Which of the following is correct for a non-ideal solution of liquids A and B showing negative deviation?

Options

A. `/_\H_("mix") = - ve`
B. `/_\V_("mix") = - ve`
C. `/_\S_("mix") = - ve`
D. `/_\G_("mix") = - ve`

Answer

To solve the question regarding the properties of a non-ideal solution of liquids A and B that show negative deviation, we can follow these steps:

### Step 1: Understand Negative Deviation
In a non-ideal solution that shows negative deviation, the intermolecular forces between the components A and B are stronger than those in the pure components A and B. This leads to a reduction in vapor pressure compared to what would be expected from Raoult's law.

**Hint:** Consider how intermolecular forces affect vapor pressure in solutions.

### Step 2: Analyze Vapor Pressure
For a non-ideal solution with negative deviation, the observed vapor pressure (P_observed) is less than the ideal vapor pressure (P_ideal). Mathematically, this can be expressed as:
- P_observed < P_ideal
- P_observed < P0A * xA (for component A)
- P_observed < P0B * xB (for component B)

**Hint:** Recall that Raoult's law applies to ideal solutions, and deviations indicate differences in intermolecular interactions.

### Step 3: Examine Enthalpy of Mixing (ΔH_mixing)
For solutions that show negative deviation, the enthalpy of mixing (ΔH_mixing) is negative. This indicates that heat is released when the solute and solvent are mixed.

**Hint:** Think about the energy changes that occur when two substances mix.

### Step 4: Consider Volume Change (ΔV_mixing)
The volume change upon mixing (ΔV_mixing) is also negative for solutions showing negative deviation. This means that the total volume of the solution is less than the sum of the volumes of the pure components.

**Hint:** Reflect on how the arrangement of molecules changes when they mix.

### Step 5: Analyze Entropy of Mixing (ΔS_mixing)
The entropy of mixing (ΔS_mixing) is negative for solutions that show negative deviation. This is because the release of heat during mixing leads to a decrease in the randomness or disorder of the system.

**Hint:** Relate entropy to the disorder of a system and how mixing affects it.

### Step 6: Evaluate Gibbs Free Energy of Mixing (ΔG_mixing)
The Gibbs free energy of mixing (ΔG_mixing) can be expressed as:
- ΔG_mixing = ΔH_mixing - TΔS_mixing
Since both ΔH_mixing and ΔS_mixing are negative, the sign of ΔG_mixing will depend on the magnitudes of these terms. Therefore, we cannot definitively say that ΔG_mixing is always negative.

**Hint:** Consider how temperature affects the relationship between enthalpy and entropy in determining the spontaneity of mixing.

### Conclusion
From the analysis, we can conclude that:
- ΔH_mixing < 0 (heat is evolved)
- ΔV_mixing < 0 (volume decreases)
- ΔS_mixing < 0 (entropy decreases)
- ΔG_mixing cannot be definitively stated as negative.

Thus, the correct options for a non-ideal solution of liquids A and B showing negative deviation are:
- ΔH_mixing is negative
- ΔV_mixing is negative
- ΔS_mixing is negative

### Final Answer
The correct options are: ΔH_mixing < 0, ΔV_mixing < 0, ΔS_mixing < 0. The statement regarding ΔG_mixing is incorrect as it depends on the magnitudes of ΔH and TΔS.