Question

Define molal elevation constant. (2)

Hint:

From \( \Delta T_b = K_b m \), put \( m=1 \): \( K_b \) is the boiling point elevation for a one molal solution; unit \( K\,kg\,mol^{-1} \).

Answer 1

Step 1: The relation. When a non-volatile solute is dissolved in a solvent, the boiling point rises. The elevation in boiling point \( \Delta T_b \) is directly proportional to the molality \( m \) of the solution:
\[ \Delta T_b = K_b \cdot m \]
where \( K_b \) is the molal elevation constant (also called the ebullioscopic constant).
Step 2: Definition. The molal elevation constant \( (K_b) \) is the elevation in boiling point produced when one mole of a non-volatile solute is dissolved in one kilogram (1000 g) of the solvent, i.e. the elevation for a one molal solution. Putting \( m = 1 \) in the equation gives \( \Delta T_b = K_b \), which shows the physical meaning.
Step 3: Units. Since \( K_b = \dfrac{\Delta T_b}{m} \), its unit is kelvin kilogram per mole, \( K\,kg\,mol^{-1} \) (or \( ^{\circ}C\,kg\,mol^{-1} \)). It is a constant characteristic of the solvent only (for water \( K_b = 0.52\ K\,kg\,mol^{-1} \)).
\[\boxed{K_b = \Delta T_b \text{ for a one molal solution; unit } K\,kg\,mol^{-1}}\]