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Colligative Properties

Colligative Properties: Formulas & Van't Hoff Factor | Chemca.in
Solutions Chapter

Colligative Properties: Formulas & Concepts

Properties of solutions that depend only on the number of solute particles, irrespective of their nature, are called Colligative Properties. These are essential for determining molar masses of solutes.

1. The Four Colligative Properties

These properties apply to dilute solutions containing non-volatile solutes.

1. Relative Lowering of Vapor Pressure
$$ \frac{P^0 - P}{P^0} = \chi_{\text{solute}} = \frac{n_2}{n_1 + n_2} $$
2. Elevation in Boiling Point
$$ \Delta T_b = K_b \times m $$

$K_b$: Ebullioscopic Constant

3. Depression in Freezing Point
$$ \Delta T_f = K_f \times m $$

$K_f$: Cryoscopic Constant

4. Osmotic Pressure
$$ \Pi = CRT $$

Best method for polymers/proteins

Colligative properties solution class 12 chart

Figure: Summary of Colligative Properties and Molar Mass Determination

2. Abnormal Molar Mass & Van't Hoff Factor ($i$)

When solutes associate or dissociate in solution, the number of particles changes, affecting colligative properties. The Van't Hoff factor ($i$) corrects this.

Calculating '$i$'

$$ i = \frac{\text{Normal Molar Mass}}{\text{Abnormal Molar Mass}} $$ $$ i = \frac{\text{Observed Colligative Property}}{\text{Calculated Colligative Property}} $$
  • Dissociation ($i > 1$): For $\text{NaCl} \rightarrow \text{Na}^+ + \text{Cl}^-$, $i \approx 2$.
  • Association ($i < 1$): For Acetic Acid dimerization in benzene, $i \approx 0.5$.
  • No Change ($i = 1$): For Urea, Glucose, Sucrose.

Modified Equations for Ionic Solutes

Always multiply the standard formula by '$i$' for electrolytes:

  • $\Delta T_b = i K_b m$
  • $\Delta T_f = i K_f m$
  • $\Pi = i CRT$

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