The ratio of the value of any colligative property of `KCl` solution to that of sugar solution is

Options

A. 1
B. 0.5
C. 2
D. 4

Explanation

To find the ratio of the value of any colligative property of a KCl solution to that of a sugar solution, we can follow these steps:

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

### Step 2: Identify the Van 't Hoff Factor (i)
The Van 't Hoff factor (i) indicates the number of particles the solute dissociates into when dissolved in a solvent.

- For KCl (potassium chloride), it dissociates into two ions: K⁺ and Cl⁻. Therefore, the Van 't Hoff factor (i) for KCl is:
\[ i_{KCl} = 2 \]

- For sugar (sucrose), which is a non-electrolyte, it does not dissociate into ions when dissolved. Therefore, the Van 't Hoff factor (i) for sugar is:
\[ i_{sugar} = 1 \]

### Step 3: Use the Formula for Colligative Properties
The value of any colligative property can be expressed as:
\[ \text{Colligative Property} = i \cdot K_b \cdot m \]
where \( K_b \) is the ebullioscopic constant and \( m \) is the molality of the solution.

### Step 4: Set Up the Ratio
Since the \( K_b \) and molality (\( m \)) will be the same for both solutions when comparing them, we can set up the ratio of the colligative properties for KCl and sugar:
\[ \frac{\text{Colligative Property of KCl}}{\text{Colligative Property of Sugar}} = \frac{i_{KCl} \cdot K_b \cdot m}{i_{sugar} \cdot K_b \cdot m} \]

### Step 5: Simplify the Ratio
Substituting the values of \( i \):
\[ \frac{\text{Colligative Property of KCl}}{\text{Colligative Property of Sugar}} = \frac{2 \cdot K_b \cdot m}{1 \cdot K_b \cdot m} = \frac{2}{1} = 2 \]

### Conclusion
Thus, the ratio of the value of any colligative property of KCl solution to that of sugar solution is:
\[ \text{Ratio} = 2 \]

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