Gibbs Free Energy Formula
Calculate Gibbs free energy with G = H - TS to predict if a chemical reaction will occur spontaneously.
Includes worked examples.
The Formula
Gibbs free energy determines whether a reaction will proceed spontaneously at constant temperature and pressure. A negative ΔG means the reaction is spontaneous. A positive ΔG means it is not.
Variables
| Symbol | Meaning |
|---|---|
| ΔG | Change in Gibbs free energy (measured in kJ/mol) |
| ΔH | Change in enthalpy — heat absorbed or released (kJ/mol) |
| T | Temperature (measured in kelvins, K) |
| ΔS | Change in entropy — disorder of the system (kJ/(mol·K)) |
Spontaneity Rules
| ΔH | ΔS | ΔG | Spontaneous? |
|---|---|---|---|
| Negative (exothermic) | Positive (more disorder) | Always negative | Always spontaneous |
| Negative | Negative | Depends on T | Spontaneous at low T |
| Positive | Positive | Depends on T | Spontaneous at high T |
| Positive (endothermic) | Negative (less disorder) | Always positive | Never spontaneous |
Example 1
A reaction has ΔH = -92 kJ/mol and ΔS = -0.199 kJ/(mol·K) at 25°C. Is it spontaneous?
Convert temperature: T = 25 + 273.15 = 298.15 K
ΔG = ΔH - TΔS = -92 - (298.15 × -0.199)
ΔG = -92 + 59.33
ΔG = -32.67 kJ/mol (negative, so the reaction is spontaneous at 25°C)
Example 2
At what temperature does the reaction above stop being spontaneous?
Set ΔG = 0: 0 = ΔH - TΔS
T = ΔH / ΔS = -92 / -0.199
T ≈ 462 K (189°C) — above this temperature, the reaction becomes non-spontaneous
When to Use It
Use the Gibbs free energy formula to predict reaction behavior:
- Determining if a chemical reaction will occur spontaneously
- Finding the temperature at which a reaction becomes favorable
- Calculating the maximum useful work a reaction can perform
- Understanding phase transitions (melting, boiling, freezing)
Key Notes
- Formula: ΔG = ΔH − TΔS: ΔH is enthalpy change (heat at constant pressure), T is absolute temperature (K), and ΔS is entropy change. ΔG < 0: spontaneous; ΔG > 0: non-spontaneous (requires energy input); ΔG = 0: system is at equilibrium.
- Four sign combinations: ΔH−/ΔS+: always spontaneous (ΔG always negative). ΔH+/ΔS−: never spontaneous (ΔG always positive). ΔH−/ΔS−: spontaneous only at low T. ΔH+/ΔS+: spontaneous only at high T. Temperature determines the outcome of the latter two cases.
- Relationship to equilibrium constant: ΔG° = −RT ln K: At standard conditions (25°C, 1 atm, 1 M concentrations). If K > 1 → ΔG° < 0 (products favored). If K < 1 → ΔG° > 0 (reactants favored). A 10-fold change in K corresponds to ~5.7 kJ/mol change in ΔG° at 25°C.
- Connection to electrochemistry: ΔG° = −nFE°: n is moles of electrons transferred; F = 96,485 C/mol (Faraday's constant); E° is the standard cell potential. A positive cell voltage means negative ΔG° — the reaction is spontaneous and will generate electrical energy.
- Applications: Gibbs free energy is used to predict whether a chemical reaction will proceed, determine equilibrium compositions in industrial processes, calculate maximum work obtainable from a reaction, analyze phase transitions, and understand biochemical energy coupling (ATP hydrolysis: ΔG° ≈ −30.5 kJ/mol).