Which of the following is correct for an ideal solution?

Options

A. `/_\H_("mix")=0" and"/_\V_("mix)=0`
B. `/_\V_("mix")=0" and"/_\S_("mix)gt0`
C. `/_\H_("mix")gt0" and"/_\S_("mix)gt0`
D. `/_\G_("mix")lt0" and"/_\S_("mix)gt0`

Answer

To determine which statements are correct for an ideal solution, we need to analyze the properties of ideal solutions based on Raoult's law and the thermodynamic changes that occur during mixing.

### Step-by-Step Solution:

1. **Understanding Ideal Solutions**:
- Ideal solutions are those that obey Raoult's law at all temperatures and pressures. This means that the vapor pressure of each component in the solution is directly proportional to its mole fraction in the solution.

2. **Raoult's Law**:
- For a solution containing components A and B, Raoult's law states:
\[ P_A = P_A^0 \cdot X_A \]
\[ P_B = P_B^0 \cdot X_B \]
where \( P_A^0 \) and \( P_B^0 \) are the vapor pressures of the pure components A and B, and \( X_A \) and \( X_B \) are their mole fractions in the solution.

3. **Thermodynamic Changes**:
- When two liquids mix to form an ideal solution, the following thermodynamic changes occur:
- **Change in Enthalpy (ΔH mixing)**: For ideal solutions, ΔH mixing = 0. This indicates that there is no heat absorbed or released during the mixing process.
- **Change in Volume (ΔV mixing)**: For ideal solutions, ΔV mixing = 0. This means that the volume of the solution is the sum of the volumes of the individual components.
- **Change in Entropy (ΔS mixing)**: For ideal solutions, ΔS mixing > 0. Mixing increases the disorder of the system, leading to a positive change in entropy.

4. **Gibbs Free Energy Change (ΔG mixing)**:
- The Gibbs free energy change for mixing can be expressed as:
\[ ΔG_{mixing} = ΔH_{mixing} - TΔS_{mixing} \]
- Since ΔH mixing = 0 and ΔS mixing > 0, it follows that:
\[ ΔG_{mixing} < 0 \]
- This indicates that the mixing process is spontaneous for ideal solutions.

5. **Evaluating the Options**:
- **Option A**: ΔH mixing = 0 and ΔV mixing = 0 (Correct)
- **Option B**: ΔV mixing = 0 (Correct)
- **Option C**: ΔH mixing > 0 (Incorrect)
- **Option D**: ΔG mixing < 0 and ΔS mixing > 0 (Correct)

### Conclusion:
The correct statements regarding ideal solutions are:
- A: ΔH mixing = 0 and ΔV mixing = 0
- B: ΔV mixing = 0
- D: ΔG mixing < 0 and ΔS mixing > 0

Thus, the correct options are A, B, and D.