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)CI-C_(6)H_(5)Br`
C. `C_(6)H_(6)-C_(6)H_(5)CH_(3)`
D. `nC_(6)H_(14)-nC_(7)H_(16)`

Explanation

To solve the problem, we will use Raoult's Law, which states that the vapor pressure of a solution is equal to the sum of the partial vapor pressures of each component in the mixture. The formula is given by:

\[ P_{solution} = P_A^0 \cdot X_A + P_B^0 \cdot X_B \]

Where:
- \( P_{solution} \) is the vapor pressure of the solution,
- \( P_A^0 \) is the vapor pressure of component A in its pure state,
- \( P_B^0 \) is the vapor pressure of component B in its pure state,
- \( X_A \) is the mole fraction of component A,
- \( X_B \) is the mole fraction of component B.

### Step-by-Step Solution:

1. **Identify the given values:**
- \( X_A = 0.4 \)
- \( P_{solution} = 580 \) torr
- \( P_A^0 = 300 \) torr
- \( P_B^0 = 800 \) torr

2. **Calculate the mole fraction of component B:**
\[ X_B = 1 - X_A = 1 - 0.4 = 0.6 \]

3. **Substitute the values into Raoult's Law:**
\[ P_{solution} = P_A^0 \cdot X_A + P_B^0 \cdot X_B \]
\[ 580 = 300 \cdot 0.4 + 800 \cdot 0.6 \]

4. **Calculate each term:**
- Calculate \( 300 \cdot 0.4 \):
\[ 300 \cdot 0.4 = 120 \text{ torr} \]
- Calculate \( 800 \cdot 0.6 \):
\[ 800 \cdot 0.6 = 480 \text{ torr} \]

5. **Add the two results to find the total vapor pressure:**
\[ P_{solution} = 120 + 480 = 600 \text{ torr} \]

6. **Compare the calculated vapor pressure with the given vapor pressure:**
- The calculated vapor pressure (600 torr) is greater than the given vapor pressure (580 torr). This indicates a positive deviation from Raoult's Law.

7. **Conclusion:**
- Since the calculated vapor pressure is greater than the observed vapor pressure, it indicates that the mixture exhibits positive deviation. Thus, the mixture of liquids A and B shows that the interactions between A and B are weaker than the interactions between A and A or B and B.

### Final Answer:
The mixture could be \( (P_A^0 = 300 \text{ torr}, P_B^0 = 800 \text{ torr}) \), and it shows positive deviation.

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