The relative lowering in vapour pressure is proportional to the ratio of number of

Options

A. solute molecules to solvent molecules
B. solvent molecules of solute molecules
C. solute molecules to the total number of molecules in solution
D. solvent molecules to the total number of molecules in solution

Explanation

To solve the question regarding the relative lowering of vapor pressure and its proportionality to the ratio of the number of particles, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Vapor Pressure**:
- The vapor pressure of a pure solvent is denoted as \( P_0 \).
- When a solute is added to the solvent, the vapor pressure of the solution becomes \( P \).

2. **Relative Lowering of Vapor Pressure**:
- The relative lowering of vapor pressure can be expressed as:
\[ \text{Relative Lowering} = \frac{P_0 - P}{P_0} \]

3. **Mole Fraction of Solute**:
- The mole fraction of the solute (denoted as \( X_2 \)) is given by:
\[ X_2 = \frac{N_2}{N_1 + N_2} \]
- Where \( N_1 \) is the number of moles of the solvent and \( N_2 \) is the number of moles of the solute.

4. **Proportionality**:
- It is known that the relative lowering of vapor pressure is proportional to the mole fraction of the solute:
\[ \frac{P_0 - P}{P_0} \propto X_2 \]

5. **Analyzing the Options**:
- The question asks for the ratio of the number of particles involved in the relative lowering of vapor pressure.
- The correct relationship is that the relative lowering of vapor pressure is proportional to the ratio of the number of moles of solute to the total number of moles in the solution (solute + solvent):
\[ \text{Relative Lowering} \propto \frac{N_2}{N_1 + N_2} \]

6. **Identifying the Correct Option**:
- From the options provided:
- Option A: Solute molecules to solvent molecules (incorrect, as it does not consider the total number of moles).
- Option B: Solvent molecules (incorrect, as it does not represent the solute).
- Option C: Solute molecules to total molecules in solution (correct).
- Option D: Solvent molecules (incorrect, as it does not represent the solute).

7. **Conclusion**:
- The correct answer is that the relative lowering of vapor pressure is proportional to the ratio of the number of solute molecules to the total number of molecules in the solution.