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Gibbs Free Energy Calculator

Chemistry

Calculate the Gibbs free energy change ΔG from enthalpy ΔH, entropy ΔS, and temperature T using ΔG = ΔH − TΔS. Determine if a reaction is spontaneous at a given temperature.

-286 kJ/mol
kJ/mol
-163 J/mol·K
J/mol·K
298 K
K

Gibbs Free Energy (ΔG°)

-237.426
Equilibrium Constant (Kc)
415,420,000,000,000,000,000,000,000,000,000,000,000,000
Spontaneity
Spontaneous (ΔG < 0)

This calculator computes your Gibbs Free Energy (ΔG°), Equilibrium Constant (Kc), Spontaneity from the values you enter.

Inputs
Enthalpy Change (ΔH°)Entropy Change (ΔS°)Temperature
Outputs
Gibbs Free Energy (ΔG°)Equilibrium Constant (Kc)Spontaneity

What is a Gibbs Free Energy?

The Gibbs Free Energy Calculator computes the standard Gibbs free energy change (ΔG°) from the enthalpy change (ΔH°), entropy change (ΔS°), and temperature (T) using the fundamental thermodynamic equation ΔG° = ΔH° − TΔS°. It also derives the equilibrium constant Kc from ΔG° = −RT ln(Kc) and classifies the reaction as spontaneous, non-spontaneous, or at equilibrium.

Gibbs free energy is the master thermodynamic criterion for chemical spontaneity. While enthalpy and entropy each capture part of the thermodynamic picture — energy release vs. disorder — ΔG combines both into a single number that directly answers whether a reaction will proceed. A negative ΔG at a given temperature means the reaction is spontaneous at those conditions; a positive ΔG means it is not. At ΔG = 0, the system is at equilibrium.

The temperature in the formula ΔG = ΔH − TΔS acts as a "weight" on the entropy term. This is why some reactions are spontaneous only above certain temperatures (entropy-driven at high T) and others only below certain temperatures (enthalpy-driven at low T). This temperature crossover behaviour is calculated directly by setting ΔG = 0 and solving for T = ΔH/ΔS.

Together with the Entropy Calculator (which extracts ΔS° from ΔH° and ΔG°) and the Equilibrium Constant Calculator (which connects Kc to ΔG°), this tool completes the core chemical thermodynamics toolkit.

How to use this Gibbs Free Energy calculator

  1. Find the standard enthalpy change ΔH° from a thermochemical table (NIST, NCERT appendix, or CRC Handbook). Enter it in kJ/mol in the Enthalpy Change (ΔH°) field — negative for exothermic.
  2. Find the standard entropy change ΔS° from the same source (or calculate it as the difference of standard molar entropies). Enter it in J/mol·K in the Entropy Change (ΔS°) field — note the units are J/mol·K, not kJ/mol·K.
  3. Enter the temperature in Kelvin in the Temperature field. For standard conditions, use 298 K; for a different temperature, note that ΔH° and ΔS° are assumed temperature-independent in this calculation.
  4. Read ΔG° (kJ/mol) and the Spontaneity verdict.
  5. Use the Kc output to connect to equilibrium analysis — compare to Kc values measured at the same temperature.

Formula & Methodology

Gibbs–Helmholtz equation:

ΔG° = ΔH° − T × ΔS°       (ΔH° in kJ/mol, T in K, ΔS° converted from J/mol·K to kJ/mol·K by ÷ 1000)

Equilibrium constant from ΔG°:

ΔG° = −RT ln(Kc) Kc = exp(−ΔG° × 1000 / (R × T))     [R = 8.314 J/(mol·K)]

Crossover temperature (ΔG = 0):

T_cross = ΔH° / ΔS°     (ΔH° in J/mol, ΔS° in J/mol·K)

Worked example — Haber process for ammonia:

N₂(g) + 3 H₂(g) → 2 NH₃(g): ΔH° = −92.4 kJ/mol, ΔS° = −198.3 J/mol·K

At T = 298 K:
ΔG° = −92.4 − (298 × −0.1983)      = −92.4 + 59.1      = −33.3 kJ/mol   (spontaneous at 298 K) Kc = exp(33,300 / (8.314 × 298)) = exp(13.44) = 6.8 × 10⁵

At T = 773 K (industrial operating temperature):
ΔG° = −92.4 − (773 × −0.1983)      = −92.4 + 153.3      = +60.9 kJ/mol   (non-spontaneous at 773 K under standard conditions) Crossover: T = 92,400 / 198.3 = 466 K

Above 466 K, the Haber process is thermodynamically non-spontaneous under standard conditions — explaining why it is run at high pressure (to shift equilibrium) and uses a catalyst (to achieve acceptable rate at the lower temperatures that are thermodynamically favourable).

