A 55.0-mL sample of a 0.102 M potassium sulfate solution is mixed with 35.0 mL of a 0.114 M lead(II) acetate solution and this precipitation reaction occurs: K₂SO₄(aq) + Pb(C₂H₃O₂)₂(aq) → 2 KC₂H₃O₂(aq) + PbSO₄(s) The solid PbSO₄ is collected, dried, and found to have a mass of 1.01 g. Determine the limiting reactant, theoretical yield, percent yield.

Verified step by step guidance

1. Determine the moles of K_2SO_4: Use the formula \( \text{moles} = \text{molarity} \times \text{volume in liters} \). Convert 55.0 mL to liters and multiply by 0.102 M to find the moles of K_2SO_4.
2. Determine the moles of Pb(C_2H_3O_2)_2: Similarly, convert 35.0 mL to liters and multiply by 0.114 M to find the moles of Pb(C_2H_3O_2)_2.
3. Identify the limiting reactant: Use the stoichiometry of the balanced equation. Compare the mole ratio of K_2SO_4 to Pb(C_2H_3O_2)_2 (1:1) to determine which reactant is limiting.
4. Calculate the theoretical yield of PbSO_4: Use the moles of the limiting reactant to find the moles of PbSO_4 produced, using the 1:1 mole ratio from the balanced equation. Then, convert moles of PbSO_4 to grams using its molar mass.
5. Calculate the percent yield: Use the formula \( \text{percent yield} = \left( \frac{\text{actual yield}}{\text{theoretical yield}} \right) \times 100\% \). Substitute the actual yield (1.01 g) and the theoretical yield calculated in the previous step.

Key Concepts

Limiting Reactant

The limiting reactant is the substance that is completely consumed first in a chemical reaction, thus determining the maximum amount of product that can be formed. To identify it, one must compare the mole ratios of the reactants based on the balanced chemical equation and the initial amounts of each reactant. The reactant that produces the least amount of product is the limiting reactant.

Theoretical Yield

The theoretical yield is the maximum amount of product that can be generated from a given amount of reactants, calculated using stoichiometry based on the balanced chemical equation. It assumes complete conversion of the limiting reactant into product without any losses. This value is essential for determining the efficiency of a reaction when compared to the actual yield obtained.

Percent Yield

Percent yield is a measure of the efficiency of a chemical reaction, calculated by dividing the actual yield of the product by the theoretical yield and multiplying by 100. It provides insight into how much of the expected product was actually produced in the experiment. A percent yield less than 100% indicates that some reactants did not convert to products, which can be due to various factors such as incomplete reactions or losses during processing.