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

Options

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

Answer

To solve the question "Which of the following is less than zero for ideal solutions?" we need to analyze each option provided in the context of ideal solutions.

### Step-by-Step Solution:

1. **Understanding Ideal Solutions**:
- An ideal solution is defined as a solution where the interactions between all particles (solute and solvent) are similar. This means that the interactions between like particles (A-A and B-B) are equal to the interactions between unlike particles (A-B).

2. **Analyzing ΔH_mix (Enthalpy of Mixing)**:
- For an ideal solution, the enthalpy of mixing (ΔH_mix) is always equal to 0. This is because there is no heat absorbed or released when the components are mixed.

3. **Analyzing ΔV_mix (Volume Change of Mixing)**:
- Similarly, for ideal solutions, the change in volume upon mixing (ΔV_mix) is also 0. This indicates that the total volume of the solution is equal to the sum of the volumes of the individual components before mixing.

4. **Analyzing ΔS_mix (Entropy of Mixing)**:
- The change in entropy upon mixing (ΔS_mix) for an ideal solution is always greater than 0. This is due to the increase in disorder when two different substances are mixed.

5. **Analyzing ΔG_mix (Gibbs Free Energy of Mixing)**:
- The Gibbs free energy of mixing (ΔG_mix) can be calculated using the formula:
\[ ΔG_{mix} = ΔH_{mix} - TΔS_{mix} \]
- Since we established that ΔH_mix = 0 and ΔS_mix > 0, we can substitute these values into the equation:
\[ ΔG_{mix} = 0 - T(ΔS_{mix}) \]
- Here, T is the temperature (which is always positive), and since ΔS_mix is positive, the entire term -TΔS_mix will be negative. Therefore, ΔG_mix will be less than 0.

6. **Conclusion**:
- Based on the analysis, the only option that is less than zero for ideal solutions is **Option C: ΔG_mix**.

### Final Answer:
The answer is **Option C: ΔG_mix**.