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Gibbs Free Energy Calculator

Calculate the Gibbs free energy: ΔG° from an equilibrium constant, K from ΔG°, ΔG from ΔH and ΔS, and ΔG for a reaction quotient Q, at your chosen temperature.

Formula

ΔG∘=−RTln⁡K\Delta G^\circ = -RT\ln K
K=exp⁡ ⁣(−ΔG∘RT)K = \exp\!\left(\dfrac{-\Delta G^\circ}{RT}\right)
ΔG=ΔH−TΔS\Delta G = \Delta H - T\Delta S
ΔG=ΔG∘+RTln⁡Q\Delta G = \Delta G^\circ + RT\ln Q
RR
gas constant, 8.314462618 J/(mol·K)
TT
absolute temperature, in kelvin
QQ
reaction quotient: products over reactants at the current concentrations

How it works

The Gibbs free energy change tells whether a reaction can proceed spontaneously at constant temperature and pressure: a negative ΔG favours the reaction as written. The standard value ΔG° is for all species at the standard state (1 M for solutes) and is tied to the equilibrium constant, ΔG° = −RT ln K, so a tenfold change in K changes ΔG° by about 5.7 kJ/mol at 25 °C.

Under other conditions ΔG = ΔG° + RT ln Q, and ΔG is zero when Q equals K, at equilibrium. The other route is ΔG = ΔH − TΔS, the balance of the enthalpy and entropy changes. A negative ΔG says a reaction is thermodynamically favourable; it says nothing about how fast it goes.

Worked example

An association with K = 10⁵ at 25 °C.

  1. T = 298.15 K, R = 8.314 J/(mol·K).
  2. ΔG° = −8.314 × 298.15 × ln(10⁵) = −28,540 J/mol.

ΔG° = −28.54 kJ/mol, which is −6.82 kcal/mol.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • Constant temperature and pressure, with ideal behaviour of the solutes.
  • For ΔH − TΔS, that ΔH and ΔS do not change with temperature, which fails when the heat capacity change is large.
  • K for the reaction as written; reversing the reaction inverts K and changes the sign of ΔG°.

Common mistakes

  • Mixing kJ and kcal (1 kcal = 4.184 kJ) or using Celsius temperatures in RT.
  • Reading a negative ΔG as a fast reaction.
  • Using ΔG° where the conditions are far from standard, for example a cell with different concentrations, without correcting with Q.

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