Assuming each salt to be `90%` dissociated which of the following will have the highest osmotic pressure?

Options

A. decimolar aluminium sulphate
B. decimolar barium chloride solution
C. decimolar sodium sulphate solution
D. solution of volume of decimolar barium choride and decimolar sodium suphate solutions

Answer

To determine which salt solution has the highest osmotic pressure when each salt is assumed to be 90% dissociated, we can follow these steps:

### Step 1: Understand the Osmotic Pressure Formula
The osmotic pressure (π) is given by the formula:
\[ \pi = C \cdot R \cdot T \cdot i \]
Where:
- \( C \) = concentration of the solution
- \( R \) = gas constant
- \( T \) = temperature
- \( i \) = Van't Hoff factor (the number of particles the solute dissociates into)

### Step 2: Identify the Van't Hoff Factor for Each Salt
We will calculate the Van't Hoff factor \( i \) for each salt based on their dissociation:

1. **Aluminum Sulfate (Al₂(SO₄)₃)**:
- Dissociates into: \( 2 \text{Al}^{3+} + 3 \text{SO}_4^{2-} \)
- Total particles = \( 2 + 3 = 5 \)
- \( i = 5 \)
- Considering 90% dissociation:
\[ i_{effective} = 0.9 \times 5 = 4.5 \]

2. **Barium Chloride (BaCl₂)**:
- Dissociates into: \( \text{Ba}^{2+} + 2 \text{Cl}^- \)
- Total particles = \( 1 + 2 = 3 \)
- \( i = 3 \)
- Considering 90% dissociation:
\[ i_{effective} = 0.9 \times 3 = 2.7 \]

3. **Sodium Sulfate (Na₂SO₄)**:
- Dissociates into: \( 2 \text{Na}^+ + \text{SO}_4^{2-} \)
- Total particles = \( 2 + 1 = 3 \)
- \( i = 3 \)
- Considering 90% dissociation:
\[ i_{effective} = 0.9 \times 3 = 2.7 \]

### Step 3: Compare the Effective Van't Hoff Factors
Now we compare the effective Van't Hoff factors we calculated:
- Aluminum Sulfate: \( i_{effective} = 4.5 \)
- Barium Chloride: \( i_{effective} = 2.7 \)
- Sodium Sulfate: \( i_{effective} = 2.7 \)

### Step 4: Determine the Highest Osmotic Pressure
Since the concentration \( C \), gas constant \( R \), and temperature \( T \) are the same for all solutions, the osmotic pressure is directly proportional to the effective Van't Hoff factor \( i \). Therefore, the solution with the highest \( i \) will have the highest osmotic pressure.

### Conclusion
The solution with the highest osmotic pressure is the **decimolar aluminum sulfate solution**.