van 't Hoff factor

The van 't Hoff factor i (named after Dutch chemist Jacobus Henricus van 't Hoff) is a measure of the effect of a solute upon 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 concentration of a substance as calculated from its mass. For most non-electrolytes dissolved in water, the van 't Hoff factor is essentially 1. For most ionic compounds dissolved in water, the van 't Hoff factor is equal to the number of discrete ions in a formula unit of the substance. This is true for ideal solutions only, as occasionally ion pairing 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 't Hoff factor to be less than that predicted in an ideal solution. The deviation for the van 't Hoff factor tends to be greatest where the ions have multiple charges.

Dissociated solutesEdit

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

 

For example, the dissociation

KCl ⇌ K+ + Cl

yields   ions, so that  

For dissociation in the absence of association, the van 't Hoff factor is:  .

Associated solutesEdit

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

 

For the dimerisation of acetic acid in benzene

2CH3COOH ⇌ (CH3COOH)2

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

 

For association in the absence of dissociation, the van 't Hoff factor is:  .

Physical significance of iEdit

 
Dimerization of a carboxylic acid by formation of hydrogen bonds (shown as dotted lines)

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.

Relation to osmotic coefficientEdit

This quantity can be related to the osmotic coefficient g by the relation:  .

See alsoEdit