Answer: The mole fraction of urea in an aqueous solution that is 47% urea by mass is 0.210.
Step-by-step explanation:
Assume we have 100g of aqueous solution.
Then, 47% urea by mass = 47g.
The remaining 53% of the solution by mass is water = 53g.
Molar mass
Urea's molar mass = 60 g/mol
Water's molar mass = 2(1) + 1(16) = 18 g/mol
Number of moles
47g of urea / (60 g/mol) = 0.783 mol urea
53 g of water / (18 g/mol) = 2.944 mol water
Total moles in solution = 3.727 mol
Mole fraction
0.783 mol urea / 3.727 mol = 0.210