Which of the following is less than zero for ideal solutions ?

Options

A. `DeltaH_("mix")`
B. `DeltaV_("mix")`
C. `DeltaG_("mix")`
D. `DeltaS_("mix")`

Explanation

To determine which of the following is less than zero for ideal solutions, we need to analyze the changes in enthalpy (ΔH), volume (ΔV), Gibbs free energy (ΔG), and entropy (ΔS) in the context of ideal solutions.

### Step-by-Step Solution:

1. **Understanding Ideal Solutions**:
- An ideal solution is one that follows Raoult's law perfectly. In an ideal solution, the interactions between the molecules of different components are similar to those between the molecules of the same component.

2. **Analyzing ΔH (Change in Enthalpy)**:
- For ideal solutions, the change in enthalpy (ΔH) is zero. This means that there is no heat absorbed or released when the solute is dissolved in the solvent.

3. **Analyzing ΔV (Change in Volume)**:
- Similarly, the change in volume (ΔV) for ideal solutions is also zero. This indicates that the volume of the solution is the same as the sum of the volumes of the solute and solvent before mixing.

4. **Analyzing ΔG (Change in Gibbs Free Energy)**:
- The change in Gibbs free energy (ΔG) is a crucial factor in determining the spontaneity of a process. For ideal solutions, ΔG is less than zero (ΔG < 0). This indicates that the mixing process is spontaneous.

5. **Analyzing ΔS (Change in Entropy)**:
- The change in entropy (ΔS) for ideal solutions is greater than zero (ΔS > 0). This reflects the increase in disorder as the solute molecules mix with the solvent molecules.

6. **Conclusion**:
- Among the four changes analyzed (ΔH, ΔV, ΔG, ΔS), the only one that is less than zero for ideal solutions is ΔG (change in Gibbs free energy).

### Final Answer:
The correct option is ΔG (change in Gibbs free energy), which is less than zero for ideal solutions.

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