Question

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: $$ \mathrm{I} . \quad \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{3} \mathrm{N}(s)+3 \mathrm{H}_{2}(g)+\mathrm{HCl}(a q) \longrightarrow $$ $$ \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{ONCl}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) $$ $$ \mathrm{II}\quad \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{ONCl}(s)+\mathrm{NaOH}(a q) \longrightarrow $$ $$ \mathrm{C}_{6} \mathrm{H}_{7} \mathrm{ON}(s)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{NaCl}(a q) $$ $$ \mathrm{III.} \quad \mathrm{C}_{6} \mathrm{H}_{7} \mathrm{ON}(s)+\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3}(l) \longrightarrow $$ $$ \mathrm{C}_{8} \mathrm{H}_{9} \mathrm{O}_{2} \mathrm{N}(s)+\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(l) $$ 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?

Short answer

a. The total percent yield by mass for the overall process can be calculated as follows: Total Percent Yield = \(\frac{3/4}{0.87 \times \frac{157}{151} \times 0.98 \times \frac{107}{157}} \times 100\% \) b. The percent yield by mass for Step III can be calculated as follows: Percent Yield of Step III = \(\frac{\text{Total Percent Yield}}{\text{Percent Yield of Step I} \times \text{Percent Yield of Step II}} = \frac{\text{Total Percent Yield}}{0.87 \times 0.98} \times 100\% \)

Step-by-step solution

Calculate Molar Masses (Optional)

Find the molar mass of each compound involved in the reaction. C_6H_5O_3N: 151 g/mol C_6H_8ONCl: 157 g/mol C_6H_7ON: 107 g/mol C_8H_9O_2N: 151 g/mol

Step I: Calculate Mass Produced

Percent yield by mass in Step I = 87%. For every mole of C6H5O3N, the reaction produces 1 mole of C6H8ONCl, and the mass ratio is: \(\frac{\text{Mass of C}_6\text{H}_8\text{ONCl}}{\text{Mass of C}_6\text{H}_5\text{O}_3\text{N}} = 0.87\) Now, let's find the mass of C6H8ONCl produced per mole of C6H5O3N: Mass of C6H8ONCl = \(0.87 \times \frac{157 \text{ g/mol}}{151 \text{ g/mol}}\)

Step II: Calculate Mass Produced

Percent yield by mass in Step II = 98%. For every mole of C6H8ONCl, the reaction produces 1 mole of C6H7ON, and the mass ratio is: \(\frac{\text{Mass of C}_6\text{H}_7\text{ON}}{\text{Mass of C}_6\text{H}_8\text{ONCl}} = 0.98\) Now, let's find the mass of C6H7ON produced per mole of C6H8ONCl: Mass of C6H7ON = \(0.98 \times \frac{107 \text{ g/mol}}{157 \text{ g/mol}}\)

Overall Reaction:

We are given that for every 4 moles of C6H5O3N, 3 moles of C8H9O2N are produced. Overall mass ratio: \(\frac{\text{Mass of C}_8\text{H}_9\text{O}_2\text{N}}{\text{Mass of C}_6\text{H}_5\text{O}_3\text{N}} = \frac{3 \cdot 151}{4 \cdot 151}\) Combine mass ratios of Step I, Step II, and the overall mass ratio: \(\frac{3}{4} = 0.87 \times \frac{157}{151} \times 0.98 \times \frac{107}{157}\)

a: Calculate Percent Yield by Mass for Overall Process

Solve for the total percent yield by mass for the overall process: Total Percent Yield = \(\frac{3/4}{0.87 \times \frac{157}{151} \times 0.98 \times \frac{107}{157}} \times 100\% \)

b: Calculate Percent Yield by Mass for Step III

To find the percent yield for Step III, divide the percent yield of the overall process by the product of the percent yield of Step I and Step II: Percent Yield of Step III = \(\frac{\text{Total Percent Yield}}{\text{Percent Yield of Step I} \times \text{Percent Yield of Step II}} = \frac{\text{Total Percent Yield}}{0.87 \times 0.98} \times 100\% \) Calculate the percent yield by mass for Step III using the values found above.

