Suppose in this reaction a limiting reagent is compound A. So the theoretical yield is calculated by the formula;

Case 2

If compound B is limiting agent in this reaction then theoretical yield is calculated by the formula;

Hence from the reaction of compound A and B the maximum amount of compound AB will be 1.5 g.

The actual yield of reaction may or may not be equal to the theoretical yield. Loss of yield is due to methods of purification of the compounds. Hence actual yield or isolated yield is always compared with theoretical yield and written in percentage. Suppose in above reaction actual yield is 1.1 g. So the percent yield can be calculated by the formula;

Hence percent yield of the reaction is 73.33 %.

Consider the reaction of methyl benzoate with lithium borohydride to produce benzyl alcohol. In this reaction for 1 mole of ester compound there is requirement of 2 moles of lithium borohydride. Calculation for the reaction is shown in table 2.

Reaction
Compound	methyl benzoate	LiAlH₄	benzyl alcohol
Molecular Wt.	136.15 g /mol	37.95 g/mol	108.14 g/mol
Amount	1g	(0.0073 x 2) x 37.95 = 0.554 g	------
Moles	1g / 136.15 g = 0.0073 moles	0.0073 x 2	0.0073 moles

Table: 2

Calculation of Theoretical Yield

Here methyl benzoate is limiting regent because it is used in least quantity. Therefore theoretical yield is calculated by the formula;

Calculation of Percent Yield

Suppose actual yield of the reaction after purification of the compound is 0.5 g; then percent yield is calculated as below;

Hence percent yield of the reaction is 62.97 %.

How to calculate overall yield of multi-step synthesis?

In organic chemistry many compounds are synthesized by linear synthesis that is the molecules required series of reactions. Each step in the synthesis has different yield of reaction. Therefore it is necessary to understand amount of final compound as a result of all the steps. This gives exact idea of productivity of the multi-step synthesis.

For example; consider a hypothetical multistep synthesis which has three steps. In this reaction scheme step 1 gives 70 % yield, step 2 has 80 % yield and step 3 gives the final product in 90 % yield. Therefore overall yield of the reaction scheme is calculated by the formula;