Before You Begin

Question #44541

Difficulty: 8/10 | 🟢 Free

The Question

Compartments A and B of equal volume are separated by a specialized chiral semipermeable membrane. Initially, Compartment A contains a $0.15\text{ M}$ aqueous solution of fully dissociated racemic 1-phenylethylammonium chloride, denoted as $(\pm)-M^+Cl^-$ . Compartment B initially contains pure water. The chiral membrane is perfectly permeable to water, the $(S)-M^+$ enantiomer, and $Cl^-$ ions, but is completely impermeable to the $(R)-M^+$ enantiomer due to stereospecific binding interactions. The system is allowed to reach thermodynamic equilibrium at $300\text{ K}$ , with external pressure applied to maintain constant and equal volumes in both compartments. What is the osmotic pressure difference ( $\Delta \pi = \pi_A - \pi_B$ ) required to maintain this equilibrium? (Given: $R = 0.082\text{ L atm K}^{-1}\text{ mol}^{-1}$ )

Options

A.
$2.46\text{ atm}$
B.
$7.38\text{ atm}$
C.
$3.69\text{ atm}$
D.
$5.54\text{ atm}$

Check Your Answer

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

Osmotic Pressure vs Diffusion|Optical Isomerism Logic

Why This Question Is Tricky

Common Mistakes

This question tests the intersection of stereochemistry (chiral recognition) and physical chemistry (Donnan membrane equilibrium).

Students typically assume osmotic pressure only depends on the initial total concentration ( $\pi = iCRT$ ).

Here, the chiral membrane acts as a stereoselective filter, but because the solute is an electrolyte, the diffusion of the permeable enantiomer is constrained by macroscopic electroneutrality.

The hidden variable is the unequal distribution of the achiral $Cl^-$ ion driven by the trapped chiral $(R)-M^+$ cation, forcing students to apply the Donnan product rule rather than simple concentration equalization.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Solutions - Class 12
Concept	Osmotic Pressure vs Diffusion
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free