The ratio of the value of any colligative property for `BaCl_(2)` solution of urea solution under similar condition is

Options

A. 2
B. 3
C. 1
D. 4

Explanation

To find the ratio of the value of any colligative property for a BaCl₂ solution compared to a urea solution under similar conditions, we will follow these steps:

### Step 1: Understand Colligative Properties
Colligative properties depend on the number of solute particles in a solution, not on the identity of the solute. Examples include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure.

### Step 2: Determine the Van't Hoff Factor (i)
The Van't Hoff factor (i) indicates the number of particles into which a solute dissociates in solution.

- For **BaCl₂**:
- It dissociates into 1 Ba²⁺ ion and 2 Cl⁻ ions.
- Thus, the total number of particles = 1 (Ba²⁺) + 2 (Cl⁻) = 3.
- Therefore, i for BaCl₂ = 3.

- For **urea**:
- Urea is a non-electrolyte and does not dissociate in solution.
- Therefore, i for urea = 1.

### Step 3: Write the Expression for a Colligative Property
Let’s consider osmotic pressure (π) as an example of a colligative property. The formula for osmotic pressure is given by:

\[ \pi = iCRT \]

Where:
- \( \pi \) = osmotic pressure
- \( i \) = Van't Hoff factor
- \( C \) = molarity of the solution
- \( R \) = universal gas constant
- \( T \) = temperature in Kelvin

### Step 4: Calculate Osmotic Pressure for Both Solutions
- For **BaCl₂**:
\[ \pi_{BaCl2} = i_{BaCl2} \cdot C_{BaCl2} \cdot R \cdot T = 3 \cdot C_{BaCl2} \cdot R \cdot T \]

- For **urea**:
\[ \pi_{urea} = i_{urea} \cdot C_{urea} \cdot R \cdot T = 1 \cdot C_{urea} \cdot R \cdot T \]

### Step 5: Find the Ratio of Osmotic Pressures
To find the ratio of the osmotic pressures of BaCl₂ solution to urea solution, we can write:

\[ \frac{\pi_{BaCl2}}{\pi_{urea}} = \frac{3 \cdot C_{BaCl2} \cdot R \cdot T}{1 \cdot C_{urea} \cdot R \cdot T} \]

### Step 6: Simplify the Ratio
The \( R \) and \( T \) terms cancel out:

\[ \frac{\pi_{BaCl2}}{\pi_{urea}} = \frac{3 \cdot C_{BaCl2}}{C_{urea}} \]

### Conclusion
Thus, the ratio of the value of any colligative property for BaCl₂ solution to urea solution is dependent on their concentrations. However, if we assume equal concentrations for both solutions, the ratio simplifies to:

\[ \frac{\pi_{BaCl2}}{\pi_{urea}} = 3 \]

### Final Answer
The ratio of the value of any colligative property for BaCl₂ solution to urea solution is **3:1**.

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