The Chalk Sample That Looked Like an Excess
A student treats 25.0 g of an impure calcium carbonate sample (assay: 84.0% CaCO₃ by mass; the rest is inert) with 250 mL of 1.20 M hydrochloric acid. The reaction is CaCO₃ + 2HCl → CaCl₂ + CO₂ + H₂O. The student collects the evolved carbon dioxide over water and obtains 2.9 g of gas, then concludes that "the reaction must have failed" because the yield is under 50%. Molar masses: CaCO₃ = 100.1 g/mol, HCl = 36.46 g/mol, CO₂ = 44.01 g/mol. Assume the molar volume of CO₂ is 24.0 L/mol under the laboratory's conditions.
1. Determine which reactant is limiting. Show the moles of each and the ratio comparison.
Read the worked answer
Moles of CaCO₃ actually present: the 25.0 g is only 84.0% pure, so mass of CaCO₃ = 25.0 × 0.840 = 21.0 g. n = 21.0 / 100.1 = 0.210 mol.
Moles of HCl: n = 0.250 L × 1.20 mol/L = 0.300 mol.
Ratio test: the equation requires 2 mol HCl per 1 mol CaCO₃.
- HCl needed to consume all the carbonate: 0.210 × 2 = 0.420 mol.
- HCl available: 0.300 mol → not enough.
Conclusion: HCl is limiting; CaCO₃ is in excess. Excess carbonate = 0.210 − 0.150 = 0.060 mol (about 6.0 g of the 21.0 g never reacts).
Note the trap: comparing raw masses (25.0 g vs 250 mL) points the wrong way. Purity must be applied before the mole comparison.
2. Calculate the theoretical mass and volume of CO₂, then the percent yield of the 2.9 g actually collected.
Read the worked answer
Moles of CO₂ - from the limiting reagent only. 0.300 mol HCl → 0.300 / 2 = 0.150 mol CO₂.
Theoretical mass: 0.150 × 44.01 = 6.60 g. Theoretical volume: 0.150 × 24.0 = 3.60 L.
Percent yield: 2.9 / 6.60 × 100 = 43.9% (≈44%).
Sanity check: the theoretical figure is set by HCl, not by the carbonate, so any calculation using 0.210 mol (which would give 9.24 g) is answering the wrong question.
3. The student calls a 44% yield a failed reaction. Assess that conclusion and state what evidence would distinguish an experimental loss from a genuinely incomplete reaction.
Read the worked answer
A low yield on its own is not evidence of failure. 44% is consistent with several ordinary losses that say nothing about whether the acid–carbonate reaction went to completion:
- CO₂ is appreciably soluble in water, and the gas was collected over water.
- Gas can escape before the collection apparatus is sealed.
- The 84.0% assay is a label value; if the true assay were lower, the carbonate would actually be limiting and the theoretical yield would shrink.
Evidence that would discriminate:
- Mass loss of the whole reaction vessel (weigh before and after) - captures all CO₂, escaped or dissolved, and is independent of collection efficiency.
- Leftover carbonate test - the calculation predicts 0.060 mol (≈6.0 g) of excess CaCO₃ surviving; if acid is truly limiting, adding more acid should restart effervescence.
- Titrate the leftover acid - if the reaction is complete, essentially no HCl should remain.
Judgement: the correct inference is that the measurement method is suspect, not that the chemistry failed. A conclusion about the reaction requires a measurement that does not depend on capturing a soluble gas quantitatively.