X is a non-volatile solute and Y is volatile solvent. The following vapour pressures are obtained by dissolving X in Y
`{:(X//molL^(-1),Y//mmHg),(0.1,P_(1)),(0.25,P_(2)),(0.01,P_(3)):}`
The correct order of vapour pressure is :

Options

A. `P_(1) lt P_(2) lt P_(3)`
B. `P_(3) lt P_(2) lt P_(1)`
C. `P_(3) lt P_(1) lt P_(2)`
D. `P_(2) lt P_(1) lt P_(3)`

Answer

To solve the problem, we need to understand how the vapor pressure of a solvent changes when a non-volatile solute is added. According to Raoult's Law, the vapor pressure of a solvent decreases when a non-volatile solute is dissolved in it. The extent of this decrease is related to the mole fraction of the solute in the solution.

### Step-by-Step Solution:

1. **Understanding the Concept**:
- When a non-volatile solute (X) is added to a volatile solvent (Y), the vapor pressure of the solvent decreases. The decrease in vapor pressure is directly related to the concentration of the solute.
- The relationship can be expressed as:
\[ P = P^0 \cdot X_Y \]
where \( P \) is the vapor pressure of the solution, \( P^0 \) is the vapor pressure of the pure solvent, and \( X_Y \) is the mole fraction of the solvent.

2. **Identifying Concentrations**:
- We have three different concentrations of the solute (X):
- 0.1 mol/L → \( P_1 \)
- 0.25 mol/L → \( P_2 \)
- 0.01 mol/L → \( P_3 \)

3. **Calculating Mole Fractions**:
- The mole fraction of the solute (X) increases with increasing concentration, which means the mole fraction of the solvent (Y) decreases.
- Therefore, for the given concentrations:
- For 0.1 mol/L (P1), the mole fraction of X is lower than that for 0.25 mol/L (P2).
- For 0.25 mol/L (P2), the mole fraction of X is the highest.
- For 0.01 mol/L (P3), the mole fraction of X is the lowest.

4. **Determining Vapor Pressure Order**:
- Since higher concentrations of solute lead to lower vapor pressures:
- \( P_2 \) (0.25 mol/L) will have the lowest vapor pressure because it has the highest concentration of solute.
- \( P_1 \) (0.1 mol/L) will have a higher vapor pressure than \( P_2 \) but lower than \( P_3 \).
- \( P_3 \) (0.01 mol/L) will have the highest vapor pressure because it has the lowest concentration of solute.

5. **Final Order of Vapor Pressures**:
- Therefore, the order of vapor pressures from highest to lowest is:
\[ P_3 > P_1 > P_2 \]

### Conclusion:
The correct order of vapor pressures is:
\[ P_3 > P_1 > P_2 \]