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.