Excess pressure required to maintain osmotic equilibrium between a solution and the
pure solvent separated by a
membrane permeable only to the solvent:
where

,

are the partial molar volume and activity of solvent

for an incompressible fluid. For ideal dilute solutions,

,
where entities

are individually moving solute molecules, ions, etc., regardless of their nature,

,

are the amount and mass concentration of the solutes, and

is the mass average molar mass of the solutes. The amount is sometimes expressed in
osmol (meaning a
mole of osmotically active entities), but this usage and the corresponding term
osmolarity are discouraged.
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