Gibbs Free Energy Calculator

At a glance:Gibbs free energy (symbol G) is the core criterion in thermodynamics for judging 'whether a chemical reaction or physical process will proceed spontaneously at constant temperature and pressure', proposed by the American scientist J. W. Gibbs. In practice we care about the free-energy change ΔG before and after the reaction, defined by ΔG = ΔH − T·ΔS, where ΔH is the enthalpy change (reflecting heat release/absorption, unit kJ/mol), T is the absolute temperature (Kelvin K), and ΔS is the entropy change (reflecting the change in disorder, unit J/(mol·K)). Note that ΔH and ΔS use different units (one kJ, one J), so before calculating ΔS must be converted to kJ/(mol·K) (divide by 1000); this calculator does that automatically. The sign of ΔG directly tells us the spontaneous direction: when ΔG < 0 the reaction is spontaneous at that temperature (exergonic, proceeds forward); when ΔG = 0 the system is at equilibrium with equal forward and reverse rates; when ΔG > 0 the forward reaction is non-spontaneous (requires external energy input), and the reverse is spontaneous. This formula captures the essence of the second law of thermodynamics: whether a process is spontaneous depends on the competition between the 'energy factor (ΔH)' and the 'disorder factor (TΔS)'. Exothermic reactions (ΔH < 0) and entropy-increasing reactions (ΔS > 0) both favour spontaneity (making ΔG smaller); endothermic (ΔH > 0) and entropy-decreasing (ΔS < 0) reactions disfavour it. In particular, temperature T is the weight of the entropy term: the higher the temperature, the greater the effect of the entropy change on ΔG. Using this tool's default (approximate combustion of hydrogen to liquid water): ΔH = −285.8 kJ/mol (strongly exothermic), ΔS = −163.2 J/(mol·K) (gas to liquid, entropy decreases), at T = 298 K (25°C), ΔG = −285.8 − 298 × (−0.1632) = −285.8 + 48.63 ≈ −237.2 kJ/mol < 0, so the reaction is highly spontaneous at room temperature. From the four combinations of ΔH, ΔS signs we can judge how spontaneity varies with temperature: (1) ΔH<0, ΔS>0: spontaneous at any temperature (ΔG always negative); (2) ΔH>0, ΔS<0: non-spontaneous at any temperature; (3) ΔH<0, ΔS<0: spontaneous at low temperature, non-spontaneous at high (e.g. freezing, exothermic polymerisation); (4) ΔH>0, ΔS>0: spontaneous at high temperature, non-spontaneous at low (e.g. ice melting, most decomposition reactions). For the last two there is a 'transition temperature' T = ΔH/ΔS (where ΔG = 0), past which the spontaneous direction reverses. Gibbs free energy has very broad uses: judging reaction feasibility, predicting direction, computing equilibrium constants from ΔG° (ΔG° = −RT ln K), linking cell potential in electrochemistry via ΔG = −nFE, and analysing spontaneity of phase changes and dissolution. When using it note: first, convert temperature to Kelvin. Second, do not mix the units of ΔH and ΔS (kJ vs J) — this calculator handles the conversion. Third, ΔG < 0 only means 'thermodynamically possibly spontaneous', not necessarily fast — reaction rate is set by activation energy and kinetics, a different level (e.g. diamond turning to graphite has ΔG<0 yet is extremely slow). In short, this calculator lets you quickly find ΔG from ΔH, T, ΔS and judge spontaneity — an indispensable tool in chemical thermodynamics.