Equal volumes of 0.1 M NaCl and 0.06 M `CaCl_(2)` solutions are separated by a semi - permeable membrane in container. For this system, choose the correct answer

Options

A. Water flows from NaCl solution towards `CaCl_(2)` solution
B. There is no movement of any solution across the membrane
C. Osmotic pressure of 0.1 M NaCl is lower than the osmotic pressure of `CaCl_(2)` (Assume complete dissociatio)
D. Water flows from `CaCl_(2)` solution towards `NaCl` soltuion

Answer

To solve the problem, we need to determine the osmotic pressures of the two solutions (0.1 M NaCl and 0.06 M CaCl₂) and analyze the direction of solvent movement through the semi-permeable membrane.

### Step-by-Step Solution:

1. **Identify the dissociation of solutes:**
- **NaCl:** Dissociates into Na⁺ and Cl⁻. Therefore, for 1 mole of NaCl, we get 2 moles of particles.
- **CaCl₂:** Dissociates into Ca²⁺ and 2 Cl⁻. Therefore, for 1 mole of CaCl₂, we get 3 moles of particles.

2. **Calculate the van 't Hoff factor (i):**
- For NaCl:
\[ i_{NaCl} = 2 \quad (\text{1 Na}^+ + 1 Cl}^-) \]
- For CaCl₂:
\[ i_{CaCl_2} = 3 \quad (\text{1 Ca}^{2+} + 2 Cl}^-) \]

3. **Calculate the osmotic pressure (π) using the formula:**
\[ \pi = i \cdot M \cdot R \cdot T \]
where:
- \(i\) = van 't Hoff factor
- \(M\) = molarity of the solution
- \(R\) = gas constant
- \(T\) = temperature (assumed constant for both solutions)

4. **Calculate osmotic pressure for NaCl:**
- Given \(M_{NaCl} = 0.1 \, M\):
\[ \pi_{NaCl} = 2 \cdot 0.1 \cdot R \cdot T = 0.2 R T \]

5. **Calculate osmotic pressure for CaCl₂:**
- Given \(M_{CaCl_2} = 0.06 \, M\):
\[ \pi_{CaCl_2} = 3 \cdot 0.06 \cdot R \cdot T = 0.18 R T \]

6. **Compare the osmotic pressures:**
- \(\pi_{NaCl} = 0.2 R T\)
- \(\pi_{CaCl_2} = 0.18 R T\)

Since \(0.2 R T > 0.18 R T\), the osmotic pressure of NaCl is greater than that of CaCl₂.

7. **Determine the direction of solvent movement:**
- According to osmosis, the solvent moves from the region of lower osmotic pressure to the region of higher osmotic pressure. Therefore, water will flow from the CaCl₂ solution (lower osmotic pressure) to the NaCl solution (higher osmotic pressure).

### Conclusion:
The correct answer is that water flows from the CaCl₂ solution to the NaCl solution.

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