Thermodynamics of Ideal Solution of Benzene and Naphthalene

To determine the correct statements regarding the mixing process of benzene and naphthalene to form an ideal solution at room temperature, we analyze the fundamental thermodynamic properties of ideal solution formation:

1. Enthalpy of Mixing ($\Delta H$): In an ideal solution, the intermolecular forces of attraction between solute-solute molecules ($A-A$), solvent-solvent molecules ($B-B$), and solute-solvent molecules ($A-B$) are equal in magnitude. Consequently, no heat is absorbed or released during the mixing process: $\Delta H_{\text{mix}} = 0$ Therefore, statement (D) is correct.

2. Entropy of System ($\Delta S_{\text{system}}$): When two liquids mix to form a homogeneous solution, the spatial disorder and randomness of the molecules increase. Quantitatively, for an ideal solution containing $n_i$ moles of components with mole fractions $x_i$: $\Delta S_{\text{system}} = -R \sum n_i \ln x_i$ Since mole fractions satisfy $0 < x_i < 1$, we have $\ln x_i < 0$, which yields: $\Delta S_{\text{system}} > 0$ Therefore, $\Delta S_{\text{system}}$ is positive, making statement (B) correct.

3. Entropy of Surroundings ($\Delta S_{\text{surroundings}}$): Since the process occurs isothermally without any enthalpy change ($\Delta H = 0$), no heat is exchanged between the system and the surroundings ($q_{\text{surroundings}} = 0$). Thus: $\Delta S_{\text{surroundings}} = \frac{q_{\text{surroundings}}}{T} = 0$ Therefore, statement (C) is correct.

4. Gibbs Free Energy ($\Delta G$): The change in Gibbs free energy for the process at constant temperature $T$ is given by: $\Delta G = \Delta H - T\Delta S_{\text{system}}$ Substituting $\Delta H = 0$ into the relation: $\Delta G = -T\Delta S_{\text{system}}$ Since $\Delta S_{\text{system}} > 0$ and $T > 0$, it follows that $\Delta G < 0$ (negative), indicating a spontaneous process. Therefore, statement (A) is incorrect.

Hence, the correct statements are B, C, and D.