Gibbs Free Energy Calculator
Compute gibbs energy using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
deltaG = deltaH - T * deltaS
Where deltaG is the Gibbs free energy change (kJ/mol), deltaH is the enthalpy change (kJ/mol), T is absolute temperature (Kelvin), and deltaS is the entropy change (J/mol*K). A negative deltaG indicates a spontaneous process.
Worked Examples
Example 1: Combustion of Methane at 298 K
Problem:Calculate deltaG for CH4 combustion: deltaH = -890.3 kJ/mol, deltaS = -242.0 J/(mol*K), T = 298.15 K.
Solution:deltaG = deltaH - T * deltaS\ndeltaG = -890.3 - (298.15)(-242.0/1000)\ndeltaG = -890.3 - (-72.15)\ndeltaG = -890.3 + 72.15\ndeltaG = -818.15 kJ/mol\n\nSince deltaG < 0, the reaction is spontaneous.\nK = exp(-deltaG / RT) = exp(818150 / (8.314 * 298.15)) = extremely large
Result:deltaG = -818.15 kJ/mol (Spontaneous) | K is astronomically large
Example 2: Equilibrium Temperature for CaCO3 Decomposition
Problem:CaCO3 -> CaO + CO2: deltaH = +178.3 kJ/mol, deltaS = +160.5 J/(mol*K). At what temperature is this spontaneous?
Solution:At equilibrium: deltaG = 0\n0 = deltaH - T*deltaS\nT = deltaH / deltaS = 178.3 / (160.5/1000)\nT = 178.3 / 0.1605 = 1110.9 K = 837.8 C\n\nAbove 1111 K, the reaction is spontaneous.
Result:Equilibrium temperature: 1110.9 K (837.8 C) | Spontaneous above this temperature
Frequently Asked Questions
What is Gibbs free energy and why is it important?
Gibbs free energy (G) is a thermodynamic potential that determines whether a process will occur spontaneously at constant temperature and pressure. The change in Gibbs free energy, deltaG = deltaH - T*deltaS, combines both the enthalpy change (heat absorbed or released) and the entropy change (disorder) into a single criterion for spontaneity. If deltaG is negative, the reaction proceeds spontaneously in the forward direction. If positive, the reverse reaction is favored. If zero, the system is at equilibrium. Gibbs free energy is arguably the most important quantity in chemical thermodynamics because it directly predicts reaction feasibility under the conditions most commonly encountered in chemistry and biology.
What is the relationship between Gibbs free energy and equilibrium constant?
Gibbs free energy is directly related to the equilibrium constant through the equation deltaG_standard = -RT * ln(K), where R is the gas constant (8.314 J/mol*K) and K is the equilibrium constant. A large negative deltaG means a very large K (products strongly favored at equilibrium). A large positive deltaG means a very small K (reactants favored). When deltaG = 0, K = 1 and products and reactants are present in equal thermodynamic amounts. This relationship is fundamental to predicting the extent of chemical reactions and is used extensively in biochemistry to understand metabolic pathways, where coupled reactions with negative deltaG drive otherwise unfavorable reactions forward.
How does temperature affect Gibbs free energy?
Temperature appears explicitly in the Gibbs equation as the coefficient of the entropy term: deltaG = deltaH - T*deltaS. As temperature increases, the entropy contribution becomes more important. For reactions with positive deltaS (increasing disorder), higher temperatures make deltaG more negative, favoring spontaneity. For reactions with negative deltaS, higher temperatures make deltaG more positive, disfavoring the reaction. The crossover temperature where deltaG = 0 can be calculated as T = deltaH/deltaS. This temperature dependence explains many natural phenomena, such as why ice melts above 273 K (positive deltaS makes the process spontaneous) and why proteins denature at high temperatures (the entropy gain of unfolding overcomes the enthalpy of hydrogen bonds).
How do living cells use Gibbs free energy to power unfavorable reactions?
Many essential biochemical reactions, like building a protein from amino acids, have a positive deltaG on their own and would never occur spontaneously. Cells solve this by coupling those reactions to ATP hydrolysis, which has a strongly negative deltaG (about -30.5 kJ/mol under cellular conditions); combining the two reactions gives a net negative deltaG for the pair, making the overall coupled process spontaneous. This deltaG-coupling strategy is the thermodynamic basis of nearly all biosynthesis, active transport across cell membranes, and muscle contraction.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy