Question

Aspirin can be made in the laboratory by reacting acetic anhydride \(\left(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3}\right)\) with salicylic acid \(\left(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}\right)\) to form aspirin \(\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\right)\) andacctic acid \(\left(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}\right) \cdot\) The balanced equation is: $$\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3}+\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3} \longrightarrow \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}+\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}$$ In a laboratory synthesis, a student begins with 3.00 \(\mathrm{mL}\) of acetic anhydride (density \(=1.08 \mathrm{g} / \mathrm{mL} )\) and 1.25 \(\mathrm{g}\) of salicylic acid. Once the reaction is complete, the student collects 1.22 \(\mathrm{g}\) of aspirin. Determine the limiting reactant, theorctical yicld of aspirin, and percent yield for the reaction.

Short answer

The limiting reactant is salicylic acid, the theoretical yield of aspirin is 1.63 g, and the percent yield is approximately 74.85%.

Step-by-step solution

Calculate the mass of acetic anhydride

Since the density of acetic anhydride is given as 1.08 g/mL, multiply the volume of acetic anhydride by its density to find the mass: Mass of acetic anhydride = Volume × Density = 3.00 mL × 1.08 g/mL = 3.24 g

Calculate the moles of acetic anhydride and salicylic acid

Use the molar masses of acetic anhydride (\( C_4H_6O_3 \) with a molar mass of about 102.09 g/mol) and salicylic acid (\( C_7H_6O_3 \) with a molar mass of about 138.12 g/mol) to calculate the number of moles of each reactant. Moles of acetic anhydride = Mass / Molar mass = 3.24 g / 102.09 g/mol ≈ 0.03173 molMoles of salicylic acid = Mass / Molar mass = 1.25 g / 138.12 g/mol ≈ 0.00905 mol

Identify the limiting reactant

Compare the mole ratio of the reactants with the coefficients in the balanced equation (which are both 1). The reactant with fewer moles is the limiting reactant. In this case, salicylic acid is the limiting reactant because it has less moles (0.00905 mol) compared to acetic anhydride (0.03173 mol).

Calculate the theoretical yield of aspirin

The theoretical yield is calculated by using the moles of the limiting reactant (salicylic acid) and the mole-to-mole ratio from the balanced equation. Since 1 mole of salicylic acid produces 1 mole of aspirin, the theoretical yield in moles of aspirin is also 0.00905 mol. Now, convert the moles of aspirin to grams using its molar mass (\( C_9H_8O_4 \) with a molar mass of about 180.16 g/mol): Theoretical yield (g) = Moles of aspirin × Molar mass of aspirin = 0.00905 mol × 180.16 g/mol = 1.63 g

Calculate the percent yield

Percent yield is calculated by dividing the actual yield by the theoretical yield and then multiplying by 100%. Percent yield = (Actual yield / Theoretical yield) × 100% = (1.22 g / 1.63 g) × 100% ≈ 74.85%

Key concepts

Limiting Reactant

When it comes to chemical reactions, not all reactants are created equal. Some get used up first, halting the reaction, and these are known as the limiting reactants. Understanding which reactant is limiting is crucial to predicting how much product can be formed. It's the ingredient in the shortest supply for a recipe, the bottleneck of the production line.

In the laboratory synthesis of aspirin, the concept of limiting reactant is demonstrated when acetic anhydride reacts with salicylic acid. Although both are necessary, one will run out before the other based on the initial amounts and the balanced equation. In our example, despite starting with a greater mass of acetic anhydride, the lower mass of salicylic acid, when converted to moles, indicated that salicylic acid was the limiting reactant. This identification dictates the maximum amount of product that can be formed and is used to calculate the theoretical yield. Thus, recognizing the limiting reactant lays the foundation for predicting the efficiency of a chemical reaction.

Theoretical Yield

Imagine you're baking a cake, and the recipe assures you'll end up with a three-layer cake. That's your theoretical yield in baking! Similarly, in chemistry, the theoretical yield is the amount of product estimated to form when a reaction goes to completion under perfect conditions, with no loss or side reactions.

For the synthesis of aspirin, the theoretical yield is calculated using stoichiometry, based on the limited supply of salicylic acid. The balanced chemical equation tells us that one mole of salicylic acid should yield one mole of aspirin. By converting the moles of the limiting reactant (salicylic acid in this case) directly to the mass of aspirin, scientists establish the maximum possible mass of aspirin that could be produced, which was 1.63 grams in the given scenario. This prediction is a critical step in evaluating the efficiency and success of a chemical synthesis, acting as the benchmark against the actual yield obtained from an experiment.

Percent Yield

In the real world, things are rarely as perfect as they are on paper, and this applies to chemical reactions as well. The percent yield is the ratio of the actual amount of product obtained to the theoretical amount possible, expressed as a percentage. It's like comparing the number of slices of cake you end up with versus how many the recipe claimed you'd have.

The percent yield is an indicator of the reaction's efficiency. For our aspirin reaction, where 1.22 grams was the actual yield and 1.63 grams was the theoretical yield, the percent yield comes out to be approximately 74.85%. This tells us and the student conducting the experiment how 'successful' their synthesis was. A percent yield below 100% might suggest inefficiencies such as incomplete reactions, impurities, product loss during transfer or measurement inaccuracies. Understanding this parameter helps students and chemists alike to refine their techniques and their expectations of real-world laboratory outcomes.