Gibbs Free Energy Calculator
Calculate Gibbs free energy ΔG = ΔH - TΔS.
Determine spontaneity, crossover temperature, and equilibrium relationship.
Essential for thermochemistry.
Gibbs Free Energy
Gibbs free energy (ΔG) is the thermodynamic potential that determines whether a process will occur spontaneously at constant temperature and pressure.
The fundamental equation:
ΔG = ΔH - TΔS
Where:
- ΔH = enthalpy change (kJ/mol) — heat released (negative) or absorbed (positive)
- T = absolute temperature (Kelvin)
- ΔS = entropy change (J/mol·K) — note the different units!
Spontaneity rules:
- ΔG < 0 → spontaneous (reaction proceeds forward)
- ΔG > 0 → non-spontaneous (requires energy input; reverse is spontaneous)
- ΔG = 0 → system is at equilibrium
Four thermodynamic cases:
| ΔH | ΔS | Spontaneous? |
|---|---|---|
| − | + | Always spontaneous |
| + | − | Never spontaneous |
| − | − | Only at low T (ΔG < 0 when T < ΔH/ΔS) |
| + | + | Only at high T (ΔG < 0 when T > ΔH/ΔS) |
Crossover temperature (where ΔG = 0):
T_crossover = ΔH / ΔS
Relationship to equilibrium constant K:
ΔG° = -RT ln K
K = e^(-ΔG°/RT)
where R = 8.314 J/mol·K.
Non-standard conditions:
ΔG = ΔG° + RT ln Q
where Q is the reaction quotient.