This Gibbs free energy calculator computes ΔG = ΔH − TΔS, reads the spontaneity of a reaction at any temperature, and converts ΔG into the equilibrium constant K — thermodynamics’ yes/no answer, with the numbers attached.
ΔS is converted from J to kJ internally — the unit mismatch between ΔH (kJ) and ΔS (J/K) is the classic thousand-fold error in this calculation, designed out here. “Spontaneous” means thermodynamically favorable — it says nothing about speed (kinetics owns that).
The Universe’s Ledger
ΔG = ΔH − TΔS weighs a reaction’s heat (ΔH) against its disorder gain (ΔS), with temperature as the exchange rate between them. Negative ΔG → the reaction can proceed on its own (and can, in principle, do work — ΔG is the maximum useful work extractable). ΔG also fixes equilibrium through ΔG° = −RT ln K: every −5.7 kJ/mol at 25 °C multiplies K by ten. The ΔH inputs are measured by the science of our Calorimetry Calculator. Part of our Chemistry Calculators collection.
The Four Sign Combinations
| ΔH | ΔS | Spontaneous when… | Intuition |
|---|---|---|---|
| − | + | Always | Heat out AND disorder up — downhill both ways |
| + | − | Never | Uphill both ways; the reverse is spontaneous |
| − | − | T below ΔH/ΔS | Exothermic but ordering — cold favors it (freezing) |
| + | + | T above ΔH/ΔS | Endothermic but disordering — heat enables it (melting, evaporation) |
Worked Example (Verified)
ΔH = −110.5 kJ/mol, ΔS = +89.5 J/mol·K, at 298 K:
- TΔS = 298 × 0.0895 = 26.7 kJ → ΔG = −110.5 − 26.7 = −137.2 kJ/mol: strongly spontaneous
- K = e^(137,200 / (8.314 × 298)) ≈ 1.1 × 10²⁴ — equilibrium is not a compromise here; it’s a rout
- Crossover example: an endothermic, disordering process with ΔH = +50 kJ/mol and ΔS = +160 J/mol·K flips spontaneous at T = 50,000 ÷ 160 = 312.5 K — why some dissolutions and reactions “switch on” with warming
Spontaneous ≠ Fast, and Other Warnings
- Diamond → graphite has ΔG < 0 at room conditions; your ring is safe on kinetic grounds. ΔG gives the destination, activation energy gives the timetable.
- Standard-state ΔG° (1 M, 1 atm, usually 298 K) differs from ΔG at real concentrations — the correction is ΔG = ΔG° + RT ln Q, and cells and organisms live in the correction.
- Biochemistry’s ΔG°′ uses pH 7 as standard — same equation, adjusted bookkeeping.
Related Tools
- Calorimetry Calculator — where ΔH numbers come from
- pH Calculator — equilibrium in acid-base dress
- Chemistry Calculators — the full collection
Frequently Asked Questions
How do you calculate Gibbs free energy?
ΔG = ΔH − TΔS, with T in kelvin and units aligned (the trap: ΔS is usually in J/mol·K while ΔH is kJ/mol — divide ΔS by 1,000). At ΔH −110.5, ΔS +89.5, 298 K: ΔG = −137.2 kJ/mol.
What does a negative ΔG mean?
The reaction is thermodynamically spontaneous in the forward direction under the stated conditions — it can proceed without net energy input (though possibly immeasurably slowly). Positive ΔG means the reverse is spontaneous; zero means equilibrium.
How is ΔG related to the equilibrium constant?
ΔG° = −RT ln K. At 298 K, every −5.7 kJ/mol of ΔG° means another factor of 10 in K — the example’s −137.2 kJ/mol corresponds to K ≈ 10²⁴, a reaction that for practical purposes completes.
At what temperature does a reaction become spontaneous?
At the crossover T = ΔH/ΔS (both in matching units), when the signs allow one: ΔH+ / ΔS+ reactions switch on above it; ΔH− / ΔS− reactions switch off above it. The widget computes it directly.
Is Gibbs free energy the same as activation energy?
No — ΔG is the net energy difference between reactants and products (thermodynamics); activation energy is the barrier between them (kinetics). Catalysts lower the barrier and change nothing about ΔG or K.
Is this Gibbs free energy calculator free?
Yes — free, instant, no sign-up.