Question

For an ideal binary liquid mixture:

• A. \( \Delta S_{\text{(mix)}} = 0; \Delta G_{\text{(mix)}} = 0 \)
• B. \( \Delta H_{\text{(mix)}} = 0; \Delta S_{\text{(mix)}} < 0 \)
• C. \( \Delta V_{\text{(mix)}} = 0; \Delta G_{\text{(mix)}} > 0 \)
• D. \( \Delta S_{\text{(mix)}} > 0; \Delta G_{\text{(mix)}} < 0 \)

Hint:

For any spontaneous mixing process (ideal or non-ideal), \( \Delta S_{\text{mix}} \) is always positive (\( > 0 \)) and \( \Delta G_{\text{mix}} \) is always negative (\( < 0 \)). These two parameters do not depend on ideal behavior.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We need to identify the thermodynamic properties that characterize an ideal binary liquid mixture during mixing.

Step 2: Detailed Explanation:
For an ideal solution formed by mixing two liquids:
- There is no change in enthalpy during mixing, so \( \Delta H_{\text{mix}} = 0 \).
- There is no change in volume during mixing, so \( \Delta V_{\text{mix}} = 0 \).
- Since mixing of two components is a spontaneous physical process, the Gibbs free energy change of mixing must be negative, i.e., \( \Delta G_{\text{mix}} < 0 \).
- As molecules of two different liquids intermingle, randomness increases, leading to a positive entropy change of mixing, i.e., \( \Delta S_{\text{mix}} > 0 \).
Analyzing the options:
- Option (A) is incorrect because \( \Delta S_{\text{mix}} \neq 0 \) and \( \Delta G_{\text{mix}} \neq 0 \).
- Option (B) is incorrect because \( \Delta S_{\text{mix}} \) must be positive (\( > 0 \)).
- Option (C) is incorrect because \( \Delta G_{\text{mix}} \) must be negative (\( < 0 \)).
- Option (D) correctly lists \( \Delta S_{\text{mix}} > 0 \) and \( \Delta G_{\text{mix}} < 0 \).

Step 3: Final Answer:
(D) \( \Delta S_{\text{(mix)}} > 0; \Delta G_{\text{(mix)}} < 0 \)