MP Board · Class 12 · Chemistry · SolutionsDefine Colligative Properties. Name the four colligative properties studied in solutions and explain Van't Hoff factor. How is Van't Hoff factor used to calculate the degree of dissociation of an electrolyte?

Definition of Colligative Properties\nColligative properties are those properties of dilute solutions that depend only upon the number of solute particles (molecules or ions) present in the solution and do not depend upon the chemical nature or identity of the solute particles. The word 'colligative' is derived from the Latin word colligare, meaning 'bound together'.

Four Major Colligative Properties

1. Relative Lowering of Vapour Pressure: The lowering of vapour pressure when a non-volatile solute is dissolved in a pure solvent.
2. Elevation of Boiling Point ($ΔT_b$): The increase in the boiling point of a solvent when a non-volatile solute is added to it.
3. Depression of Freezing Point ($ΔT_f$): The lowering of the freezing point of a solvent upon the addition of a non-volatile solute.
4. Osmotic Pressure ($Π$): The extra hydrostatic pressure applied on the solution side to prevent the flow of solvent into the solution through a semipermeable membrane.

Van't Hoff Factor ($i$)\nWhen electrolytes are dissolved in water, they undergo dissociation or association, which changes the total number of particles in the solution. To account for this anomaly in colligative properties, Jacobus Henricus van't Hoff introduced a factor known as the Van't Hoff factor ($i$).

\nIt is defined as: $$i = \frac{\text{Observed colligative property}}{\text{Calculated (normal) colligative property}} = \frac{\text{Normal molar mass}}{\text{Abnormal molar mass}} = \frac{\text{Total number of moles of particles after association/dissociation}}{\text{Number of moles of particles before association/dissociation}}$$

Degree of Dissociation ($\alpha$) and Van't Hoff Factor\nConsider an electrolyte that dissociates into $n$ ions:

$$\text{Electrolyte} \rightleftharpoons n(\text{Ions})$$

• Initial moles at $t = 0$: $1$ mole, $0$ ions
• Moles at equilibrium: $(1 - \alpha)$ moles, $n\alpha$ moles \nTotal moles at equilibrium ($N$) = $1 - \alpha + n\alpha = 1 + \alpha(n - 1)$ \nSince the Van't Hoff factor $i$ is equal to the total moles after dissociation divided by initial moles: $$i = \frac{1 + \alpha(n - 1)}{1} = 1 + \alpha(n - 1)$$ \nRearranging the formula to calculate the degree of dissociation ($\alpha$): $$\alpha = \frac{i - 1}{n - 1}$$\nThis relationship allows chemists to determine the exact extent to which weak electrolytes dissociate in aqueous solutions by measuring their colligative properties experimentally.