This Gibbs free energy calculator computes ΔG = ΔH − TΔS to predict reaction spontaneity at any temperature, converts between ΔG° and the equilibrium constant K using ΔG° = −RT × ln K, finds ΔG from electrochemical cell voltages via ΔG = −nFE, and calculates ΔG° from standard Gibbs energies of formation — with complete step-by-step working and interactive free energy diagrams. Use this delta G calculator for any thermodynamics problem.

Gibbs Free Energy — ΔG = ΔH − TΔS

Gibbs free energy (G) is the thermodynamic potential that determines whether a chemical reaction or physical process at constant temperature and pressure is spontaneous. The change in Gibbs free energy, written ΔG = ΔH − TΔS, balances two competing thermodynamic driving forces: enthalpy (ΔH — the heat released or absorbed) and entropy (ΔS — the change in disorder), weighted by the absolute temperature T in Kelvin.

The spontaneity rules from ΔG = ΔH − TΔS are:

• ΔG < 0 (negative ΔG): Spontaneous — the forward reaction proceeds without external energy input. A negative delta G means the products are thermodynamically more stable than the reactants at that temperature. The reaction releases free energy.
• ΔG > 0 (positive ΔG): Non-spontaneous — the forward reaction is not thermodynamically favorable. A positive delta G means the reverse reaction is spontaneous instead. External energy must be supplied to drive the reaction forward.
• ΔG = 0: The system is at equilibrium — no net reaction occurs in either direction.

The formula ΔG = ΔH − TΔS is named after Josiah Willard Gibbs, who developed it in the 1870s. It defines the standard free energy change ΔG° when conditions are standard (298.15 K, 1 atm, 1 M concentrations). Under non-standard conditions, ΔG (without the degree symbol) depends on the actual concentrations via ΔG = ΔG° + RT ln Q.

Standard Free Energy of Formation — ΔGf° Tables

The standard Gibbs free energy of formation (ΔGf°) is defined as the change in Gibbs free energy when exactly 1 mole of a compound is formed from its constituent elements in their standard states at 298.15 K and 1 atm. The standard Gibbs free energy of formation table allows calculating ΔG° for any reaction directly, without needing separate ΔH° and ΔS° values.

Key rules for the standard Gibbs free energy of formation:

• Elements in their standard state (H₂(g), O₂(g), C(graphite), Fe(s), etc.) have ΔGf° = 0 by definition.
• Non-standard allotropes do NOT have ΔGf° = 0 — for example, C(diamond) has ΔGf° = +2.900 kJ/mol.
• The standard Gibbs free energy of formation table gives values at exactly 298.15 K. Temperature dependence requires recalculating using ΔG° = ΔH° − TΔS°.

Spontaneity — The Four Cases of ΔH and ΔS

The spontaneity chart captures all four sign combinations of ΔH and ΔS in the formula ΔG = ΔH − TΔS. Understanding these four cases is essential for predicting whether a reaction is spontaneous, non-spontaneous, or temperature-dependent.

The crossover temperature (where ΔG = 0 and spontaneity switches) is found by setting ΔG = ΔH − TΔS = 0:

Key interpretations of the spontaneity chart:

• Always spontaneous (ΔH < 0, ΔS > 0): Both enthalpy release and entropy increase drive the reaction forward at all temperatures. Example: 2H₂(g) + O₂(g) → 2H₂O(l), ΔG = −237 kJ/mol.
• Spontaneous at low T only (ΔH < 0, ΔS < 0): Enthalpy wins at low temperature, but as T increases, the −TΔS term (which is positive since ΔS < 0) grows until it exceeds ΔH. Non-spontaneous reaction sets in above T_cross. Example: Haber process N₂+3H₂→2NH₃.
• Spontaneous at high T only (ΔH > 0, ΔS > 0): Endothermic reactions can be spontaneous when TΔS exceeds ΔH. Example: CaCO₃(s)→CaO(s)+CO₂(g), spontaneous above ~840°C.
• Never spontaneous (ΔH > 0, ΔS < 0): Both enthalpy and entropy oppose the reaction. ΔG is always positive at all temperatures. The reverse reaction is always spontaneous instead.

Can endothermic reactions be spontaneous? Yes — when ΔS > 0 and temperature is high enough that TΔS > ΔH. Dissolving NaCl in water is a perfect example: ΔH = +3.88 kJ/mol (endothermic) but ΔS = +43.4 J/mol·K (entropy-driven), giving ΔG = −9.05 kJ/mol at 298 K — spontaneous because entropy dominates. If entropy is positive (ΔS > 0), the reaction becomes more spontaneous as temperature increases.

ΔG° and Equilibrium Constant K — ΔG° = −RT ln K

The standard Gibbs free energy change ΔG° is directly and quantitatively connected to the equilibrium constant K through the fundamental equation ΔG° = −RT × ln K, one of the most important relationships in physical chemistry. This equation, sometimes written ΔG° = −RT ln K or delta G RT ln K, allows chemists to predict equilibrium positions from thermodynamic data and vice versa.

The relationship between ΔG° = −RT ln K and equilibrium position:

• ΔG° < 0: K > 1 — products are favored at equilibrium. The more negative ΔG°, the larger K. At ΔG° = −RT ln K gives K = e^(+|ΔG°|/RT).
• ΔG° > 0: K < 1 — reactants are favored at equilibrium. Non-spontaneous under standard conditions.
• ΔG° = 0: K = 1 — equal concentrations of reactants and products at equilibrium.

The non-standard Gibbs free energy ΔG (without degree symbol) uses the reaction quotient Q:

ΔG and Electrochemistry — ΔG = −nFE

The Gibbs free energy provides the fundamental link between thermodynamics and electrochemistry through the equation ΔG = −nFE_cell, where n is the number of moles of electrons transferred, F = 96,485 C/mol is Faraday's constant, and E_cell is the cell voltage. This equation ΔG = −nFE is one of the most important in electrochemical thermodynamics.

The sign relationship in ΔG = −nFE governs cell spontaneity:

• E_cell > 0 → ΔG < 0 → Spontaneous: A positive cell voltage means the reaction is spontaneous — the cell operates as a galvanic (voltaic) cell, generating electrical energy from chemical energy.
• E_cell < 0 → ΔG > 0 → Non-spontaneous: A negative cell voltage means the reaction requires electrical energy input — this is an electrolytic cell.
• E_cell = 0 → ΔG = 0: The cell is at equilibrium — dead battery condition.

Free Energy Diagrams — Visualizing ΔG

A free energy diagram (Gibbs free energy diagram) plots the Gibbs free energy G on the vertical axis against the reaction coordinate on the horizontal axis. The Gibbs free energy graph shows reactants at the left, products at the right, and an activation energy barrier (transition state hump) in the middle.

• The height difference between reactants and products = ΔG (thermodynamics — tells you IF the reaction is spontaneous)
• The height of the hump = E_a (activation energy — kinetics, tells you HOW FAST the reaction goes)
• Spontaneous reaction (ΔG < 0): Products are lower on the free energy diagram — the arrow points downward from reactants to products.
• Non-spontaneous reaction (ΔG > 0): Products are higher on the free energy diagram — the arrow points upward.

The ΔG vs temperature graph — plotting ΔG = ΔH − TΔS as a linear function of T — is perhaps the most instructive visualization in thermodynamics. The slope of the line equals −ΔS, the y-intercept equals ΔH, and the line crosses zero at T_cross = ΔH×1000/ΔS. This single straight line encodes all four cases of the spontaneity chart simultaneously, making the abstract become geometric.

Standard Entropy — ΔS° Values and Tables

The standard molar entropy S° is the absolute entropy of 1 mole of a substance at 298.15 K and 1 atm. Unlike standard enthalpies and standard Gibbs free energies of formation, elements do NOT have S° = 0. This follows from the Third Law of Thermodynamics: only a perfect crystal at 0 K has zero entropy.

Rules for predicting the sign of ΔS° (without looking up the standard entropy table):

• Gases have much higher S° than liquids, which have higher S° than solids: S°(H₂O(g)) = 188.83 vs S°(H₂O(l)) = 69.95 J/mol·K — a difference of 119 J/mol·K just from phase change.
• More moles of gas on product side → ΔS > 0 (entropy increases). Reactions producing gas from solids/liquids always have large positive ΔS°.
• Larger, more complex molecules have higher S°: C₃H₈(g): 270.20 vs CH₄(g): 186.26 J/mol·K — more atoms = more ways to store energy.
• Dissolution of ionic solids usually increases entropy (ions in solution have more freedom than a crystal lattice).

Reading the Gibbs Free Energy Tables

The Gibbs free energy table (ΔGf° values), the standard entropy table (S° values), and the standard enthalpies of formation table (ΔHf° values) are the three essential thermodynamic data tables in chemistry. Using them correctly allows you to calculate ΔG° for any reaction without running experiments.

Two equivalent methods to find ΔG° — they should give the same answer (small differences arise from rounding in tabulated values):

Why do the two methods give slightly different ΔG° values? The standard Gibbs free energy of formation table values (ΔGf°) are measured directly and precisely. The ΔH° and ΔS° values are also measured independently. Both sets of data carry experimental uncertainties, and the tables use slightly different reference conditions. Small discrepancies (typically <1 kJ/mol) are normal and expected.

Common Mistakes in Gibbs Free Energy Problems

Worked Examples — 8 Complete Problems

Frequently Asked Questions

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