Question

Which of the following statements are true for the elevation of boiling point?
(A) The boiling point of a solution is always higher than the boiling point of the pure solvent in which the solution is prepared.
(B) The boiling point of a solution is always lower than the boiling point of the pure solvent in which the solution is prepared.
(C) The elevation of boiling point is directly proportional to the molal concentration of the solute in solution.
(D) Unit of \(K_b = \text{K kg mol}^{-1}\)
Choose the correct answer from the options given below:

• A. (A), (B) and (D) only
• B. (B), (C) and (D) only
• C. (A), (B), (C) and (D)
• D. (A), (C) and (D) only

Hint:

Both the ebullioscopic constant (\(K_b\)) and cryoscopic constant (\(K_f\)) have the exact same unit: \(\text{K kg mol}^{-1}\) (or \(\text{K m}^{-1}\)).
Solute addition increases boiling point (\(\Delta T_b > 0\)) but lowers freezing point (\(\Delta T_f > 0\)).

Answer 1

The Correct Option is D

Concept:
The addition of a non-volatile solute to a volatile solvent lowers the escaping tendency and vapor pressure of the solvent.
Because a liquid boils when its vapor pressure equals the prevailing external atmospheric pressure, the solution must be heated to a higher temperature than the pure solvent, leading to elevation of boiling point (\(\Delta T_b\)).

Step 1: Evaluation of Statements Regarding Boiling Point Comparison:
Because non-volatile solute particles occupy part of the liquid surface, the equilibrium vapor pressure of the solution is lower than that of the pure liquid at all temperatures.
Consequently, a higher temperature is required for the solution to reach atmospheric pressure, meaning:
\[ T_b > T_b^\circ \] where \(T_b\) is the boiling point of the solution and \(T_b^\circ\) is that of the pure solvent.
Hence, statement (A) is correct, while statement (B) is incorrect.

Step 2: Proportionality to Solute Concentration:
For dilute solutions, thermodynamic derivation shows that the elevation in boiling point is directly proportional to the molality (\(m\)) of the dissolved solute:
\[ \Delta T_b \propto m \implies \Delta T_b = K_b \cdot m \] where \(K_b\) is the molal elevation constant or ebullioscopic constant.
Hence, statement (C) is correct.

Step 3: Verification of the Unit of \(K_b\):
From the relation \(K_b = \frac{\Delta T_b}{m}\), we express the units as:
\[ \text{Unit of } K_b = \frac{\text{K}}{\text{mol kg}^{-1}} = \text{K kg mol}^{-1} \] Hence, statement (D) is correct.
Final Answer:
The true statements are (A), (C), and (D), which corresponds to option (D).