Van 't Hoff factor

The degree of dissociation is the fraction of the original solute molecules that have dissociated. It is usually indicated by the Greek symbol ${\displaystyle \alpha }$ . There is a simple relationship between this parameter and the van 't Hoff factor. If a fraction ${\displaystyle \alpha }$  of the solute dissociates into ${\displaystyle n}$  ions, then

${\displaystyle i=1+\alpha (n-1).}$ 

For example, the dissociation KCl ⇌ K⁺ + Cl⁻ yields ${\displaystyle n=2}$  ions, so that ${\displaystyle i=1+\alpha }$ .

For dissociation in the absence of association, the van 't Hoff factor is: ${\displaystyle i>1}$ .

Similarly, if a fraction ${\displaystyle \alpha }$  of ${\displaystyle n}$  moles of solute associate to form one mole of an n-mer (dimer, trimer, etc.), then

${\displaystyle i=1-\left(1-{\frac {1}{n}}\right)\alpha .}$ 

For the dimerisation of acetic acid in benzene:

2 CH₃COOH ⇌ (CH₃COOH)₂

2 moles of acetic acid associate to form 1 mole of dimer, so that

${\displaystyle i=1-\left(1-{\frac {1}{2}}\right)\alpha =1-{\frac {\alpha }{2}}.}$ 

For association in the absence of dissociation, the van 't Hoff factor is: ${\displaystyle i<1}$ .

• When solute particles associate in solution, i is less than 1. For example, carboxylic acids such as acetic acid (ethanoic acid) or benzoic acid form dimers in benzene, so that the number of solute particles is half the number of acid molecules.
• When solute particles dissociate in solution, 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, i equals 1 (e.g. glucose in water).

The value of 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.

This quantity can be related to the osmotic coefficient g by the relation: ${\displaystyle i=ng}$ .

• Colligative properties
• Thermodynamic activity
• Raoult's law
• Law of dilution
• Van 't Hoff equation
• Dissociation (chemistry)
• Osmosis
• Osmotic coefficient

• Tro, Nivaldo J. (2020). Chemistry : A Molecular Approach (Fifth ed.). Hoboken, NJ. pp. 613–614. ISBN 978-0-13-498889-4. OCLC 1048659501.{{cite book}}: CS1 maint: location missing publisher (link)