Van't Hoff Factor ($i$)
Abnormal Molar Masses & Association/Dissociation | Solutions
1. Why do we need the Van't Hoff Factor?
Colligative properties depend on the number of solute particles.
- If a solute dissociates (e.g., $NaCl \to Na^+ + Cl^-$), the number of particles increases.
- If a solute associates (e.g., dimerization of Ethanoic acid), the number of particles decreases.
2. Defining the Van't Hoff Factor ($i$)
$$ i = \frac{\text{Observed Colligative Property}}{\text{Calculated Colligative Property}} $$
$$ i = \frac{\text{Normal (Theoretical) Molar Mass}}{\text{Abnormal (Observed) Molar Mass}} $$
$$ i = \frac{\text{Normal (Theoretical) Molar Mass}}{\text{Abnormal (Observed) Molar Mass}} $$
Summary of Cases
| Case | Value of $i$ | Effect on Colligative Property | Effect on Molar Mass |
|---|---|---|---|
| No Association/Dissociation (e.g., Urea, Glucose) |
$i = 1$ | Same as calculated | Normal |
| Dissociation (e.g., $NaCl, K_2SO_4$) |
$i > 1$ | Increases | Decreases (Abnormal low) |
| Association (e.g., Benzoic acid in Benzene) |
$i < 1$ | Decreases | Increases (Abnormal high) |
3. Calculating $i$ from Degree of Ionization ($\alpha$)
Case A: Dissociation
If one molecule breaks into $n$ ions:
$$ A_n \rightleftharpoons nA $$
$$ i = 1 + (n - 1)\alpha $$
Example: For $BaCl_2$, $n=3$ (gives $Ba^{2+} + 2Cl^-$). If $\alpha = 100\% (1)$, then $i = 3$.
Case B: Association
If $n$ molecules combine to form one giant molecule:
$$ nA \rightleftharpoons A_n $$
$$ i = 1 + \left(\frac{1}{n} - 1\right)\alpha $$
Example: Dimerization of Acetic Acid, $n=2$. If $\alpha = 100\%$, then $i = 0.5$.
4. Modified Colligative Property Equations
Multiply the standard formulas by $i$:
- RLVP: $\frac{P^\circ - P}{P^\circ} = i \cdot \chi_{solute}$
- Elevation in BP: $\Delta T_b = i \cdot K_b \cdot m$
- Depression in FP: $\Delta T_f = i \cdot K_f \cdot m$
- Osmotic Pressure: $\pi = i \cdot C \cdot R \cdot T$
Practice Quiz
Test your knowledge on Van't Hoff Factor.
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