Question

For the following question, enter the correct numerical value up to TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numerical value 5 will be written as 5.00 and 2.346 will be written as 2.35) Elevation in boiling point of an aqueous urea solution is \(0.52^\circ\). (\(K_b = 0.52\,\text{mol}^{-1}\,\text{kg}\)). Hence, mole fraction of urea in this solution is _____

Hint:

First find molality using \( \Delta T_b = K_b m \), then convert molality into mole fraction.

Answer 1

Correct Answer: 0.02

Step 1: Elevation in boiling point is given by \[ \Delta T_b = K_b \, m \]
Step 2: Substituting given values, \[ 0.52 = 0.52 \times m \Rightarrow m = 1\,\text{mol kg}^{-1} \]
Step 3: Molality \( m = 1 \) means 1 mole of urea is dissolved in 1 kg (1000 g) of water. Moles of water: \[ \text{Moles of water} = \frac{1000}{18} = 55.56 \]
Step 4: Mole fraction of urea: \[ X_{\text{urea}} = \frac{1}{1 + 55.56} = 0.0177 \]
Step 5: Rounding off to two decimal places, \[ X_{\text{urea}} \approx 0.02 \] Hence, the mole fraction of urea is \[ \boxed{0.02} \]