The total vapour pressure of a binary solution is gives by
P = (`100X_(A) + 260 X_(B)`)mm Hg
where,`X_(A)and X_(B)`are the molefractions of components A and B. This indicates that the:

Options

A. vapour pressure of solution is less than the pure B component
B. vapour pressure of solution is less than the pure A component
C. vapour pressure of pure A is 100 mm Hg and that of pure B is 260 mm Hg
D. the vapour pressure of pure A and B are 260 mm Hg and 100 mm hg respectively

Answer

To solve the problem, we need to analyze the given equation for the total vapor pressure of a binary solution and derive the implications from it.

### Step-by-Step Solution:

1. **Understanding the Equation**:
The total vapor pressure \( P \) of the binary solution is given by:
\[ P = 100X_A + 260X_B \text{ mm Hg} \]
where \( X_A \) and \( X_B \) are the mole fractions of components A and B, respectively.

2. **Identifying the Pure Component Pressures**:
From the equation, we can identify that:
- The vapor pressure of pure component A (\( P^0_A \)) is 100 mm Hg.
- The vapor pressure of pure component B (\( P^0_B \)) is 260 mm Hg.

3. **Vapor Pressure of the Solution**:
According to Raoult's Law, the total vapor pressure of a solution is the sum of the partial pressures of each component:
\[ P = X_A P^0_A + X_B P^0_B \]
This means that the vapor pressure of the solution is influenced by the mole fractions of each component and their respective pure vapor pressures.

4. **Analyzing the Statements**:
- **Statement A**: The vapor pressure of the solution is less than that of the pure component.
- This is true because the presence of a solute (if it is non-volatile) lowers the vapor pressure of the solvent.
- **Statement B**: The vapor pressure of the solution is less than that of pure component B.
- This is also true for the same reason as above.
- **Statement C**: The vapor pressure of pure A is 100 mm Hg and for B is 260 mm Hg.
- This is true as we derived from the equation.
- **Statement D**: The vapor pressure of pure A and B are given incorrectly.
- This is false because we have correctly identified the vapor pressures.

5. **Conclusion**:
The correct statements are A, B, and C. Therefore, the answer to the question is that statements A, B, and C are correct.