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Question #44165

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The Question

Three separate $1.0 \text{ molal}$ solutions of $o$ -dichlorobenzene, $m$ -dichlorobenzene, and $p$ -dichlorobenzene are prepared in a non-polar solvent ( $\ce{CCl4}$ ) at $298 \text{ K}$ . In this solvent, the polar solute molecules undergo dimerization exclusively due to dipole-dipole interactions. The dimerization equilibrium constant ( $K_d$ ) is directly proportional to the square of the resultant dipole moment of the solute molecule ( $\mu_{res}^2$ ).

For the $m$ -dichlorobenzene solution, the van 't Hoff factor ( $i$ ) is observed to be $0.75$ .

Assuming the relative lowering of vapor pressure is directly proportional to the effective molality of the solute, what is the ratio of the relative lowering of vapor pressure of the $o$ -dichlorobenzene solution to that of the $p$ -dichlorobenzene solution?

Options

A.
$\frac{2}{3}$
B.
$\frac{5}{8}$
C.
$\frac{8}{9}$
D.
$\frac{3}{4}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Numerical_Precision

Improve calculation stamina and avoid rounding errors in high-stakes competitive examinations.

Concepts Behind This Question

Dipole Moment Vector Addition|Vapor Pressure Lowering (Mole Fraction)

Why This Question Is Tricky

Common Mistakes

The question tests the intersection of molecular dipole moments, chemical equilibrium (dimerization), and colligative properties.

The 'hidden variable' is that polar molecules in non-polar solvents aggregate via dipole-dipole interactions, reducing the effective particle count ( $i < 1$ ).

Students often blindly apply Raoult's Law assuming $i=1$ for non-electrolytes.

Furthermore, the extent of dimerization depends on the resultant dipole moment, requiring vector addition of the individual bond dipoles.

The trap is failing to recognize that $p$ -dichlorobenzene has a zero dipole moment and thus does not dimerize ( $i=1$ ), while the ortho and meta isomers dimerize to different extents based on their bond angles ( $60^\circ$ vs $120^\circ$ ).

Another trap is incorrectly formulating the $K_d$ expression for dimerization by forgetting the stoichiometric coefficients.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Chemical Bonding and Molecular Structure - Class 11 Part 1
Concept	Dipole Moment Vector Addition
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free