For an ideal solution containing a nonvolatile solute, which of the following expression represents the vapour pressure of the solute ? `(x_(1)rarr` mole fraction of solvent)

Options

A. `p = x_(2) p_(2)`
B. `p = x_(1)p_(2)`
C. `p = x_(1)p_(1)`
D. `p_(1) - p = x_(2)`

Answer

To determine the expression that represents the vapor pressure of a solute in an ideal solution containing a non-volatile solute, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Components**:
- In an ideal solution, we have a solvent and a non-volatile solute. The mole fraction of the solvent is denoted as \( x_1 \) and the mole fraction of the solute can be denoted as \( x_2 \).

2. **Vapor Pressure of Pure Solvent**:
- The vapor pressure of the pure solvent is represented as \( P_0 \). This is the pressure exerted by the vapor of the solvent when it is in equilibrium with its liquid phase.

3. **Raoult's Law**:
- According to Raoult's Law, the vapor pressure of the solvent in the solution is directly proportional to the mole fraction of the solvent. The law states:
\[ P = x_1 \cdot P_0 \]
- Here, \( P \) is the vapor pressure of the solution, \( x_1 \) is the mole fraction of the solvent, and \( P_0 \) is the vapor pressure of the pure solvent.

4. **Vapor Pressure of Solute**:
- Since the solute is non-volatile, it does not contribute to the vapor pressure of the solution. Therefore, the vapor pressure of the solute itself is considered to be zero in this context.

5. **Final Expression**:
- Thus, the expression that represents the vapor pressure of the solution containing a non-volatile solute is:
\[ P = x_1 \cdot P_0 \]
- This indicates that the vapor pressure of the solution depends on the mole fraction of the solvent and the vapor pressure of the pure solvent.

### Conclusion:
The correct expression representing the vapor pressure of the solution containing a non-volatile solute is:
\[ P = x_1 \cdot P_0 \]