Question

Molality of an aqueous solution of urea is 4.44 m. Mole fraction of urea in solution is x × 10^–3. Value of x is _______. (integer answer)

Answer 1

Correct Answer: 74

To determine the mole fraction of urea in an aqueous solution from its molality, we utilize fundamental definitions and calculations.

Molality (m) is defined as the molar amount of solute per kilogram of solvent. In this context, the solute is urea (CH₄N₂O).

Given: Molality (m) = 4.44 m

Assuming a solvent mass of 1 kg of water, the moles of urea present are 4.44 moles, as molality is defined as moles of solute per kg of solvent.

The formula for the mole fraction of a solute (urea) is:

\[ \text{Mole fraction of urea} = \frac{\text{moles of urea}}{\text{moles of urea} + \text{moles of water}} \]

Moles of water: With a water mass of 1 kg (1000 g) and a molar mass of water of 18 g/mol:

\[ \text{Moles of water} = \frac{1000}{18} \approx 55.56 \text{ moles} \]

Substituting these values into the equation yields:

\[ \text{Mole fraction of urea} = \frac{4.44}{4.44 + 55.56} \]

\[ \text{Mole fraction of urea} = \frac{4.44}{60} \approx 0.074 \]

To express the mole fraction in the form \( x \times 10^{-3} \):

\[ 0.074 = x \times 10^{-3} \]

\[ x = 0.074 \times 10^{3} = 74 \]

Consequently, the value of \( x \) is determined to be 74, falling within the range of (74 to 74).