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.]

A 10$$\ \ \%\ $$ by weight $$(w/w)$$ aqueous urea solution means:

• 10 g urea in 100 g solution
• Therefore, water = 90 g

Step 1: Moles of Urea

Urea formula = $$CO(NH_{2})_2$$​

Molar mass of urea:

$$12+16+2(14)+4(1)$$

$$=12+16+28+4=60g mol^{−1}$$

Moles of urea:

$$\ \ \frac{10}{60}=\frac{1}{6}mol$$

Step 2: Moles of Water

Water = $$H_2O$$

Molar Mass $$=2+16=18\ g\ mol^{-1}$$

Moles:

$$\frac{90}{18}=5\ mol$$

Step 3: Mole Fraction of a water

$$X_{H_2O}=\frac{moles\ of\ water}{total\ moles}=\frac{5}{5+\frac{1\ }{6}}$$

$$=\frac{5}{\frac{31}{6}}=\frac{30}{31\ }\approx\ 0.967$$

Hence, Option D is correct