The mole fraction of water in a 10% (w/w) aqueous solution of urea is x × 10^-3. Find the value of x.

A 10% (w/w) solution means:

• 10 g urea
• 90 g water

Assume 100 g solution.

Molar mass of urea:

CO(NH₂)₂ = 12 + 16 + 28 + 4

= 60 g mol^-1

Moles of urea:

10/60

= 0.1667 mol

Moles of water:

90/18

= 5 mol

Mole fraction of water:

X_water = 5/(5 + 0.1667)

= 0.9677

Expressing in the required form:

0.9677 ≈ 968 × 10^-3

Therefore:

x = 968

Mole fraction is an important concentration term because it is independent of temperature and is widely used in colligative property calculations such as boiling point elevation, freezing point depression, and osmotic pressure.

x = 968