Question

Acetylsalicylic acid, the active ingredient in aspirin, is prepared from salicylic acid by reaction with acetic anhydride. $$\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}+\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3} \quad \longrightarrow \quad \mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4} \quad+\quad \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}$$ (salicylic acid) (acetic anhydride) (acetylsalicylic acid) (acetic acid) (a) Calculate the theoretical yield if \(47 \mathrm{~g}\) of salicylic acid is reacted with \(25 \mathrm{~g}\) of acetic anhydride. (b) What is the percent yield if only \(35 \mathrm{~g}\) is obtained?

Short answer

Theoretical yield: 44.12 g, Percent yield: 79.3%.

Step-by-step solution

Determine Molar Masses

First, calculate the molar mass of each compound involved in the reaction: For salicylic acid \(C_{7}H_{6}O_{3} = 7(12.01) + 6(1.01) + 3(16.00) = 138.12 \, g/mol\)For acetic anhydride \(C_{4}H_{6}O_{3} = 4(12.01) + 6(1.01) + 3(16.00) = 102.09 \, g/mol\)For acetylsalicylic acid \(C_{9}H_{8}O_{4} = 9(12.01) + 8(1.01) + 4(16.00) = 180.18 \, g/mol\) .

Convert Mass to Moles

Convert the masses of salicylic acid and acetic anhydride to moles using their molar masses:For salicylic acid: \(\frac{47 \, g}{138.12 \, g/mol} \approx 0.34 \, mol\)For acetic anhydride: \(\frac{25 \, g}{102.09 \, g/mol} \approx 0.245 \, mol\).

Identify Limiting Reagent

Determine the limiting reagent by comparing the mole ratio. The balanced equation shows a 1:1 mole ratio:Salicylic acid: \(0.34 \, mol\)Acetic anhydride: \(0.245 \, mol\).Since acetic anhydride has fewer moles, it is the limiting reagent.

Calculate Theoretical Yield of Product

The theoretical yield of acetylsalicylic acid is determined by the moles of the limiting reagent:Using acetic anhydride: \(0.245 \, mol \, C_{9}H_{8}O_{4} \times 180.18 \, g/mol = 44.12 \, g\).Thus, the theoretical yield of acetylsalicylic acid is 44.12 g.

Calculate Percent Yield

Calculate the percent yield using the actual yield and theoretical yield:Percent yield = \(\frac{35 \, g}{44.12 \, g} \times 100 \approx 79.3\%\).

Key concepts

Theoretical Yield in Stoichiometry

In stoichiometry, the theoretical yield is the maximum amount of product that can be formed in a chemical reaction. This is based on the complete conversion of the limiting reactant into the desired product under perfect conditions. To determine the theoretical yield, it is essential to:

• Use a balanced chemical equation to understand the mole-to-mole relationships between reactants and products.
• Identify the limiting reagent, which is the reactant that gets consumed first and limits the amount of product produced.
• Convert the moles of the limiting reagent into the moles of product.
• Finally, use the molar mass of the product to calculate the theoretical yield in grams.

In the given exercise, the calculation of the theoretical yield starts by recognizing acetic anhydride as the limiting reagent. With its moles determined, the theoretical yield of acetylsalicylic acid is calculated as 44.12 grams. This result represents an ideal scenario where no external factors affect the reaction.

Understanding the Limiting Reagent

The concept of a limiting reagent is crucial in stoichiometry as it determines when a chemical reaction will stop, thus dictating the maximum amount of product that can form. To find the limiting reagent:

• Calculate the moles of all reactants using their given masses and molar masses.
• Examine the balanced chemical equation to identify the reactant ratios needed for the reaction.
• Compare the amounts of each reactant (in moles) to see which one is present in the smallest stoichiometric amount.

In our specific exercise, the reaction between salicylic acid and acetic anhydride has a 1:1 mole ratio. Hence, converting their respective masses to moles revealed that acetic anhydride has fewer moles compared to salicylic acid. This makes acetic anhydride the limiting reagent, meaning it will deplete first and thus limit the amount of acetylsalicylic acid formed.

Calculating Percent Yield

Percent yield is a practical measure of how successful a reaction is compared to its theoretical outcome. It evaluates the efficiency of a chemical process by showing the ratio of the actual yield (what is obtained) to the theoretical yield (maximum possible amount) as a percentage: Percent yield = \(\frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100\).In practice, percent yield less than 100% often results from losses during the reaction processes such as incomplete reactions, impurities, or side-products. In this exercise, the actual yield of acetylsalicylic acid was measured at 35 grams. When compared with the theoretical yield of 44.12 grams, the percent yield is calculated to be approximately 79.3%. This percentage reflects the efficiency of the experimental process under the conditions in which it was carried out.