Q.Match the laws given in Column I with expressions given in Column II.
Column I:

The key idea is matching each colligative property or solution law to its defining equation.

Step 1 – Raoult’s law gives the total vapour pressure of an ideal binary mixture: $p = x_1 p_1^{o} + x_2 p_2^{o}$. This matches (c).

Step 2 – Henry’s law states that the partial pressure of a gas above a liquid is proportional to its mole fraction in the liquid: $p = K_H \cdot x$. This matches (e). …

The key to solving this cleanly is to recall what each law says — not just the formula, but the physical idea behind it. Once you know the concept, the expression follows naturally.

1. Raoult’s law describes the vapour pressure of an ideal liquid-liquid solution. It says: the partial pressure of each component above the solution equals its mole fraction times its pure vapour pressure. For a two-component mixture, the total pressure is

$p = x_1 p_1^\circ + x_2 p_2^\circ$.

That matches option (c).

2. Henry’s law governs the solubility of a gas in a liquid. It states: at constant temperature, the partial pressure of the gas above the liquid is directly proportional to its mole fraction in the liquid.

$p = K_H \cdot x$

Here $K_H$ is Henry’s constant. That’s option (e).

3. Elevation of boiling point — when a non-volatile solute is added to a solvent, the boiling point rises. The change is proportional to the molality of the solution:

$\Delta T_b = K_b m$

where $K_b$ is the ebullioscopic constant. That’s option (d).

4. Depression in freezing point — similarly, adding a solute lowers the freezing point. The depression is:

$\Delta T_f = K_f m$

where $K_f$ is the cryoscopic constant. That’s option (a). …

Method: Direct Concept Matching

This is a recognition-based matching problem. The method involves recalling the defining equation for each colligative or solution law, then matching it to the correct expression in Column II.

Steps

1. Recall the standard formula for each law from memory (no calculation needed).

2. Match each law to its expression:

   • (i) Raoult's law For a mixture of two volatile liquids:

 → Matches with **(c)**.

• (ii) Henry's law Solubility of a gas in a liquid:

 → Matches with **(e)**.

• (iii) Elevation of boiling point

 → Matches with **(d)**.

• (iv) Depression in freezing point

 → Matches with **(a)**.

• (v) Osmotic pressure

 → Matches with **(b)**.

3. Write the final matched pairs:

✗ Mistake 1: Confusing Raoult’s law with Henry’s law

Why it happens:

Both laws have a similar-looking equation:

• Raoult’s law: $p = x_1 p_1^\circ + x_2 p_2^\circ$ (for ideal liquid mixtures)
• Henry’s law: $p = K_H \cdot x$ (for gas solubility in a liquid)

Students often swap them because both involve partial pressure and mole fraction.

How to avoid:

• Raoult’s law uses the pure vapour pressure of each component ($p^\circ$).
• Henry’s law uses a Henry’s constant ($K_H$), not the pure vapour pressure.
• Remember: Raoult’s law applies to solvent in an ideal solution; Henry’s law applies to solute (especially gases).

✓ Correct match:

• (i) Raoult’s law → (c) $p = x_1 p_1^\circ + x_2 p_2^\circ$
• (ii) Henry’s law → (e) $p = K_H \cdot x$

✗ Mistake 2: Mixing up boiling point elevation and freezing point depression formulas

Why it happens:

Both formulas look nearly identical:

• $\Delta T_b = K_b m$
• $\Delta T_f = K_f m$

Students often match them incorrectly because they forget which constant ($K_b$ or $K_f$) goes with which.

How to avoid:

• Boiling point elevation → uses $K_b$ (b for boiling).
• Freezing point depression → uses $K_f$ (f for freezing).
• Mnemonic: b for boil, f for freeze.

✓ Correct match:

• (iii) Elevation of boiling point → (d) $\Delta T_b = K_b m$
• (iv) Depression in freezing point → (a) $\Delta T_f = K_f m$

✗ Mistake 3: Forgetting the osmotic pressure formula

Why it happens:

Osmotic pressure ($\Pi = CRT$) looks similar to the ideal gas law ($PV = nRT$), so students sometimes confuse it with other colligative property formulas.

How to avoid:

• Osmotic pressure is the only colligative property that uses concentration $C$ (molarity) and $RT$ directly.
• No $K$ constant, no $m$ (molality) — just $C$, $R$, $T$.

✓ Correct match:

• (v) Osmotic pressure → (b) $\Pi = CRT$

✗ Mistake 4: Not reading the notation carefully

Why it happens: …