Question

6 g urea is dissolved in 200 g water. Calculate the elevation in boiling point. Molal elevation constant for water is 0.52 K kg mol$^{-1$.}

Hint:

For colligative properties, always convert solvent mass to kilograms and use moles of solute. Urea is non-electrolyte (van't Hoff factor \(i=1\)).

Answer 1

Elevation of boiling point is given by \(\Delta T_b = K_b \times m\).
Here \(K_b = 0.52 \, \text{K kg mol}^{-1}\) and \(m\) is molality.

Step 1: Moles of urea (solute).
Molar mass of urea \(= 60 \, \text{g mol}^{-1}\).
\(n = \dfrac{6}{60} = 0.10 \, \text{mol}\).

Step 2: Mass of solvent (water) in kg.
\(200 \, \text{g} = 0.200 \, \text{kg}\).

Step 3: Molality.
\(m = \dfrac{0.10}{0.200} = 0.50 \, \text{mol kg}^{-1}\).

Step 4: Elevation in boiling point.
\(\Delta T_b = K_b \times m = 0.52 \times 0.50 = 0.26 \, \text{K}\).
\[ \boxed{\Delta T_b = 0.26 \, \text{K}} \]