What this calculator does
Gibbs free energy is enthalpy minus temperature times entropy, and its sign decides whether a reaction proceeds. A reaction releasing 92.4 kJ/mol but losing 198.4 J/(mol·K) of entropy gives −33.247 kJ/mol at room temperature, so it runs.
That same reaction stops running if it gets hot enough. At 600 K the entropy term has grown to −119 kJ/mol and outweighs the enthalpy, giving a positive ΔG. The crossover sits at about 466 K, which is the temperature where the two terms exactly balance. This is why many industrial syntheses have an optimum temperature rather than simply going faster when heated.
The formula
ΔG is ΔH minus T times ΔS. The units differ by a factor of a thousand, since enthalpy is conventionally quoted in kJ/mol and entropy in J/(mol·K), and the calculator handles that conversion. A negative ΔG means the reaction is thermodynamically favourable; it says nothing about how fast it will go, which is a kinetic question.
| Term | Meaning |
|---|---|
| ΔG | Gibbs free energy change. Negative means spontaneous. |
| ΔH | Enthalpy change. Negative means heat is released. |
| ΔS | Entropy change. Positive means disorder increases. |
| Spontaneous | Thermodynamically favourable. It does not mean fast, and many spontaneous reactions never visibly proceed. |
The inputs explained
| Field | What to enter |
|---|---|
| Enthalpy change ΔH (kJ/mol) | Enthalpy change in kJ/mol. Negative for an exothermic reaction. |
| Entropy change ΔS (J/(mol·K)) | Entropy change in J/(mol·K). Note the joules, not kilojoules. |
| Temperature (K) | Temperature in kelvin. |
When to use it
Predicting whether a reaction will go
The sign of ΔG is the thermodynamic verdict, independent of any reaction pathway.
Finding a crossover temperature
Where enthalpy and entropy oppose each other, there is a temperature at which the verdict flips.
Understanding industrial conditions
The choice of operating temperature often balances a thermodynamic penalty against a kinetic benefit.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does temperature change the verdict?
The same reaction at a range of temperatures.
| Temperature | Gibbs free energy ΔG | T·ΔS term | Spontaneity |
|---|---|---|---|
| 200 K | -52.720 kJ/mol | -39.680 kJ/mol | spontaneous (favourable) at this temperature |
| 298.15 K | -33.247 kJ/mol | -59.153 kJ/mol | spontaneous (favourable) at this temperature |
| 400 K | -13.040 kJ/mol | -79.360 kJ/mol | spontaneous (favourable) at this temperature |
| 600 K | 26.640 kJ/mol | -119.040 kJ/mol | non-spontaneous at this temperature |
Questions
Does spontaneous mean fast?
No, and this is the most common misreading. Spontaneous means thermodynamically favourable. Diamond converting to graphite is spontaneous at room temperature and takes geological time, because the activation barrier is enormous. Rate is a separate question answered by kinetics.
What are the four sign combinations?
Negative ΔH with positive ΔS is spontaneous at all temperatures. Positive ΔH with negative ΔS is never spontaneous. The mixed cases depend on temperature: negative-negative favours low temperatures and positive-positive favours high ones.
Why do enthalpy and entropy use different units?
Convention. Enthalpy changes are large and quoted in kJ/mol; entropy changes are smaller and quoted in J/(mol·K). Forgetting the factor of a thousand is the classic error, and it produces an answer wrong by 1,000 in the entropy term.
How do I find the crossover temperature?
Set ΔG to zero and solve, giving T equal to ΔH over ΔS. For the reaction above that is 92,400 J/mol divided by 198.4 J/(mol·K), about 466 K. Above that temperature the sign of ΔG reverses.
For entropy values, see the entropy calculator. For equilibrium constants, see the Kp and Kc conversion calculator.