Identifying an Unknown Carbonate by Back-Titration
A student receives a 2.500 g sample of an unknown Group 2 metal carbonate, MCO3, contaminated with inert NaCl. The student dissolves the sample in 50.00 mL of 1.000 M HCl, boils off the CO2, then titrates the excess acid with 0.5000 M NaOH, requiring 28.40 mL to reach the endpoint. The student claims the metal is calcium (molar mass of CaCO3 = 100.09 g/mol) based on a rough flame test that showed a faint orange-red color. A classmate points out that the sample's mass is inconsistent with a pure carbonate and that the flame test is unreliable with sodium present from the NaCl contamination.
1. Calculate the mass of MCO3 in the sample and determine the identity of the metal. Show each stoichiometric step.
Read the worked answer
Step 1 - moles of acid added: 50.00 mL × 1.000 M = 0.05000 mol HCl.
Step 2 - moles of excess acid: NaOH reacts 1:1 with HCl: 0.5000 M × 0.02840 L = 0.01420 mol NaOH = 0.01420 mol excess HCl.
Step 3 - moles of HCl consumed by carbonate: 0.05000 − 0.01420 = 0.03580 mol HCl.
Step 4 - carbonate stoichiometry: MCO3 + 2HCl → MCl2 + CO2 + H2O, so moles MCO3 = 0.03580 / 2 = 0.01790 mol.
Step 5 - molar mass: 2.500 g / 0.01790 mol = 139.7 g/mol.
Step 6 - identify the metal: M = 139.7 − 60.01 (CO3) = 79.7 g/mol, which matches barium (Ba, 137.33; BaCO3 = 197.3 g/mol).
Cross-check: If the sample were pure CaCO3, 2.500 g would contain 0.02498 mol and consume 0.04996 mol HCl, leaving essentially no excess acid - inconsistent with 0.01420 mol of excess found. The data rule out calcium.
2. The student's flame test was orange-red, which superficially supports calcium. Explain why this observation cannot be used to confirm the metal here, and describe one cleaner confirmatory test.
Read the worked answer
Sodium from the NaCl contamination produces an intense yellow-orange flame that masks or mimics the faint brick-red of calcium; flame color is a low-confidence test in mixtures, especially with a strong emitter like Na present. The quantitative back-titration is the reliable evidence and points to barium.
A cleaner confirmatory test: precipitate the metal as the sulfate. BaSO4 is famously insoluble (Ksp ~1×10⁻¹⁰), while CaSO4 is slightly soluble (~0.015 M). Add dilute H2SO4 to a solution of the dissolved sample; a dense white precipitate that persists in dilute acid supports Ba²⁺. Alternatively, a gravimetric sulfate determination gives a molar mass check: if 0.01790 mol of MSO4 weighs about 4.18 g, M ≈ 137, confirming barium.