Gibbs Free Energy Calculators

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Gibbs free energy (G) is a thermodynamic potential that predicts whether a process will occur spontaneously at constant temperature and pressure: ΔG = ΔH − TΔS. When ΔG < 0, the process is spontaneous (exergonic); when ΔG > 0, it is non-spontaneous (endergonic) and requires energy input; when ΔG = 0, the system is at equilibrium. In biochemistry, Gibbs free energy drives metabolic reactions — cells use exergonic reactions (like ATP hydrolysis) to power endergonic reactions (like biosynthesis) through coupled reactions. The actual ΔG under cellular conditions often differs significantly from the standard ΔG°.

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ΔG Formula

ΔG = ΔH − TΔS

ΔH = enthalpy change; T = absolute temperature (K); ΔS = entropy change. ΔG < 0: spontaneous (exergonic). ΔG > 0: non-spontaneous (endergonic). ΔG = 0: equilibrium.

Standard Free Energy and Equilibrium

ΔG° = −RT ln(Keq)

R = 8.314 J/mol/K; T = 298 K (25°C). Keq > 1: ΔG° < 0 (products favored). At 25°C: every 5.7 kJ/mol change in ΔG° changes Keq by 10-fold.

Actual ΔG vs. Standard ΔG°

ΔG = ΔG° + RT ln(Q)

Q = reaction quotient (product of concentrations/reactant concentrations). In the cell: actual concentrations differ from standard (1 M). ATP hydrolysis: ΔG° = −30.5 kJ/mol; actual ΔG ≈ −50 to −60 kJ/mol in cells (due to low ADP/ATP ratio and Pi in cytoplasm).

Coupled Reactions in Biochemistry

Cells couple exergonic reactions (ΔG < 0) to endergonic reactions (ΔG > 0) by sharing a common intermediate: Glucose-6-phosphate synthesis: glucose + Pi → G6P + H₂O; ΔG° = +13.8 kJ/mol. ATP hydrolysis: ATP → ADP + Pi; ΔG° = −30.5 kJ/mol. Coupled: glucose + ATP → G6P + ADP; ΔG° = +13.8 + (−30.5) = −16.7 kJ/mol (spontaneous). ATP coupling makes biochemically unfavorable reactions thermodynamically possible.

Glossary

Gibbs Free Energy (ΔG)
ΔH − TΔS; the thermodynamic criterion for spontaneity at constant T and P; ΔG < 0 = exergonic (spontaneous); ΔG > 0 = endergonic; ΔG = 0 = equilibrium; ΔG° = −RT ln(Keq).
Coupled Reactions
Biochemical strategy linking exergonic reactions (ATP hydrolysis, ΔG < 0) to endergonic biosynthetic reactions (ΔG > 0) via shared intermediates; enables thermodynamically unfavorable reactions to proceed.
Standard Free Energy (ΔG°)
The free energy change under standard conditions (1 M, 25°C, pH 7 in biochemistry); fixed for a given reaction; related to equilibrium by ΔG° = −RT ln(Keq); actual ΔG depends on real concentrations.

Frequently Asked Questions

Gibbs free energy (G) is a thermodynamic potential combining enthalpy and entropy: ΔG = ΔH − TΔS. Spontaneity criteria at constant T and P: ΔG < 0: spontaneous (exergonic); system releases usable energy. ΔG > 0: non-spontaneous (endergonic); requires energy input. ΔG = 0: equilibrium; no net reaction. ΔG is more useful than ΔH alone (which doesn't account for entropy) and more directly relevant to chemistry and biology than ΔS alone. ΔH − TΔS accounts for both the energy content of bonds and the thermodynamic favorability of increasing molecular disorder.

ΔG° = −RT ln(Keq). R = 8.314 J/mol·K; T = temperature in Kelvin. Relationships: Keq = 1 → ΔG° = 0 (products and reactants equally favored). Keq > 1 → ΔG° < 0 (products thermodynamically favored). Keq < 1 → ΔG° > 0 (reactants favored). At 25°C (298 K): ΔG° = −5.7 kJ/mol corresponds to Keq = 10 (10-fold products). Each 5.7 kJ/mol change shifts Keq by 10-fold. ATP hydrolysis: ΔG° = −30.5 kJ/mol; Keq = e^(30,500/8.314/298) = e^12.3 = 2.2 × 10⁵ (strongly favoring ADP + Pi).

ATP hydrolysis: ATP + H₂O → ADP + Pi; ΔG° = −30.5 kJ/mol; actual ΔG ≈ −50 to −60 kJ/mol under cellular conditions (low [ADP], [Pi]). Cells use this exergonic reaction to drive endergonic (biosynthetic) reactions by coupling: the 'coupling' usually involves covalent intermediates where ATP phosphorylates a substrate first, making it reactive. Example: Amino acid activation for protein synthesis: amino acid + ATP → aminoacyl-AMP + PPi; ΔG° ≈ −30 kJ/mol (driven by ATP hydrolysis to AMP + PPi). Pyrophosphate (PPi) is rapidly hydrolyzed by pyrophosphatase (PPi → 2 Pi; ΔG° = −33.5 kJ/mol) — driving the reaction even further toward completion. This double coupling explains how cells efficiently drive thermodynamically difficult biosynthetic reactions.

ΔG°: standard free energy change under standard conditions (1 M concentrations of all reactants and products, 25°C, 1 atm, pH 7 in biochemistry). It is a fixed constant for a given reaction. ΔG: the actual free energy change under the real conditions in the system. ΔG = ΔG° + RT ln(Q), where Q = reaction quotient (current concentration ratio). When Q < Keq: ΔG < ΔG° — reaction is pulled forward. When Q > Keq: ΔG > ΔG° — reaction is pushed backward. At equilibrium: Q = Keq and ΔG = 0. Biological significance: metabolic reactions rarely occur at standard conditions — the actual ΔG in the cell depends on substrate and product concentrations maintained by metabolism. Cells regulate metabolite concentrations to keep ΔG favorable for their energy needs.