According to Raoult's law the relative lowering of vapour pressure for a solution is equal to

Options

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

Answer

To solve the question regarding Raoult's law and the relative lowering of vapor pressure for a solution, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Raoult's Law**:
- Raoult's law states that the partial vapor pressure of each component in a solution is directly proportional to its mole fraction in the solution.

2. **Identifying Components**:
- In a solution, we typically have a volatile solvent and a non-volatile solute. The vapor pressure of the solvent is affected by the presence of the solute.

3. **Expressing Partial Vapor Pressure**:
- Let \( P_1^0 \) be the vapor pressure of the pure solvent and \( x_1 \) be the mole fraction of the solvent. According to Raoult's law, the partial vapor pressure \( P_1 \) of the solvent in the solution can be expressed as:
\[ P_1 = P_1^0 \cdot x_1 \]

4. **Calculating the Reduction in Vapor Pressure**:
- The reduction in vapor pressure (\( \Delta P_1 \)) due to the presence of the solute is given by:
\[ \Delta P_1 = P_1^0 - P_1 \]
- Substituting the expression for \( P_1 \):
\[ \Delta P_1 = P_1^0 - P_1^0 \cdot x_1 = P_1^0 (1 - x_1) \]

5. **Relating Mole Fractions**:
- Since the sum of the mole fractions of all components in a solution equals 1, we can express the mole fraction of the solute (\( x_2 \)) as:
\[ x_2 = 1 - x_1 \]

6. **Substituting for Mole Fraction of Solute**:
- Substituting \( x_2 \) into the equation for \( \Delta P_1 \):
\[ \Delta P_1 = P_1^0 \cdot x_2 \]

7. **Calculating Relative Lowering of Vapor Pressure**:
- The relative lowering of vapor pressure is defined as:
\[ \frac{\Delta P_1}{P_1^0} = \frac{P_1^0 \cdot x_2}{P_1^0} = x_2 \]
- This shows that the relative lowering of vapor pressure is equal to the mole fraction of the solute.

8. **Conclusion**:
- Therefore, according to Raoult's law, the relative lowering of vapor pressure for a solution is equal to the mole fraction of the solute.

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

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