Question

Given below are two statements:} A semipermeable membrane separates two chambers:

Statement I:} \(H_2O\) molecules move from chamber 1 to chamber 2. Statement II:} The osmotic pressure of a solution prepared by dissolving \(50\,\text{mg}\) of potassium sulphate \((\text{molar mass}=174\,\text{g mol}^{-1})\) in \(2\,\text{L}\) of water (at \(27^\circ\text{C}\)) is \(0.0107\,\text{bar}\). \((R=0.083\,\text{dm}^3\text{bar K}^{-1}\text{mol}^{-1})\) Choose the correct answer.

• A. Both Statement I and Statement II are true
• B. Both Statement I and Statement II are false
• C. Statement I is true but Statement II is false
• D. Statement I is false but Statement II is true

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The statements concern the direction of osmosis and the calculation of osmotic pressure for an electrolyte.
Step 2: Key Formula or Approach:
- Osmosis direction: Solvent moves from lower solute concentration (hypotonic) to higher (hypertonic).
- Osmotic pressure: \(\pi = iCRT\) where \(i\) is the van't Hoff factor.
Step 3: Detailed Explanation:
1. Statement I:
- Molarity 1: \(18\text{ g glucose} = 0.1\text{ mol}\) in 0.1 L \(\Rightarrow 1.0\text{ M}\).
- Molarity 2: \(30\text{ g glucose} \approx 0.167\text{ mol}\) in 0.25 L \(\Rightarrow 0.668\text{ M}\).
- Water moves from lower (Chamber 2) to higher (Chamber 1) concentration. Statement I is False.
2. Statement II:
- \(\text{K}_2\text{SO}_4 \rightarrow 2\text{K}^{+} + \text{SO}_4^{2-}\) so \(i = 3\).
- \(C = \frac{50 \times 10^{-3} / 174}{2} \text{ mol/L}\).
- \(\pi = 3 \times \frac{0.05}{174 \times 2} \times 0.083 \times 300 \approx 0.0107\text{ bar}\). Statement II is True.
Step 4: Final Answer:
Statement I is false, and Statement II is true.