If a non-volatile solute is dissolved in a volatile solvent relative lowering of vapour pressure is equal to

Options

A. Moles of solute
B. Moles of solvent
C. Mole fraction of solute
D. Mole fraction of solvent

Answer

To solve the question regarding the relative lowering of vapor pressure when a non-volatile solute is dissolved in a volatile solvent, we can follow these steps:

### Step-by-Step Solution:

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

2. **Defining Relative Lowering of Vapor Pressure**:
- The relative lowering of vapor pressure (RLVP) is defined as the decrease in vapor pressure of the solvent when a solute is added, compared to the original vapor pressure of the pure solvent.

3. **Using Raoult's Law**:
- According to Raoult's Law, the vapor pressure of a solution (P_solution) is directly proportional to the mole fraction of the solvent (X_solvent):
\[ P_{\text{solution}} = X_{\text{solvent}} \cdot P^0_{\text{solvent}} \]
- Where \(P^0_{\text{solvent}}\) is the vapor pressure of the pure solvent.

4. **Calculating Relative Lowering**:
- The relative lowering of vapor pressure can be expressed as:
\[ \text{Relative Lowering} = \frac{P^0_{\text{solvent}} - P_{\text{solution}}}{P^0_{\text{solvent}}} \]
- Substituting for \(P_{\text{solution}}\) from Raoult's Law:
\[ \text{Relative Lowering} = \frac{P^0_{\text{solvent}} - (X_{\text{solvent}} \cdot P^0_{\text{solvent}})}{P^0_{\text{solvent}}} \]
- This simplifies to:
\[ \text{Relative Lowering} = \frac{P^0_{\text{solvent}}(1 - X_{\text{solvent}})}{P^0_{\text{solvent}}} = 1 - X_{\text{solvent}} \]

5. **Relating to Mole Fraction of Solute**:
- Since the sum of the mole fractions of solute and solvent is 1, we have:
\[ X_{\text{solute}} = 1 - X_{\text{solvent}} \]
- Therefore, the relative lowering of vapor pressure can also be expressed in terms of the mole fraction of the solute:
\[ \text{Relative Lowering} = X_{\text{solute}} \]

6. **Conclusion**:
- The relative lowering of vapor pressure when a non-volatile solute is dissolved in a volatile solvent is equal to the mole fraction of the solute.

### Final Answer:
The relative lowering of vapor pressure is equal to the mole fraction of the solute.