Gibbs Free Energy Calculator

About the Gibbs Free Energy Calculator

Gibbs free energy (G) is the thermodynamic potential that determines whether a process will occur spontaneously at constant temperature and pressure. The change in Gibbs energy, ΔG = ΔH - TΔS, combines the enthalpy change (ΔH) and entropy change (ΔS) into a single criterion: if ΔG < 0, the process is spontaneous; if ΔG > 0, it is non-spontaneous; and if ΔG = 0, the system is at equilibrium.

Named after Josiah Willard Gibbs, this quantity is arguably the most important in chemical thermodynamics. It determines reaction feasibility, phase equilibria, electrochemical cell potentials (ΔG = -nFE°), and the equilibrium constant (ΔG° = -RT ln K). Understanding Gibbs energy allows you to predict which reactions will occur, at what temperatures they become favorable, and how much useful work they can perform.

This calculator computes ΔG from ΔH and ΔS at any temperature, determines the crossover temperature where ΔG changes sign, and relates ΔG° to the equilibrium constant K. It also calculates ΔG°rxn from standard free energies of formation.

When This Page Helps

Gibbs energy calculations require careful attention to units (kJ vs J, K vs °C) and signs. This calculator handles all conversions, determines spontaneity, computes the crossover temperature, and provides the corresponding K value.

How to Use the Inputs

1. Select the calculation mode: ΔG from ΔH and ΔS, or ΔG°rxn from formation data.
2. Enter ΔH in kJ/mol and ΔS in J/(mol·K) for the direct method.
3. Enter the temperature in K (or °C — will be converted).
4. For formation data mode, enter ΔGf° values for products and reactants.
5. Click a preset to load common reaction data.
6. Review ΔG, spontaneity assessment, crossover temperature, and K.
7. Check the temperature profile table to see how ΔG changes with T.

Example Calculation

Tips & Best Practices

• Watch units: ΔH is usually in kJ/mol, but ΔS in J/(mol·K). Convert ΔS to kJ/(mol·K) by dividing by 1000 before using ΔG = ΔH - TΔS.
• Four spontaneity cases: ΔH<0, ΔS>0 → always spontaneous. ΔH>0, ΔS<0 → never spontaneous. Others depend on T.
• At body temperature (310 K), biochemical reactions like ATP hydrolysis have ΔG ≈ -30 kJ/mol.
• ΔG tells you the direction; it does NOT tell you the rate. A thermodynamically favorable reaction can still be slow.
• For electrochemistry: ΔG = -nFE, where n = electrons transferred, F = 96,485 C/mol.
• The maximum non-expansion work obtainable from a process equals -ΔG.

The Four Spontaneity Cases

The sign of ΔG = ΔH - TΔS depends on the signs of ΔH and ΔS. Case 1: ΔH < 0, ΔS > 0 — always spontaneous (exothermic + more disorder). Case 2: ΔH > 0, ΔS < 0 — never spontaneous. Case 3: ΔH < 0, ΔS < 0 — spontaneous at low T (enthalpy-driven). Case 4: ΔH > 0, ΔS > 0 — spontaneous at high T (entropy-driven, like CaCO₃ decomposition).

Gibbs Energy and Coupled Reactions

In biology, unfavorable reactions (ΔG > 0) are driven by coupling them with favorable ones. ATP hydrolysis (ΔG = -30.5 kJ/mol) drives countless otherwise non-spontaneous biochemical processes. The overall ΔG for coupled reactions is the sum of individual ΔG values.

Temperature Dependence and Phase Diagrams

The crossover temperature T_eq = ΔH/ΔS determines phase transition temperatures (melting, boiling) and reaction feasibility boundaries. Phase diagrams are essentially maps of where ΔG changes sign for different phases as functions of T and P.

Frequently Asked Questions

• What is Gibbs free energy?

  Gibbs free energy (G) is a thermodynamic state function that predicts whether a process will occur spontaneously at constant T and P. ΔG < 0 means the process is spontaneous.

• What does ΔG = 0 mean?

  ΔG = 0 means the system is at equilibrium. The forward and reverse processes occur at equal rates, and there is no net change.

• How does temperature affect spontaneity?

  Temperature determines the relative importance of ΔH and TΔS. Endothermic reactions with positive ΔS become spontaneous at high temperatures; exothermic reactions with negative ΔS become spontaneous at low temperatures.

• What is the crossover temperature?

  It's the temperature where ΔG = 0, calculated as T = ΔH/ΔS. Below this temperature, one sign of ΔG dominates; above it, the other does.

• How does ΔG relate to the equilibrium constant?

  ΔG° = -RT ln K. A negative ΔG° means K > 1 (products favored). Every ~5.7 kJ/mol of ΔG° corresponds to about one order of magnitude change in K at 298 K.

• What is the difference between ΔG and ΔG°?

  ΔG° is the free energy change under standard conditions (1 bar, 1 M). ΔG is the actual free energy change: ΔG = ΔG° + RT ln Q, where Q is the reaction quotient.