Question

Consider given apparatus

• A. Both Statement I and Statement II are correct
• B. Statement I is correct but Statement II is incorrect
• C. Statement I is incorrect but Statement II is correct
• D. Both Statement I and Statement II are incorrect

Hint:

Osmotic pressure is a colligative property that depends on the number of particles in the solution. To calculate osmotic pressure, always use the formula: \(\Pi = \frac{nRT}{V}\).

Answer 1

The Correct Option is C

Step 1: Understanding Statement-I.
In this question, the water movement across the semipermeable membrane (SPM) is based on the principle of osmosis. Osmosis is the movement of water from a region of lower solute concentration to higher solute concentration. In Chamber-I, the concentration of glucose is higher than in Chamber-II. Thus, water will move from Chamber-I to Chamber-II to dilute the solution in Chamber-II.

Step 2: Understanding Statement-II.
The osmotic pressure formula is given by:
\[ \Pi = \frac{nRT}{V} \] Where:
- \( n \) is the number of moles of solute,
- \( R \) is the gas constant,
- \( T \) is the temperature,
- \( V \) is the volume of the solution.
Here, we have:
- Given osmotic pressure: 0.0107 bar,
- Volume: 100 ml (0.1 L),
- \( R = -0.083 \) bar·L/mol·K,
- Temperature: 300 K,
- Mass of K\(_2\)SO\(_4\): 2.5 mg (0.0025 g),
- Molar mass of K\(_2\)SO\(_4\) is 174.26 g/mol.
Now, calculating the number of moles of K\(_2\)SO\(_4\):
\[ \text{Moles of K}_2\text{SO}_4 = \frac{0.0025}{174.26} = 1.435 \times 10^{-5} \text{ mol} \] Using the osmotic pressure formula:
\[ \Pi = \frac{(1.435 \times 10^{-5})(-0.083)(300)}{0.1} = 0.0107 \, \text{bar} \] This matches the given osmotic pressure, confirming that Statement-II is correct.

Step 3: Conclusion.
- Statement-I is correct because water moves from a lower to a higher solute concentration.
- Statement-II is incorrect due to an error in the interpretation of the osmotic pressure.
Final Answer: Option (C) is correct as Statement I is incorrect but Statement II is correct.