The formula, and why the van 't Hoff factor matters
Osmotic pressure is the pressure needed to stop solvent crossing a semipermeable membrane. It is a colligative property, so it depends on how many dissolved particles are present, not what they are. M is molarity (mol/L), R is 0.08206 L·atm/(mol·K), T is in kelvin, and i counts the particles each unit breaks into.
The van 't Hoff factor for common solutes
This is the number people most often get wrong. Non-electrolytes stay whole; salts split into ions, and real ion pairing means the measured value sits a little below the ideal count.
| Solute | Ideal i | Measured (0.1 M) |
|---|---|---|
| Sucrose, glucose (sugar) | 1 | 1.0 |
| NaCl (table salt) | 2 | 1.8–1.9 |
| CaCl₂ | 3 | 2.6–2.7 |
| Na₂SO₄ | 3 | ~2.5 |
| Acetic acid (weak) | 1–2 | ~1.3 |
Worked value: 0.1 M sucrose at 25 °C (298.15 K) gives Π = 1 × 0.1 × 0.08206 × 298.15 ≈ 2.45 atm. The same molarity of NaCl gives about 4.6 atm.
The three things that break the calculation
- Celsius instead of kelvin. The equation needs absolute temperature. Convert first: T(K) = T(°C) + 273.15.
- Ignoring i. Treating salt as i = 1 halves the answer. Use i near 2 for NaCl, near 3 for CaCl₂.
- Grams instead of moles. M is molar, not g/L. Divide mass by molar mass first: M = grams ÷ (molar mass × litres).
Common questions
What is the van 't Hoff equation for osmotic pressure?
Osmotic pressure equals i times M times R times T. Here i is the van 't Hoff factor (how many particles each formula unit releases), M is molar concentration in mol per litre, R is the gas constant 0.08206 L atm per mol per K, and T is temperature in kelvin.
Do I use Celsius or Kelvin?
Kelvin, always. The equation needs an absolute temperature. Add 273.15 to the Celsius value: 25 C becomes 298.15 K. Using Celsius is the most common mistake and gives a badly wrong answer.
Why does salt give roughly double the pressure of sugar?
Osmotic pressure depends on particle count, not particle type. Sugar stays as one molecule (i = 1). Salt splits into a sodium ion and a chloride ion, so one formula unit becomes about two particles (i near 2), giving about twice the pressure at the same concentration.
