Osmotic Pressure (Π = MRT)

Separate a solution from pure water by a membrane that passes only water, and water flows in until the extra hydrostatic pressure — the osmotic pressure Π — stops it. Van 't Hoff noticed that dilute solutes behave like an ideal gas trapped in the solution, so Π = MRT with the same gas constant, R = 8.314 J/(mol·K). Physiological saline (0.154 M NaCl, which dissociates into about 0.308 mol/L of particles) at body temperature gives Π = 308 mol/m³ × 8.314 × 310 K ≈ 7.9 × 10⁵ Pa — roughly 7.7 atm, which is why IV fluids must match blood's osmolarity or red cells swell and burst.

The effect is enormous per mole: even a 0.010 M sugar solution at 25 °C pushes with about 0.24 atm, equivalent to a 2.5 m column of water. That sensitivity makes osmotic pressure the classic method for measuring the molar mass of polymers and proteins, where a tiny molar concentration of huge molecules still produces a comfortably measurable pressure. Reverse osmosis simply runs the equation backwards — seawater's ~27 atm of osmotic pressure sets the minimum pressure a desalination pump must beat.