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Question #44729

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The Question

A $2.085 \text{ g}$ sample of \ce{PCl5} ( $M_w = 208.5 \text{ g/mol}$ ) is added to $100 \text{ g}$ of an acyclic dialkyl ether (\ce{R2O}), which serves as the solvent ( $K_f = 4.5 \text{ K kg mol}^{-1}$ ). The mixture is gently warmed until \ce{PCl5} completely cleaves the ether, converting entirely into a stable phosphorus oxychloride and alkyl chlorides.

In a parallel experiment, $1.335 \text{ g}$ of anhydrous \ce{AlCl3} ( $M_w = 133.5 \text{ g/mol}$ ) is dissolved in $100 \text{ g}$ of the same ether, where it forms a stable coordination complex without cleavage.

Assuming all products and complexes remain dissolved as non-volatile, non-electrolytic solutes, let $\Delta T_{f1}$ and $\Delta T_{f2}$ be the observed freezing point depressions for the \ce{PCl5} and \ce{AlCl3} solutions, respectively.

What is the ratio $\Delta T_{f1} / \Delta T_{f2}$ and the apparent molar mass of \ce{PCl5} calculated from its freezing point depression?

Options

A.
Ratio = $3$ , Apparent Mass = $69.5 \text{ g/mol}$
B.
Ratio = $6$ , Apparent Mass = $69.5 \text{ g/mol}$
C.
Ratio = $2$ , Apparent Mass = $104.25 \text{ g/mol}$
D.
Ratio = $1$ , Apparent Mass = $208.5 \text{ g/mol}$

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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

Molecular Mass Abnormalities|Ether Cleavage Patterns|Oxidation State Traps

Why This Question Is Tricky

Common Mistakes

This problem tests the 'Chemical Exception' where a solute chemically reacts with the solvent, drastically altering the number of particles and the observed colligative properties.

Students often mechanically apply the formula $\Delta T_f = K_f \cdot m$ assuming the solute dissolves inertly.

Here, \ce{PCl5} acts as a cleavage agent for ethers, tripling the particle count ( $i=3$ ).

Furthermore, it tests a hidden variable in coordination chemistry: \ce{AlCl3} is typically a dimer ( $i=0.5$ ) in non-polar media, but in Lewis basic solvents like ether, it undergoes symmetric cleavage to form a monomeric adduct ( $i=1$ ).

Failing to account for the ether cleavage by \ce{PCl5} or the monomeric nature of the \ce{AlCl3}-etherate leads to incorrect ratios and apparent masses.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Solutions - Class 12
Concept	Molecular Mass Abnormalities
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free