Thermodynamics: Criteria for Spontaneity

Criteria for Spontaneity

A process is spontaneous if it occurs naturally without external intervention. In thermodynamics, spontaneity is determined by changes in enthalpy (ΔH), entropy (ΔS), and Gibbs free energy (ΔG).

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1. Gibbs Free Energy (ΔG)

ΔG = ΔH − TΔS

Where:

• ΔG: Change in Gibbs free energy (J/mol)
• ΔH: Change in enthalpy (J/mol)
• ΔS: Change in entropy (J/mol·K)
• T: Absolute temperature (K)

Criteria Based on ΔG (at constant T and P):

ΔG	Spontaneity	Description
ΔG < 0	Spontaneous	Process occurs naturally
ΔG = 0	Equilibrium	No net change
ΔG > 0	Non-spontaneous	Requires energy input

Key Rule: A reaction is spontaneous only if ΔG is negative.

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2. Role of ΔH and ΔS

Spontaneity depends on the signs of ΔH and ΔS, and the temperature.

ΔH	ΔS	ΔG = ΔH − TΔS	Spontaneity
− (exothermic)	+ (↑ disorder)	Always negative	Always spontaneous
− (exothermic)	− (↓ disorder)	Negative at low T	Spontaneous only at low T
+ (endothermic)	+ (↑ disorder)	Negative at high T	Spontaneous only at high T
+ (endothermic)	− (↓ disorder)	Always positive	Never spontaneous

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3. Temperature Effect on Spontaneity

• Exothermic + Entropy increase: Spontaneous at all temperatures (e.g., combustion).
• Endothermic + Entropy increase: Spontaneous only above a certain temperature (e.g., melting ice at T > 0°C).
• Exothermic + Entropy decrease: Spontaneous only below a certain temperature (e.g., water freezing at T < 0°C).
• Endothermic + Entropy decrease: Never spontaneous.

Critical Temperature Calculation

At equilibrium: ΔG = 0 → ΔH = TΔS → T = ^ΔH⁄_ΔS

Use this to find the temperature where a reaction switches from spontaneous to non-spontaneous.

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4. Summary: Decision Flowchart

1. Calculate or determine ΔH and ΔS.
2. Compute ΔG = ΔH − TΔS at given T.
3. Check sign of ΔG:
   • ΔG < 0 → Spontaneous
   • ΔG > 0 → Non-spontaneous
   • ΔG = 0 → Equilibrium

Remember: Spontaneity tells you if a reaction can happen, not how fast. (Rate depends on kinetics!)

Test Your Knowledge

1. For a process to be spontaneous at constant temperature and pressure, what must be true about ΔG?

• A) ΔG > 0
• B) ΔG = 0
• C) ΔG < 0
• D) ΔG can be any value

Correct Answer: C) ΔG < 0
Explanation: A negative Gibbs free energy change (ΔG < 0) is the only criterion for spontaneity under constant T and P.

Correct Answer: C) ΔG < 0

2. A reaction has ΔH = −100 kJ/mol and ΔS = −50 J/mol·K. At what temperature range is it spontaneous?

• A) At all temperatures
• B) Only at high temperatures
• C) Only at low temperatures
• D) Never spontaneous

Correct Answer: C) Only at low temperatures
Explanation: ΔH < 0 (exothermic), ΔS < 0 (↓ entropy) → ΔG = ΔH − TΔS is negative only when T is low (TΔS term is small).

3. Which combination always results in a spontaneous reaction regardless of temperature?

• A) ΔH > 0, ΔS > 0
• B) ΔH < 0, ΔS < 0
• C) ΔH < 0, ΔS > 0
• D) ΔH > 0, ΔS < 0

Correct Answer: C) ΔH < 0, ΔS > 0
Explanation: Exothermic and entropy-increasing reactions have ΔG < 0 at all temperatures.

4. The melting of ice at 25°C is:

• A) Spontaneous, ΔH < 0, ΔS < 0
• B) Spontaneous, ΔH > 0, ΔS > 0
• C) Non-spontaneous, ΔH > 0, ΔS < 0
• D) At equilibrium

Correct Answer: B) Spontaneous, ΔH > 0, ΔS > 0
Explanation: Melting is endothermic (ΔH > 0) and increases disorder (ΔS > 0). At T > 0°C, TΔS > ΔH → ΔG < 0.

5. At what condition does ΔG = 0 for a reaction?

• A) When the reaction is spontaneous
• B) When the reaction is at equilibrium
• C) When ΔH = 0
• D) When T = 0 K

Correct Answer: B) When the reaction is at equilibrium
Explanation: ΔG = 0 defines the equilibrium state (no net driving force).