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Question #44656

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The Question

An aqueous solution is prepared by dissolving $200\text{ g}$ of \ce{Fe2(SO4)3} (Molar mass $= 400\text{ g mol}^{-1}$ ) in $1000\text{ g}$ of water. The freezing point of this solution is found to be $-3.255^\circ\text{C}$ . If the density of the solution at $300\text{ K}$ is $1.44\text{ g mL}^{-1}$ , what is the osmotic pressure of the solution at $300\text{ K}$ ?\n\n(Given: $K_f\text{ of water} = 1.86\text{ K kg mol}^{-1}$ , $R = 0.082\text{ L atm K}^{-1}\text{ mol}^{-1}$ . Assume the Van't Hoff factor remains constant across the temperature range.)

Options

A.
$43.05\text{ atm}$
B.
$51.66\text{ atm}$
C.
$61.50\text{ atm}$
D.
$73.80\text{ atm}$

Check Your Answer

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

Dimensional Consistency of Constants|Colligative Property Definition|Van’t Hoff Factor (i) Application

Why This Question Is Tricky

Common Mistakes

This problem tests two major conceptual traps in colligative properties.

First, it forces the student to calculate the experimental Van't Hoff factor ( $i = 3.5$ ) rather than assuming ideal complete dissociation ( $i = 5$ for \ce{Fe2(SO4)3}).

Second, it exploits the dimensional mismatch between molality ( $m$ ) and molarity ( $M$ ).

Students frequently approximate $M \approx m$ for aqueous solutions, which is only valid for highly dilute solutions at $4^\circ\text{C}$ .

By providing a high-density solution ( $1.44\text{ g mL}^{-1}$ ), the approximation fails catastrophically.

Osmotic pressure strictly requires volume-based Molarity ( $M = 0.6\text{ M}$ ), while freezing point depression uses mass-based Molality ( $m = 0.5\text{ m}$ ).

Using $m$ in the osmotic pressure formula yields the distractor $43.05\text{ atm}$ .

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Some Basic Concepts of Chemistry - Class 11 Part 1
Concept	Dimensional Consistency of Constants
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free