Osmotic Pressure: Why Water Climbs Against Gravity

A membrane that plays favourites

A semipermeable membrane lets small solvent molecules — usually water — pass freely while blocking larger dissolved solute. Put pure water on one side and a solute solution on the other, and the two sides start out with different water chemical potentials: dissolving solute lowers water's chemical potential on that side. Water spontaneously flows from where its chemical potential is higher (the pure side) to where it's lower (the solution side), diluting the solution, exactly the way heat flows from hot to cold.

The van't Hoff equation

The pressure needed to exactly stop that net flow — the osmotic pressure Π — follows a strikingly simple relation for dilute solutions, discovered empirically by Jacobus van't Hoff:

Π = i M R T

  i  van't Hoff factor (particles produced per formula unit dissolved)
  M  molarity of solute
  R  gas constant
  T  absolute temperature

The form is the same shape as the ideal gas law P = (n/V)RT, which is why the two are often taught side by side — though the physical mechanism behind osmotic pressure is a membrane-mediated chemical-potential balance, not molecules literally striking a container wall.

The osmometer: pressure balances flow

A membrane osmometer makes this measurable directly: a solution sits in a chamber sealed by a semipermeable membrane, connected to a thin open capillary. Water flows in through the membrane, and the liquid column in the capillary rises. As it rises, the hydrostatic pressure at the membrane (ρgh, from the taller column of liquid) grows and pushes back against further net inflow. The column stops rising exactly when hydrostatic pressure equals the osmotic pressure, giving a direct physical measurement of Π from the equilibrium height h.

Colligative — it only counts particles

Osmotic pressure belongs to the family of colligative properties, alongside boiling-point elevation, freezing-point depression and vapor-pressure lowering — properties that depend on how many solute particles are dissolved, not on what those particles chemically are. That's exactly why the van't Hoff factor i matters: sugar stays as one intact molecule in solution (i = 1), while NaCl dissociates into Na+ and Cl- (i ≈ 2), so equal molar amounts of the two produce roughly double the osmotic pressure for the salt.

Reverse osmosis: fighting the gradient

Apply an external mechanical pressure to the solution side that exceeds its natural osmotic pressure, and the direction of net water flow reverses: water is pushed backward through the membrane, from the concentrated side to the pure side, leaving dissolved solute behind since the membrane still only passes solvent. That is reverse osmosis, the basis of most modern seawater desalination and household water-purification systems.

Frequently asked questions

Try it live

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