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 the Concept**:
- When a non-volatile solute is added to a volatile solvent, the vapor pressure of the solvent decreases. This phenomenon is known as the relative lowering of vapor pressure.

2. **Defining Vapor Pressure**:
- Let \( P_0 \) be the vapor pressure of the pure solvent.
- Let \( P_t \) be the vapor pressure of the solution after the solute has been added.

3. **Using Raoult's Law**:
- According to Raoult's Law, the relative lowering of vapor pressure can be expressed as:
\[ \text{Relative lowering of vapor pressure} = \frac{P_0 - P_t}{P_0} \]
- This can also be written as:
\[ \frac{P_0 - P_t}{P_0} = \frac{n_{solute}}{n_{solute} + n_{solvent}} \]
- Here, \( n_{solute} \) is the number of moles of the solute and \( n_{solvent} \) is the number of moles of the solvent.

4. **Mole Fraction**:
- The mole fraction of the solute (\( X_{solute} \)) can be defined as:
\[ X_{solute} = \frac{n_{solute}}{n_{solute} + n_{solvent}} \]
- Therefore, the relative lowering of vapor pressure can also be expressed as:
\[ \text{Relative lowering of vapor pressure} = X_{solute} \]

5. **Conclusion**:
- From the above derivation, we conclude that the relative lowering of vapor pressure 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**.