The mole fraction of glucose (C₆H₁₂O₆ ) in an aqueous binary solution is 0.1. The mass percentage of water in it, to the nearest integer, is _______.

Solution

Chemistry ma’am · 3 steps

Take one mole of solution in total, turn each mole count into grams, and the percentage follows.

1. Pick a total. A mole fraction does not depend on how much solution you take, so take 1 mol of solution in total. Glucose is 0.1 mol and water is 1 - 0.1 = 0.9 mol.
2. Convert to grams. Glucose: 0.1 × 180 = 18 g. Water: 0.9 × 18 = 16.2 g. Total mass is 18 + 16.2 = 34.2 g.

   mass % of water = 16.2/34.2 × 100 = 47.37

3. So. The mass percentage of water is about 47.4, which rounds to 47.

The common slip: 53. Working out the mass percentage of glucose instead of water gives 18/34.2 × 100 ≈ 53, not 47.

The idea to keep. To go from mole fraction to mass percentage, assume 1 mol of solution in total, multiply each mole count by its molar mass, then divide by the total mass.

Answer from the NTA final answer key. Solution by PrepWiser.