Question

Define molal elevation constant. Calculate the boiling point of an aqueous solution containing 0.6 g of urea (molar mass = 60) in 100 g of water. The value of molal elevation constant for water is 0.52 K kg mol\(^{-1}\) and boiling point of water is 373.15 K.

Hint:

The increase in boiling point is proportional to the molality of the solute, and molal elevation constant (\( K_b \)) is solvent-specific.

Answer 1

Step 1: Definition: The molal elevation constant (\( K_b \)) is the increase in boiling point when 1 mole of a non-volatile solute is dissolved in 1 kg of solvent. 

Step 2: Formula for Boiling Point Elevation:} \[ \Delta T_b = K_b \times m \] where, \[ m = \frac{\text{moles of solute}}{\text{mass of solvent (kg)}} \] 

Step 3: Calculate Molality: \[ \text{Moles of urea} = \frac{0.6}{60} = 0.01 \text{ mol} \] \[ m = \frac{0.01}{0.1} = 0.1 \text{ mol/kg} \] 

Step 4: Calculate Boiling Point Elevation: \[ \Delta T_b = 0.52 \times 0.1 = 0.052 \text{ K} \] 

Step 5: Final Boiling Point: \[ T_b = 373.15 + 0.052 = 373.202 \text{ K} \] Thus, the boiling point of the solution is 373.20 K.