van't Hoff law (1887): osmotic pressure Π of an ideal dilute solution equals the "pressure" the solute would exert as an ideal gas at the same number density. R = 8.314 J/mol·K.
i is the van't Hoff factor: i=1 for non-electrolytes, i≈2 for NaCl, i≈3 for MgCl₂ (if fully dissociated). Activity corrections reduce i at high concentration.
Virial expansion: real solutions have B₂ (second virial coefficient) due to solute–solute interactions. Positive B₂ → larger pressure; negative B₂ → association.
External [solute] < cell interior. Net water influx. Cell swells, may lyse (cytolysis). Example: pure water around red blood cell.
External [solute] ≈ cell interior (~0.9% NaCl for human cells, ~290 mOsm). No net water flow. Cell maintains shape.
External [solute] > cell interior. Net water efflux. Cell shrinks (crenation). Example: seawater or concentrated saline.