a) Which is the limiting reactant? Given the density of acetic anhydride is 1.030 g/ml? b) What is the percent yield of this reaction?

To solve this problem, we first need to determine the molar masses of the reactants and products, then calculate the moles of each reactant to find the limiting reactant, and finally use the limiting reactant to calculate the theoretical yield and percent yield.

The balanced chemical equation is: $\text{C}_7H_6O_3 + (CH_3CO)_2O \rightarrow C_9H_8O_4 + CH_3\text{COOH}$ (Salicylic acid) + (Acetic anhydride) $\rightarrow$ (Aspirin) + (Acetic acid)

Molar masses: • Salicylic acid ($\text{C}_7H_6O_3$): $(7 \times 12.01) + (6 \times 1.008) + (3 \times 16.00) = 84.07 + 6.048 + 48.00 = 138.118 \text{ g/mol}$ • Acetic anhydride ($\text{(CH}_3CO)_2\text{O}$ or $\text{C}_4H_6O_3$): $(4 \times 12.01) + (6 \times 1.008) + (3 \times 16.00) = 48.04 + 6.048 + 48.00 = 102.088 \text{ g/mol}$ • Aspirin ($\text{C}_9H_8O_4$): $(9 \times 12.01) + (8 \times 1.008) + (4 \times 16.00) = 108.09 + 8.064 + 64.00 = 180.154 \text{ g/mol}$

a) Which is the limiting reactant?

Step 1: Calculate the moles of salicylic acid. $\text{Moles of salicylic acid} = \frac{mass}{molar mass} = \frac{3.0779 g}{138.118 g/mol} = 0.022284 \text{ mol}$

Step 2: Calculate the mass of acetic anhydride using its density and volume. $\text{Mass of acetic anhydride} = density \times volume = 1.080 g/mL \times 5.050 mL = 5.454 \text{ g}$

Step 3: Calculate the moles of acetic anhydride. $\text{Moles of acetic anhydride} = \frac{mass}{molar mass} = \frac{5.454 g}{102.088 g/mol} = 0.053426 \text{ mol}$

Step 4: Determine the limiting reactant. From the balanced equation, the stoichiometric ratio between salicylic acid and acetic anhydride is 1:1. Since $0.022284 \text{ mol}$ (salicylic acid) is less than $0.053426 \text{ mol}$ (acetic anhydride), salicylic acid is the limiting reactant.

The limiting reactant is salicylic acid. $\boxed{Salicylic acid}$

b) What is the percent yield of this reaction?

Step 5: Calculate the theoretical yield of aspirin. Based on the balanced equation, 1 mole of salicylic acid produces 1 mole of aspirin. $\text{Moles of aspirin (theoretical)} = moles of limiting reactant = 0.022284 \text{ mol}$ $\text{Theoretical yield of aspirin} = moles \times molar mass = 0.022284 mol \times 180.154 g/mol = 4.0148 \text{ g}$

Step 6: Calculate the percent yield. $\text{Percent yield} = \frac{actual yield}{theoretical yield} \times 100\%$ $\text{Percent yield} = \frac{3.281 g}{4.0148 g} \times 100\% = 81.72\%$

The percent yield of this reaction is 81.72%. $\boxed{81.72\%}$

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