What is the correct sequence of osmotic pressure of `0.01 M aq.` solution of `:`
`(a) Al_(2)(SO_(4))_(3)" "(b) Na_(3)PO_(4)" "(c ) BaCl_(2)" " (d) Gluc ose`

Options

A. `pi_(4) gt pi_(2) gt pi_(3) gt pi_(1)`
B. `pi_(3) gt pi_(4) gt pi_(2) gt pi_(1)`
C. `pi_(3) gt pi_(4) gt pi_(1) gt pi_(2)`
D. `pi_(1) gt pi_(2) gt pi_(3) gt pi_(4)`

Answer

To determine the correct sequence of osmotic pressure for the given 0.01 M aqueous solutions of the compounds, we will follow these steps:

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

### Step 2: Identify the Van't Hoff Factor for Each Compound
We need to find the Van't Hoff factor (i) for each of the given compounds:

1. **Aluminum Sulfate \((Al_2(SO_4)_3)\)**:
- Dissociates into: 2 \(Al^{3+}\) and 3 \(SO_4^{2-}\)
- Total ions = 2 + 3 = 5
- \( i = 5 \)

2. **Sodium Phosphate \((Na_3PO_4)\)**:
- Dissociates into: 3 \(Na^{+}\) and 1 \(PO_4^{3-}\)
- Total ions = 3 + 1 = 4
- \( i = 4 \)

3. **Barium Chloride \((BaCl_2)\)**:
- Dissociates into: 1 \(Ba^{2+}\) and 2 \(Cl^{-}\)
- Total ions = 1 + 2 = 3
- \( i = 3 \)

4. **Glucose**:
- Glucose does not dissociate in solution (it is a non-electrolyte).
- \( i = 1 \)

### Step 3: Compare the Van't Hoff Factors
Now we can compare the Van't Hoff factors:
- \( Al_2(SO_4)_3 \): \( i = 5 \)
- \( Na_3PO_4 \): \( i = 4 \)
- \( BaCl_2 \): \( i = 3 \)
- Glucose: \( i = 1 \)

### Step 4: Determine the Sequence of Osmotic Pressure
Since the osmotic pressure is directly proportional to the Van't Hoff factor (when concentration, R, and T are constant), we can arrange the compounds in order of their osmotic pressure based on their \( i \) values:

1. **Aluminum Sulfate**: Highest osmotic pressure (i = 5)
2. **Sodium Phosphate**: Second highest osmotic pressure (i = 4)
3. **Barium Chloride**: Third highest osmotic pressure (i = 3)
4. **Glucose**: Lowest osmotic pressure (i = 1)

### Final Sequence of Osmotic Pressure
Thus, the correct sequence of osmotic pressure for the 0.01 M aqueous solutions is:
\[ \text{(a) Al}_2(SO_4)_3 > \text{(b) Na}_3PO_4 > \text{(c) BaCl}_2 > \text{(d) Glucose} \]