Question

Match Column I with Column II and choose the correct option :

Column I	Column II
a. Osmotic pressure	i. \( \Delta \mathrm{T_f} = \mathrm{K_f}\,m \)
b. Elevation of boiling point	ii. \( \pi = CRT \)
c. Depression of freezing point	iii. \( \frac{\mathrm{P_1^0 - P_1}}{\mathrm{P_1^0}} = \frac{\mathrm{W_2 \times M_1}}{\mathrm{M_2 \times W_1}} \)
d. Relative lowering of vapour pressure	iv. \( \Delta \mathrm{T_b} = \mathrm{K_b}\,m \)

• A. a-i, b-ii, c-iii, d-iv
• B. a-ii, b-i, c-iii, d-iv
• C. a-iv, b-iii, c-ii, d-i
• D. a-ii, b-iv, c-i, d-iii

Hint:

Osmotic pressure is pi = CRT, boiling point rise uses Kb, freezing point fall uses Kf, and relative lowering uses the vapour pressure ratio.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
Each colligative property in Column I has one formula in Column II. We match them one by one and then pick the option that has all four pairs right.

Step 2: Match (a) Osmotic pressure:
Osmotic pressure is the extra pressure needed to stop solvent flow through a semipermeable membrane. For a dilute solution, \( \pi = CRT \), where C is molarity. This is (ii).

Step 3: Match (b) Elevation of boiling point:
A non-volatile solute raises the boiling point of the solvent. The rise is \( \Delta T_b = K_b m \), where m is molality. This is (iv).

Step 4: Match (c) Depression of freezing point:
A solute lowers the freezing point of the solvent. The fall is \( \Delta T_f = K_f m \). This is (i).

Step 5: Match (d) Relative lowering of vapour pressure:
This is the fall in vapour pressure divided by the vapour pressure of the pure solvent. For a dilute solution, \[ \frac{P_1^0 - P_1}{P_1^0} = \frac{W_2 \times M_1}{M_2 \times W_1} \] This is (iii).

Step 6: Why the other options are wrong:
Option (A) gives osmotic pressure the freezing point formula, so it is wrong.
Option (B) pairs a with ii correctly, but b-i and c-iii are both wrong. The boiling point rise does not use the freezing formula.
Option (C) pairs osmotic pressure with the boiling point formula (a-iv), so it is wrong.

Final Answer:
The correct matching is a-ii, b-iv, c-i, d-iii, which is option (D). \[ \boxed{\text{(D)}} \]