Notes › Physical Chemistry

Solutions & Colligative Properties

1. Raoult's Law

The partial vapour pressure of a component is proportional to its mole fraction: $P_A = P_A^\circ x_A$.

  • Ideal Solutions: $\Delta H_{mix} = 0$, $\Delta V_{mix} = 0$.
  • Non-Ideal: Show positive or negative deviations from Raoult's law.

2. Colligative Properties

Properties that depend only on the number of solute particles, not their nature.

  • Relative Lowering of Vapour Pressure
  • Elevation of Boiling Point: $\Delta T_b = i K_b m$
  • Depression of Freezing Point: $\Delta T_f = i K_f m$
  • Osmotic Pressure: $\pi = iCRT$

🧪 van't Hoff Factor ($i$)

Don't forget $i$! For dissociation (e.g., $NaCl$), $i > 1$. For association (e.g., acetic acid in benzene), $i < 1$.

3. Henry's Law

The solubility of a gas in a liquid is proportional to its partial pressure: $p = K_H x$. A higher $K_H$ means lower solubility. Gas solubility falls as temperature rises. This is why soft drinks are bottled under $CO_2$ pressure, and why divers use helium-diluted air to avoid the bends.

4. Deviations from Raoult's Law

  • Positive deviation: A–B attractions weaker than A–A and B–B. $\Delta H_{mix} > 0$, $\Delta V_{mix} > 0$. Examples: ethanol + acetone, carbon disulphide + acetone. Large positive deviations give minimum-boiling azeotropes, such as ethanol–water at about 95% ethanol.
  • Negative deviation: A–B attractions stronger. $\Delta H_{mix} < 0$, $\Delta V_{mix} < 0$. Example: chloroform + acetone (H-bonding), nitric acid + water. These form maximum-boiling azeotropes.

Interactive diagram: open this page in a browser to use it.

5. Concentration Terms

  • Molarity (M) = moles of solute per litre of solution; changes with temperature.
  • Molality (m) = moles of solute per kg of solvent; independent of temperature, which is why it is used for $\Delta T_b$ and $\Delta T_f$.
  • Mole fraction $x_A = \frac{n_A}{n_A + n_B}$.

6. Relative Lowering of Vapour Pressure

$$\frac{P^\circ - P}{P^\circ} = x_{solute} = \frac{n_2}{n_1 + n_2}$$

7. Abnormal Molar Mass

$i = \frac{\text{normal molar mass}}{\text{observed molar mass}}$. For dissociation into $n$ particles, $\alpha = \frac{i - 1}{n - 1}$. For association of $n$ molecules into one, $\alpha = \frac{1 - i}{1 - 1/n}$. Ethanoic acid dimerises in benzene, so its observed molar mass is close to 120 g/mol.

💡 Osmosis in Practice

Isotonic solutions have equal osmotic pressure (0.9% NaCl is isotonic with blood). Red blood cells swell in a hypotonic solution and shrink in a hypertonic one. Applying pressure greater than the osmotic pressure drives reverse osmosis, used in desalination.

Practice questions

  1. Which property of a solution does not change with temperature?

    1. Molarity
    2. Molality
    3. Normality
    4. Formality
    Answer

    B. Molality uses the mass of solvent, which does not change with temperature; molarity uses volume, which does.

  2. A mixture of chloroform and acetone shows:

    1. Positive deviation
    2. Negative deviation
    3. Ideal behaviour
    4. No azeotrope
    Answer

    B. Hydrogen bonding between CHCl₃ and acetone makes A–B attraction stronger, giving negative deviation and a maximum-boiling azeotrope.

  3. The van't Hoff factor for K₄[Fe(CN)₆] assuming complete dissociation is:

    1. 2
    2. 4
    3. 5
    4. 10
    Answer

    C. It gives 4K⁺ + [Fe(CN)₆]⁴⁻, i.e. 5 particles.

  4. The solubility of a gas in water decreases with:

    1. Increase in pressure
    2. Increase in temperature
    3. Decrease in temperature
    4. Increase in K_H only at low pressure
    Answer

    B. Dissolving a gas is usually exothermic, so solubility falls as temperature rises.

  5. 0.9% NaCl solution relative to human blood is:

    1. Hypotonic
    2. Hypertonic
    3. Isotonic
    4. Not comparable
    Answer

    C. 0.9% (w/v) saline has the same osmotic pressure as blood plasma.

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