A sample of sodium bicarbonate ( NaHCO₃ ) is heated strongly until a constant weight is achieved. If the total mass loss due to the evolution of gases is 3.1 g, what was the initial mass of the sample? (Given: Molar mass of Na, H, C and O are 23 , 1 , 12 and 16 g mol ⁻¹ respectively)

Step-by-step solution

The thermal decomposition of sodium bicarbonate is given by: 2NaHCO₃(s) Na₂CO₃(s) + H₂O(g) + CO₂(g) Molar mass of NaHCO₃ = 23 + 1 + 12 + 3 16 = 84 g mol ⁻¹ From the balanced equation, heating 2 moles of NaHCO₃ ( 2 84 = 168 g) results in the loss of 1 mole of H₂O and 1 mole of CO₂ as gases. Total mass loss for 2 moles of NaHCO₃ = 18 g ( H₂O ) + 44 g ( CO₂ ) = 62 g. Let the initial mass of the sample be m . Since 62 g of mass is lost from 168 g of NaHCO₃ , a mass loss of 3.1 g corresponds to: m = 168 62 3.1 = 8.4 g.