van't Hoff equation: Π = iMRT, where i is the van't Hoff factor (number of particles per formula unit), M is molar concentration (mol/L), R = 0.08206 L·atm/(mol·K), and T is temperature. This describes the osmotic pressure — the pressure needed to stop net solvent flow across a semipermeable membrane.
The simulation shows random-walk water (blue) and solute (green) molecules. The semipermeable membrane passes only water. Net flux from low-concentration to high-concentration side builds up a pressure difference visible as a height difference Δh = Π/(ρg). At equilibrium the chemical potentials equalize.
Osmosisvan't HoffChemical potentialColligative propertiesMembrane transport