Gibbs Free Energy
deltaG = deltaH - T(deltaS)
Gibbs free energy determines reaction spontaneity by combining enthalpy and entropy. A negative deltaG indicates a spontaneous reaction; positive deltaG indicates non-spontaneous.
Variables
Free energy change in kJ/mol
Heat of reaction in kJ/mol
Absolute temperature in Kelvin
Entropy change in kJ/(mol·K)
Example Calculation
Scenario
For a reaction with deltaH = -100 kJ/mol and deltaS = -0.200 kJ/(mol·K), calculate deltaG at 25°C.
Given Data
Calculation
deltaG = deltaH - T(deltaS) = -100 - (298)(-0.200) = -100 + 59.6
Result
deltaG = -40.4 kJ/mol
Interpretation
Since deltaG is negative, the reaction is spontaneous at 25°C. However, as temperature increases, the positive TdeltaS term grows, and eventually deltaG becomes positive.
When to Use This Formula
- ✓Predicting if a reaction is spontaneous
- ✓Finding the temperature at which spontaneity changes
- ✓Calculating maximum useful work from a reaction
- ✓Relating to equilibrium constant (deltaG° = -RT ln K)
Common Mistakes
- ✗Forgetting to convert temperature to Kelvin
- ✗Using inconsistent units (kJ vs J)
- ✗Not converting deltaS units to match deltaH
- ✗Confusing deltaG with deltaG° (standard conditions)
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Common questions about this formula
When deltaG = 0, the system is at equilibrium. No net change occurs in either direction. You can use deltaG = 0 to find the temperature at which a reaction becomes non-spontaneous.
deltaG° = -RT ln K. A large negative deltaG° means a large K (products favored). deltaG (not standard) tells you which direction the reaction will proceed from current conditions to reach equilibrium.