Question

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?

Short answer

The overall percentage yield is 49.64%.

Step-by-step solution

Determine the percentage yield

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.

Identification of the overall reaction

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

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

Calculate the yield of reactant and product

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

Determine the yield of the overall reaction 

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:

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