What is the correct order of osmotic pressure of 0.01 M aqueous solution os
(1) `Al_2(SO_4)_3`
(2) `K_3PO_4`
(3) `BaCl_2`
(4) Urea

Options

A. `pi_4 gt pi_3 gt pi_2 gt pi_1`
B. `pi_1 gt pi_2 gt pi_3 gt pi_4`
C. `pi_1 = pi_2 = pi_3 = pi_4`
D. `pi_2 gt pi_4 gt pi_1 gt pi_3`

Answer

To determine the correct order of osmotic pressure for the given 0.01 M aqueous solutions of the compounds, we will 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 (0.01 M for all in this case)
- \(R\) = gas constant (which is constant for all)
- \(T\) = temperature (which is also constant for all)

Since \(C\), \(R\), and \(T\) are constant for all solutions, we can focus on the van 't Hoff factor \(i\) to compare the osmotic pressures.

### Step 1: Calculate the van 't Hoff factor \(i\) for each solute

1. **For \(Al_2(SO_4)_3\)**:
- It dissociates into 2 Al³⁺ ions and 3 SO₄²⁻ ions.
- Total ions = 2 + 3 = 5
- Therefore, \(i = 5\).

2. **For \(K_3PO_4\)**:
- It dissociates into 3 K⁺ ions and 1 PO₄³⁻ ion.
- Total ions = 3 + 1 = 4
- Therefore, \(i = 4\).

3. **For \(BaCl_2\)**:
- It dissociates into 1 Ba²⁺ ion and 2 Cl⁻ ions.
- Total ions = 1 + 2 = 3
- Therefore, \(i = 3\).

4. **For Urea (NH₂CONH₂)**:
- Urea does not dissociate in solution.
- Therefore, \(i = 1\).

### Step 2: Compare the values of \(i\)

Now we have the values of \(i\) for each solute:
- \(Al_2(SO_4)_3\): \(i = 5\)
- \(K_3PO_4\): \(i = 4\)
- \(BaCl_2\): \(i = 3\)
- Urea: \(i = 1\)

### Step 3: Determine the order of osmotic pressure

Since osmotic pressure is directly proportional to \(i\), we can arrange the solutes in order of decreasing osmotic pressure based on their \(i\) values:

1. \(Al_2(SO_4)_3\) (5)
2. \(K_3PO_4\) (4)
3. \(BaCl_2\) (3)
4. Urea (1)

Thus, the correct order of osmotic pressure from highest to lowest is:

\[ Al_2(SO_4)_3 > K_3PO_4 > BaCl_2 > Urea \]

### Final Answer

The correct order of osmotic pressure is:

**(1) \(Al_2(SO_4)_3 > K_3PO_4 > BaCl_2 > Urea\)**

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