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Analogical ReasoningLevel 2 · Application

A cucumber shrivels when placed in concentrated salt water but swells when placed in distilled water. A red blood cell bursts in distilled water but shrinks in concentrated saline. Both involve a membrane and water movement. What single principle, stated in one sentence, explains all four observations?

✦Real Life Hook

Singapore, Israel, and the Gulf states quench their thirst using reverse osmosis — forcing sea water through membranes at high pressure (60–80 bar) to push water against its natural osmotic flow. The membranes remove 99.99% of dissolved salts. A single large RO plant in Dubai produces 140 million litres of drinking water per day. The same physics that makes a raisin swell in water makes desalination possible — just running the process in reverse by applying enough pressure to overcome the osmotic gradient.

Osmosis and Semipermeable Membranes

Osmosis is the spontaneous net flow of solvent molecules through a semipermeable membrane (SPM) from the region of lower solute concentration to the region of higher solute concentration.

A semipermeable membrane allows solvent molecules to pass through but blocks solute molecules/ions. Examples: cellophane, pig bladder, biological cell membranes.

Osmotic pressure ( $\pi$ ) is the external pressure that must be applied to the solution side to just stop net osmotic flow.

Van't Hoff Equation for Osmotic Pressure

For dilute solutions:
$\pi = MRT$

where:

$\pi$ = osmotic pressure (in Pa or bar)
$M$ = molarity of the solution (mol/L) — note: osmotic pressure uses molarity, not molality
$R$ = gas constant = 0.0831 L·bar/(mol·K)
$T$ = temperature in Kelvin

This equation is analogous to the ideal gas law ( $pV = nRT$ ), with $M = n/V$ .

Concentration types relative to the cell:

Isotonic ( $\pi_{\text{solution}} = \pi_{\text{cell}}$ ) → no net osmotic flow → cells maintain shape
Hypotonic ( $\pi_{\text{solution}} < \pi_{\text{cell}}$ ) → water enters cell → cell swells/bursts
Hypertonic ( $\pi_{\text{solution}} > \pi_{\text{cell}}$ ) → water leaves cell → cell shrinks (crenation)

🖼 Image PendingOsmosis diagram showing water movement through semipermeable membrane from dilute to concentrated solution

AI Generation Prompt

Osmosis apparatus diagram. A U-tube or glass vessel divided by a semipermeable membrane (shown as a mesh/grid in the middle). Left side labelled "Pure water / dilute solution" with fewer orange dots (solute particles). Right side labelled "Concentrated solution" with many orange dots. Arrows showing water molecules (small blue dots) moving predominantly left to right through the membrane. Right side liquid level is higher than left, showing pressure buildup. Label the height difference as "π = osmotic pressure". Inset diagram showing (A) cell in hypotonic solution — swollen, (B) normal isotonic cell, (C) cell in hypertonic solution — crenated/shrunken. Dark background, orange accent labels, clean technical illustration style.

📸 Osmosis: water flows from the dilute side (left) to the concentrated side (right) until osmotic pressure π is reached

📖NCERT 2.12NCERT Intext

Problem

200 cm³ of an aqueous solution of a protein contains 1.26 g of the protein. The osmotic pressure at 300 K is found to be $2.57 \times 10^{-3}$ bar. Calculate the molar mass of the protein. ( $R = 0.0831$ L·bar·mol⁻¹·K⁻¹)

✦JEE / NEET Exam InsightJEE / NEET

◆Osmotic pressure vs other colligative properties for large molecules:

\pi

is most sensitive for large molecules (proteins, polymers). A 1 g/L protein solution has undetectable

\Delta T_f

but measurable

\pi

. This is why osmometry is used for molar mass of macromolecules.

◆Reverse osmosis: Apply pressure >

\pi

to concentrated side → water flows backward → desalination.

◆Medical importance: IV saline is 0.9% NaCl (isotonic — same osmotic pressure as blood plasma ≈ 7.91 bar). 5% glucose is also approximately isotonic. Using pure water in an IV would lyse red blood cells.

◆Units trap: In

\pi = MRT

, R = 0.0831 L·bar·mol⁻¹·K⁻¹ when

\pi

is in bar and M in mol/L.

Quick Check

Q1.In osmosis, the net flow of solvent occurs from: