Gibbs Free Energy Calculator
Compute Gibbs free energy changes (ΔG and ΔG°) from enthalpy and entropy or from the equilibrium constant. Instantly see whether a reaction is spontaneous, at equilibrium, or non‑spontaneous at a given temperature.
How this Gibbs free energy calculator works
This tool implements the core thermodynamic relationships used in chemistry, biochemistry, and engineering to connect enthalpy, entropy, equilibrium, and spontaneity.
1. From enthalpy and entropy: ΔG = ΔH − TΔS
At constant temperature and pressure:
\\(\Delta G = \Delta H - T \Delta S\\)
- \\(\Delta G\\): Gibbs free energy change (kJ/mol)
- \\(\Delta H\\): enthalpy change (kJ/mol)
- \\(T\\): absolute temperature (K)
- \\(\Delta S\\): entropy change (kJ/(mol·K))
The calculator automatically converts units so you can enter:
- ΔH in kJ/mol or J/mol
- ΔS in J/(mol·K) or kJ/(mol·K)
- T in K or °C (internally converted to kelvin)
2. From equilibrium constant: ΔG° = −RT ln K
For a reaction at equilibrium at temperature \\(T\\):
\\(\Delta G^\circ = -RT \ln K\\)
- \\(\Delta G^\circ\\): standard Gibbs free energy change (kJ/mol)
- \\(R = 8.314\\ \text{J·mol}^{-1}\text{·K}^{-1}\\): gas constant
- \\(T\\): temperature (K)
- \\(K\\): equilibrium constant (dimensionless)
The calculator:
- Converts T from °C to K if needed.
- Computes ΔG° in J/mol, then reports it in kJ/mol for readability.
- Interprets the sign of ΔG° to tell you whether products or reactants are favored at equilibrium.
3. From ΔG° and reaction quotient Q: ΔG = ΔG° + RT ln Q
Under non‑standard conditions:
\\(\Delta G = \Delta G^\circ + RT \ln Q\\)
- \\(\Delta G\\): Gibbs free energy change under actual conditions
- \\(\Delta G^\circ\\): standard Gibbs free energy change
- \\(Q\\): reaction quotient (same form as K, but using current activities)
This lets you see how far a system is from equilibrium and in which direction it will shift.
Interpreting the sign of ΔG
- ΔG < 0: reaction is spontaneous in the forward direction at this T.
- ΔG = 0: system is at equilibrium.
- ΔG > 0: reaction is non‑spontaneous in the forward direction (reverse is spontaneous).
Remember: “spontaneous” does not mean “fast” — it only refers to thermodynamic favorability, not kinetics.
Temperature dependence and the sign of ΔH and ΔS
The signs of ΔH and ΔS determine how temperature affects spontaneity:
| ΔH | ΔS | Spontaneity |
|---|---|---|
| − (exothermic) | + (entropy increases) | Spontaneous at all temperatures |
| + (endothermic) | − (entropy decreases) | Non‑spontaneous at all temperatures |
| − | − | Spontaneous at low T, non‑spontaneous at high T |
| + | + | Non‑spontaneous at low T, spontaneous at high T |
Common pitfalls and unit mistakes
- Mixing J and kJ: Always convert ΔS to kJ/(mol·K) if ΔH is in kJ/mol.
- Using °C instead of K: The formulas require absolute temperature in kelvin.
- Using negative or zero K: K and Q must be positive; ln(K) and ln(Q) are undefined for ≤ 0.
FAQ
Is Gibbs free energy the same as “usable energy”?
In chemistry at constant T and P, −ΔG represents the maximum non‑expansion work that can be extracted from a process (for example, electrical work in a galvanic cell). In real systems, kinetic barriers and irreversibilities mean you usually get less than this theoretical maximum.
How does Gibbs free energy relate to equilibrium?
At equilibrium, ΔG = 0 and the system has no net driving force in either direction. The equilibrium constant K encodes this balance, and ΔG° = −RT ln K connects thermodynamics to measurable equilibrium compositions.