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

Options

A. `1.0`
B. `0.5`
C. `2.0`
D. `2.5`

Answer

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

### Step-by-Step Solution:

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

2. **Identifying the Solutes**:
- KCl (Potassium Chloride) is a strong electrolyte, which means it dissociates into ions when dissolved in water.
- Sugar (e.g., sucrose) is a non-electrolyte, which means it does not dissociate into ions in solution.

3. **Determining the Van 't Hoff Factor (i)**:
- For KCl, when it dissolves, it dissociates into two ions: K⁺ and Cl⁻. Therefore, the van 't Hoff factor (i) for KCl is 2.
- For sugar, since it does not dissociate, the van 't Hoff factor (i) is 1.

4. **Calculating the Ratio of Colligative Properties**:
The ratio of any colligative property for KCl solution to that for sugar solution can be expressed as:
\[ \text{Ratio} = \frac{i_{\text{KCl}}}{i_{\text{sugar}}} \]
Substituting the values:
\[ \text{Ratio} = \frac{2}{1} = 2 \]

5. **Conclusion**:
The ratio of the value of any colligative property for KCl solution to that for sugar solution is nearly 2.