Colligative Properties & Van't Hoff
Master the physical properties of solutions that depend entirely on the number of particles, not their identity. Decode Phase Diagrams, Osmotic Pressure, and the Van't Hoff Factor ($i$).
Module Focus: The Power of Numbers
Colligative Properties (from Latin colligatus: bound together) are properties of dilute solutions that depend ONLY on the number of solute particles (molecules or ions) present, and are completely independent of the chemical nature of the solute. A solution of 1M Glucose behaves identically to a 1M solution of Urea in terms of these properties.
1. The Four Colligative Properties
Before introducing the Van't Hoff factor, let's establish the four fundamental formulas assuming the solute is non-volatile and does not dissociate or associate (e.g., Glucose, Urea, Sucrose).
The drop in vapor pressure relative to the pure solvent is equal to the mole fraction of the solute ($X_B$).
The excess pressure applied to the solution side to prevent osmosis. It is proportional to molarity ($C$) and temperature ($T$).
2. Elevation of BP & Depression of FP
When a non-volatile solute is added, the vapor pressure drops. Consequently, the solution must be heated to a higher temperature to make its vapor pressure equal to atmospheric pressure (Elevation of Boiling Point, $\Delta T_b$). Similarly, the freezing point drops (Depression of Freezing Point, $\Delta T_f$).
Notice how the lower Vapor Pressure curve of the solution shifts BOTH the freezing point down and the boiling point up.
$K_b$ = Ebullioscopic Constant (Molal elevation constant). Units: $\text{K kg mol}^{-1}$.
$m$ = Molality of the solution.
$K_f$ = Cryoscopic Constant (Molal depression constant). Units: $\text{K kg mol}^{-1}$.
Application: Ethylene glycol acts as an antifreeze in car radiators.
3. Osmosis & Osmotic Pressure
Osmosis is the spontaneous flow of pure solvent molecules through a Semi-Permeable Membrane (SPM) from a region of lower solute concentration to a region of higher solute concentration.
- Isotonic Solutions: Two solutions with the exact same osmotic pressure ($\pi_1 = \pi_2$). 0.9% (mass/volume) NaCl is isotonic with fluid inside Red Blood Cells (RBCs).
- Hypertonic Trap: If RBCs are placed in a solution $> 0.9\%$ NaCl, water flows OUT of the cells via osmosis, causing them to shrink (plasmolysis).
- Hypotonic Trap: If RBCs are placed in pure water or $< 0.9\%$ NaCl, water flows INTO the cells, causing them to swell and burst.
4. The Mega Concept: Van't Hoff Factor ($i$)
Colligative properties depend on the *number* of particles. If an electrolyte dissociates (breaks apart) or associates (groups together), the number of particles changes, leading to abnormal molar masses.
Salts break into multiple ions, multiplying the effect.
$K_2SO_4 \rightarrow 2K^+ + SO_4^{2-}$ (i = 3)
$Al_2(SO_4)_3 \rightarrow 2Al^{3+} + 3SO_4^{2-}$ (i = 5)
If degree of dissociation ($\alpha$) is given:
Molecules hydrogen bond together (dimerize), reducing the number of particles.
$2CH_3COOH \rightleftharpoons (CH_3COOH)_2$ (i = 0.5)
If degree of association ($\alpha$) is given:
To solve any real problem, simply multiply the original formula by the Van't Hoff factor ($i$).
NEET Grand Test: Colligative Properties
15 High-Yield Questions targeting Van't Hoff comparisons, biological osmosis, and formula applications.
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