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

Options

A. Decinormal `Al_(2)(SO_(4))_(3)`
B. Decinormal `BaCl_(2)`
C. Decinormal `Na_(2)SO_(4)`
D. A solution obtained by mixing equal volumes of (b) and (c) and filtering

Explanation

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

### Step 1: Understand the formula for osmotic pressure
The osmotic pressure (\( \pi \)) of a solution can be calculated using the formula:
\[ \pi = iCRT \]
where:
- \( i \) = van 't Hoff factor (number of particles the solute dissociates into)
- \( C \) = molar concentration of the solution
- \( R \) = universal gas constant
- \( T \) = temperature in Kelvin

### Step 2: Identify the dissociation of each salt
We need to determine the van 't Hoff factor (\( i \)) for each salt based on its dissociation in solution. The dissociation of the salts is as follows:
1. **NaCl** dissociates into 2 ions: \( Na^+ + Cl^- \) → \( i = 2 \)
2. **BaCl\(_2\)** dissociates into 3 ions: \( Ba^{2+} + 2Cl^- \) → \( i = 3 \)
3. **Na\(_2\)SO\(_4\)** dissociates into 3 ions: \( 2Na^+ + SO_4^{2-} \) → \( i = 3 \)
4. **MgSO\(_4\)** dissociates into 3 ions: \( Mg^{2+} + SO_4^{2-} \) → \( i = 3 \)
5. **Al\(_2\)(SO\(_4\))\(_3\)** dissociates into 5 ions: \( 2Al^{3+} + 3SO_4^{2-} \) → \( i = 5 \)

### Step 3: Calculate the effective van 't Hoff factor considering 90% dissociation
Since each salt is 90% dissociated, we can calculate the effective \( i \) for each salt:
- For **NaCl**: \( i = 2 \times 0.9 + 0.1 = 1.9 \)
- For **BaCl\(_2\)**: \( i = 3 \times 0.9 + 0.1 = 2.7 \)
- For **Na\(_2\)SO\(_4\)**: \( i = 3 \times 0.9 + 0.1 = 2.7 \)
- For **MgSO\(_4\)**: \( i = 3 \times 0.9 + 0.1 = 2.7 \)
- For **Al\(_2\)(SO\(_4\))\(_3\)**: \( i = 5 \times 0.9 + 0.1 = 4.6 \)

### Step 4: Compare the effective van 't Hoff factors
Now we can compare the effective \( i \) values:
- NaCl: \( i = 1.9 \)
- BaCl\(_2\): \( i = 2.7 \)
- Na\(_2\)SO\(_4\): \( i = 2.7 \)
- MgSO\(_4\): \( i = 2.7 \)
- Al\(_2\)(SO\(_4\))\(_3\): \( i = 4.6 \)

### Step 5: Determine the highest osmotic pressure
Since osmotic pressure is directly proportional to the van 't Hoff factor (\( i \)), the salt with the highest \( i \) will have the highest osmotic pressure. From our calculations, **Al\(_2\)(SO\(_4\))\(_3\)** has the highest effective \( i \) of 4.6.

### Conclusion
Thus, the salt that will have the highest osmotic pressure when each salt is assumed to be 90% dissociated is **Al\(_2\)(SO\(_4\))\(_3\)**.

---