Raoult's Law & Colligative Properties
Raoult's Law:
For volatile liquid solutions, partial vapour pressure of each component equals vapour pressure of pure component multiplied by its mole fraction: $p_1 = p_1^\circ x_1$.
Four Colligative Properties:
- Relative Lowering of Vapour Pressure: $\frac{p_1^\circ - p_1}{p_1^\circ} = x_2 = \frac{n_2}{n_1 + n_2}$
- Elevation of Boiling Point: $\Delta T_b = K_b \cdot m$ ($K_b$: Ebullioscopic constant)
- Depression of Freezing Point: $\Delta T_f = K_f \cdot m$ ($K_f$: Cryoscopic constant)
- Osmotic Pressure: $\Pi = C R T = \frac{n_2}{V} R T$
Van 't Hoff Factor ($i$)
$$i = \frac{\text{Experimental Colligative Property}}{\text{Calculated Colligative Property}} = \frac{\text{Total moles of particles after association/dissociation}}{\text{Initial moles of solute}}$$
- Dissociation: $i = 1 + (n - 1)\alpha$ (e.g., $NaCl \rightarrow i \approx 2$).
- Association: $i = 1 + \left(\frac{1}{n} - 1\right)\beta$ (e.g., Acetic acid dimerization $\rightarrow i \approx 0.5$).
