Gibbs Free Energy Calculator
Four calculation modes in one tool: the classic ΔG = ΔH - TΔS formula, reverse-solve for any missing variable, standard Gibbs free energy from the equilibrium constant K, and non-standard ΔG from the reaction quotient Q. Enter values in kelvin, Celsius, or Fahrenheit, and in kJ, J, or kcal.
Formula
Worked example
Ammonia synthesis at 298.15 K: ΔH = -92.2 kJ/mol, ΔS = -198.7 J/(mol·K). Convert ΔS to -0.1987 kJ/(mol·K), so T·ΔS = 298.15 × (-0.1987) = -59.24 kJ/mol. Then ΔG = -92.2 - (-59.24) = -32.96 kJ/mol. Since ΔG is negative, the reaction is spontaneous. The crossover temperature is (-92.2) / (-0.1987) = 464.0 K (190.8 °C): above this, ΔG becomes positive.
What Gibbs free energy tells you
Gibbs free energy, ΔG, is the thermodynamic quantity that decides whether a chemical reaction or physical change can happen on its own at constant temperature and pressure. It balances two competing tendencies: the enthalpy change ΔH, which favours states of lower energy, and the entropy change ΔS, which favours states of greater disorder. The equation ΔG = ΔH - TΔS weighs these against each other, with temperature setting how much the entropy term counts. A negative ΔG marks a spontaneous, energetically favourable process; a positive ΔG marks one that requires energy input; and a value of zero means the system has reached equilibrium with no net driving force in either direction.
Why temperature can flip spontaneity
Because the entropy term is multiplied by temperature, the sign of ΔG often depends on how hot or cold the system is. When ΔH and ΔS have the same sign, the two terms pull ΔG in opposite directions, and there is a crossover temperature, T = ΔH / ΔS, where ΔG equals zero. Below that point one direction is favoured; above it the other takes over. This is why ice melts spontaneously above 0 °C but water freezes spontaneously below it, even though the underlying enthalpy and entropy changes barely move. Keeping units consistent matters: enthalpy is usually tabulated in kJ/mol while entropy is in J/(mol·K), so the entropy figure must be divided by 1000 before the two terms are combined. This calculator handles that conversion automatically regardless of which unit you choose.
Standard free energy and the equilibrium constant
The standard Gibbs free energy ΔG° describes the reaction when every species is in its standard state (pure substances at 1 bar, solutes at 1 mol/L). It is related to the equilibrium constant K by the equation ΔG° = -RT ln K, where R = 8.314 J/(mol·K) is the ideal gas constant. A large K (products strongly favoured at equilibrium) gives a large negative ΔG°, confirming the reaction is thermodynamically downhill. Conversely, a tiny K indicates a large positive ΔG° and almost no product at equilibrium. Use the K mode in this calculator to convert directly between K and ΔG°.
Non-standard conditions and the reaction quotient Q
Real systems rarely operate at standard conditions. The reaction quotient Q measures the current ratio of product to reactant activities. When Q is less than K, the system has not yet reached equilibrium and the forward reaction is still favoured (ΔG < 0). When Q is greater than K, the reverse reaction is favoured (ΔG > 0). The equation ΔG = ΔG° + RT ln Q quantifies this: at equilibrium, Q = K and ΔG = 0 exactly. The Q mode in this calculator lets you enter any current composition and find the actual driving force under those conditions, not just the standard-state tendency.
Reverse-solve modes: finding ΔH, ΔS, or the crossover temperature
Sometimes you know ΔG from experiment and need to extract an unknown enthalpy or entropy. Rearranging ΔG = ΔH - TΔS gives ΔH = ΔG + TΔS and ΔS = (ΔH - ΔG) / T. Both reverse modes are available here. The crossover temperature mode goes one step further: setting ΔG = 0 and solving T = ΔH / ΔS tells you the exact temperature at which the reaction changes from spontaneous to non-spontaneous (or vice versa). This is particularly useful in industrial chemistry and material science where processes must operate within a specific temperature window.
How the signs of ΔH and ΔS control spontaneity
| ΔH | ΔS | Result | Example |
|---|---|---|---|
| Negative | Positive | Spontaneous at all temperatures | Combustion of hydrogen |
| Negative | Negative | Spontaneous below T_c | Ammonia synthesis (T_c ≈ 464 K) |
| Positive | Positive | Spontaneous above T_c | Dissolving ammonium nitrate |
| Positive | Negative | Never spontaneous | Ozone from O2 at standard state |
The combination of enthalpy and entropy signs determines when ΔG is negative. T_c is the crossover temperature = ΔH / ΔS.
Frequently asked questions
What does a negative ΔG mean?
A negative ΔG means the forward reaction is spontaneous at the given temperature and pressure: it can proceed without continuous outside energy. It describes feasibility and direction, not how fast the reaction goes. A favourable reaction can still be extremely slow if the activation energy is high.
Why is temperature entered in kelvin?
The Gibbs equation requires an absolute temperature, and only the kelvin scale starts at absolute zero with no negative values. This calculator accepts Celsius and Fahrenheit and converts them automatically, so you can enter 25 °C and get the same result as entering 298.15 K.
What is the difference between ΔG and ΔG°?
ΔG° is the standard Gibbs free energy, calculated when all species are in their standard states (1 bar or 1 mol/L). It is a fixed property of a reaction at a given temperature, related to the equilibrium constant by ΔG° = -RT ln K. ΔG is the actual free energy change under current (possibly non-standard) conditions, calculated as ΔG = ΔG° + RT ln Q where Q is the reaction quotient reflecting the real composition.
How do I find the temperature where a reaction switches from spontaneous to non-spontaneous?
Set ΔG = 0 in the equation ΔG = ΔH - TΔS and solve for T to get T = ΔH / ΔS. This crossover temperature is the point where the enthalpy and entropy contributions exactly cancel. Use the "Solve for crossover T" mode in this calculator, or read the crossover temperature directly from the standard mode output.
What units can I enter for ΔH and ΔS?
This calculator accepts enthalpy in kJ/mol, J/mol, kcal/mol, or cal/mol. Entropy can be entered in J/(mol·K), kJ/(mol·K), cal/(mol·K), or kcal/(mol·K). All values are converted to a common kJ/mol scale before the calculation, so the unit combination you choose does not affect the result.
Can I solve for ΔH or ΔS instead of ΔG?
Yes. Use the "Solve for ΔH" or "Solve for ΔS" modes. These rearrange the Gibbs equation algebraically: ΔH = ΔG + TΔS and ΔS = (ΔH - ΔG) / T. Enter the three known quantities and the calculator returns the fourth.