If liquids A and B form an ideal solution, the:

Enthalpy of mixing is zero

The correct answer is option 1. Enthalpy of mixing is zero.

Let us delve into the concepts involved to clarify why the correct answer is that the enthalpy of mixing is zero for an ideal solution.

An ideal solution is one where the interactions between different molecules (A-B) are identical to the interactions between like molecules (A-A and B-B). This ideal behavior implies that when the two components mix, the overall energy of the system doesn't change.

Thermodynamic Properties of Mixing:

1. Enthalpy of Mixing (\(\Delta H_{mix}\)):

For an ideal solution, the enthalpy of mixing is zero. This is because the energy required to break the intermolecular forces between like molecules (A-A and B-B) is exactly compensated by the energy released when forming the intermolecular forces between unlike molecules (A-B).

Mathematically, \(\Delta H_{mix} = 0\).

2. Entropy of Mixing (\(\Delta S_{mix}\)):

The entropy of mixing is always positive. When two substances mix, the number of possible microstates (arrangements of molecules) increases, leading to an increase in disorder.

Therefore, \(\Delta S_{mix} > 0\).

3. Free Energy of Mixing (\(\Delta G_{mix}\)):

The free energy change of mixing is given by the equation:

\(\Delta G_{mix} = \Delta H_{mix} - T\Delta S_{mix}\)

Since \(\Delta H_{mix} = 0\) for an ideal solution and \(\Delta S_{mix}\) is positive, the term \(- T\Delta S_{mix}\) is negative. This means \(\Delta G_{mix} < 0\), indicating that the mixing process is spontaneous and results in a decrease in free energy.

Examination of the Options:

1. Enthalpy of mixing is zero:

Correct, as explained above, for an ideal solution, the enthalpy of mixing is zero because the energy of interactions between different types of molecules is the same as that between like molecules.

2. Entropy of mixing is zero:

Incorrect, because the mixing process increases the disorder of the system, leading to a positive entropy change.

3. Free energy of mixing is zero:

Incorrect, because the free energy change of mixing for an ideal solution is negative due to the positive entropy change.

4. Free energy as well as the entropy of mixing are each zero:

Incorrect, as both the free energy change and the entropy change cannot be zero for the mixing process in an ideal solution.

Conclusion: The only correct statement is that the enthalpy of mixing is zero for an ideal solution. This reflects the fact that the energy required to mix the substances is balanced by the energy released, resulting in no net enthalpy change.