Crystallisation with hydrates: Cooling 100 kg of an aqueous Na2SO4 solution from 30% (w/w) to a mother-liquor concentration of 10% (w/w) precipitates Na2SO4·10H2O crystals. What is the mass of crystals formed?

Introduction / Context:Hydrate crystallisation problems are common in chemical process calculations. Correctly accounting for solute in the crystal lattice water is key to obtaining the right crystal mass and mother-liquor composition.

Given Data / Assumptions:

• Feed: 100 kg solution at 30% w/w Na2SO4 (anhydrous basis).
• Final mother liquor: 10% w/w Na2SO4.
• Crystals: Na2SO4·10H2O (decahydrate).
• Molar masses (kg/kmol): Na2SO4 ≈ 142.04; 10H2O ≈ 180.16; crystal ≈ 322.20.

Concept / Approach:Perform component balances on anhydrous Na2SO4. In the hydrate crystals, only a fraction of the mass is Na2SO4; the rest is water of crystallisation. Mass fraction of Na2SO4 in crystals = 142.04 / 322.20 ≈ 0.441. Use this to link crystal mass to solute removed from solution.

Step-by-Step Solution:

Verification / Alternative check:Water balance (optional) would show the remaining water plus the 55.9% crystal water equals the original 70 kg less liquor water removal—consistent within rounding.

Why Other Options Are Wrong:

• 20, 32.2, 45.35: Each fails the Na2SO4 balance when the hydrate fraction is applied.

Common Pitfalls:Using 10% of the original solution instead of mother liquor mass, or forgetting that crystals contain substantial water; both lead to significant underestimation.

Final Answer:58.65