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Question #44531

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The Question

An organic base \ce{B} (molar mass = $100 \text{ g mol}^{-1}$ ) is studied in two different solvents to understand its solvation thermodynamics.

Experiment 1: $10.0 \text{ g}$ of \ce{B} is dissolved in $100 \text{ g}$ of benzene ( $K_b = 2.53 \text{ K kg mol}^{-1}$ ). The boiling point of the solution is elevated by $1.518 \text{ K}$ . In benzene, \ce{B} undergoes partial dimerization due to intermolecular hydrogen bonding.

Experiment 2: $10.0 \text{ g}$ of \ce{B} is dissolved in $100 \text{ g}$ of water ( $K_b = 0.52 \text{ K kg mol}^{-1}$ ). The boiling point elevation is observed to be $0.5252 \text{ K}$ . In water, \ce{B} acts as a weak monobasic amine.

Experiment 3: $0.05 \text{ mol}$ of anhydrous \ce{HCl} gas is dissolved in the aqueous solution from Experiment 2 (assume no change in the mass of the solvent and no volume change).

Assuming the molarity of the aqueous solution is approximately equal to its molality, calculate the dimerization equilibrium constant ( $K_d$ ) of \ce{B} in benzene, the base ionization constant ( $K_b$ ) in water, and the new boiling point elevation ( $\Delta T_b'$ ) of the solution in Experiment 3.

Options

A.
$10 \text{ kg mol}^{-1}$ , $1.01 \times 10^{-4} \text{ M}$ , $0.780 \text{ K}$
B.
$0.1 \text{ kg mol}^{-1}$ , $1.0 \times 10^{-2} \text{ M}$ , $1.045 \text{ K}$
C.
$10 \text{ kg mol}^{-1}$ , $1.01 \times 10^{-4} \text{ M}$ , $1.045 \text{ K}$
D.
$2.0 \text{ kg mol}^{-1}$ , $2.02 \times 10^{-4} \text{ M}$ , $0.780 \text{ K}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Exception_Exposure

Learn to identify edge cases and boundary exceptions that JEE examiners hide in math problems.

Concepts Behind This Question

Boiling Point Elevation (Solvent vs Solution)|Molecular Mass Abnormalities|Basicity-Solvation Competition

Why This Question Is Tricky

Common Mistakes

The problem tests the Basicity-Solvation Competition and the dynamic nature of the van't Hoff factor ( $i$ ).

Students must distinguish between physical association (dimerization, $i < 1$ ) in non-polar solvents and chemical ionization ( $i > 1$ ) in polar solvents.

The 'Hidden Variable' is the acid-base neutralization in Experiment 3.

A common trap is assuming \ce{HCl} simply adds to the existing particle count without reacting (leading to $\Delta T_b' = 1.045 \text{ K}$ ), failing to recognize that converting a weak base into a strong electrolyte salt drastically alters the effective molality.

Another trap is calculating the dissociation constant instead of the association constant for benzene.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Solutions - Class 12
Concept	Boiling Point Elevation (Solvent vs Solution)
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free