Gibbs Free Energy Calculator
Delta G and the equilibrium constant K from enthalpy, entropy, and temperature.
What it does
Two drives decide whether a reaction wants to run: enthalpy, the heat it releases or soaks up, and entropy, the disorder it creates or destroys. Gibbs free energy combines them into one number, DG = DH - T x DS, and its sign is the classic spontaneity test.
The tool above takes a reaction's standard enthalpy and entropy changes plus any temperature, and returns delta G, the equilibrium constant that delta G implies, the temperature where the two terms balance, and a plain-language read on spontaneity.
The defaults use ammonia-synthesis-style numbers: DH of -91.8 kJ/mol and DS of -198.1 J/(mol K) at 298 K. That gives DG of -32.77 kJ/mol and a K of 5.5 x 10^5, with a crossover at 463 K. Warm the reaction to 573 K and DG flips positive at +21.71 kJ/mol with K down to 0.01, which is exactly why that industrial reaction prefers lower temperatures for yield.
The equations and their worked examples follow the free-energy chapters in OpenStax Chemistry and the LibreTexts thermodynamics library: standard-state values, the R = 8.314 J/(mol K) gas constant, and the relationship between delta G and K.
How to use
- Enter the standard enthalpy change in kJ/mol; exothermic reactions are negative.
- Enter the standard entropy change in J per mole per kelvin; watch the units.
- Set the temperature in kelvin.
- Read delta G, then K, then the crossover temperature.
- Check the spontaneity line for the sign story in words.
Formula
- DG
- Gibbs free energy change at the chosen temperature, in kJ/mol.
- DH
- Enthalpy change of the reaction, in kJ/mol.
- DS
- Entropy change of the reaction, in J/(mol K).
- K
- Thermodynamic equilibrium constant at that temperature.
The units are the usual trap: DH arrives in kilojoules while DS arrives in joules per kelvin, so the tool divides DS by 1,000 before subtracting. The crossover temperature only exists as a positive number when DH and DS share a sign; when they disagree, one term dominates at every temperature and the reaction is spontaneous everywhere or nowhere. Standard states (pure substances at 1 bar) describe the bench conditions behind DH and DS, while real mixtures shift things through the reaction quotient Q, and thermodynamics says nothing about how fast a spontaneous reaction gets anywhere.
Worked example
Example: DH -91.8 kJ/mol, DS -198.1 J/(mol K) at 298 K
Defaults: exothermic reaction with decreasing entropy, scored at room temperature.
- Entropy term: T x DS = 298 x -198.1 / 1000 = -59.03 kJ/mol.
- DG: -91.8 - (-59.03) = -32.77 kJ/mol, so the reaction is spontaneous at 298 K.
- K: exp(32,770 / (8.314 x 298)) = 5.5 x 10^5, a strong product-favored constant.
- Crossover: DH / DS = -91,800 / -198.1 = about 463 K.
- At 573 K, DG = -91.8 + 113.51 = +21.71 kJ/mol and K falls to 0.01: the entropy term wins.
Reference table
| DH | DS | Spontaneous when | Typical case |
|---|---|---|---|
| Negative | Positive | At every temperature | Combustion |
| Negative | Negative | Below T = DH / DS | Ammonia synthesis |
| Positive | Positive | Above T = DH / DS | Dissolving ammonium nitrate |
| Positive | Negative | Never under standard conditions | No natural driver |
Limits
- Uses standard-state DH and DS values, assumed constant over temperature.
- Does not include the reaction quotient Q for non-standard mixtures.
- Says nothing about reaction kinetics or catalysts.
- R is fixed at 8.314 J/(mol K), the standard gas constant.
Common mistakes
- Subtracting DS without converting joules to kilojoules.
- Reading a negative DG as a prediction of speed.
- Using standard values for a real mixture at real concentrations.
- Expecting a crossover temperature when DH and DS have opposite signs.
- Quoting K at a temperature other than the one entered.
Try it yourself
Quick checks. Answers sit tucked under each question.
The same reaction at 573 K?
DG = +21.71 kJ/mol and K = 0.01: not spontaneous, because you are above the 463 K crossover.
DH +50 kJ/mol, DS +100 J/(mol K)?
Crossover at 500 K. At 298 K, DG = +20.2 kJ/mol; above 500 K the entropy term takes over.
DH -100 kJ/mol, DS +50 J/(mol K)?
DG = -114.9 kJ/mol at 298 K, spontaneous at every temperature, with K = 1.4 x 10^20.
Questions
What does delta G actually mean?
It is the maximum useful work the reaction can supply at constant temperature and pressure; its sign is the standard test for whether a reaction is product-favored.
Does spontaneous mean it happens quickly?
No. Diamond turning to graphite is spontaneous and effectively never observed. DG is about direction, not speed; kinetics decides speed.
What is the crossover temperature?
The temperature where DH and T x DS cancel, DG hits zero, and the reaction sits at equilibrium with K = 1.
What does K tell me?
How far the reaction runs at equilibrium: K well above 1 favors products, well below 1 favors reactants, and near 1 means a meaningful mixture.
Why is R 8.314?
That is the gas constant in joules per mole per kelvin, the units that match DH and T in the K = exp(-DG / RT) formula.
Can I use these numbers at other temperatures?
Approximately, for small temperature jumps. Real DH and DS drift with temperature, so the crossover figure is an estimate drawn from constant-value thermodynamics.