If liquids A and B form an ideal solution.

Options

A. The free energy of mixing is zero
B. The free energy as well as the entropy of mixing are each zero
C. The enthalpy of mixing is zero
D. The entropy of mixing is zero

Answer

To solve the question regarding the characteristics of an ideal solution formed by liquids A and B, we will analyze the properties of ideal solutions step by step.

### Step-by-Step Solution:

1. **Understanding Ideal Solutions**:
- An ideal solution is one where the interactions between the molecules of the components (A-A and B-B) are equal to the interactions between the different components (A-B).
- Mathematically, this can be expressed as:
\[ \text{A-A interaction} + \text{B-B interaction} = \text{A-B interaction} \]

**Hint**: Remember that the key characteristic of ideal solutions is the equality of interactions.

2. **Enthalpy of Mixing (ΔH)**:
- For an ideal solution, the change in enthalpy upon mixing (ΔH) is zero:
\[ \Delta H_{\text{mix}} = 0 \]
- This means that no heat is absorbed or released when the two liquids are mixed.

**Hint**: ΔH = 0 indicates that mixing does not involve any heat change.

3. **Volume of Mixing (ΔV)**:
- The change in volume upon mixing (ΔV) is also zero for ideal solutions:
\[ \Delta V_{\text{mix}} = 0 \]
- This means that the total volume of the solution is the sum of the volumes of the individual components.

**Hint**: ΔV = 0 means the volume remains constant upon mixing.

4. **Free Energy of Mixing (ΔG)**:
- The change in Gibbs free energy (ΔG) for an ideal solution is always negative:
\[ \Delta G_{\text{mix}} < 0 \]
- This indicates that the mixing process is spontaneous.

**Hint**: A negative ΔG signifies a spontaneous process.

5. **Entropy of Mixing (ΔS)**:
- The change in entropy (ΔS) upon mixing is always positive for ideal solutions:
\[ \Delta S_{\text{mix}} > 0 \]
- This reflects an increase in randomness or disorder when the two liquids are mixed.

**Hint**: ΔS > 0 indicates an increase in randomness.

6. **Evaluating the Options**:
- Based on the characteristics discussed:
- **Option 1**: Free energy of mixing is zero. (False)
- **Option 2**: Free energy and entropy of mixing are both zero. (False)
- **Option 3**: Enthalpy of mixing is zero. (True)
- **Option 4**: Entropy of mixing is zero. (False)

**Hint**: Carefully evaluate each option against the characteristics of ideal solutions.

### Conclusion:
From the analysis, we conclude that the only true statement regarding the ideal solution formed by liquids A and B is that the enthalpy of mixing is zero.