Key concepts

Acetaminophen Production

Acetaminophen, a common pain reliever and fever reducer, is synthesized through a series of chemical reactions. The entire process involves three main steps, each contributing to the overall yield of the product. This synthesis starts with a compound called phenyl nitrobenzoate, and through a series of transformations, it ends with acetaminophen, known chemically as \( \text{C}_8 \text{H}_9 \text{O}_2 \text{N} \).

The initial step in the synthesis reduces nitro compounds to amine derivatives. In the second step, these amine derivatives undergo further reactions to form intermediates necessary for the final drug. The third step culminates in the formation of acetaminophen itself, formed by adding acetic anhydride to 4-aminophenol.

These reactions have to be meticulously controlled to maximize the yield and quality of acetaminophen. This process not only requires a chemical understanding but also a keen attention to reaction conditions like temperature and pH.

Percent Yield Calculation

The percent yield of a reaction helps determine the efficiency of the chemical process. Simply put, it compares the actual amount of product obtained to the theoretical maximum. Calculating percent yield is crucial for evaluating how successful a chemical reaction was.

To find the percent yield, the equation used is:

• \( \text{Percent Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100 \% \)

In our example, acetaminophen is produced in three steps and the yield of each step affects the overall yield. The given problem mentions percent yields for the first two steps: 87% and 98%, respectively. The challenge is to calculate the total percent yield of the sequence and identify the individual percent yield of Step III.

Understanding how each step contributes to the overall yield helps chemists optimize processes to increase efficiency and reduce waste, which is vital in large-scale industrial production.

Stoichiometry

Stoichiometry is the chemical math that dictates the proportions of reactants and products in a reaction. It provides the quantitative basis for chemical reactions and helps predict yields. In the production of acetaminophen, stoichiometry dictates how much of each reactant is needed and how much product can be formed.

The stoichiometric coefficients, such as the 3:4 mole ratio mentioned for acetaminophen production, indicate the exact balance between moles of reactants and products. This balance is derived from the balanced chemical equations, ensuring mass conservation.

Using stoichiometry, chemists can precisely calculate amounts of reactants to avoid excess waste and determine the anticipated mass of products formed. In the acetaminophen process, understanding how the yield of each step relates to stoichiometric calculations can guide adjustments to improve the entire process.

Molar Mass

Molar mass is a key concept in chemistry that refers to the mass of a single mole of a substance, typically expressed in grams per mole (g/mol). It provides a way to convert between the mass of a substance and the amount in moles, which is crucial for stoichiometric calculations.

In the context of acetaminophen production, calculating the molar mass of each reactant and product allows chemists to determine how much of each substance is involved in the reactions. For instance, knowing the molar mass of acetaminophen (151 g/mol) helps quantify yields and assess the efficiency of each step.

The molar masses of other intermediates involved, such as \( \text{C}_6 \text{H}_5 \text{O}_3 \text{N} \) and \( \text{C}_6 \text{H}_8 \text{ONCl} \), play an equally important role. Correct calculations and understanding of molar mass support the accurate application of stoichiometry, ensuring that all chemical equations are balanced and proportional in practice.

Chemical Reactions

Chemical reactions form the backbone of chemical synthesis, transforming reactants into products through bond-breaking and bond-forming processes. In acetaminophen production, each of the three chemical reactions involves distinct molecular changes.

One of the core aspects of these reactions is maintaining equilibrium to optimize product formation. This involves controlling variables such as temperature, pressure, and the presence of catalysts, all of which can shift equilibrium, impacting yields.

Chemists must thoroughly understand the mechanisms underlying each reaction, including how reactants interact and transition to products. In the synthesis of acetaminophen, steps involve additions, eliminations, and rearrangements. These processes highlight the diverse nature of chemical reactions and the importance of tailoring conditions to achieve the maximum desired yield.