Osmotic Pressure and van't Hoff Factor

Osmotic Pressure and the van't Hoff Factor: Colligative Properties Calculations

By StudyStore · Published 2026-11-04 · 1 min read · 302 words

Colligative properties depend on the number of dissolved particles, not their identity. The van't Hoff factor (i) counts how many particles one formula unit gives in solution.

The equations

Property	Equation	Direction
Osmotic pressure	pi = iMRT	Solute raises it
Freezing point depression	delta T_f = i K_f m	Freezing point falls
Boiling point elevation	delta T_b = i K_b m	Boiling point rises
Vapor pressure lowering	P = X_solvent P° (Raoult)	Vapor pressure falls

M is molarity, m is molality, R = 0.0821 L atm/(mol K), and T is in kelvin.

van't Hoff factor

Solute	Ideal i
Glucose, sucrose, urea	1
NaCl, KBr	2
CaCl₂, Na₂SO₄	3
AlCl₃	4

Real values are slightly lower than ideal because of ion pairing, more so for concentrated solutions and highly charged ions.

Worked example

Compare 0.1 M glucose with 0.1 M NaCl at 300 K. Glucose: pi = 1 x 0.1 x 0.0821 x 300 = 2.5 atm. NaCl: i = 2, so pi = about 4.9 atm. The NaCl solution has twice the osmotic pressure, so water moves toward it across a semipermeable membrane.

Osmosis direction

Water moves from low solute concentration (hypotonic) to high solute concentration (hypertonic). Compare osmolarity (i x M), not molarity. A cell in a hypotonic solution swells; in a hypertonic solution it shrinks.

Common traps

Forgetting i. 0.1 M NaCl acts like 0.2 M of particles.
Using Celsius for T.
Reversing the freezing and boiling directions. Freezing point goes down, boiling point goes up.

One-minute recap

Count particles: osmolarity = iM.
pi = iMRT; water flows toward higher osmolarity.
Solutes lower freezing point and raise boiling point.

Check yourself: 5-question mini-quiz

Try each question first, then click it to reveal the answer.

1. What is the ideal van't Hoff factor for CaCl2?

Three.

2. Which equation gives osmotic pressure?

pi = iMRT.

3. Which has higher osmotic pressure, 0.1 M glucose or 0.1 M NaCl?

NaCl, because it gives about twice as many particles.

4. Which way does water move across a semipermeable membrane?

Toward the side with higher solute concentration.

5. What happens to the boiling point when a nonvolatile solute is added?

It rises.

Free MCAT sampler

Enter your email and download a real page set from a paid pack: the 3-page Amino Acids, Proteins and Enzymes cheat sheet (PDF). Confirm your email and short MCAT lessons follow. Free, no card.

Prefer not to sign up? The sampler is open to everyone: free notes, practice sets and the study schedule generator.

Written by StudyStore from standard scientific facts. Study aid only. Always check values against the reference your exam provides.