Editing Osmotic pressure (section)

==Theory and measurement==
[[File:Pfeffer Osmotische Untersuchungen-1-3.jpg|thumb|right|200 px|A [[Pfeffer cell]] used for early measurements of osmotic pressure]]

[[Jacobus Henricus van 't Hoff|Jacobus van&nbsp;'t Hoff]] found a quantitative relationship between osmotic pressure and solute concentration, expressed in the following equation:
:<math>\Pi = icRT</math>
where <math>\Pi</math> is osmotic pressure, ''i'' is the dimensionless [[van 't Hoff factor|van&nbsp;'t Hoff index]], ''c'' is the [[molar concentration]] of solute, ''R'' is the [[ideal gas constant]], and ''T'' is the [[absolute temperature]] (usually in [[kelvins]]). This formula applies when the solute concentration is sufficiently low that the solution can be treated as an [[ideal solution]]. The proportionality to concentration means that osmotic pressure is a [[colligative property]]. Note the similarity of this formula to the [[ideal gas law]] in the form <math display="inline">P = \frac{n}{V} RT = c_\text{gas} RT</math> where {{mvar|n}} is the total number of moles of gas molecules in the volume ''V'', and ''n''/''V'' is the molar concentration of gas molecules. [[Harmon Northrop Morse]] and Frazer showed that the equation applied to more concentrated solutions if the unit of concentration was [[molal]] rather than [[molar (unit)|molar]];<ref name=":0">{{Cite journal|  vauthors = Lewis GN | date=1908-05-01| title=The Osmotic Pressure of Concentrated Solutions and the Laws of the Perfect Solution.| journal=Journal of the American Chemical Society| volume=30| issue=5| pages=668–683| doi=10.1021/ja01947a002| issn=0002-7863| url=https://zenodo.org/record/1428858| access-date=2019-07-04| archive-date=2022-06-18| archive-url=https://web.archive.org/web/20220618111258/https://zenodo.org/record/1428858| url-status=live}}</ref> so when the molality is used this equation has been called the '''Morse equation'''.

For more concentrated solutions the van&nbsp;'t Hoff equation can be extended as a power series in solute concentration, ''c''. To a first approximation,

:<math> \Pi = \Pi_0 + A c^2 </math>

where <math>\Pi_0 </math> is the ideal pressure and ''A'' is an empirical parameter. The value of the parameter ''A'' (and of parameters from higher-order approximations) can be used to calculate [[Pitzer parameter]]s. Empirical parameters are used to quantify the behavior of solutions of ionic and non-ionic solutes which are not [[ideal solution]]s in the thermodynamic sense.

The [[Wilhelm Pfeffer|Pfeffer cell]] was developed for the measurement of osmotic pressure.