Identifying an Unknown Carbonate by Back-Titration
A first-year laboratory has an unlabelled bottle of a white, water-soluble solid believed to be a group 1 or group 2 carbonate. A 2.000 g sample is dissolved and made up to 250.0 mL. A 25.00 mL aliquot is treated with 50.00 mL of 0.2000 mol/L HCl, and the mixture is warmed to expel CO2. The excess acid is then titrated with 0.1000 mol/L NaOH, requiring 22.40 mL to reach the phenolphthalein endpoint. The solid dissolves without residue, and a flame test on the original sample gives a persistent brick-red colour. A student suggests the sample is calcium carbonate because 'carbonates fizz with acid and calcium gives a red flame'.
1. Calculate the amount of carbonate in the 25.00 mL aliquot and hence the molar mass of the solid. State whether the student's identification is supported.
Read the worked answer
Amount of HCl added = 0.05000 L × 0.2000 mol/L = 1.000 × 10⁻² mol. Amount of NaOH used = 0.02240 L × 0.1000 mol/L = 2.240 × 10⁻³ mol, which equals the unreacted HCl. So HCl consumed by carbonate = 1.000 × 10⁻² − 2.240 × 10⁻³ = 7.760 × 10⁻³ mol. Since CO3²⁻ + 2H⁺ → CO2 + H2O, moles of carbonate = 7.760 × 10⁻³ / 2 = 3.880 × 10⁻³ mol in 25.00 mL. Total in 250.0 mL = 3.880 × 10⁻² mol, so M = 2.000 g / 3.880 × 10⁻² mol ≈ 51.5 g/mol. This is far too low for CaCO3 (100.1 g/mol) and matches no simple carbonate; the result is internally inconsistent, so the data or the assumed 2:1 stoichiometry must be questioned. The brick-red flame is actually characteristic of calcium, so the flame test supports Ca while the titration does not - the two pieces of evidence conflict and the identification is not supported by the titration.
2. Give two specific reasons the calculated molar mass might be unreliable, and describe one modification that would test your explanation.
Read the worked answer
First, loss of HCl as vapour or incomplete expulsion of CO2 would change the excess-acid titre; if CO2 remained, it would consume NaOH and inflate the apparent excess, lowering the calculated carbonate and raising M - but here M is already too low, so an alternative is that the solid is a hydrated or impure carbonate, or a hydrogencarbonate. A hydrogencarbonate reacts 1:1 with H⁺, so the same titre would imply twice the moles and a molar mass near 25.8 g/mol, still inconsistent, indicating the sample is likely not pure. Second, the 2.000 g may include surface moisture or the balance may be poorly calibrated, directly scaling M. A modification: dry the solid in a desiccator and reweigh, or run the titration on a known mass of analytical-grade CaCO3 as a control to check the method's recovery. If the control returns 100 g/mol, the method is sound and the sample is impure; if not, the procedure needs correction.