Frequently Asked Questions

Gibbs free energy (G) is a thermodynamic state function that combines enthalpy (H) and entropy (S) into a single spontaneity criterion: ΔG = ΔH − TΔS. A negative ΔG means the process is thermodynamically spontaneous under the given conditions — it can occur without input of external energy. A positive ΔG means the process is non-spontaneous. At equilibrium, ΔG = 0. Gibbs free energy was introduced by Josiah Willard Gibbs in 1875 and is the most widely used thermodynamic potential in chemistry.
The standard Gibbs free energy change is ΔG° = ΔH° − TΔS°, where ΔH° is the standard enthalpy change (kJ/mol), T is the absolute temperature in Kelvin, and ΔS° is the standard entropy change (J/mol·K, converted to kJ/mol·K by dividing by 1000). All three quantities must be in consistent units. The non-standard Gibbs free energy is ΔG = ΔG° + RT ln Q, where Q is the reaction quotient.
A negative ΔG means the reaction is spontaneous — it proceeds in the forward direction without external energy input under the specified conditions. This does not necessarily mean the reaction is fast: a large negative ΔG (thermodynamic favourability) says nothing about the activation energy barrier (kinetic barrier). Diamond converting to graphite has ΔG° = −2.9 kJ/mol at room temperature (thermodynamically favourable) yet the rate is immeasurably slow.
At standard conditions, ΔG° = −RT ln(Kc), where R = 8.314 J/(mol·K) and T is in Kelvin. A negative ΔG° gives a Kc greater than 1 (products favoured); a positive ΔG° gives a Kc less than 1 (reactants favoured). At ΔG° = 0, Kc = 1. This relationship directly links thermodynamics to equilibrium: the [Equilibrium Constant Calculator](/equilibrium-constant-calculator/) computes Kc from equilibrium concentrations, while this calculator derives Kc from ΔH° and ΔS°.
The spontaneity depends on the signs of ΔH° and ΔS°: (1) ΔH < 0, ΔS > 0 — spontaneous at all temperatures (always negative ΔG); (2) ΔH > 0, ΔS < 0 — non-spontaneous at all temperatures (always positive ΔG); (3) ΔH < 0, ΔS < 0 — spontaneous at low temperatures but non-spontaneous above a crossover temperature T = ΔH/ΔS; (4) ΔH > 0, ΔS > 0 — non-spontaneous at low temperatures but spontaneous above the crossover temperature. The crossover temperature is where ΔG = 0.
Temperature acts as the weighting factor for entropy in ΔG = ΔH − TΔS. At low temperature, the TΔS term is small and ΔH dominates: exothermic reactions (ΔH < 0) tend to be spontaneous. At high temperature, TΔS is large and ΔS dominates: entropy-increasing reactions (ΔS > 0) tend to be spontaneous. This explains why endothermic reactions like dissolution of some salts become spontaneous only above certain temperatures, and why some exothermic reactions become non-spontaneous at high temperature.
Enter the standard enthalpy change ΔH° in kJ/mol, the standard entropy change ΔS° in J/mol·K, and the temperature T in Kelvin. The calculator computes ΔG° = ΔH° − TΔS° (converting ΔS° from J to kJ internally), reports ΔG° in kJ/mol, derives Kc from ΔG° = −RT ln(Kc), and classifies the reaction as Spontaneous (ΔG < 0), Non-spontaneous (ΔG > 0), or At equilibrium (ΔG = 0).
ΔG° is the Gibbs free energy change under standard conditions (1 bar pressure, specified concentration of 1 mol/L for solutes, at temperature T — usually 298 K). ΔG is the Gibbs free energy change under actual non-standard conditions. They are related by ΔG = ΔG° + RT ln Q. At equilibrium (Q = Kc), ΔG = 0, which gives the fundamental equation ΔG° = −RT ln Kc. Use ΔG° to calculate equilibrium constants and overall thermodynamic favourability; use ΔG to determine spontaneity under specific reaction conditions.
In older NCERT and some state board textbooks in India, Gibbs free energy is sometimes called 'Gibbs energy' or 'free energy', omitting the word 'Gibbs'. The symbol G is universal. The Chapter 6 (Thermodynamics) of NCERT Class 11 Chemistry uses 'Gibbs energy' (ΔG) extensively, and questions on ΔG = ΔH − TΔS appear regularly in CBSE board examinations and JEE Main. The relationship ΔG° = −RT ln K is specifically tested in JEE Advanced.
The crossover temperature is the temperature at which ΔG = 0 — the boundary between spontaneous and non-spontaneous. It is given by T_cross = ΔH° / ΔS° (with both in consistent units, e.g., ΔH in J/mol and ΔS in J/mol·K). Below T_cross, the enthalpy term dominates; above T_cross, the entropy term dominates. For a reaction with ΔH° = −50 kJ/mol and ΔS° = −100 J/mol·K, T_cross = 50,000 / 100 = 500 K — the reaction is spontaneous below 500 K and non-spontaneous above it.
Extensively — Gibbs free energy governs drug solubility, crystallisation, polymorphism, and stability. The thermodynamic driving force for drug dissolution into biological fluids is determined by ΔG_dissolution. Different crystal polymorphs of the same API (active pharmaceutical ingredient) have different ΔG values and therefore different solubility and bioavailability — a critical quality parameter under CDSCO guidelines. Pfizer's sildenafil (Viagra) polymorphism issues and various Indian API manufacturers' polymorph selection processes all ultimately trace back to Gibbs free energy differences between crystal forms.