Question

Aspirin (acetyl salicylic acid) is prepared by heating salicylic acid with acetic anhydride. In an experiment, \(5 \mathrm{~g}\) of salicylic acid is heated with \(8 \mathrm{~g}\) of acetic anhydride. The theoretical yield of aspirin is (a) \(5.46 \mathrm{~g}\) (b) \(3.84 \mathrm{~g}\) (c) \(6.52 \mathrm{~g}\) (d) \(4.95 \mathrm{~g}\)

Short answer

Question: In a synthesis of aspirin, 5 g of salicylic acid and 8 g of acetic anhydride are used. Calculate the theoretical yield of aspirin. Answer: (c) 6.52 g

Step-by-step solution

Write the balanced chemical equation

Write the balanced chemical equation for the reaction between salicylic acid and acetic anhydride to produce aspirin and acetic acid: \(C_7H_6O_3 + C_4H_6O_3 \rightarrow C_9H_8O_4 + C_2H_4O_2\)

Calculate the moles of reactants

To determine the limiting reactant, we need to know the number of moles of salicylic acid and acetic anhydride. Use their molar masses to convert given masses in grams into moles: - Salicylic acid: \(C_7H_6O_3\) has a molar mass of 138.12 g/mol - Acetic anhydride: \(C_4H_6O_3\) has a molar mass of 102.09 g/mol Moles of salicylic acid = \(\frac{5 \mathrm{~g}}{138.12 \mathrm{~g/mol}} = 0.0362\) moles Moles of acetic anhydride = \(\frac{8 \mathrm{~g}}{102.09 \mathrm{~g/mol}} = 0.0784\) moles

Determine the limiting reactant

According to the balanced chemical equation, it's a 1:1 ratio between salicylic acid and acetic anhydride. We compare the number of moles of salicylic acid and acetic anhydride to determine the limiting reactant: Since there is less salicylic acid (0.0362 moles) than acetic anhydride (0.0784 moles), salicylic acid is the limiting reactant.

Calculate the theoretical yield of aspirin

Using the moles of the limiting reactant (salicylic acid), we can calculate the moles of aspirin (\(C_9H_8O_4\)) formed. According to the balanced chemical equation, the ratio between salicylic acid and aspirin is 1:1: Moles of aspirin = 0.0362 moles Now, we can convert moles of aspirin to grams using its molar mass (180.16 g/mol): Theoretical yield of aspirin = \(0.0362 \mathrm{~moles} \times 180.16 \mathrm{~g/mol} = 6.52 \mathrm{~g}\) So, the correct answer is (c) \(6.52 \mathrm{~g}\).

Key concepts

Chemical Equation Balancing

Understanding the basics of chemical equation balancing is essential in chemistry, particularly when working on reactions like the synthesis of aspirin. Balancing chemical equations ensures the law of conservation of mass is followed: matter is neither created nor destroyed during a chemical reaction.

Balancing a chemical equation involves adjusting the coefficients (the numbers in front) of the reactants and products so that the number of atoms of each element is the same on both sides of the equation. For example, the reaction for producing aspirin from salicylic acid and acetic anhydride can be balanced as follows:
\[C_7H_6O_3 + C_4H_6O_3 \rightarrow C_9H_8O_4 + C_2H_4O_2\]
This shows a one-to-one ratio between the reactants and products, which is critical in subsequent steps such as stoichiometry and limiting reactant calculations.

Stoichiometry

Stoichiometry is the study of the quantitative relationships between the amounts of reactants used and products formed in a chemical reaction. It is fundamentally based on the balanced chemical equation and uses the concept of moles to relate these quantities.

To carry out stoichiometric conversions, we need to use the coefficients from the balanced equation as conversion factors. These coefficients denote the ratio in which reactants combine and products form. For instance, the balanced equation for aspirin synthesis shows a 1:1 stoichiometric ratio between salicylic acid and acetic anhydride. This means that for each mole of salicylic acid reacting, one mole of aspirin is expected to form, assuming complete conversion and no side reactions.

Limiting Reactant Calculation

The limiting reactant in a chemical reaction is the substance that is completely consumed first and thus limits the amount of product that can be formed. Determining the limiting reactant is a critical step in predicting the theoretical yield of a reaction.

To find the limiting reactant, we compare the mole ratio of the reactants to that required by the balanced chemical equation. In the synthesis of aspirin, the balanced equation indicated a 1:1 ratio between salicylic acid and acetic anhydride. By calculating the moles of each reactant, we can identify which one is present in the lesser amount relative to the stoichiometric requirements. This reactant will be the limiting one and will dictate the maximum amount of product that can be made.

Molar Mass

The molar mass is a physical property of a substance and is defined as the mass of one mole of that substance. The unit for molar mass is grams per mole (g/mol). It serves as a bridge between the mass of a substance and the number of moles, making it a crucial factor for stoichiometric calculations in chemistry.

In the process of calculating the theoretical yield of aspirin, we use the molar masses of the reactants to convert the given masses in grams to moles. Subsequently, knowing the molar mass of the produced aspirin allows us to convert moles back to grams to determine the theoretical yield. For example, with the molar mass of aspirin being 180.16 g/mol, we can directly relate the moles of aspirin to the final mass expected from the reaction.