Editing Colligative properties (section)

== Osmotic pressure ==
{{details|Osmotic pressure}}
The osmotic pressure of a solution is the difference in pressure between the solution and the pure liquid solvent when the two are in equilibrium across a [[semipermeable membrane]], which allows the passage of solvent molecules but not of solute particles. If the two phases are at the same initial pressure, there is a net transfer of solvent across the membrane into the solution known as [[osmosis]]. The process stops and equilibrium is attained when the pressure difference equals the osmotic pressure.

Two laws governing the osmotic pressure of a dilute solution were discovered by the German botanist [[Wilhelm Pfeffer|W. F. P. Pfeffer]] and the Dutch chemist [[Jacobus Henricus van 't Hoff|J. H. van't Hoff]]:

# The [[osmotic pressure]] of a dilute solution at constant temperature is directly proportional to its concentration.
# The osmotic pressure of a solution is directly proportional to its absolute temperature.<ref>{{Cite web |title=Van't Hoff's Laws of Osmotic Pressure - QS Study |url=https://qsstudy.com/vant-hoffs-laws-osmotic-pressure/ |access-date=2022-03-08 |website=qsstudy.com |language=en-US}}</ref>

These are analogous to [[Boyle's law]] and [[Charles's law]] for gases. Similarly, the combined [[ideal gas law]], <math>PV = nRT</math>, has as an analogue for ideal solutions <math>\Pi V = n R T i</math>, where <math>\Pi</math> is osmotic pressure; ''V'' is the volume; ''n'' is the number of moles of solute; ''R'' is the molar [[gas constant]] 8.314 J K<sup>−1</sup> mol<sup>−1</sup>; ''T'' is absolute temperature; and ''i'' is the [[Van 't Hoff factor]].

The osmotic pressure is then proportional to the [[molar concentration]] <math>c = n/V</math>, since

:<math>\Pi = \frac {n R T i}{V} = c R T i</math>

The osmotic pressure is proportional to the concentration of solute particles ''ci'' and is therefore a colligative property.

As with the other colligative properties, this equation is a consequence of the equality of solvent [[chemical potential]]s of the two phases in equilibrium. In this case the phases are the pure solvent at pressure ''P'' and the solution at total pressure (''P'' + <math>\Pi</math>).<ref>Engel and Reid p.207</ref>