-40.37
kJ/mol
-59.63
kJ/mol
500
K
0.4037
1
-40.37
kJ/mol
-59.63
kJ/mol
500
K
0.4037
1
The Gibbs Free Energy Calculator determines whether a process or chemical reaction occurs spontaneously at given conditions. Gibbs free energy, denoted $$G$$, is the most important thermodynamic potential for systems at constant temperature and pressure—precisely the conditions under which most chemical reactions and biological processes occur.
The Gibbs free energy change is defined as: $$\Delta G = \Delta H - T\Delta S$$ where $$\Delta H$$ is the enthalpy change (heat of reaction), $$T$$ is the absolute temperature, and $$\Delta S$$ is the entropy change. The sign of $$\Delta G$$ determines spontaneity:
Named after Josiah Willard Gibbs, this quantity elegantly balances two competing thermodynamic drives: the tendency toward minimum energy (favored by negative ΔH) and the tendency toward maximum disorder (favored by positive ΔS). Temperature acts as a weighting factor for the entropy contribution—at high temperatures, the TΔS term dominates, and entropy-driven processes become more favorable.
Gibbs free energy is indispensable in chemistry, biochemistry, materials science, and chemical engineering. It predicts reaction spontaneity, determines equilibrium constants through $$\Delta G^\circ = -RT\ln K$$, governs electrochemical cell voltages via $$\Delta G = -nFE$$, and controls phase transitions. In biochemistry, ATP hydrolysis (ΔG = −30.5 kJ/mol) drives virtually all cellular energy-requiring processes.
This calculator allows you to quickly determine spontaneity by entering the enthalpy change, temperature, and entropy change. The results include ΔG in both joules and kilojoules, the magnitude of the TΔS term, and a clear spontaneity indicator. It is valuable for chemistry students, researchers planning reactions, and engineers evaluating process feasibility.
The Gibbs free energy calculator applies the fundamental Gibbs equation:
$$\Delta G = \Delta H - T\Delta S$$
where:
Spontaneity Criteria:
$$\Delta G < 0 \Rightarrow \text{Spontaneous (favorable)}$$
$$\Delta G = 0 \Rightarrow \text{Equilibrium}$$
$$\Delta G > 0 \Rightarrow \text{Non-spontaneous (unfavorable)}$$
The four possible combinations of ΔH and ΔS signs determine temperature dependence: (1) ΔH < 0, ΔS > 0: always spontaneous; (2) ΔH > 0, ΔS < 0: never spontaneous; (3) ΔH < 0, ΔS < 0: spontaneous at low T; (4) ΔH > 0, ΔS > 0: spontaneous at high T.
The primary result, ΔG, tells you whether the process is thermodynamically favorable. A large negative ΔG (e.g., −200 kJ) indicates a strongly spontaneous process, while a large positive ΔG (e.g., +150 kJ) means the process requires significant energy input. The TΔS term shows how much the entropy change contributes to the free energy balance. When |TΔS| is much larger than |ΔH|, the process is entropy-driven; when |ΔH| dominates, it is enthalpy-driven. Note that 'spontaneous' means thermodynamically favorable, not necessarily fast—diamond converting to graphite has ΔG < 0 but is kinetically so slow as to be unobservable at room temperature.
Inputs
Results
Methane combustion: CH₄ + 2O₂ → CO₂ + 2H₂O. With ΔH = −890.4 kJ and ΔS = −242.8 J/K, ΔG = −818 kJ at 298 K. Strongly spontaneous despite the entropy decrease, because the large exothermic enthalpy dominates.
Inputs
Results
NH₄NO₃ dissolving in water is endothermic (ΔH = +25.7 kJ) but has a large entropy increase (ΔS = +108.7 J/K). At 298 K, TΔS = 32.4 kJ exceeds ΔH, giving ΔG = −6.7 kJ. The dissolution is spontaneous, driven by the entropy increase of ions dispersing in water.
Gibbs free energy represents the maximum amount of non-expansion work (useful work) that can be extracted from a system at constant temperature and pressure. For a chemical reaction, |ΔG| is the maximum useful work obtainable (if ΔG < 0) or the minimum work that must be supplied (if ΔG > 0). In electrochemistry, this appears directly as electrical work: ΔG = −nFE, where n is the number of electrons transferred, F is Faraday's constant, and E is the cell voltage.
No. Spontaneous (ΔG < 0) means thermodynamically favorable, not fast. The rate of a reaction depends on kinetics (activation energy, catalysts), not thermodynamics. Diamond converting to graphite has ΔG < 0 at standard conditions, but the rate is essentially zero at room temperature because the activation energy barrier is enormous. A catalyst can speed up a spontaneous reaction but cannot make a non-spontaneous reaction occur.
Temperature determines the relative importance of ΔH and TΔS in the Gibbs equation. For reactions with ΔH > 0 and ΔS > 0 (endothermic, entropy increase), increasing temperature favors spontaneity because TΔS eventually exceeds ΔH. The crossover temperature is T = ΔH/ΔS. For reactions with ΔH < 0 and ΔS < 0, they become non-spontaneous above T = ΔH/ΔS. This explains why some reactions are spontaneous only at high or low temperatures.
At equilibrium, ΔG = 0. The standard Gibbs energy relates to the equilibrium constant through ΔG° = −RT ln K. A large negative ΔG° means K >> 1 (products favored at equilibrium). A large positive ΔG° means K << 1 (reactants favored). At non-standard conditions, ΔG = ΔG° + RT ln Q, where Q is the reaction quotient. The reaction proceeds spontaneously until Q = K and ΔG = 0.
Be careful with units! ΔH is often tabulated in kJ/mol while ΔS is in J/(mol·K). You must use consistent units—either convert ΔH to J (multiply kJ by 1000) or convert ΔS to kJ/K (divide J/K by 1000) before applying ΔG = ΔH − TΔS. This calculator uses joules for ΔH and J/K for ΔS. Common mistake: using ΔH in kJ and ΔS in J/K gives results that are off by a factor of 1000.
The standard Gibbs free energy of formation (ΔG°_f) is the free energy change when one mole of a compound is formed from its constituent elements in their standard states at 1 bar and 25°C. By convention, ΔG°_f = 0 for elements in their most stable form. For any reaction, ΔG°_rxn = Σ ΔG°_f(products) − Σ ΔG°_f(reactants). This allows calculation of reaction spontaneity from tabulated data without knowing ΔH and ΔS separately.
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