# Van't Hoff Factor : Explanation Of Abnormal Molar Mass

Why do we need van’t Hoff factor? In colligative properties of solution, we have read about the methods used for measurements of molecular masses of various substances. We now know that colligative properties such as relative lowering of vapour pressure, elevation of boiling point, freezing point depression and osmotic pressure are used for the determination of molar masses. As science advanced further, it has been experimentally observed that some of the molar mass measurements were different from the theoretical values, that is, they were either less or more than the ones calculated using the colligative properties. This abnormality in mass from the theoretical value was referred as abnormal molar mass. Van’t Hoff, in 1880 came up with the explanation for this abnormality and gave van’t Hoff factor in order to account for this abnormality.

## Explanation of Abnormal Molar Mass

As science advanced further, it has been experimentally observed that some of the molar mass measurements were different from the theoretical values, that is, they were either less or more than the ones calculated using the colligative properties. This abnormality in mass from the theoretical value was referred as abnormal molar mass. Van’t Hoff, in 1880 came up with the explanation for this abnormality and gave van’t Hoff factor in order to account for this abnormality.

Van’t Hoff explained that when solutes are dissolved in a solvent they dissociate into ions. Since colligative properties depend only on the number of solute particles, the dissociation of solute molecules into ions results in an increase in the number of particles and hence affects the colligative property. Suppose 1 mole of NaCl was dissolved in 1 Kg of water, now if all the molecules of NaCl dissociate in water ,then there will be 1 mol of Cl ions and 1 mole of Na+ ions and hence a total of 2 moles of ions in the solution. But while calculating the molar mass using the colligative properties ,we consider only 1 mol of NaCl to be present in the solution.

Some of the substances tend to associate in aqueous state and for such molecules the number of ions/molecules present in the solution is less than the actual number of molecules. So , for those substances that dissociate in solution, the observed molar mass will always be less than the real mass and for those substances that associate in solutions, the real mass will always be less than the observed molar mass. We do not know the extent of association or dissociation for all the substance.

### Van’t Hoff Factor

To solve this problem, Van’t Hoff introduced van’t Hoff factor (i) to account for these abnormalities. The van’t Hoff factor is defined as:

$i=\frac{Normal Molar Mass}{Abnormal/Observed Molar Mass}$

$i=\frac{Observed Colligative Property}{Calculated Colligative Property}$

$i=\frac{Number of moles of solute after association/dissociation}{Number of moles of solute before association/dissociation}$

Hence for those substances that dissociate in aqueous state, the value of i will be greater than 1 and for those that associate in it, it will be less than 1. If you have any query, get in touch with the mentors at BYJU’s.’

#### Practise This Question

The density of a 0.438 M solution of potassium chromate at 298 K is 1.063 g cm3. Calculate the vapour pressure of water above this solution. Given : P0 (water) = 23.79 mm Hg.