Osmotic Pressure

Osmotic pressure: π = M·R·T (van't Hoff equation)

Osmotic pressure is the pressure needed to stop solvent flow across a semipermeable membrane from a less-concentrated to a more-concentrated solution. Jacobus van't Hoff (1886) derived π = M·R·T for dilute solutions, where M is the solute molarity, R = 0.0821 L·atm/(mol·K), and T is the absolute temperature in K. The equation earned him the first Nobel Prize in Chemistry (1901). For electrolytes, multiply by the van't Hoff factor i (NaCl → i ≈ 2, since it dissociates into Na⁺ and Cl⁻). Example: physiological saline (0.9% NaCl) is isotonic with blood at ~308 mOsm/L, giving π ≈ 7.7 atm at 37 °C — matching the osmotic pressure inside red blood cells. Osmosis itself is the spontaneous solvent flow from low to high solute concentration, opposing this pressure.

Applications

Medicine (IV fluids must be isotonic — hypertonic or hypotonic solutions injected rapidly can lyse or shrink red blood cells), nephrology (hemodialysis exploits osmotic gradients to remove urea), food preservation (salt and sugar dehydrate bacteria by osmosis), botany (cell turgor pressure keeps plants rigid), and reverse osmosis desalination (applying >50 atm forces solvent through a membrane against the natural osmotic gradient).

FAQ

What is the van't Hoff factor i? The number of particles produced per formula unit in solution. Non-electrolytes (glucose, urea) give i = 1; NaCl gives i ≈ 2; CaCl₂ gives i ≈ 3. Real values are slightly lower than ideal due to ion pairing.

Why is the formula identical in shape to the ideal gas law? Both treat dilute "particles" (solute or gas) as non-interacting; van't Hoff noted the analogy explicitly. The formula breaks down at high concentrations, just as PV = nRT fails for dense gases.

Isotonic, hypertonic, hypotonic — what's the difference? Isotonic matches the cell's internal osmotic pressure (0.9% NaCl for human cells); hypertonic is higher (cells shrink); hypotonic is lower (cells swell, possibly bursting). Critical in clinical fluid management.