A binary ideal solution of AB type has:

\(\Delta H_{mix} = 0\), \(\Delta V_{mix} = 0\)

The correct answer is option 2. \(\Delta H_{mix} = 0\), \(\Delta V_{mix} = 0\).

For a binary ideal solution of the AB type, the characteristics of mixing are defined by Raoult’s Law, which states that the properties of an ideal solution are such that:

Enthalpy of Mixing (\(\Delta H_{mix}\)): For an ideal solution, the enthalpy of mixing is zero. This is because the intermolecular forces between the components of an ideal solution are exactly the same as those between the molecules of the pure components. Therefore, there is no net heat absorbed or released during mixing.

Volume of Mixing (\(\Delta V_{mix}\)): The volume of mixing for an ideal solution can vary. In an ideal solution, the volume change upon mixing can be zero or non-zero. It depends on whether the volumes of the components are additive or not. For many ideal solutions, the volume of mixing is not necessarily zero, as the molecules of the components might occupy the same volume differently than the sum of their individual volumes.

Analysis of Each Option:

1.\(\Delta H_{mix} = 0\), \(\Delta V_{mix} \neq 0\):

The option is correct. For an ideal solution, the enthalpy of mixing (\(\Delta H_{mix}\)) is zero because the mixing process does not involve any heat exchange. The volume of mixing (\(\Delta V_{mix}\)) can be non-zero, meaning the total volume of the solution might not be the sum of the volumes of the pure components.

2. \(\Delta H_{mix} = 0\), \(\Delta V_{mix} = 0\):

The option is possible but not necessarily true. While \(\Delta H_{mix}\) is indeed zero, \(\Delta V_{mix}\) being zero is not a requirement for an ideal solution. It is possible for \(\Delta V_{mix}\) to be zero, but it is not a defining characteristic of an ideal solution.

3. \(\Delta H_{mix} \neq 0\), \(\Delta V_{mix} \neq 0\):

The option is incorrect. For an ideal solution, \(\Delta H_{mix}\) must be zero. Therefore, this option is incorrect as it contradicts the fact that the enthalpy of mixing for an ideal solution is zero.

4. \(\Delta H_{mix} \neq 0\), \(\Delta V_{mix} = 0\):

The option is incorrect. This option is incorrect because \(\Delta H_{mix}\) for an ideal solution should be zero. Therefore, this option does not describe an ideal solution.

Conclusion: The correct description for a binary ideal solution of AB type is: 1. \(\Delta H_{mix} = 0\), \(\Delta V_{mix} \neq 0\). This accurately reflects that the enthalpy of mixing is zero while the volume of mixing may vary.