MP Board · Class 12 · Chemistry · SolutionsWhat is van't Hoff factor? How is it related to the degree of dissociation of an electrolyte?

The van't Hoff factor ($i$) is a dimensionless parameter that accounts for the extent of association or dissociation of solute particles in solution. It is defined as the ratio of the normal (calculated) molar mass to the abnormal (observed) molar mass of a solute, or equivalently, as the ratio of the observed colligative property to the calculated colligative property. Mathematically, $i = \frac{\text{Observed colligative property}}{\text{Calculated colligative property}} = \frac{\text{Normal molar mass}}{\text{Abnormal molar mass}} = \frac{\text{Total moles of particles after association/dissociation}}{\text{Number of moles of particles before association/dissociation}}$. When an electrolyte undergoes dissociation in a solution, producing $n$ ions per molecule, let $\alpha$ be the degree of dissociation. The total number of moles of particles after dissociation is given by $1 - \alpha + n\alpha$. Thus, the van't Hoff factor $i = 1 + \alpha(n - 1)$, rearranging which gives the degree of dissociation as $\alpha = \frac{i - 1}{n - 1}$. This relationship is extremely important for correcting colligative property measurements for ionic solutes.