JEE Advance - Chemistry (2013 - Paper 1 Offline - No. 7)
Explanation
When dealing with solutions and thermodynamics, particularly with ideal solutions, several key aspects must be considered to understand the behavior of the system and its interactions with the surroundings. Let's analyze each option in the context of forming an ideal solution from benzene and naphthalene at room temperature:
Option A: $$\Delta G$$ is positive
For an ideal solution, the Gibbs free energy change ($$\Delta G$$) upon mixing can be described as follows:
$$\Delta G = \Delta H - T\Delta S$$
An ideal solution has the characteristic that there is no enthalpy change upon mixing ($$\Delta H = 0$$) because the intermolecular forces between unlike molecules are assumed to be equal to those between like molecules. Additionally, when two or more components form an ideal solution, the entropy of the system ($$\Delta S$$) increases due to the mixing of different molecules, which is a manifestation of increased randomness or disorder.
Since $$\Delta H = 0$$ and $$\Delta S > 0$$ for an ideal solution, applying these to the Gibbs free energy equation yields:
$$\Delta G = 0 - T\Delta S = -T\Delta S$$
Given that $$T > 0$$ and $$\Delta S > 0$$, $$\Delta G$$ will ultimately be negative, indicating a spontaneous process. Therefore, Option A is false.
Option B: $$\Delta S_{system}$$ is positive
As mentioned earlier, the entropy of the system increases in the formation of an ideal solution. This is because the different molecules of benzene and naphthalene mix, increasing the randomness or disorder of the system. Therefore, Option B is true.
Option C: $$\Delta S_{surroundings}$$ = 0
In the formation of an ideal solution, there is no heat exchange with the surroundings since $$\Delta H = 0$$. Without a heat exchange, there is no change in the entropy of the surroundings, as entropy change in the surroundings is generally associated with heat exchange according to the relation $$\Delta S = \frac{q}{T}$$ for reversible processes. Therefore, Option C is true.
Option D: $$\Delta H$$ = 0
In the context of an ideal solution, it is assumed that the enthalpy change ($$\Delta H$$) is zero because the energy required to break interactions among similar molecules is exactly balanced by the energy released from the formation of new interactions between different types of molecules. This implies no net heat effect. Therefore, Option D is true.
In summary, Options B, C, and D are true, while Option A is false for the ideal solution of benzene and naphthalene at room temperature.
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