For different aqueous solutions of `0.1M` urea, `0.1M NaCl, 0.1M Na_(2)SO_(4)` and `0.1M Na_(3)PO_(4)` solution at `27^(@)C`, select the correct statements:

Options

A. The order of osmotic pressure is, urea `gtNaClgtNa_(2)SO_(4)gtNa_(3)PO_(4)`
B. The order of vapour pressure is , `Na_(3)PO_(4)gtNa_(2)SO_(4)gtNaClgt`urea
C. The order of boiling point `(T_(B))` is urea,`gt NaClgtNa_(2)SO_(4)gtNa_(3)PO_(4)`
D. The order of freezing point `(T_(f))` is, urea `gtNaClgtNa_(2)SO_(4)gtNa_(3)PO_(4)`

Explanation

To solve the problem, we need to analyze the van't Hoff factors (i) for each of the given solutes and how they affect various colligative properties such as osmotic pressure, vapor pressure, boiling point, and freezing point.

### Step-by-Step Solution:

1. **Identify the van't Hoff factor (i) for each solute:**
- **Urea (NH2CONH2):** Urea is a non-electrolyte and does not dissociate in solution. Therefore, \( i = 1 \).
- **Sodium Chloride (NaCl):** NaCl dissociates into two ions: Na⁺ and Cl⁻. Thus, \( i = 2 \).
- **Sodium Sulfate (Na₂SO₄):** Na₂SO₄ dissociates into three ions: 2 Na⁺ and SO₄²⁻. Thus, \( i = 3 \).
- **Sodium Phosphate (Na₃PO₄):** Na₃PO₄ dissociates into four ions: 3 Na⁺ and PO₄³⁻. Thus, \( i = 4 \).

2. **Determine the order of osmotic pressure (π):**
- The osmotic pressure is directly proportional to the van't Hoff factor:
\[ \pi = iCRT \]
- Therefore, the order of osmotic pressure based on the van't Hoff factor is:
\[ \text{Na}_3\text{PO}_4 > \text{Na}_2\text{SO}_4 > \text{NaCl} > \text{Urea} \]
- Correct statement: The osmotic pressure is highest for Na₃PO₄ and lowest for urea.

3. **Determine the order of vapor pressure (P):**
- Vapor pressure is inversely proportional to the van't Hoff factor:
\[ P \propto \frac{1}{i} \]
- Thus, the order of vapor pressure is:
\[ \text{Urea} > \text{NaCl} > \text{Na}_2\text{SO}_4 > \text{Na}_3\text{PO}_4 \]
- Correct statement: The vapor pressure is highest for urea and lowest for Na₃PO₄.

4. **Determine the order of boiling point (T_b):**
- The boiling point elevation is directly proportional to the van't Hoff factor:
\[ \Delta T_b \propto i \]
- Therefore, the order of boiling point is:
\[ \text{Na}_3\text{PO}_4 > \text{Na}_2\text{SO}_4 > \text{NaCl} > \text{Urea} \]
- Correct statement: The boiling point is highest for Na₃PO₄ and lowest for urea.

5. **Determine the order of freezing point (T_f):**
- The freezing point depression is also directly proportional to the van't Hoff factor:
\[ \Delta T_f \propto i \]
- Thus, the order of freezing point is:
\[ \text{Urea} > \text{NaCl} > \text{Na}_2\text{SO}_4 > \text{Na}_3\text{PO}_4 \]
- Correct statement: The freezing point is highest for urea and lowest for Na₃PO₄.

### Summary of Results:
- **Osmotic Pressure Order:** Na₃PO₄ > Na₂SO₄ > NaCl > Urea
- **Vapor Pressure Order:** Urea > NaCl > Na₂SO₄ > Na₃PO₄
- **Boiling Point Order:** Na₃PO₄ > Na₂SO₄ > NaCl > Urea
- **Freezing Point Order:** Urea > NaCl > Na₂SO₄ > Na₃PO₄

### Final Conclusion:
The correct statements based on the analysis are:
- The osmotic pressure is highest for Na₃PO₄.
- The vapor pressure is highest for urea.
- The boiling point is highest for Na₃PO₄.
- The freezing point is highest for urea.