The problem asks for the correct thermodynamic statements regarding the formation of an ideal solution by mixing benzene and naphthalene at room temperature.

Step-by-Step Analysis:

1. Definition of an Ideal Solution: An ideal solution is one where the intermolecular forces of attraction between molecules of different components (solute-solvent) are the same as those between molecules of the same components (solute-solute and solvent-solvent). For mixing components A and B to form an ideal solution, the A-B interactions are equal in strength to the A-A and B-B interactions.

2. Analysis of Enthalpy Change ($\\\Delta H$): For an ideal solution, the enthalpy of mixing ($\\\Delta H_{mix}$) is zero. This is because no net energy is released or absorbed during the mixing process. The energy required to break the existing interactions (benzene-benzene, naphthalene-naphthalene) is exactly balanced by the energy released when new interactions (benzene-naphthalene) are formed. $\\\Delta H = \\\Delta H_{mix} = 0$ Therefore, statement (D) is true.

3. Analysis of System Entropy Change ($\\\Delta S_{system}$): Mixing is a process that increases the randomness or disorder of the system. When two pure substances are mixed, the number of possible arrangements of the molecules increases. This leads to an increase in the entropy of the system. $\\\Delta S_{system} = \\\Delta S_{mix} > 0$ For any spontaneous mixing process, the entropy of the system will increase. Therefore, statement (B) is true.

4. Analysis of Surroundings Entropy Change ($\\\Delta S_{surroundings}$): The change in the entropy of the surroundings is related to the heat exchanged with the system at a constant temperature T. $\\\Delta S_{surroundings} = \frac{-q_{sys}}{T}$ For a process at constant pressure, the heat exchanged by the system is equal to the enthalpy change of the system, $q_{sys} = \\\Delta H_{sys}$. Since we established that for an ideal solution, $\\\\Delta H_{sys} = 0$, then: $\\\Delta S_{surroundings} = \frac{-0}{T} = 0$ Therefore, statement (C) is true.

5. Analysis of Gibbs Free Energy Change ($\\\Delta G$): The Gibbs free energy change for a process is given by the equation: \\\Delta G = \\\Delta H - T\\\\[S_{system} For the formation of an ideal solution:

   • \\\\[H = 0
   • \\\\[S_{system} > 0
   • T (temperature in Kelvin) is positive.

   Substituting these values into the equation: $\\\Delta G = 0 - T(\\\text{positive value})$ $\\\Delta G < 0$ A negative value of \\\\[G indicates that the process is spontaneous. The mixing of benzene and naphthalene to form a solution is a spontaneous process. Statement (A) says \\\\[G is positive, which would imply a non-spontaneous process. Therefore, statement (A) is false.

Conclusion:

Based on the analysis, the true statements are (B), (C), and (D).