Assertion (A): Vapour pressure of `0.5 M` sugar solution is more than `0.5 M KCl` solution. Reason (R): Relative lowering of vapour pressure is directly proportional to the number of species present in the solution.

Options

A. If both `(A)` and `(R )` are correct, and `(R )` is the correct explanation of `(A)`.
B. If both `(A)` and `(R )` are correct, but `(R )` is not the correct explanation of `(A)`.
C. If `(A)` is correct, but `(R )` is incorrect.
D. If `(A)` is correct, but `(R )` is correct.

Explanation

To solve the question, we need to analyze the assertion and reason provided:

**Assertion (A):** The vapor pressure of a 0.5 M sugar solution is more than that of a 0.5 M KCl solution.

**Reason (R):** The relative lowering of vapor pressure is directly proportional to the number of species present in the solution.

### Step-by-Step Solution:

1. **Understanding Vapor Pressure:**
- Vapor pressure is the pressure exerted by the vapor in equilibrium with its liquid or solid phase. When a non-volatile solute is added to a solvent, the vapor pressure of the solvent decreases.

2. **Colligative Properties:**
- The relative lowering of vapor pressure is a colligative property, which means it depends on the number of solute particles in the solution, not on their identity.

3. **Analyzing the Sugar Solution:**
- Sugar (sucrose) is a non-electrolyte and does not dissociate in solution. Therefore, a 0.5 M sugar solution contains 0.5 moles of sugar molecules per liter of solution.

4. **Analyzing the KCl Solution:**
- KCl is an ionic compound that dissociates into two ions in solution: K⁺ and Cl⁻. Therefore, a 0.5 M KCl solution will produce 0.5 moles of K⁺ ions and 0.5 moles of Cl⁻ ions, resulting in a total of 1.0 mole of particles per liter of solution (0.5 + 0.5 = 1.0).

5. **Comparing the Relative Lowering of Vapor Pressure:**
- Since the relative lowering of vapor pressure is proportional to the number of solute particles, the KCl solution, which has 1.0 mole of particles, will have a greater relative lowering of vapor pressure compared to the sugar solution, which has only 0.5 mole of particles.

6. **Conclusion:**
- Because the KCl solution has a greater relative lowering of vapor pressure, it will have a lower vapor pressure than the sugar solution. Thus, the assertion that the vapor pressure of the sugar solution is greater than that of the KCl solution is correct.

7. **Evaluating the Reason:**
- The reason provided is also correct because it accurately states that the relative lowering of vapor pressure is directly proportional to the number of species present in the solution.

### Final Answer:
Both the assertion (A) and the reason (R) are correct, and the reason (R) is the correct explanation for the assertion (A).