Question

Match List I with List II

LIST I	LIST II
A. \( \Delta H = -ve, \Delta S = -ve, \Delta G = -ve \)	I. Reaction will be non-spontaneous at high temperature
B. \( \Delta H = -ve, \Delta S = -ve, \Delta G = +ve \)	II. Reaction will be non-spontaneous at low temperature
C. \( \Delta H = +ve, \Delta S = +ve, \Delta G = +ve \)	III. Reaction will be spontaneous at low temperature
D. \( \Delta H = +ve, \Delta S = +ve, \Delta G = -ve \)	IV. Reaction will be spontaneous at high temperature

Choose the correct answer from the options given below:

• A. (A)- (II), (B)- (III), (C)- (I), (D)- (IV)
• B. (A)- (III), (B)- (I), (C)- (II), (D)- (IV)
• C. (A)- (III), (B)- (II), (C)- (IV), (D)- (I)
• D. (A)- (II), (B)- (IV), (C)- (I), (D)- (III)

Hint:

The signs of ∆H and ∆S determine the temperature dependence of the spontaneity of a reaction.

Answer 1

The Correct Option is B

To correctly match the thermodynamic parameters from List I with their corresponding descriptions in List II, we need to analyze each case based on the Gibbs free energy equation: \[ \Delta G = \Delta H - T \Delta S \] Where:

• \( \Delta G \): Change in Gibbs free energy
• \( \Delta H \): Change in enthalpy
• \( \Delta S \): Change in entropy
• \( T \): Temperature in Kelvin

The spontaneity of a reaction depends on the sign of \( \Delta G \):

• If \( \Delta G < 0 \), the reaction is spontaneous.
• If \( \Delta G > 0 \), the reaction is non-spontaneous.

Additionally, the effect of temperature on spontaneity varies based on the signs of \( \Delta H \) and \( \Delta S \):

• Exothermic (\( \Delta H < 0 \)) and Decreasing Entropy (\( \Delta S < 0 \)):
  - Spontaneous at low temperatures.
  - Non-spontaneous at high temperatures.
• Exothermic (\( \Delta H < 0 \)) and Increasing Entropy (\( \Delta S > 0 \)):
  - Spontaneous at all temperatures.
• Endothermic (\( \Delta H > 0 \)) and Increasing Entropy (\( \Delta S > 0 \)):
  - Spontaneous at high temperatures.
  - Non-spontaneous at low temperatures.
• Endothermic (\( \Delta H > 0 \)) and Decreasing Entropy (\( \Delta S < 0 \)):
  - Non-spontaneous at all temperatures.

Now, let’s analyze each item in List I and match it with the appropriate description in List II.

1. List I Item A: \( \Delta H = -\text{ve}, \Delta S = -\text{ve}, \Delta G = -\text{ve} \)
   Interpretation: \[ \Delta G = \Delta H - T \Delta S = (-) - T(-) = -\text{ve} + T\Delta S \] - Since \( \Delta H < 0 \) and \( \Delta S < 0 \), the reaction is spontaneous (\( \Delta G < 0 \)) at low temperatures and non-spontaneous (\( \Delta G > 0 \)) at high temperatures.
   - Matching Description: The reaction is spontaneous at low temperature.
   - Corresponding List II Item: III. Reaction will be spontaneous at low temperature.
2. List I Item B: \( \Delta H = -\text{ve}, \Delta S = -\text{ve}, \Delta G = +\text{ve} \)
   Interpretation: \[ \Delta G = \Delta H - T \Delta S = (-) - T(-) = -\text{ve} + T\Delta S \] - Given \( \Delta G > 0 \), the reaction is non-spontaneous.
   - With \( \Delta H < 0 \) and \( \Delta S < 0 \), the reaction becomes non-spontaneous at high temperatures.
   - Matching Description: Reaction will be non-spontaneous at high temperature.
   - Corresponding List II Item: I. Reaction will be non-spontaneous at high temperature.
3. List I Item C: \( \Delta H = +\text{ve}, \Delta S = +\text{ve}, \Delta G = +\text{ve} \)
   Interpretation: \[ \Delta G = \Delta H - T \Delta S = (+) - T(+) \] - Given \( \Delta G > 0 \), the reaction is non-spontaneous.
   - With \( \Delta H > 0 \) and \( \Delta S > 0 \), the reaction is non-spontaneous at low temperatures and becomes spontaneous at high temperatures.
   - Matching Description: Reaction will be spontaneous at high temperature.
   - Corresponding List II Item: IV. Reaction will be spontaneous at high temperature.
4. List I Item D: \( \Delta H = +\text{ve}, \Delta S = +\text{ve}, \Delta G = -\text{ve} \)
   Interpretation: \[ \Delta G = \Delta H - T \Delta S \] - With \( \Delta H > 0 \) and \( \Delta S > 0 \), the reaction is spontaneous at high temperatures and non-spontaneous at low temperatures.
   - Matching Description: Reaction will be non-spontaneous at low temperature.
   - Corresponding List II Item: II. Reaction will be non-spontaneous at low temperature.

Summary of Matching:
\[ \text{(A)} \, -\Delta H, -\Delta S, -\Delta G \rightarrow \text{III. Spontaneous at low temp} \\ \text{(B)} \, -\Delta H, -\Delta S, +\Delta G \rightarrow \text{I. Non-spontaneous at high temp} \\ \text{(C)} \, +\Delta H, +\Delta S, +\Delta G \rightarrow \text{II. Non-spontaneous at low temp} \\ \text{(D)} \, +\Delta H, +\Delta S, -\Delta G \rightarrow \text{IV. Spontaneous at high temp} \] Therefore, the correct matching is:
\[ \boxed{\text{(A) - (III), (B) - (I), (C) - (II), (D) - (IV)}} \]