Aspirin \(\left(\mathrm{C}, \mathrm{H}_{8} \mathrm{O}_{4}\right)\) is synthesized by reacting salicylic acid \(\left(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}\right)\) with acetic anhydride \(\left(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3}\right)\). The balanced equa- tion is $$ \mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}+\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3} \longrightarrow \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}+\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2} $$ a. What mass of acetic anhydride is needed to completely consume \(1.00 \times 10^{2} \mathrm{~g}\) salicylic acid? b. What is the maximum mass of aspirin (the theoretical yield) that could be produced in this reaction?

Step by step solution

01

Find the molar mass of salicylic acid

Calculate the molar mass by adding up the mass of each atom in salicylic acid: C: 7 × 12.01 g/mol = 84.07 g/mol H: 6 × 1.01 g/mol = 6.06 g/mol O: 3 × 16.00 g/mol = 48.00 g/mol The molar mass of salicylic acid is \(138.13 \thinspace g/mol\).

02

Calculate the moles of salicylic acid

Divide the given mass of salicylic acid by its molar mass to find the moles: \(1.00 \times 10^2 \thinspace g \div 138.13 \thinspace g/mol = 0.7238 \thinspace mol\) Step 2: Use the balanced equation to find the moles of acetic anhydride and aspirin

03

Moles of acetic anhydride

From the balanced equation, 1 mole of salicylic acid reacts with 1 mole of acetic anhydride. Thus, 0.7238 moles of salicylic acid need 0.7238 moles of acetic anhydride to completely react.

04

Moles of aspirin

From the balanced equation, 1 mole of salicylic acid produces 1 mole of aspirin. Thus, 0.7238 moles of salicylic acid can produce 0.7238 moles of aspirin. Step 3: Calculate the mass of acetic anhydride and aspirin

05

Find the molar mass of acetic anhydride

Calculate the molar mass by adding up the mass of each atom in acetic anhydride: C: 4 × 12.01 g/mol = 48.04 g/mol H: 6 × 1.01 g/mol = 6.06 g/mol O: 3 × 16.00 g/mol = 48.00 g/mol The molar mass of acetic anhydride is \(102.10 \thinspace g/mol\).

06

Calculate the mass of acetic anhydride

Multiply the moles of acetic anhydride by its molar mass to find the mass: \(0.7238 \thinspace mol \times 102.10 \thinspace g/mol = 73.92 \thinspace g\)

07

Find the molar mass of aspirin

Calculate the molar mass by adding up the mass of each atom in aspirin: C: 9 × 12.01 g/mol = 108.09 g/mol H: 8 × 1.01 g/mol = 8.08 g/mol O: 4 × 16.00 g/mol = 64.00 g/mol The molar mass of aspirin is \(180.17 \thinspace g/mol\).

08

Calculate the mass of aspirin

Multiply the moles of aspirin by its molar mass to find the mass: \(0.7238 \thinspace mol \times 180.17 \thinspace g/mol = 130.40 \thinspace g\) Answers: a. The mass of acetic anhydride needed to completely consume 100 g salicylic acid is 73.92 g. b. The maximum mass of aspirin that could be produced in this reaction is 130.40 g.

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