Article — Gibbs Free Energy Calculator
How the Gibbs free energy calculator works
Gibbs free energy combines enthalpy and entropy into a single sign-bearing number that predicts spontaneity at constant temperature and pressure. The defining equation is ΔG = ΔH − TΔS. Negative ΔG means the forward reaction is spontaneous; positive means the reverse direction is favored; zero means equilibrium. The calculator above reports ΔG in kJ/mol from your inputs and also computes the equilibrium constant K from ΔG° = −RT ln K.
Josiah Willard Gibbs introduced the function in the 1870s as the natural thermodynamic potential for laboratory-style conditions where temperature and pressure are held constant — the everyday situation in chemistry.
What is Gibbs free energy
Gibbs free energy G is a state function defined by G = H − TS. The change ΔG during a process equals the maximum non-expansion work the process can deliver. For a chemical reaction at constant T and P, ΔG < 0 is the criterion for spontaneity — it does not say the reaction is fast, only that the products are more stable than the reactants under those conditions.
Two related potentials exist for different constraints: Helmholtz free energy A = U − TS for constant V and T, and the grand potential for constant chemical potential. For chemistry under atmospheric pressure, Gibbs is the right choice.
The Gibbs free energy formula
The central equation is:
ΔG = ΔH − TΔS
Units convention: ΔH is reported in kJ/mol, ΔS in J/(K·mol) (note the units mismatch — the calculator handles the 1000-fold conversion internally). T is absolute temperature in kelvin.
R 8.314 J/(mol K) or 0.008314 kJ/(mol K)T standard 298.15 K (25 °C)P standard 1 bar (or 1 atm in older tables)F (Faraday) 96,485 C/molGibbs energy spontaneity regimes
The signs of ΔH and ΔS combine into four regimes:
- ΔH < 0 and ΔS > 0 — ΔG is always negative; the reaction is spontaneous at every temperature. Combustion of fuels lives here.
- ΔH > 0 and ΔS < 0 — ΔG is always positive; the reaction never proceeds spontaneously in the forward direction. Photosynthesis turns this around with energy input from sunlight.
- ΔH < 0 and ΔS < 0 — spontaneous at low T only; the enthalpy term wins until T grows large enough to make the entropy penalty dominate. Crystallization fits here.
- ΔH > 0 and ΔS > 0 — spontaneous at high T only; the entropy benefit eventually overcomes the enthalpy penalty. Melting, vaporization, and many endothermic dissolutions live here.
The same chemistry can shift regime when conditions change. Mixing dinitrogen tetroxide and water at room temperature has small enthalpy but a strongly favorable entropy from gas dispersion. At high pressure where the gas behaves more like a liquid the entropy advantage shrinks — this is why catalysis matters in industrial chemistry.
The switch temperature explained
For the two mixed-sign regimes (both signs equal), there is a temperature where ΔG crosses zero:
Tswitch = ΔH / ΔS
Below Tswitch one direction is favored; above it the other. The classic example is ice melting: ΔHfus = +6.01 kJ/mol, ΔSfus = +22.0 J/(K·mol). Tswitch = 6010 / 22.0 = 273.2 K, which is exactly 0 °C — the experimental melting point.
For decomposition of calcium carbonate, CaCO3 → CaO + CO2, ΔH = +178 kJ/mol and ΔS = +160 J/(K·mol). Tswitch = 1113 K (840 °C), the temperature above which CaCO3 decomposes — the basis for lime kilns.
Gibbs energy and the equilibrium constant
For standard-state ΔG° the connection to the equilibrium constant is:
ΔG° = −RT ln K
Rearranging gives K = exp(−ΔG°/RT). At 298 K, every 5.7 kJ/mol of ΔG° shifts K by one order of magnitude. A ΔG° of −57 kJ/mol gives K = 1010; a ΔG° of +57 kJ/mol gives K = 10−10. Equilibrium thermodynamics is built on this single relation.
Gibbs free energy predicts thermodynamic feasibility, not reaction rate. Diamond converting to graphite at room temperature has ΔG of −2.9 kJ/mol but takes geological ages to actually occur because the activation energy is enormous. Rate is governed by the height of the activation barrier (Arrhenius), not by ΔG.
Gibbs energy in electrochemistry
For an electrochemical cell, the work done by transferring n moles of electrons at potential E°cell:
ΔG° = −nFE°cell
where F = 96,485 C/mol is the Faraday constant. A positive cell potential corresponds to negative ΔG° — the cell does work spontaneously. The Daniell cell (Zn/Cu) has E° = 1.10 V and n = 2, giving ΔG° = −212 kJ/mol, corresponding to K ≈ 1037. The reverse direction is essentially never observed.
Gibbs free energy of formation
Standard Gibbs energy of formation ΔG°f is the change in Gibbs energy when one mole of a compound forms from its elements in their reference states at 298.15 K. Like enthalpy of formation, ΔG°f = 0 for elements in their standard form (O2 gas, C graphite, Hg liquid). All other values are referenced against those zeros.
For any reaction, ΔG° = Σ ni ΔG°f(products) − Σ ni ΔG°f(reactants). Some useful benchmarks: water (l) −237.13 kJ/mol; CO2 (g) −394.36; methane (g) −50.72; glucose (s) −910; aluminum oxide −1582. The very negative values for oxides and carbonates explain why aluminum mining requires enormous energy — you have to reverse the formation step electrolytically.
Common Gibbs free energy pitfalls
- Units mismatch — ΔH in kJ/mol and ΔS in J/(K·mol) need a 1000-fold correction before combining
- Celsius instead of Kelvin — T must be absolute; subtracting 273.15 by mistake gives meaningless results near room temperature
- Standard vs non-standard — ΔG° refers to standard state (1 bar, 1 M); ΔG = ΔG° + RT ln Q at any other condition
- Confusing ΔG with ΔG° — at equilibrium ΔG = 0 but ΔG° is non-zero
- Assuming ΔH and ΔS are temperature-independent — tables are valid near 298 K; far from that, Kirchhoff corrections become important
For a quick sanity check on any calculation, recompute TΔS in kJ/mol and confirm that its magnitude is comparable to ΔH. If TΔS is 1000-fold larger or smaller than ΔH you almost certainly have a units error somewhere.
One last reminder: living systems run on negative-ΔG reactions coupled to positive-ΔG ones. ATP hydrolysis releases −30.5 kJ/mol under cellular conditions; that energy drives muscle contraction, protein synthesis, and active transport against concentration gradients. Each step has its own ΔG, but the network as a whole must have net ΔG < 0 for the organism to stay alive. Biochemistry is essentially applied Gibbs energy bookkeeping at molecular scale.