## Theoretical yield formula

The quantity of a product obtained from a reaction is expressed in terms of the yield of the reaction. The amount of product predicted by stoichiometry is called the theoretical yield, whereas the amount obtained actually is called the actual yield. A reaction yield is reported as a percent yield which gives the percentage of the theoretical amount.

The formula for percent yield is given by

$\dpi{120}&space;\large&space;Percent\;&space;yield&space;=\frac{Actual\;&space;yield}{Theoretical\;&space;yield}\times&space;100\%$

Rearrange the above formula to obtain theoretical yield formula

$\dpi{120}&space;\large&space;Theoretical\;&space;yield&space;=\frac{Actual\;&space;yield}{percent\;&space;yield}\times&space;100\%$

Example 1

Determine the theoretical yield of the formation of geranyl formate from 375g of geraniol. A chemist making geranyl formate uses 375g of starting material and collects 417g of purified product. Percent yield is given as 94.1%

Solution

The actual yield is 417g which is the quantity of the desired product.

Percent yield is 94.1%

Therefore,

$\dpi{120}&space;\large&space;Theoretical\;&space;yield&space;=\frac{Actual\;&space;yield}{percent\;&space;yield}\times&space;100\%$

= 417 / 94.1× 100%

= 443g

Example 2

For the industrial production of hydrogen cyanide, the yield of the synthesis is 97.5%. Calculate how many kgs of methane and how many of ammonia should be used to produce 1.50 × 105 kg of HCN.

Solution

Rearrange the equation for percent yield to find the theoretical yield that gives an actual yield of 1.50 × 105 kg

$\dpi{120}&space;\large&space;Theoretical\;&space;yield&space;=\frac{Actual\;&space;yield}{percent\;&space;yield}\times&space;100\%$

= 1.50×105 kg / 97.5% × 100%

Theoretical yield = 1.528 × 105 kg HCN