JEE Advanced level
A JEE Advanced-level example on Mole Concept and Stoichiometry
Question. A mixture of anhydrous Na2CO3 and NaHCO3 weighing 22.1 g is heated strongly until constant mass is reached. The residue weighs 15.9 g. This residue is then dissolved in water and treated with excess dilute HCl. Find (a) the mass of each component in the original mixture, and (b) the volume of CO2 evolved at STP when the residue reacts with HCl. (Molar masses: Na2CO3 = 106, NaHCO3 = 84)
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- On heating, Na2CO3 is stable but NaHCO3 decomposes: 2NaHCO3 → Na2CO3 + H2O + CO2. Let mass of Na2CO3 = a g and NaHCO3 = b g.
- From the reaction, b g of NaHCO3 gives (106/168) × b = (53b/84) g of Na2CO3. So residue mass = a + 53b/84.
- Setting up equations: a + b = 22.1 and a + 53b/84 = 15.9. Subtracting gives 31b/84 = 6.2, so b = 16.8 g (NaHCO3) and a = 5.3 g (Na2CO3).
- Total Na2CO3 in residue = original 5.3 g + formed from NaHCO3 = 5.3 + 10.6 = 15.9 g = 0.15 mol.
- Residue reacts: Na2CO3 + 2HCl → 2NaCl + H2O + CO2. Moles of CO2 = 0.15 mol. Volume at STP = 0.15 × 22.4 = 3.36 L.
Answer: (a) Na2CO3 = 5.3 g, NaHCO3 = 16.8 g; (b) Volume of CO2 at STP = 3.36 L
This example was solved twice independently and both solutions agree.