Van’t Hoff Factor:
In 1886, Van’t Hoff introduced a factor called Van’t Hoff factor, ‘i’ to express the extent of association or dissociation of solutes in an electrolytic solution. It is the ratio of the normal and observed molar masses (or abnormal molar mass) of the solute, i.e.,
|i = Normal molar mass / Observed molar mass|
In case of an association, observed molar mass being more than the normal, the factor ‘i’ has a value less than 1.
But in the case of dissociation, the Van’t Hoff factor is more than 1 because the observed molar mass has a lesser value.
In the case of solutes that do not undergo any association or dissociation in a solvent, Van’t Hoff factor ‘i’ will be equal to 1 because the observed and normal molar masses will be the same.
Since the molar masses are inversely proportional to the colligative property, Van’t Hoff factor may also be expressed as:
|i = Observed value of colligative property / Normal value of colligative property|
The normal value of colligative property is the theoretically calculated value assuming no association of dissociation.
Inclusion of Van’t Hoff factor (i) modified the equations for colligative properties as follows-
- PA° – PA / PA° = ixB
- ΔTb = iKbm
- ΔTf = iKfm
- π = iCRT
Van’t Hoff factor and Extent of Dissociation or Association in an Electrolytic Solution:
Van’t Hoff factor can be used to calculate the extent of dissociation or association in terms of the degree of dissociation or association of a substance in solution.
(1) Degree of Dissociation- It is defined as the fraction of total substance that undergoes dissociation into ions i.e.,
|Degree of dissociation = No. of moles of the substance dissociated / Total number of moles of the substance taken|
Van’t Hoff factor ‘i’ is related to the degree of dissociation (α) as-
|α = (i – 1) / (m – 1)|
For the electrolytes of the type AB, such as KCl, NaCl, etc., the number of particles in solution i.e., m = 2
|∴ α = i – 1|
For the electrolytes of the type AB2 like CaCl2, Ba(NO3)2 etc. the value of m = 3, so that
|∴ α = (i – 1) / 2|
(2) Degree of Association- It is defined as the fraction of the total number of molecules that combine to form associated molecules i.e.,
|Degree of association = No. of moles of the substance associated / Total number of moles of substance taken|
Relation between Vant’s Hoff factor ‘i’ and degree of association is given as-
| α = (i – 1) / [(1/n) – 1]|
But, i = Normal molar mass / Observed molar mass
Thus, knowing ‘n’ the number of simple molecules which combine to give associated molecule, observed molar mass, degree of associated (α) can be calculated.