Two successive reactions,$\mathbf{A}\mathbf{\to }\mathbf{B}$and $\mathbf{B}\mathbf{\to }\mathbf{C}$have yields of 73% and 68%, respectively. What is the overall percent yield for conversion of A to C?

The percentage yield is calculated as:

$\mathbf{Percentage}\mathbf{}\mathbf{yield}\mathbf{=}\frac{\mathbf{Actual}\mathbf{}\mathbf{yield}}{\mathbf{Theoretical}\mathbf{}\mathbf{yield}}\mathbf{\times }\mathbf{100}\mathbf{\%}$

The theoretical yield is the amount of product made in the reaction, whereas the actual yield is the amount of product actually produced.

In the given successive reaction, $\mathbf{B}$is intermediate, so the overall reaction is:

$\mathbf{A}\underset{\mathbf{}}{\mathbf{\to }}\mathbf{C}$

Consider 100% reactant initially present in the reaction. So, the amount of intermediate is:

$\begin{array}{c}\mathbf{}\mathbf{A}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\stackrel{\mathbf{}}{\mathbf{\to }}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{B}\mathbf{}\mathbf{}\mathbf{}\\ \mathbf{100}\mathbf{\%}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{73}\mathbf{\%}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\end{array}$

The final product is 68% of the intermediate present in the reaction. So, the yield of the final product is calculated as:

role="math" localid="1657102530698" $\begin{array}{c}\mathbf{}\mathbf{B}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\stackrel{\mathbf{}}{\mathbf{\to }}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{C}\mathbf{}\mathbf{}\mathbf{}\\ \mathbf{}\mathbf{73}\mathbf{\%}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{68}\mathbf{\%}\mathbf{\times }\frac{\mathbf{73}\mathbf{\%}}{\mathbf{100}\mathbf{\%}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\end{array}$

The yield of the overall reaction is calculated as:

$\begin{array}{c}\mathbf{}\mathit{A}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\stackrel{\mathbf{}}{\mathbf{\to }}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{C}\mathbf{}\mathbf{}\mathbf{}\\ \mathbf{}\mathbf{100}\mathbf{\%}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{68}\mathbf{\%}\mathbf{\times }\frac{\mathbf{73}\mathbf{\%}}{\mathbf{100}\mathbf{\%}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\end{array}$

Therefore, the percentage yield of the reaction is:

$$\begin{gathered} \mathbf{Percentage}\mathbf{}\mathbf{yield}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\mathbf{}\mathbf{68}\mathbf{\%}\mathbf{\times }\frac{\mathbf{73}\mathbf{\%}}{\mathbf{100}\mathbf{\%}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{49}\mathbf{.}\mathbf{64}\mathbf{\%} \end{gathered}$$