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)