Question

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

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

• 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:

Match by symbol: pi goes with osmotic pressure, Kb with boiling point, Kf with freezing point, and the ratio of P values with relative lowering.

Answer 1

The Correct Option is D

Step 1: Name each formula in Column II.
(i) \( \Delta T_f = K_f m \) uses the freezing point constant, so it is the depression of freezing point.
(ii) \( \pi = CRT \) gives the pressure across a semipermeable membrane, so it is osmotic pressure.
(iii) The ratio \( (P_1^0 - P_1)/P_1^0 \) is the fraction by which vapour pressure falls. It is the relative lowering of vapour pressure.
(iv) \( \Delta T_b = K_b m \) uses the boiling point constant, so it is the elevation of boiling point.

Step 2: Match with Column I.
a. Osmotic pressure goes with ii.
b. Elevation of boiling point goes with iv.
c. Depression of freezing point goes with i.
d. Relative lowering of vapour pressure goes with iii.

Step 3: Compare with the options.
(A) pairs a with i, which is wrong.
(B) pairs b with i, which is wrong.
(C) pairs a with iv, which is wrong.
(D) gives a-ii, b-iv, c-i, d-iii, which is exactly our matching.

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