How to Calculate Theoretical Yield

Theoretical yield is basically the amount of products that are formed in a chemical reaction, when none of the reactants are wasted and the entire reaction is completed. Such reactants that react completely are called the limiting reagents of the reaction. It is based on the stoichiometry of the reaction (i.e. the relation between the quantities of substances that take part in a reaction or form a compound, [typically a ratio of whole integers]) and ideal conditions in which starting material is completely exhausted, undesired side reactions or reverse reactions do not occur, and there are no losses in the entire work-up procedure.

Theoretical yield helps in determining the overall efficiency of the reaction, which further assists in maximizing profitability in various industrial settings. A low theoretical yield means that the conditions were not optimal and could have been improved. Also, there were competing reactions occurring at the same time or some of the products may have got lost during the entire process. However, the amount of product actually formed by the reaction is the actual yield, which is generally less than the theoretical yield. Therefore, the efficiency of the reaction which is basically the ratio of actual yield to theoretical yield can be expressed as:

Yield (in %) = (actual yield (grams) / theoretical yield (grams)) x 100

Calculating Theoretical Yield
General mechanism for calculating theoretical yield is as follows:

• Balancing the reaction and determining the ratios of reactants to products.
• Calculating the number of moles of each starting material used.
• Finding the limiting reagent. For solids, divide the mass (in grams) of a reactant used by its molecular weight (in g/mol). For liquids and gases, multiply the volume times the density and then divide by the molecular weight. Multiply the molecular weight by the number of moles in the equation and whichever reactant has the lowest number is the limiting reagent.
• Calculating the moles of product expected, if the yield is 100% based on the limiting reagent.
• Calculating the grams of product corresponding to the number of moles expected.

Example: What is the theoretical yield of ethylene in the acid-catalyzed production of ethylene from ethanol, if you start with 100 g of ethanol?

CH₃CH₂OH -------> H₂C=CH₂ + H₂O

The reaction above is balanced, as one mole of ethanol (CH₃CH₂OH) producing one mole of ethylene (H₂C=CH₂), hence the stoichiometry or ratio is 1:1.

Now to calculate the theoretical yield, we have to determine the number of moles of each reactant. In this example the sole reactant is ethanol. Since, the molecular weight of ethanol is 46 g/mole, convert the 100 g to moles from the following calculation:

100(grams) x (1 (mole) / 46 (grams)) = 2.17 moles

Since, there is only one reactant, it will also act as a limiting reagent. The theoretical number of moles of ethylene is 2.17. Since, the molecular weight of ethylene is 28 g/mole, the theoretical yield is:

2.17(mole) x (28 (gram) / 1 (mole)) = 61 grams

Therefore, theoretical yield for this chemical reaction is 61 grams. Now to determine the percentage yield, suppose you start with 100 g of ethanol and isolate 50 g of ethylene, then the percentage yield is:

(50 (grams) / 61 (grams)) x 100 = 82%

Since, the value of actual yield is usually less than the theoretical yield, the percentage yield is always less than 100%. Well, this was all about theoretical yield. I hope the information given on how to calculate theoretical yield proves to be helpful, to all those who are struggling or finding it difficult to calculate.