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Problem 86

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

## Discussion

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The aspirin substitute, acetaminophen $\left(\mathrm{C}_{8} \mathrm{H}_{9} \mathrm{O}_{2} \mathrm{N}\right),$ is produced by the following three-step synthesis:

$$

\mathrm{I} . \quad \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{3} \mathrm{N}(s)+3 \mathrm{H}_{2}(g)+\mathrm{HCl}(a q) \longrightarrow

$$

$$

\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{ONCl}(s)+2 \mathrm{H}_{2} \mathrm{O}(l)

$$

$$

\mathrm{II}\quad \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{ONCl}(s)+\mathrm{NaOH}(a q) \longrightarrow

$$

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\mathrm{C}_{6} \mathrm{H}_{7} \mathrm{ON}(s)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{NaCl}(a q)

$$

$$

\mathrm{III.} \quad \mathrm{C}_{6} \mathrm{H}_{7} \mathrm{ON}(s)+\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3}(l) \longrightarrow

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$$

\mathrm{C}_{8} \mathrm{H}_{9} \mathrm{O}_{2} \mathrm{N}(s)+\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(l)

$$

The first two reactions have percent yields of 87$\%$ and 98$\%$ by mass, respectively. The overall reaction yields 3 moles of acetaminophen product for every 4 moles of $\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{3} \mathrm{N}$ reacted.

a. What is the percent yield by mass for the overall process?

b. What is the percent yield by mass of Step III?

The reactions shown here can be combined to make the overall reaction $\mathrm{C}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}(g)+\mathrm{H}_{2}(g)$ by reversing some and/or dividing all the coefficients by a number. As a group, determine how the reactions need to be modified to sum to the overall process. Then have each group member determine the value of $K$ for one of the reactions to be combined. Finally, combine all the values of $K$ to determine the value of $K$ for the overall reaction.

$$

\begin{array}{ll}{\text { a. } C(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)} & {K=1.363 \times 10^{69}} \\ {\text { b. } 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)} & {K=1.389 \times 10^{80}} \\ {\text { c. } 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)} & {K=1.477 \times 10^{90}}\end{array}

$$