Question

Aspirin (acetylsalicylic acid, \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\) ) is made by reacting salicylic acid \(\left(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}\right)\) with acetic anhydride \(\left[\left(\mathrm{CH}_{3} \mathrm{CO}\right)_{2} \mathrm{O}\right]:\) $$ \mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}(s)+\left(\mathrm{CH}_{3} \mathrm{CO}\right)_{2} \mathrm{O}(l) \longrightarrow \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}(s)+\mathrm{CH}_{3} \mathrm{COOH}(l) $$ In one preparation, \(3.077 \mathrm{~g}\) of salicylic acid and \(5.50 \mathrm{~mL}\) of acetic anhydride react to form \(3.281 \mathrm{~g}\) of aspirin. (a) Which is the limiting reactant (the density of acetic anhydride is \(1.080 \mathrm{~g} / \mathrm{mL}) ?\) (b) What is the percent yield of this reaction? (c) What is the percent atom economy of this reaction?

Short answer

Limiting reactant: salicylic acid; Percent yield: 81.73%; Percent atom economy: 75%.

Step-by-step solution

- Calculate Moles of Salicylic Acid

First, determine the molar mass of salicylic acid (C7H6O3). Molecules mass: \(7 \times 12 + 6 \times 1 + 3 \times 16 = 138 \ \text{g/mol}\). Then, calculate the moles of salicylic acid: \(\frac{3.077 \ \text{g}}{138 \ \text{g/mol}} = 0.0223 \ \text{mol}\).

- Calculate Moles of Acetic Anhydride

Find the mass of acetic anhydride using its density: \(5.50 \, \text{mL} \times 1.080 \ \text{g/mL} = 5.94 \ \text{g}\). Determine the molar mass of acetic anhydride (C4H6O3): \(4 \times 12 + 6 \times 1 + 3 \times 16 = 102 \ \text{g/mol}\). Then, calculate the moles of acetic anhydride: \(\frac{5.94 \ \text{g}}{102 \ \text{g/mol}} = 0.0582 \ \text{mol}\).

- Identify the Limiting Reactant

Compare the mole ratios to determine the limiting reactant. The balanced equation shows a 1:1 ratio between salicylic acid and acetic anhydride. Since 0.0223 mol of salicylic acid is less than 0.0582 mol of acetic anhydride, salicylic acid is the limiting reactant.

- Calculate Theoretical Yield of Aspirin

The stoichiometry of the reaction shows that 1 mol of salicylic acid yields 1 mol of aspirin (C9H8O4). Therefore, the theoretical yield of aspirin is 0.0223 mol. Calculate the mass of aspirin: \(0.0223 \, \text{mol} \times 180 \ \text{g/mol} = 4.014 \ \text{g}\).

- Calculate Percent Yield

Percent yield is calculated by \(\frac{\text{actual yield}}{\text{theoretical yield}} \times 100\%\). Here, \(\frac{3.281 \ \text{g}}{4.014 \ \text{g}} \times 100\% = 81.73\%\).

- Calculate Percent Atom Economy

Percent atom economy is given by \(\frac{\text{molecular mass of desired product}}{\text{total mass of reactants}} \times 100\%\). Total mass of reactants is the mass of salicylic acid plus acetic anhydride: 138 + 102 = 240 g/mol. The molecular mass of aspirin is 180 g/mol. So, \(\frac{180 \ \text{g/mol}}{240 \ \text{g/mol}} \times 100\% = 75\%\).

Key concepts

limiting reactant

In any chemical reaction, the limiting reactant is the substance that is completely consumed first and thus determines the amount of product formed. To identify the limiting reactant, we first need to calculate the moles of each reactant. For instance, if we have 3.077 g of salicylic acid \(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}\) and enough acetic anhydride \[\left(\mathrm{CH}_{3} \mathrm{CO}\right)_{2} \mathrm{O}\],\ we can determine the moles for both.

percent yield

Percent yield helps us understand the efficiency of a reaction. It is calculated by comparing the actual yield (what we obtained) to the theoretical yield (what we expected).
Percent yield gives insight into how well a reaction proceeded and can also reveal losses or errors during the experiment. For example, if the theoretical yield of aspirin was 4.014 g but we obtained 3.281 g, the percent yield would be \(\frac{3.281}{4.014} \times 100\% = 81.73\%\).

atom economy

Atom economy measures how efficient a chemical reaction is in terms of the atoms used to form the desired product. It's calculated using the ratio of the molecular mass of the desired product to the total mass of reactants. High atom economy is desirable for green chemistry.
For example, in the synthesis of aspirin, if the mass of aspirin (\(180 \ \text{g/mol}\)) is divided by the total mass of reactants (\(240 \ \text{g/mol}\)), the percent atom economy is \(\frac{180}{240} \times 100\% = 75\%\).

stoichiometry

Stoichiometry is the part of chemistry that deals with the quantitative relationships between reactants and products. It relies on balanced chemical equations and mole ratios.
In the aspirin synthesis, the balanced reaction is: \[\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3} + \left(\mathrm{CH}_{3} \mathrm{CO}\right)_{2} \mathrm{O} \rightarrow \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4} + \mathrm{CH}_{3} \mathrm{COOH}\],\ which shows the 1:1 mole ratio between salicylic acid and acetic anhydride.

chemical reaction equation

A chemical reaction equation represents the reactants converting into products. It must be balanced to follow the law of conservation of mass, meaning the same number of each type of atom must appear on both sides of the equation.
For example, for aspirin production, the equation is: \[\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3} + \left(\mathrm{CH}_{3} \mathrm{CO}\right)_{2} \mathrm{O} \rightarrow \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4} + \mathrm{CH}_{3} \mathrm{COOH}\],\ which ensures that the number of carbon, hydrogen, and oxygen atoms are equal on both sides.