STATEMENT-1 : 0.1 M solution of `Na_(2)SO_(4)` has greater osmotic pressure than 0.1 M solution of urea at same temperature.
and
STATEMENT-2 : The value of van't Hoff factor for `Na_(2)SO_(4)` is less than urea.

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-6
B. Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-6
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True

Answer

To solve the given problem, we need to analyze both statements regarding the osmotic pressure of solutions and the van't Hoff factor.

### Step-by-Step Solution:

**Step 1: Understand Osmotic Pressure**
Osmotic pressure (π) is given by the formula:
\[ \pi = iCRT \]
where:
- \(i\) = van't Hoff factor (number of particles the solute dissociates into)
- \(C\) = molarity of the solution
- \(R\) = universal gas constant
- \(T\) = temperature in Kelvin

**Step 2: Analyze Statement 1**
The first statement claims that a 0.1 M solution of \(Na_2SO_4\) has greater osmotic pressure than a 0.1 M solution of urea at the same temperature.

- For \(Na_2SO_4\):
- It dissociates into 3 ions: \(2Na^+\) and \(SO_4^{2-}\).
- Therefore, the van't Hoff factor \(i\) for \(Na_2SO_4\) is 3.

- For urea:
- Urea does not dissociate in solution.
- Therefore, the van't Hoff factor \(i\) for urea is 1.

**Step 3: Calculate Osmotic Pressure for Both Solutions**
Using the formula for osmotic pressure:
- For \(Na_2SO_4\):
\[ \pi_{Na_2SO_4} = i \cdot C \cdot R \cdot T = 3 \cdot 0.1 \cdot R \cdot T \]

- For urea:
\[ \pi_{urea} = i \cdot C \cdot R \cdot T = 1 \cdot 0.1 \cdot R \cdot T \]

**Step 4: Compare the Osmotic Pressures**
From the calculations:
\[ \pi_{Na_2SO_4} = 0.3 \cdot R \cdot T \]
\[ \pi_{urea} = 0.1 \cdot R \cdot T \]
Clearly, \(0.3 \cdot R \cdot T > 0.1 \cdot R \cdot T\), which means:
\[ \pi_{Na_2SO_4} > \pi_{urea} \]
Thus, Statement 1 is **True**.

**Step 5: Analyze Statement 2**
The second statement claims that the van't Hoff factor for \(Na_2SO_4\) is less than that for urea.

- As established earlier, the van't Hoff factor for \(Na_2SO_4\) is 3, while for urea it is 1.
- Therefore, the van't Hoff factor for \(Na_2SO_4\) is **greater** than that for urea.

Thus, Statement 2 is **False**.

### Final Conclusion:
- Statement 1 is True.
- Statement 2 is False.