A binary liqiud (AB) shows positive deviation from Raoult's law when

Options

A. `P_(A)gtP_(A)^(@)X_(A)^("liquid")" and "P_(B)gt P_(B)^(@)X_(B)^("liquid")`
B. Intermolecular forces
`A-A, B-BgtA-B`
C. `DeltaV_("mix")gt0`
D. `DeltaH_("mix")gt0`

Answer

To determine when a binary liquid (AB) shows positive deviation from Raoult's law, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Raoult's Law**:
- Raoult's law states that the partial vapor pressure of a solvent in a solution is equal to the partial vapor pressure of that solvent in its pure state multiplied by the mole fraction of that solvent in the solution.
- Mathematically, it can be expressed as:
\[ P_A = P_A^0 \cdot X_A \]
where \( P_A \) is the partial vapor pressure of solvent A in the solution, \( P_A^0 \) is the vapor pressure of pure solvent A, and \( X_A \) is the mole fraction of solvent A in the solution.

2. **Ideal vs Non-Ideal Solutions**:
- Ideal solutions obey Raoult's law perfectly, while non-ideal solutions do not.
- In ideal solutions, the enthalpy change and volume change upon mixing are both zero.
- Non-ideal solutions can show either positive or negative deviations from Raoult's law.

3. **Positive Deviation from Raoult's Law**:
- A binary liquid shows positive deviation when the interactions between the different components (A and B) are weaker than the interactions between the same components (A-A and B-B).
- This results in a higher vapor pressure than predicted by Raoult's law.

4. **Characteristics of Positive Deviation**:
- The partial vapor pressure of the solvent in the solution is greater than the expected value calculated using Raoult's law:
\[ P_A > P_A^0 \cdot X_A \]
- The enthalpy change of mixing is greater than zero (\( \Delta H_{mix} > 0 \)).
- The volume change of mixing is also greater than zero (\( \Delta V_{mix} > 0 \)).

5. **Conclusion**:
- A binary liquid (AB) shows positive deviation from Raoult's law when the intermolecular forces between the components (A and B) are weaker than those between the same components (A-A and B-B).
- This leads to an increase in vapor pressure, a positive enthalpy change, and a positive volume change upon mixing.