A 1.84 g mixture of calcium carbonate ( CaCO₃ ) and magnesium carbonate ( MgCO₃ ) is heated strongly to a constant weight. If the total mass of the solid residue obtained is 0.96 g, what was the mass of CaCO₃ in the original mixture? (Given: Molar mass of Ca, Mg, C and O are 40 , 24 , 12 and 16 g mol ⁻¹ respectively)

Step-by-step solution

Let the number of moles of CaCO₃ and MgCO₃ in the mixture be x and y respectively. The molar masses are: CaCO₃ = 100 g mol ⁻¹ MgCO₃ = 84 g mol ⁻¹ The initial mass of the mixture is: 100x + 84y = 1.84 ... (i) The thermal decomposition reactions are: CaCO₃(s) CaO(s) + CO₂(g) MgCO₃(s) MgO(s) + CO₂(g) The solid residue consists of CaO (molar mass = 56 g mol ⁻¹ ) and MgO (molar mass = 40 g mol ⁻¹ ). The mass of the residue is: 56x + 40y = 0.96 ... (ii) Alternatively, the mass loss is due to the evolution of CO₂ gas: Mas