Consider a binary mixture of volatile liquides. If at `X_(A)=0.4`, the vapour pressure of solution is 580 torr then the mixture could be `(p_A^@=300 "torr" ,P_(B)^@=800 "torr")` :

Options

A. `CHCl_(3)-CH_(3)COCH_(3)`
B. `C_(6)H_(5)Cl-C_(6)H_(5)Br`
C. `C_(6)H_(6)-C_(6)-C_(6)H_(5)CH_(3)`
D. `nC_(6)H_(14)` and `C_(6)H_(5)CH_(3)`

Explanation

To solve the problem, we will use Raoult's Law, which states that the vapor pressure of a component in a solution is equal to the vapor pressure of the pure component multiplied by its mole fraction in the solution.

### Step-by-Step Solution:

1. **Identify Given Values**:
- Vapor pressure of component A (P₀A) = 300 torr
- Vapor pressure of component B (P₀B) = 800 torr
- Mole fraction of A (Xₐ) = 0.4
- Mole fraction of B (Xᵦ) = 1 - Xₐ = 0.6

2. **Apply Raoult's Law**:
According to Raoult's Law, the total vapor pressure (P_total) of the solution can be calculated as:
\[ P_{\text{total}} = P_{0A} \cdot X_A + P_{0B} \cdot X_B \]

3. **Substitute the Values**:
Substitute the known values into the equation:
\[ P_{\text{total}} = (300 \, \text{torr} \cdot 0.4) + (800 \, \text{torr} \cdot 0.6) \]

4. **Calculate Each Term**:
- Calculate the contribution from component A:
\[ 300 \, \text{torr} \cdot 0.4 = 120 \, \text{torr} \]
- Calculate the contribution from component B:
\[ 800 \, \text{torr} \cdot 0.6 = 480 \, \text{torr} \]

5. **Sum the Contributions**:
Now, add the contributions from both components to find the total vapor pressure:
\[ P_{\text{total}} = 120 \, \text{torr} + 480 \, \text{torr} = 600 \, \text{torr} \]

6. **Compare with Experimental Vapor Pressure**:
The experimental vapor pressure given in the problem is 580 torr. According to the principles of Raoult's Law, the observed vapor pressure should be less than or equal to the calculated vapor pressure. Since 580 torr is less than 600 torr, this is consistent with the behavior of the mixture.

7. **Conclusion**:
The calculated total vapor pressure of the solution is 600 torr, which is greater than the observed vapor pressure of 580 torr. This indicates that the mixture behaves ideally under the given conditions.