Q81P - Chemistry: Molecular Nature Of Matter And Change

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?

Step-by-Step Solution

Answer

The overall percentage yield is 49.64%. 

Step 1: 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.

Step 2: Identification of the overall reaction

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

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

Step 3: 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:

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

Step 4: 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:

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