11.3 Limiting-Reactant & Percent-Yield Calculations
Key Takeaways
- The limiting reactant is the species that runs out first and caps the theoretical yield; identify it by comparing mole-to-coefficient ratios, not gram masses.
- Percent yield = (actual yield / theoretical yield) × 100; values over 100% usually indicate impurity, solvent mass, or measurement error.
- The Bulletin's acetic-anhydride acetylation/hydrolysis problem structure requires balancing an organic reaction, computing molar masses, and converting between mass and moles.
- Always convert all given reactant masses to moles before comparing; using grams directly is the most common stoichiometry error on the PA-CAT.
- Theoretical yield is computed from the limiting reactant through the balanced equation's mole ratio, not from the reactant present in excess.
Limiting Reactant and Percent Yield
Quick Answer: Stoichiometry on the PA-CAT rewards a rigid four-step pipeline: balance the equation → convert all given masses to moles → identify the limiting reactant by comparing mole/coefficient ratios → scale to product using the mole ratio. Percent yield compares what you actually isolate to what the limiting reactant theoretically allows.
Bloom's Application is 54% of the PA-CAT, and the Bulletin of Information, rev. 20240815 sample items include an acetic-anhydride acetylation/hydrolysis problem that is solved with this exact pipeline. Chemistry is 16% of the exam (~38 items), so expect 2–4 stoichiometry items.
The Pipeline
- Balance the equation — coefficients give the mole ratio.
- Convert masses to moles — divide by molar mass.
- Find the limiting reactant — for each reactant, compute moles ÷ coefficient; the smallest value limits.
- Compute theoretical yield — multiply limiting-reactant moles by the product coefficient / limiting-reactant coefficient, then convert to grams.
- Percent yield = (actual / theoretical) × 100.
Worked Example 1 — Aspirin Synthesis (Acetylation)
Salicylic acid (C7H6O3, MW 138.12 g/mol) reacts with acetic anhydride (C4H6O3, MW 102.09 g/mol) to give acetylsalicylic acid (C9H8O4, MW 180.16 g/mol) and acetic acid:
C7H6O3 + C4H6O3 → C9H8O4 + C2H4O2
Suppose 2.00 g salicylic acid and 5.00 mL acetic anhydride (density 1.08 g/mL) are combined.
Step 1 — Equation is already balanced (1:1:1:1).
Step 2 — Moles: salicylic acid = 2.00 / 138.12 = 0.01448 mol. Acetic anhydride mass = 5.00 mL × 1.08 g/mL = 5.40 g; moles = 5.40 / 102.09 = 0.0529 mol.
Step 3 — Coefficients are both 1, so compare moles directly. Salicylic acid (0.01448) is far less than acetic anhydride (0.0529), so salicylic acid is limiting.
Step 4 — Theoretical yield of aspirin: 0.01448 mol aspirin × 180.16 g/mol = 2.609 g.
Step 5 — If 2.18 g of dry aspirin is recovered, percent yield = (2.18 / 2.609) × 100 = 83.6%.
Worked Example 2 — Hydrolysis of Acetic Anhydride
Acetic anhydride hydrolyzes in water: C4H6O3 + H2O → 2 C2H4O2. Given 10.0 g acetic anhydride in excess water, how much acetic acid (MW 60.05) forms?
Moles anhydride = 10.0 / 102.09 = 0.09795 mol. Coefficient ratio 2 acetic acid : 1 anhydride → moles acetic acid = 2 × 0.09795 = 0.1959 mol → mass = 0.1959 × 60.05 = 11.76 g.
If water were limited—say 1.50 g H2O (0.0833 mol), coefficient 1—the mole/coefficient ratios would be: anhydride 0.09795/1 = 0.09795, water 0.0833/1 = 0.0833. Water would then be limiting, giving 2 × 0.0833 = 0.1666 mol acetic acid = 10.0 g.
Common Error Patterns
| Error | Wrong result | Fix |
|---|---|---|
| Comparing grams instead of moles | Wrong limiting reactant | Convert to moles first |
| Using coefficient ratio inverted | Yield too small/large by factor | Limiting × (product coeff / reactant coeff) |
| Forgetting product molar mass | Units of moles reported as grams | Always × molar mass at end |
| Using excess reactant for theoretical yield | Overstates yield | Use limiting reactant only |
Why Yields Are Below 100%
Real organic yields fall below theoretical for several reasons PA-CAT items may name: incomplete reaction, side products (e.g., polymerization of salicylic acid), loss during recrystallization, and competing hydrolysis of acetic anhydride by atmospheric moisture. A reported yield over 100% almost always means the product is wet with solvent or unreacted starting material—never that mass was created.
Worked Example — Aspirin Synthesis Percent Yield
Aspirin (acetylsalicylic acid) is synthesized from salicylic acid and acetic anhydride:
C7H6O3 + (CH3CO)2O → C9H8O4 + CH3COOH
A student starts with 2.00 g salicylic acid (molar mass 138.12 g/mol) and excess acetic anhydride, and isolates 2.18 g aspirin (molar mass 180.16 g/mol).
- Moles salicylic acid = 2.00 ÷ 138.12 = 0.01448 mol — the limiting reactant.
- Theoretical moles aspirin = 0.01448 mol (1:1 stoichiometry).
- Theoretical mass aspirin = 0.01448 × 180.16 = 2.609 g.
- Percent yield = (2.18 ÷ 2.609) × 100 = 83.6%.
The unaccounted 16% reflects transfer losses, incomplete reaction, and recrystallization discard — not a violation of conservation of mass. If acetic anhydride were in short supply instead, you would compute product from the anhydride and take the smaller value as the theoretical yield. The PA-CAT rewards candidates who identify the limiting reactant before computing theoretical yield, because percent yield is meaningless unless the denominator is the maximum the limiting reactant allows.
In the aspirin synthesis, 2.00 g salicylic acid (MW 138.12) and 5.40 g acetic anhydride (MW 102.09) are combined in a 1:1 reaction. Which is the limiting reactant, and what is the maximum moles of aspirin producible?