0.1 M NaCl and 0.05 M `BaCl_(2)` solutions are separated by a semi-permeable membrane in a container. For this system, choose the correct answer

Options

A. (a) There is no movement of any solution across the membrane
B. (b) Water flows from `BaCl_(2)` solution towards NaCl solution
C. (c) Water flows from NaCl solution towards `BaCl_(2)` solution
D. (d) Osmotic pressure of 0.1 M NaCl is lower than the osmotic pressure of `BaCl_(2)`(assume complete dissociation)

Answer

To solve the problem of the movement of water between 0.1 M NaCl and 0.05 M BaCl₂ solutions separated by a semi-permeable membrane, we will calculate the osmotic pressures of both solutions and determine the direction of water movement based on these pressures.

### Step-by-step Solution:

1. **Identify the Van't Hoff Factor (I)**:
- For NaCl:
- NaCl dissociates into Na⁺ and Cl⁻.
- Therefore, for every 1 mole of NaCl, we get 2 particles (1 Na⁺ + 1 Cl⁻).
- Thus, the Van't Hoff factor (I) for NaCl = 2.
- For BaCl₂:
- BaCl₂ dissociates into Ba²⁺ and 2 Cl⁻.
- Therefore, for every 1 mole of BaCl₂, we get 3 particles (1 Ba²⁺ + 2 Cl⁻).
- Thus, the Van't Hoff factor (I) for BaCl₂ = 3.

2. **Calculate the Osmotic Pressure (π)**:
- The formula for osmotic pressure is given by:
\[ \pi = I \cdot C \cdot R \cdot T \]
- For NaCl (0.1 M):
\[ \pi_1 = I \cdot C \cdot R \cdot T = 2 \cdot 0.1 \cdot R \cdot T = 0.2RT \]
- For BaCl₂ (0.05 M):
\[ \pi_2 = I \cdot C \cdot R \cdot T = 3 \cdot 0.05 \cdot R \cdot T = 0.15RT \]

3. **Compare the Osmotic Pressures**:
- We find that:
\[ \pi_1 (NaCl) = 0.2RT \quad \text{and} \quad \pi_2 (BaCl₂) = 0.15RT \]
- Since \( \pi_1 > \pi_2 \), it indicates that the osmotic pressure of the NaCl solution is greater than that of the BaCl₂ solution.

4. **Determine the Direction of Water Movement**:
- Water will move from the area of lower osmotic pressure to the area of higher osmotic pressure.
- Therefore, water will flow from the BaCl₂ solution (lower osmotic pressure) to the NaCl solution (higher osmotic pressure).

5. **Conclusion**:
- The correct answer is that water flows from the BaCl₂ solution towards the NaCl solution.

### Final Answer:
Water flows from BaCl₂ solution towards NaCl solution.