What is the mole fraction of water in 10 % by weight (w/w) of aqueous urea solution? [Given: Molar mass of H, O, C and N are 1 , 16 , 12 and 14 g mol ⁻¹ respectively.]

Step-by-step solution

10 % w/w aqueous urea solution means 10 g of urea is present in 100 g of solution. Mass of urea = 10 g Mass of water = 100 - 10 = 90 g Molar mass of urea ( NH ₂ CONH ₂ ) = 14 + 2 + 12 + 16 + 14 + 2 = 60 g mol ⁻¹ Molar mass of water ( H ₂ O ) = 18 g mol ⁻¹ Moles of urea, n_ urea = 10 60 = 1 6 mol Moles of water, n_ water = 90 18 = 5 mol Total moles = 5 + 1 6 = 31 6 mol Mole fraction of water, x_ water = n_ water n_ water + n_ urea = 5 31 6 = 30 31 0.967 Answer: 0.967