Benzene and naphthalene form an ideal solution at room temperature. For this process, the true statement(s) is (are)

Engineering

Chemistry

Ideal Solution

First Law and Various Process

Gibbs Free Energy Calculations and Third Law

Question

Benzene and naphthalene form an ideal solution at room temperature. For this process, the true statement(s) is (are)

$∆$ G is positive

$∆$ H = 0

$∆$ S_system is positive

$∆$ S_surroundings = 0

For ideal solution

$∆$ H_solution = 0

$∆$ S_solution = +ve

$∴ ∆$ G_solution = – ve

$∆$ S_surrounding = 0

(As no heat exchange takes place)

When benzene and naphthalene form an ideal solution at room temperature, several thermodynamic properties can be analyzed. An ideal solution follows Raoult's law, meaning there are no net intermolecular interactions between the different components (benzene and naphthalene) beyond those in the pure liquids.

Step 1: Analyze ΔH (Enthalpy Change)
For an ideal solution, the enthalpy change of mixing is zero because there is no heat absorbed or released during the process. The intermolecular forces between like molecules (benzene-benzene and naphthalene-naphthalene) are equal to those between unlike molecules (benzene-naphthalene). Therefore, $Δ H = 0$ .

Step 2: Analyze ΔS_system (Entropy Change of the System)
When two substances mix to form a solution, the number of possible arrangements of molecules increases, leading to a higher disorder or randomness. This results in a positive entropy change for the system. $Δ S_{s y s t e m} > 0$ .

Step 3: Analyze ΔG (Gibbs Free Energy Change)
The Gibbs free energy change is given by $Δ G = Δ H - T Δ S$ . Since $Δ H = 0$ and $Δ S > 0$ , $Δ G = - T Δ S < 0$ . Thus, ΔG is negative, indicating the mixing process is spontaneous.

Step 4: Analyze ΔS_surroundings (Entropy Change of the Surroundings)
Since $Δ H = 0$ , no heat is exchanged with the surroundings. The entropy change of the surroundings, related to heat transfer by $Δ S_{s u r r} = - \frac{Δ H}{T}$ , is therefore zero. $Δ S_{s u r r o u n d i n g s} = 0$ .

Final Answer: The true statements are:
- $Δ H = 0$
- $Δ S_{s y s t e m}$ is positive
- $Δ S_{s u r r o u n d i n g s} = 0$

Detailed Solution

Related Topics and Formulae

Detailed Solution

Related Topics and Formulae

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