Question

Which of the following is CORRECT with respect to the property mentioned against it?

• A. Osmotic pressure at 298K : 0.1M NaCl solution<0.1M Urea solution
• B. Concentration of NaCl in the solution : 2ppm>2M
• C. \(\Delta\)T\(_b\) : 0.02M Urea solution>0.02M NaCl solution
• D. Vapour pressure at 298K : Salt water<Pure water

Hint:

For all colligative properties, remember that adding a non-volatile solute to a solvent will:

• Lower the freezing point.
• Elevate the boiling point.
• Lower the vapour pressure.
• Increase the osmotic pressure.

Also, always account for the Van't Hoff factor (i) for electrolytes.

Answer 1

The Correct Option is D

Step 1: Understanding Colligative Properties and Van't Hoff Factor (i).
Colligative properties (osmotic pressure, elevation in boiling point, depression in freezing point, relative lowering of vapour pressure) depend on the number of solute particles in a solution. For electrolytes like NaCl, we must consider their dissociation using the Van't Hoff factor (i).

• For NaCl, which dissociates into Na\(^+\) and Cl\(^-\), the theoretical Van't Hoff factor is i=2.
• For Urea, a non-electrolyte, i=1.

The effective concentration for colligative properties is i \(\times\) Molarity.
Step 2: Evaluating each statement.
(A) Osmotic pressure (\(\pi\)) = iCRT:

• For 0.1M NaCl: effective concentration = i \(\times\) 0.1 M = 2 \(\times\) 0.1 M = 0.2 M.
• For 0.1M Urea: effective concentration = i \(\times\) 0.1 M = 1 \(\times\) 0.1 M = 0.1 M.

Since osmotic pressure is proportional to the effective concentration, the osmotic pressure of 0.1M NaCl solution should be greater than that of 0.1M Urea solution. The statement says the opposite, so it is incorrect.
(B) Concentration of NaCl in the solution: 2ppm>2M:

• 2 ppm (parts per million) is a very dilute concentration (e.g., 2 mg of solute per 1 kg of solution).
• 2M (2 Molar) means 2 moles of solute per 1 litre of solution. Molar mass of NaCl \(\approx\) 58.5 g/mol. So, 2M NaCl is 2 \(\times\) 58.5 = 117 g of NaCl per litre.

Clearly, 2M is a much, much higher concentration than 2ppm. The statement is incorrect.
(C) Elevation in boiling point (\(\Delta\)T\(_b\)) = iK\(_b\)m:

• For 0.02M Urea: effective concentration \(\approx\) 1 \(\times\) 0.02 M = 0.02 M.
• For 0.02M NaCl: effective concentration \(\approx\) 2 \(\times\) 0.02 M = 0.04 M.

Since \(\Delta\)T\(_b\) is proportional to the effective concentration, the boiling point elevation for NaCl solution will be greater than for Urea solution. The statement says the opposite, so it is incorrect.
(D) Vapour pressure at 298K: Salt water<Pure water: This refers to the lowering of vapour pressure, a colligative property. According to Raoult's law, when a non-volatile solute (like salt) is dissolved in a solvent (like water), the vapour pressure of the solution is lower than that of the pure solvent. This is because the solute particles occupy some of the surface area, reducing the rate of evaporation of the solvent molecules. This statement is correct.
Step 3: Final Answer.
The correct statement is (D).