The ratio of real colligative characteristics to theoretical colligative properties is known as the Van’t Hoff factor i. In other way the ratio of the aberrant or experimental molar mass to the real or theoretical molar mass.The proportion of total ions remaining after dissociation or association to total ions remaining before dissociation or association.
For dissociation, the Van’t Hoff factor is more than one, for association, it is lower than one, and for the non-electrolyte solute, it is equal to one. As we know, when a solute or electrolyte is dissolved in a solvent, it never entirely dissociates or associates, but only up to a fraction known as the degree of dissociation, which is represented by the symbol α.
To obtain the relation between Van’t Hoff factor and degree of dissociation, consider an electrolyte that gives the following reaction An⇌nA
Hence, from this the Van’t Hoff factor is defined as the ratio of total particles after dissociation to the total particles before dissociation
∴i = 1−α+nα/1
∴i = 1−α(1−n)
Making degree of dissociation the subject of equation,
∴ α = i−1/n−1 , where n is the total number of ions of the electrolyte possible
This is the relation between the Van’t Hoff factor and the Degree of dissociation.