Free Energy Change Calculation: ΔG Formula and Example

Free energy change, ΔG, is calculated from the change in enthalpy and entropy using ΔG = ΔH − TΔS, with temperature in kelvins and consistent energy units. This calculator estimates ΔG from those three inputs and returns the result in joules per mole; a negative value indicates a thermodynamically favorable direction under the stated conditions, not necessarily a fast reaction.

Formula

The Gibbs free-energy change at constant temperature and pressure is ΔG = ΔH − TΔS. In the calculator, ΔG = ΔH − T × ΔS / 1000. ΔG is the Gibbs free-energy change in kJ/mol; ΔH is the enthalpy change in kJ/mol; T is the absolute temperature in kelvins (K); and ΔS is the entropy change in joules per mole per kelvin, J/(mol·K). The factor 1000 converts joules to kilojoules so that the subtraction uses matching units.

For a chemical reaction, these changes are usually molar quantities per mole of reaction as written in the balanced equation. If the supplied ΔH is instead in J/mol, convert it to kJ/mol by dividing by 1000 before using this calculator. Celsius temperatures must be converted to kelvins by adding 273.15.

Worked Example

Using exactly the default inputs, ΔH = −10 kJ/mol, ΔS = 50 J/(mol·K), and T = 298.15 K:

1. Convert the entropy contribution to kilojoules: TΔS / 1000 = 298.15 × 50 / 1000 = 14.9075 kJ/mol.
2. Subtract it from the enthalpy change: ΔG = −10 − 14.9075 = −24.9075 kJ/mol.
3. Rounded to the calculator’s three decimal places, ΔG = −24.908 kJ/mol.

Assumptions

• The input values refer to the same reaction, reaction direction, and stoichiometric basis.
• ΔH and ΔS are treated as constant over the temperature used. This is an approximation if the temperature range is broad or heat capacities change significantly.
• The formula gives a Gibbs-energy change for the conditions represented by the inputs. It does not automatically convert standard-state values to actual mixture conditions.

What Free Energy Change Tells You

Gibbs free energy combines enthalpy, often associated with heat released or absorbed at constant pressure, and entropy, which describes how energy and matter are distributed among accessible states. At constant temperature and pressure, a process that proceeds spontaneously in the forward direction has ΔG < 0. At equilibrium, ΔG = 0 for the actual composition. If ΔG > 0, the forward process is unfavorable under those conditions, while the reverse direction is favorable.

These signs describe thermodynamic direction, not reaction speed. A reaction with a strongly negative ΔG can still proceed extremely slowly if it has a large activation-energy barrier. Catalysts can change reaction rates but do not change the equilibrium free-energy difference between the same initial and final states.

The formula is especially useful when temperature, enthalpy change, and entropy change are known or estimated. It also shows why a reaction’s favorability can depend on temperature: the entropy term is multiplied by T. For example, if both ΔH and ΔS are negative, the enthalpy contribution favors the forward direction, while the entropy contribution opposes it; the balance can change as temperature changes.

Standard and Actual Free Energy

A key distinction is between standard Gibbs free-energy change, ΔG°, and the actual ΔG for a mixture. Standard values use specified standard states. For a reaction at a given temperature, actual free energy is related to the standard value by ΔG = ΔG° + RT ln Q, where R is the gas constant, T is in kelvins, and Q is the dimensionless reaction quotient formed from activities. For ideal dilute solutions, concentrations are sometimes used as approximations to activities, with the standard concentration included to make the quotient dimensionless.

Because Q changes as reactants are consumed and products form, ΔG can change during a reaction even when ΔG° is fixed at a given temperature. At equilibrium, Q equals the equilibrium constant K and ΔG is zero. The relationship then gives ΔG° = −RT ln K. Thus a negative ΔG° indicates that equilibrium favors products relative to the chosen standard states, but it does not mean every starting mixture has a negative actual ΔG.

This calculator uses the direct ΔH − TΔS relation. It does not calculate Q, K, activities, or composition effects. For a nonstandard mixture, use suitable thermodynamic data and the reaction quotient rather than treating ΔG° as the actual free-energy change.

Choosing Inputs and Checking Units

• Use the same reaction basis. If ΔH and ΔS refer to a balanced equation as written, both apply to that equation. Multiplying every reaction coefficient by a factor multiplies ΔH, ΔS, and ΔG by the same factor.
• Use kelvins. A temperature of 25 °C is 298.15 K, not 25 K. Kelvin is required because the entropy term depends on absolute temperature.
• Match energy units. This calculator accepts ΔH in kJ/mol and ΔS in J/(mol·K), then explicitly divides TΔS by 1000. If both inputs are in kJ-based units, do not apply that conversion again.
• Check signs and definitions. Entropy and enthalpy changes are signed changes for the specified process. Reversing a reaction reverses the signs of ΔH, ΔS, and ΔG.

Reported thermodynamic values depend on the substance, phase, concentration, pressure, and reference conditions. Check that data sources describe compatible states and temperatures. Rounding inputs too early can affect the final digits; keep extra precision through the calculation and round the reported result to a precision justified by the data.

Limits and Common Misconceptions

The simple expression assumes ΔH and ΔS do not change appreciably across the temperature considered. If heat-capacity data are important, enthalpy and entropy may need to be adjusted with temperature before calculating ΔG. The equation also does not identify a reaction mechanism, predict a rate, or establish that a process is safe or experimentally practical.

A negative ΔG is often called “spontaneous,” but that word has a specific thermodynamic meaning: the forward direction is favored under the specified conditions. It does not mean the process happens instantly, and it does not mean energy is created. In a closed system moving toward equilibrium, the available Gibbs free energy decreases for a spontaneous change at constant temperature and pressure.

Do not confuse ΔG with ΔG°. The first refers to the actual conditions and composition; the second refers to a defined standard state. Nor should the temperature be inserted in Celsius: doing so can give a numerically plausible but physically incorrect entropy contribution. Where bench work is implied, follow your lab method, the safety data sheet (SDS) and your supervisor.

Frequently Asked Questions

What is the formula for free energy change?
At constant temperature and pressure, ΔG = ΔH − TΔS. Use kelvins and ensure the enthalpy and entropy terms are converted to matching energy units.

What does a negative ΔG mean?
It means the forward change is thermodynamically favorable under the conditions represented by the calculation. It does not establish how quickly the process occurs.

Can I use Celsius in the formula?
No. Convert Celsius to kelvins by adding 273.15. For example, 25 °C is 298.15 K.

Why can ΔG differ from ΔG°?
ΔG° applies to standard states. Actual ΔG also depends on mixture composition through ΔG = ΔG° + RT ln Q.

When is ΔG equal to zero?
At equilibrium, the actual Gibbs free-energy change for the reaction is zero. A standard free-energy change, ΔG°, is not generally zero at equilibrium.

Related

• Moles to Grams Calculator: Mass of a Compound From Moles
• Molecules to Moles Calculator: Divide by the Avogadro Constant
• Mass to Mole Calculator: Grams to Moles From the Molar Mass

in dh | Enthalpy change ΔH | kJ/mol | -10 | -
in ds | Entropy change ΔS | J/(mol·K) | 50 | -
in t | Temperature T | K | 298.15 | 0
out dg | Free energy change ΔG | kJ/mol | dh - t * ds / 1000 | 3