The correct order of osmotic pressure of 0.01M aqueous solution of the following is

Options

A. `"Sucrose" gt CH_3COOH gt KCl`
B. `CH_3 COOH gt "Sucrose" gt KCl`
C. `"Sucrose " gt KCl gt CH_3COOH`
D. `KCl gt CH_3COOH gt" Sucrose"`

Explanation

To determine the correct order of osmotic pressure for a 0.01 M aqueous solution of the given substances, we can use the formula for osmotic pressure:

\[ \pi = iCRT \]

Where:
- \(\pi\) = osmotic pressure
- \(i\) = van 't Hoff factor (number of particles the solute dissociates into)
- \(C\) = concentration of the solution (in this case, 0.01 M)
- \(R\) = universal gas constant (constant for all solutions)
- \(T\) = temperature (assumed constant for this problem)

Since \(C\), \(R\), and \(T\) are constants in this scenario, the osmotic pressure is directly proportional to the van 't Hoff factor \(i\). Therefore, we need to determine the \(i\) values for each solute.

### Step 1: Determine the van 't Hoff factor \(i\) for each solute
1. **KCl (Potassium Chloride)**:
- KCl dissociates into K\(^+\) and Cl\(^-\).
- Therefore, \(i = 2\) (1 K\(^+\) + 1 Cl\(^-\)).

2. **Acetic Acid (CH₃COOH)**:
- Acetic acid is a weak acid and does not fully dissociate in solution.
- It dissociates into H\(^+\) and CH₃COO\(^-\), but since it is not 100% dissociated, we can estimate \(i\) to be slightly less than 2. For practical purposes, we can take \(i \approx 1.2\).

3. **Sucrose (C₁₂H₂₂O₁₁)**:
- Sucrose does not dissociate in solution; it remains as one molecule.
- Therefore, \(i = 1\).

### Step 2: Compare the values of \(i\)
- KCl: \(i = 2\)
- Acetic Acid: \(i \approx 1.2\)
- Sucrose: \(i = 1\)

### Step 3: Determine the order of osmotic pressure
Since osmotic pressure is proportional to \(i\), we can arrange the substances in order of decreasing osmotic pressure:
1. KCl (highest osmotic pressure, \(i = 2\))
2. Acetic Acid (middle osmotic pressure, \(i \approx 1.2\))
3. Sucrose (lowest osmotic pressure, \(i = 1\))

### Final Order of Osmotic Pressure
The correct order of osmotic pressure for the 0.01 M aqueous solutions is:
\[ \text{KCl} > \text{Acetic Acid} > \text{Sucrose} \]

### Conclusion
Thus, the correct answer is option D, which matches our findings.