Editing Van 't Hoff factor

{{short description|Measure of solute effect}}
The '''van&nbsp;'t Hoff factor {{mvar|i}}''' (named after Dutch chemist [[Jacobus Henricus van 't Hoff]]) is a measure of the effect of a solute on [[colligative properties]] such as [[osmotic pressure]], relative lowering in [[vapor pressure]], [[boiling-point elevation]] and [[freezing-point depression]]. The van 't Hoff factor is the ratio between the ''actual concentration'' of particles produced when the substance is dissolved and the ''[[formal concentration]]'' that would be expected from its chemical formula. For most non-[[electrolyte]]s dissolved in water, the van&nbsp;'t Hoff factor is essentially 1.

For most [[ionic compound]]s dissolved in water, the van&nbsp;'t Hoff factor is equal to the number of discrete ions in a [[formula unit]] of the substance. This is true for [[ideal solution]]s only, as occasionally [[ion pair]]ing occurs in solution. At a given instant a small percentage of the ions are paired and count as a single particle. Ion pairing occurs to some extent in all electrolyte solutions. This causes the measured van&nbsp;'t Hoff factor to be less than that predicted in an ideal solution. The deviation for the van&nbsp;'t Hoff factor tends to be greatest where the ions have multiple charges.

The factor binds [[osmolarity]] to [[molarity]] and [[osmolality]] to [[molality]].

==Dissociated solutes==
The degree of dissociation is the fraction of the original solute molecules that have [[dissociation (chemistry)|dissociated]]. It is usually indicated by the Greek symbol <math>\alpha</math>. There is a simple relationship between this parameter and the van&nbsp;'t Hoff factor. If a fraction <math>\alpha</math> of the solute dissociates into <math>n</math> ions, then

:<math> i = 1 + \alpha (n - 1). </math>

For example, the dissociation KCl {{Eqm}} K<sup>+</sup> + Cl<sup>−</sup> yields <math>n = 2</math> ions, so that <math>i = 1 + \alpha</math>.

For dissociation in the absence of association, the van&nbsp;'t Hoff factor is:
<math>i > 1 </math>.

==Associated solutes==
Similarly, if a fraction <math>\alpha</math> of <math>n</math> moles of solute associate to form one mole of an ''n''-mer ([[Dimer (chemistry)|dimer]], [[Trimer (chemistry)|trimer]], etc.), then

: <math> i = 1 - \left(1 - \frac{1}{n}\right)\alpha. </math>

For the [[Dimer (chemistry)|dimerisation]] of [[acetic acid]] in [[benzene]]:

: 2 CH<sub>3</sub>COOH {{Eqm}} (CH<sub>3</sub>COOH)<sub>2</sub>

2 moles of acetic acid associate to form 1 mole of dimer, so that
: <math>i = 1 - \left(1 - \frac{1}{2}\right)\alpha = 1 - \frac{\alpha}{2}.</math>

For association in the absence of dissociation, the van&nbsp;'t Hoff factor is:
<math>i <1 </math>.

== Physical significance of {{mvar|i}} ==

[[File:Carboxylic acid dimers.svg|thumb|Dimerization of a carboxylic acid by formation of [[hydrogen bond]]s (shown as dotted lines)]]
* When solute particles associate in solution, {{mvar|i}} is less than 1. For example, [[carboxylic acid]]s such as [[acetic acid]] (ethanoic acid) or [[benzoic acid]] form [[Dimer (chemistry)|dimers]] in benzene, so that the number of solute particles is half the number of acid molecules.
* When solute particles [[dissociate]] in solution, {{mvar|i}} is greater than 1 (e.g. [[sodium chloride]] in water, [[potassium chloride]] in water, [[magnesium chloride]] in water).
* When solute particles neither dissociate nor associate in solution, {{mvar|i}} equals 1 (e.g. [[glucose]] in water).
The value of {{mvar|i}} is the actual number of particles in solution after dissociation divided by the number of formula units initially dissolved in solution and means the number of particles per formula unit of the solute when a solution is dilute.

== Relation to osmotic coefficient ==
This quantity can be related to the [[osmotic coefficient]] g by the relation: 
<math>i = n g</math>.

== See also ==
* [[Colligative properties]]
* [[Thermodynamic activity]]
* [[Raoult's law]]
* [[Law of dilution]]
* [[Van 't Hoff equation]]
* [[Dissociation (chemistry)]]
* [[Osmosis]]
* [[Osmotic coefficient]]

== References ==
* {{cite book | last=Tro | first=Nivaldo J. | url=https://www.worldcat.org/oclc/1048659501 | title=Chemistry : A Molecular Approach | date=2020 | isbn=978-0-13-498889-4 | edition=Fifth | location=Hoboken, NJ | oclc=1048659501 | pages=613–614}}

[[Category:Physical chemistry]]
[[Category:Dimensionless numbers of physics]]
[[Category:Jacobus Henricus van 't Hoff]]