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 find the mole fraction of urea in an aqueous solution given the molality, we start by noting the essential relationships and calculations.

Molality (m) is defined as the number of moles of solute per kilogram of solvent. Here, the solute is urea (CH₄N₂O).

Given: Molality (m) = 4.44 m

Let the mass of water be 1 kg. This implies the number of moles of urea is 4.44 moles since molality is moles of solute per kg of solvent.

The mole fraction of a solute (urea) is given by:

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

Moles of water: Given the mass of water is 1 kg (1000 g) and the molar mass of water is 18 g/mol:

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

Substitute these values into the equation:

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

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

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

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

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

Therefore, the value of \( x \) is 74, which lies within the range (74 to 74).

Answer 2

Molality ($m$) of urea is given as 4.44 $m$, meaning 4.44 moles of urea are dissolved in 1000 g of water.
Step 1: Mole fraction formula
\[ X_{\text{urea}} = \frac{\text{Moles of urea}}{\text{Moles of urea} + \text{Moles of water}} \]
Step 2: Calculate moles of water
\[ \text{Mass of water} = 1000 \, \text{g}, \quad \text{Molar mass of water} = 18 \, \text{g/mol}. \] \[ \text{Moles of water} = \frac{1000}{18} = 55.56. \]
Step 3: Substitute values into the mole fraction formula
\[ X_{\text{urea}} = \frac{4.44}{4.44 + 55.56}. \] \[ X_{\text{urea}} = \frac{4.44}{60.00} = 0.0740. \]
Step 4: Express mole fraction as $x \times 10^{-3}$
\[ X_{\text{urea}} = 74 \times 10^{-3}. \] \[ x = 74. \]
Final Answer: 74