A binary solution of liquids A and B will show positive deviation from Raoult's law if it fulfils the following condition:

Options

A. (a) `P_(A) gt X_(A)P_(A^(@)) "and"P_(B) gtX_(B)P_(B^(@)`
B. (b) The intermolecular forces of `A -B lt A - A, B - B`
C. (c) `/_\H `mixing is positive
D. (d) `/_\V` mixing is negative

Answer

To determine the conditions under which a binary solution of liquids A and B shows positive deviation from Raoult's law, we can follow these steps:

### Step 1: Understand Raoult's Law
Raoult's law states that the vapor pressure of a component in a solution is directly proportional to its mole fraction in the solution. For a component A, the equation is:
\[ P_A = x_A \cdot P^0_A \]
where:
- \( P_A \) = vapor pressure of component A in the solution
- \( x_A \) = mole fraction of component A
- \( P^0_A \) = vapor pressure of pure component A

### Step 2: Identify Positive Deviation
A positive deviation from Raoult's law occurs when the observed vapor pressure of the solution is greater than what is predicted by Raoult's law. This can be expressed as:
\[ P_{observed} > P_{ideal} \]
This means:
\[ P_A > x_A \cdot P^0_A \]
and
\[ P_B > x_B \cdot P^0_B \]
for components A and B respectively.

### Step 3: Analyze Intermolecular Forces
For a solution to show positive deviation, the interactions between the molecules of the different components (AB) must be weaker than the interactions between the molecules of the same component (AA and BB). Therefore, the intermolecular forces in the mixture are less than those in the pure components.

### Step 4: Consider Enthalpy and Volume Changes
In solutions that exhibit positive deviation:
- The change in enthalpy upon mixing (\( \Delta H_{mixing} \)) is positive, indicating that energy is absorbed when the components are mixed.
- The change in volume upon mixing (\( \Delta V_{mixing} \)) is also positive, indicating an increase in volume.

### Step 5: Conclusion
Based on the above analysis, the conditions for a binary solution of liquids A and B to show positive deviation from Raoult's law are:
1. \( P_A > x_A \cdot P^0_A \) and \( P_B > x_B \cdot P^0_B \)
2. The intermolecular forces between AB are weaker than those between AA and BB.
3. Both \( \Delta H_{mixing} > 0 \) and \( \Delta V_{mixing} > 0 \).

### Final Answer
The correct conditions for a binary solution of liquids A and B to show positive deviation from Raoult's law are:
- \( P_A > x_A \cdot P^0_A \)
- \( P_B > x_B \cdot P^0_B \)
- Intermolecular forces of AB are less than those of AA and BB.
- \( \Delta H_{mixing} > 0 \) and \( \Delta V_{mixing} > 0 \).