Question

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?

Short answer

a. The mass of acetic anhydride needed to completely consume \(100\thinspace g\) salicylic acid is \(73.92\thinspace g\). b. The maximum mass of aspirin that could be produced in this reaction is \(130.40\thinspace g\).

Step-by-step solution

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 \(138.13 \thinspace g/mol\).

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

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.

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

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 \(102.10 \thinspace g/mol\).

Calculate the mass of acetic anhydride

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

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 \(180.17 \thinspace g/mol\).

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.

Key concepts

Balanced Chemical Equation

A balanced chemical equation is crucial because it ensures the law of conservation of mass is maintained during a chemical reaction. This means that the number of atoms of each element on the reactant side must be equal to the number on the product side. In the synthesis of aspirin from salicylic acid and acetic anhydride, the balanced equation is displayed as follows:
\[ \mathrm{C}_7 \mathrm{H}_6 \mathrm{O}_3 + \mathrm{C}_4 \mathrm{H}_6 \mathrm{O}_3 \rightarrow \mathrm{C}_9 \mathrm{H}_8 \mathrm{O}_4 + \mathrm{HC}_2 \mathrm{H}_3 \mathrm{O}_2 \]
Here, each type of atom is accounted for and equal on both sides:

• Carbon (C): 7 from salicylic acid + 4 from acetic anhydride = 9 in aspirin + 2 in acetic acid product.
• Hydrogen (H): 6 in salicylic acid + 6 in acetic anhydride = 8 in aspirin + 4 in acetic acid product.
• Oxygen (O): 3 in salicylic acid + 3 in acetic anhydride = 4 in aspirin + 2 in acetic acid product.

This balance confirms that no atoms are lost or gained, just rearranged to form new compounds.

Molar Mass Calculation

Molar mass calculation is a fundamental skill in stoichiometry, involving finding the mass of one mole of a compound's atoms. For example, in the synthesis of aspirin:

For salicylic acid \((\mathrm{C}_7\mathrm{H}_6\mathrm{O}_3)\):
The molar mass is calculated by summing the masses multiplied by the number of each type of atom:

• Carbon (C): \(7 \times 12.01 \space g/mol = 84.07 \space g/mol\)
• Hydrogen (H): \(6 \times 1.01 \space g/mol = 6.06 \space g/mol\)
• Oxygen (O): \(3 \times 16.00 \space g/mol = 48.00 \space g/mol\)

Total molar mass of salicylic acid is \(138.13 \space g/mol\).

Similarly, find the molar mass for other compounds by adding the atomic masses for each element according to its formula.
Molar mass allows conversion from a gram measure to moles which is essential in determining how much of each reactant is required, and knowing exactly how much product can be expected under perfect conditions.

Theoretical Yield

Theoretical yield signifies the maximum amount of product that can be obtained from a chemical reaction if it proceeds perfectly, without any loss, based on the stoichiometry of the balanced chemical equation. It provides an ideal scenario against which actual yields can be measured.
In the reaction that synthesizes aspirin, theoretical yield is calculated from the moles of the limiting reactant, which defines the maximum possible moles of product:

• Start by using the balanced equation to find that 1 mole of salicylic acid produces 1 mole of aspirin.
• Given 0.7238 moles of salicylic acid (calculated from the provided 100 g), it should produce 0.7238 moles of aspirin when fully reacted.

To find the theoretical mass of aspirin, the moles are multiplied by the molar mass:
\(0.7238 \space mol \times 180.17 \space g/mol = 130.40 \space g\)
This calculation anticipates a perfect conversion under ideal conditions with no waste.