Question

Aspirin $\left({\mathrm{C}}_9{\mathrm{H}}_8{\mathrm{O}}_4\right)$ is produced from salicylic acid $\left({\mathrm{C}}_7{\mathrm{H}}_6{\mathrm{O}}_3\right)$ and acetic anhydride $\left({\mathrm{C}}_4{\mathrm{H}}_6{\mathrm{O}}_3\right):$ $${\mathrm{C}}_7{\mathrm{H}}_6{\mathrm{O}}_3+{\mathrm{C}}_4{\mathrm{H}}_6{\mathrm{O}}_3⟶{\mathrm{C}}_9{\mathrm{H}}_8{\mathrm{O}}_4+{\mathrm{HC}}_2{\mathrm{H}}_3{\mathrm{O}}_2$$ (a) How much salicylic acid is required to produce $1.5\times {10}^2\mathrm{kg}$ of aspirin, assuming that all of the salicylic acid is converted to aspirin? (b) How much salicylic acid would be required if only $80\mathrm{\%}$ of the salicylic acid is converted to aspirin? (c) What is the theoretical yield of aspirin if $185\mathrm{kg}$ of salicylic acid is allowed to react with $125\mathrm{kg}$ of acetic anhydride? (d) If the situation described in part (c) produces $182\mathrm{kg}$ of aspirin, what is the percentage yield?

Short answer

(a) 114.9 kg of salicylic acid is required to produce 1.5 x 10^2 kg of aspirin assuming all the salicylic acid is converted to aspirin. (b) 143.626 kg of salicylic acid is required for 80% conversion to aspirin. (c) The theoretical yield of aspirin is 220.342 kg. (d) The percentage yield is 82.60%.

Step-by-step solution

(a) Find moles of Aspirin and Salicylic acid needed to produce the given Aspirin mass

Given mass of aspirin: $1.5\times {10}^{2}kg=150000g$ Molar mass of aspirin (C9H8O4): $(9\times 12.01)+(8\times 1.01)+(4\times 16.00)=180.157g/mol$ Moles of aspirin: ${\displaystyle \frac{150000}{180.157}}=832.38mol$ Looking at the balanced equation, the mole ratio of salicylic acid (C7H6O3) to aspirin (C9H8O4) is 1:1, so the required moles of salicylic acid are equal to the moles of aspirin, which is 832.38 mol. Now, find the mass of salicylic acid needed: Molar mass of salicylic acid (C7H6O3): $(7\times 12.01)+(6\times 1.01)+(3\times 16.00)=138.121g/mol$ Mass of salicylic acid: $832.38\times 138.121=114900.1078g=114.9kg$ Therefore, 114.9 kg of salicylic acid is required to produce 1.5 x 10^2 kg of aspirin assuming all the salicylic acid is converted to aspirin.

(b) Calculate the required salicylic acid for 80% conversion

If only 80% of the salicylic acid is converted to Aspirin: Required moles of salicylic acid: ${\displaystyle \frac{832.38}{0.8}}=1040.475mol$ Mass of salicylic acid needed: $1040.475\times 138.121=143625.760975g=143.626kg$ Therefore, 143.626 kg of salicylic acid is required for 80% conversion to aspirin.

(c) Calculate the theoretical yield of Aspirin

Given mass of salicylic acid: 185 kg = 185000 g Given mass of acetic anhydride: 125 kg = 125000 g Moles of salicylic acid: ${\displaystyle \frac{185000}{138.121}}=1339.862mol$ Moles of acetic anhydride: ${\displaystyle \frac{125000}{102.088}}=1223.565mol$ The mole ratio of salicylic acid to acetic anhydride to aspirin is 1:1:1. Since moles of acetic anhydride is 1223.565 mol, which is less than 1339.862 mol of salicylic acid, acetic anhydride is the limiting reactant. Theoretical moles of Aspirin: 1223.565 mol (same as moles of limiting reactant) Theoretical yield of Aspirin: $1223.565\times 180.157=220342.036505g=220.342kg$ The theoretical yield of aspirin is 220.342 kg.

(d) Calculate the percentage yield

Actual yield of Aspirin: 182 kg Theoretical yield of Aspirin: 220.342 kg Percentage yield: ${\displaystyle \frac{182}{220.342}}\times 100\mathrm{\%}=82.60\mathrm{\%}$ Therefore, the percentage yield is 82.60%.

Key concepts

Understanding Theoretical Yield

The concept of theoretical yield is foundational to stoichiometry and chemistry. Theoretical yield refers to the maximum amount of product that a chemical reaction could produce based on calculated stoichiometry, assuming perfect efficiency and no losses due to side reactions or incomplete reactions. It's a benchmark for chemists to gauge how a real-life reaction compares to the ideal.

To determine the theoretical yield, one must first examine the balanced chemical equation for the reactants and products. The amounts of reactants used in the calculation are based on their molar ratio from the balanced equation. If we look at the example from the exercise, where salicylic acid reacts with acetic anhydride to produce aspirin, we can calculate the theoretical yield of aspirin by finding the limiting reactant and using its amount to determine the maximum possible amount of aspirin.

Importance of Molar Ratios

In the case of aspirin production, the molar ratio is 1:1, meaning one mole of salicylic acid will ideally produce one mole of aspirin. By converting the given mass of reactants to moles, applying the mole ratio, and then converting moles of product back to mass, we arrive at the theoretical yield—an essential step for any chemist or student learning about chemical reactions.

Identifying the Limiting Reactant

The limiting reactant in a chemical reaction is the substance that runs out first, thus determining the quantity of product formed. It's an important concept because in real-world conditions, reactants are rarely supplied in perfect stoichiometric amounts. The limiting reactant limits the extent of the reaction and hence, the amount of product that can be formed.

In our aspirin example, by comparing the moles of salicylic acid to the moles of acetic anhydride, we determined that acetic anhydride is the limiting reactant because it was present in a lesser amount relative to the stoichiometric ratio. This knowledge directly influences the yield of aspirin that can be expected from the reaction.

Practical Application

Understanding the limiting reactant is crucial for efficient resource utilization in industrial chemistry. It helps in optimizing reactant quantities to maximize product formation while minimizing waste. In classroom settings, identifying the limiting reactant helps students learn to predict realistic outcomes of reactions and connect theoretical concepts with practical laboratory experiences.

Calculating Percentage Yield

Percentage yield is a measure that allows chemists to evaluate the efficiency of a chemical reaction. It is calculated by dividing the actual yield obtained from an experiment by the theoretical yield and multiplying by 100%. The actual yield is the measured amount of product obtained from a reaction, which is usually less than the theoretical yield due to losses or side reactions.

In our exercise with aspirin production, the actual yield of aspirin was given as 182 kg, whereas the theoretical yield was calculated to be 220.342 kg. By using the percentage yield formula, we calculated that the reaction efficiency was 82.60%.

Significance of Percentage Yield

A high percentage yield indicates a reaction that is close to achieving the projected maximum efficiency. In an educational setting, percentage yield exercises help students understand that real chemical processes often deviate from the theoretical predictions due to imperfect conditions. In industry, maximizing percentage yield is essential for cost-effectiveness and reducing environmental impact by minimizing waste and the consumption of reactants.