Gibbs Free Energy Calculator - Predict Spontaneity

Gibbs free energy is a value used in chemistry and physics to predict whether a reaction or process will happen on its own, without outside help. It is written as ΔG and combines a system's heat content with its disorder into one number.

What is Gibbs free energy?

Every chemical reaction either releases or absorbs heat, and either increases or decreases disorder. Gibbs free energy, named after the American scientist Josiah Willard Gibbs, weighs these two effects against each other at a given temperature. The result tells chemists whether a reaction is spontaneous, meaning it can proceed on its own once it starts, or non-spontaneous, meaning it needs a steady input of energy to continue.

Gibbs free energy does not say how fast a reaction goes. A reaction can be spontaneous and still take years, because speed depends on a separate factor called activation energy, not on ΔG.

Gibbs free energy formula

At constant temperature and pressure, the change in Gibbs free energy is ΔG = ΔH − TΔS:

$\Delta G = \Delta H - T \Delta S$

• ΔG — the change in Gibbs free energy
• ΔH — the change in enthalpy, the heat released or absorbed during the process
• T — the absolute temperature, measured in kelvin (K)
• ΔS — the change in entropy, a measure of disorder

This calculator uses kJ/mol for ΔH, kelvin for T, and kJ/(mol·K) for ΔS, so the result comes out in kJ/mol. Many textbooks list entropy in joules instead of kilojoules (J/(mol·K)). To use a textbook value here, divide it by 1000 first — for example, 50 J/(mol·K) becomes 0.050 kJ/(mol·K).

How to calculate Gibbs free energy

1. Find or measure the enthalpy change (ΔH) of the process, in kJ/mol. A negative value means the process releases heat; a positive value means it absorbs heat.
2. Convert the temperature to kelvin if it is not already (K = °C + 273.15). Temperature must be greater than 0 K.
3. Find or measure the entropy change (ΔS), in kJ/(mol·K). A positive value means disorder increases; a negative value means it decreases.
4. Multiply T by ΔS, then subtract that result from ΔH. The answer is ΔG, in kJ/mol.

Worked example

Take the calculator's sample values: ΔH = −100 kJ/mol, T = 298 K, and ΔS = 0.05 kJ/(mol·K).

$\Delta G = -100 - (298 \times 0.05) = -100 - 14.9 = -114.9 \text{ kJ/mol}$

Because ΔG is negative, the process is spontaneous at 298 K.

What does the sign of ΔG mean?

• ΔG < 0 — the process is spontaneous. It can occur without a continuous outside energy source.
• ΔG = 0 — the system is at equilibrium. There is no further net change.
• ΔG > 0 — the process is non-spontaneous. It needs energy input to proceed as written.

Finding the temperature where a reaction becomes spontaneous

Because temperature multiplies ΔS in the formula, a reaction with a positive ΔH and a positive ΔS can switch from non-spontaneous to spontaneous as temperature rises. The switch happens where ΔG = 0, which gives:

$T = \frac{\Delta H}{\Delta S}$

For example, if ΔH = 15.0 kJ/mol and ΔS = 0.050 kJ/(mol·K), the reaction reaches equilibrium at T = 15.0 ÷ 0.050 = 300 K. Below 300 K the reaction is non-spontaneous; above 300 K it becomes spontaneous.

Standard Gibbs free energy (ΔG°)

Standard Gibbs free energy (ΔG°) is the value calculated when reactants and products are in their standard states: 1 bar pressure for gases and 1 M concentration for dissolved substances, often at 298.15 K. It uses the same formula, written ΔG° = ΔH° − TΔS°, with standard enthalpy and entropy values.

ΔG° also links to the equilibrium constant K of a reaction through ΔG° = −RT ln(K), where R is the gas constant, 8.314 J/(mol·K). For conditions away from standard state, the full relationship is ΔG = ΔG° + RT ln(Q), where Q is the reaction quotient.

Where Gibbs free energy is used

• Chemistry: predicting whether a reaction will proceed and choosing conditions that favor the desired product.
• Biochemistry: explaining how cells couple energy-releasing reactions, such as breaking down glucose, to energy-requiring ones, such as building proteins.
• Materials science: predicting which phase of a material, such as solid or liquid, is stable at a given temperature.
• Engineering: designing industrial processes, from metal refining to fuel cells, around favorable energy conditions.

History of Gibbs free energy

Josiah Willard Gibbs (1839–1903), an American scientist, introduced this concept in his paper "On the Equilibrium of Heterogeneous Substances." It appeared in the Transactions of the Connecticut Academy between 1875 and 1878. The work laid the foundation of chemical thermodynamics, but its value was not widely known for years. Its heavy mathematics made it hard for most chemists to read. Wilhelm Ostwald translated it into German, and Henri Le Chatelier translated the first part into French.

Frequently asked questions

What is Gibbs free energy in simple terms? It is a number that tells whether a chemical reaction or physical change can happen by itself. A negative value means it can; a positive value means it needs outside energy.

Can an endothermic reaction be spontaneous? Yes. An endothermic reaction (ΔH > 0) can still be spontaneous if entropy increases enough and the temperature is high enough that TΔS is larger than ΔH, making ΔG negative.

What is the difference between ΔG and ΔG°? ΔG is the free energy change under whatever conditions actually apply. ΔG° is the free energy change under standard conditions: 1 bar pressure, 1 M concentration, and often 298.15 K.

Does a negative ΔG mean a reaction happens quickly? No. ΔG describes whether a reaction is thermodynamically favorable, not how fast it runs. A spontaneous reaction can still be slow if it has a high activation energy.

What units does this calculator use? Enthalpy in kJ/mol, temperature in kelvin, and entropy in kJ/(mol·K). If a source lists entropy in J/(mol·K), divide the value by 1000 before entering it.

How is Gibbs free energy related to equilibrium? At equilibrium, ΔG equals zero. The standard free energy change ΔG° connects to the equilibrium constant K by ΔG° = −RT ln(K).

References

1. OpenStax, Rice University. Chemistry 2e, section 16.4 "Free Energy". OpenStax Chemistry 2e, 16.4 — ΔG = ΔH − TΔS; sign of ΔG and spontaneity; ΔG° = −RT ln K; ΔG = ΔG° + RT ln Q; standard state of 1 bar and 1 M.
2. National Institute of Standards and Technology. CODATA Value: molar gas constant. NIST CODATA molar gas constant — R = 8.314 462 618 J mol⁻¹ K⁻¹ (exact).
3. MacTutor History of Mathematics, University of St Andrews. J Willard Gibbs (1839–1903) – Biography. MacTutor: Josiah Willard Gibbs — Gibbs's birth and death years.
4. Bumstead, H. A. Biographical Sketch, in The Scientific Papers of J. Willard Gibbs, Volume 1 (Longmans, Green, 1906), scanned at the Internet Archive. Scientific Papers of J. Willard Gibbs, Volume 1 — publication of "On the Equilibrium of Heterogeneous Substances" (1875–1878), its slow recognition, and the Ostwald and Le Chatelier translations.