Limestone Purity by Two Methods: Gas Volume and Residue Mass
A student is given 5.00 g of powdered limestone that may contain calcium carbonate mixed with insoluble sand. She adds 100.0 cm³ of 1.00 mol/L hydrochloric acid at 25 °C and collects the gas produced over water in a 1,000 cm³ gas syringe. When bubbling stops she reads 780 cm³ of gas at a total pressure of 101 kPa; the vapour pressure of water at 25 °C is 3.2 kPa. The reaction is CaCO₃(s) + 2HCl(aq) → CaCl₂(aq) + CO₂(g) + H₂O(l). A second 5.00 g sample is treated with excess acid, washed, dried and weighed, leaving 1.70 g of residue. The student says the acid must have been the limiting reagent because some acid remained at the end, and that the limestone is at least 90% calcium carbonate because '5 g should give about 1.1 L of gas'. The class must check the stoichiometry, calculate the purity, and explain why the dry solid does not conduct electricity while the filtrate does.
1. Correct the gas volume for water vapour, calculate the moles of CO₂, identify the limiting reagent, and compute the percentage of calcium carbonate in the limestone.
Read the worked answer
The gas in the syringe is CO₂ plus water vapour, so the CO₂ partial pressure is 101 − 3.2 = 97.8 kPa.
n(CO₂) = PV/RT = (97,800 Pa)(7.80 × 10⁻⁴ m³)/(8.314 × 298 K) = 76.28/2477.6 = 0.0308 mol.
From the equation, 1 mol CaCO₃ gives 1 mol CO₂ and consumes 2 mol HCl. n(CaCO₃) = 0.0308 mol, mass = 0.0308 × 100.09 = 3.08 g. Percentage = 3.08/5.00 × 100 = 61.6%.
HCl available = 0.1000 L × 1.00 mol/L = 0.100 mol. Required = 2 × 0.0308 = 0.0616 mol. Since 0.0616 < 0.100, HCl is in excess and the limestone is the limiting reagent.
The student's inference is backwards: leftover acid is the signature of an excess, not of a limiting reagent. A limiting reagent is the one completely consumed, and here that is the carbonate in the solid.
2. The residue method gives a different purity. Calculate it, explain the disagreement, and judge which value is more trustworthy.
Read the worked answer
If the acid is in excess and the residue is washed free of soluble CaCl₂, the residue is the insoluble sand: 1.70 g. So CaCO₃ = 5.00 − 1.70 = 3.30 g, purity = 66.0%.
This disagrees with the gas result (61.6%) by about 4 percentage points. Both methods have known loss routes. The gas method loses CO₂ in three ways: some dissolves in the water and the acidic solution, some escapes before the syringe is connected, and the syringe reading may be taken before the apparatus cools to room temperature. All of these make the gas result too low. The residue method can lose fine sand during decanting and washing, which lowers the residue and makes purity too high; if the solid were not washed thoroughly, residual CaCl₂ (0.0308 mol × 111 g/mol ≈ 3.4 g) would make the residue far larger than 1.70 g, so thorough washing is essential.
The two results bracket roughly 62–66%, and neither alone pins the value down. The gas method is more trustworthy only if the apparatus is sealed before acid addition, a blank correction is made for dissolved CO₂, and the syringe is read at room temperature. To decide, repeat with a closed system and compare, or determine Ca²⁺ by titration. Merely averaging the two numbers would hide two systematic errors of opposite sign.
The '90%' claim is also wrong: 0.0500 mol of pure CaCO₃ would produce 0.0500 × 2477.6/97,800 = 1.27 × 10⁻³ m³ = 1.27 L of damp gas at 101 kPa, which exceeds the 1.00 L syringe. The apparatus cannot even measure a pure sample, so the quoted 1.1 L expectation is not a valid benchmark.
3. Explain why the dry limestone does not conduct electricity but the filtrate does, and why adding more acid after bubbling stops produces no further gas.
Read the worked answer
Solid CaCO₃ is an ionic compound: it is a lattice of Ca²⁺ and CO₃²⁻ ions. In the solid the ions are held in fixed positions and cannot migrate, so there is no ionic current. Sand (SiO₂) is a covalent network solid and has no mobile charged particles either. The dry mixture therefore does not conduct.
When dissolved, the lattice is broken up by water and the ions become mobile. The filtrate contains Ca²⁺, Cl⁻ and excess H⁺, all free to move under an applied potential, so the solution conducts. Conductivity requires mobile charge carriers, not merely the presence of ions - this is the key distinction.
Adding more acid produces no gas because all the carbonate has already reacted; the fizzing stops when the limiting reagent is used up. Any further acid simply dilutes into the already-acidic solution. Gas evolution would restart only if more carbonate were added, which is also the standard test to distinguish a carbonate from a chloride: acid plus limewater turning milky indicates CO₂.