Change in Gibbs Free Energy: Formula and Meaning

The change in Gibbs free energy is calculated as ΔG = ΔH − TΔS, where enthalpy change and entropy change describe a process and temperature is measured in kelvin. This calculator estimates ΔG from those three inputs and returns the result in joules per mole; a negative value indicates thermodynamic favorability under the stated conditions, not necessarily a fast reaction.

Formula

The standard relation is ΔG = ΔH − TΔS. This calculator reports ΔG in kJ/mol and converts the inputs as follows:

• ΔG is the Gibbs free-energy change, in kJ/mol.
• ΔH is the enthalpy change, entered here in kJ/mol.
• T is absolute temperature in kelvin. For an input in degrees Celsius, the conversion is T = t + 273.15.
• ΔS is the entropy change, entered here in J/(mol·K). To combine it with enthalpy in kJ/mol, the calculator divides TΔS by 1000 because 1000 J = 1 kJ.

Thus the calculator expression is ΔG = ΔH − ((t + 273.15) × ΔS / 1000). The formula assumes that ΔH and ΔS refer to the same process, direction, and amount of substance, and that the values apply at the temperature being considered. If they are standard-state quantities, the result is a standard Gibbs-energy change, conventionally written ΔG°; otherwise it is a Gibbs-energy change for the specified conditions.

Worked Example

Using the calculator defaults, ΔH = −10 kJ/mol, ΔS = 50 J/(mol·K), and t = 25 °C:

1. Convert temperature: T = 25 + 273.15 = 298.15 K.
2. Calculate the entropy term in kJ/mol: TΔS / 1000 = 298.15 × 50 / 1000 = 14.9075 kJ/mol.
3. Subtract the entropy term: ΔG = −10 − 14.9075 = −24.9075 kJ/mol.

Rounded to the calculator’s three decimal places, the result is −24.908 kJ/mol.

Assumptions

• The enthalpy and entropy changes describe the same chemical or physical process and are expressed per mole on the same basis.
• Both values are treated as applicable at the entered temperature. The simple equation does not account for their possible variation with temperature.
• Temperature is converted from Celsius to kelvin using +273.15; the entropy term is converted from joules to kilojoules using /1000.
• The calculation is thermodynamic bookkeeping, not a prediction of reaction speed or a substitute for equilibrium data.

What the Sign of ΔG Tells You

At constant temperature and pressure, a process with ΔG < 0 is thermodynamically favorable in the forward direction as written. If ΔG > 0, the forward direction is unfavorable under those conditions, while the reverse direction is favorable. If ΔG = 0, the system is at equilibrium with respect to that process. These statements describe direction and equilibrium, not how quickly the process occurs.

A reaction can have a negative ΔG and still proceed too slowly to observe without overcoming a substantial activation-energy barrier. A catalyst can speed up the approach to equilibrium, but it does not change the reaction’s ΔG or equilibrium constant at a given temperature. Conversely, a positive ΔG for an isolated step does not rule out its occurrence when it is coupled to another process whose free-energy decrease is larger.

Temperature and Entropy: Why the Result Can Change

The relation makes the role of temperature explicit: the entropy contribution is TΔS. When ΔS is positive, increasing temperature makes the subtracted term larger and tends to lower ΔG. When ΔS is negative, increasing temperature tends to raise ΔG. Enthalpy also matters, so the direction cannot be inferred from entropy or temperature alone.

For example, if ΔH is positive and ΔS is positive, the process may be unfavorable at lower temperatures but favorable above a crossover temperature. Setting ΔG to zero gives T = ΔH/ΔS, provided the units match and ΔH and ΔS remain approximately constant over the relevant range. Convert ΔH to J/mol before dividing by ΔS in J/(mol·K); the resulting temperature is kelvin. This estimate is only as good as the constant-enthalpy and constant-entropy approximation.

Standard and Nonstandard Gibbs Energy

A frequent source of confusion is the difference between ΔG and ΔG°. The standard value applies to substances in their defined standard states. Actual reaction mixtures may have different concentrations or partial pressures, so their Gibbs-energy change can differ. For a reaction under nonstandard conditions:

ΔG = ΔG° + RT ln Q

Here, R = 8.31446261815324 J/(mol·K), T is in kelvin, and Q is the dimensionless reaction quotient constructed using activities (often approximated with concentrations or pressures when appropriate). Do not insert a dimensional concentration directly into a logarithm. At equilibrium, ΔG = 0 and Q = K, yielding ΔG° = −RT ln K. A negative ΔG° therefore corresponds to an equilibrium constant greater than 1 for the reaction as written, but it does not mean every mixture will move forward regardless of its composition.

Common Calculation Mistakes and Limits

• Mixing joules and kilojoules: If ΔH is in kJ/mol and ΔS in J/(mol·K), divide TΔS by 1000, as this calculator does.
• Using Celsius directly: The temperature multiplier must be in kelvin. Add 273.15 to degrees Celsius before calculating TΔS.
• Inconsistent reaction direction: Reversing a reaction reverses the signs of ΔH, ΔS, and ΔG. Keep all values tied to the same written equation.
• Treating favorability as speed: ΔG says nothing by itself about reaction rate or activation energy.
• Applying one temperature’s data everywhere: ΔH and ΔS can change with temperature, especially across phase changes or broad temperature ranges. More detailed thermodynamic data may be needed.

For a reaction in a mixture, ΔH − TΔS using standard values gives ΔG° rather than the actual ΔG unless the conditions match the standard states. Use the reaction-quotient equation when concentration or pressure effects matter. For laboratory work, follow your lab method, the safety data sheet (SDS) and your supervisor.

Frequently Asked Questions

What is the formula for change in Gibbs free energy?
At constant temperature and pressure, use ΔG = ΔH − TΔS. Use kelvin for T and consistent energy units for the enthalpy and entropy terms.

Does negative ΔG mean a reaction happens quickly?
No. Negative ΔG means the forward process is thermodynamically favorable under the specified conditions. The reaction rate depends on kinetic factors, including activation energy.

Can I use Celsius in the Gibbs free-energy formula?
Not directly. Convert Celsius to kelvin by adding 273.15, then use that absolute temperature in TΔS.

What is the difference between ΔG and ΔG°?
ΔG describes a process at its actual conditions. ΔG° is the standard-state value. Their relationship is ΔG = ΔG° + RT ln Q.

When is ΔG equal to zero?
At equilibrium for the process under consideration, ΔG is zero. This means there is no net thermodynamic driving force in either direction, although forward and reverse molecular events can continue.

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in dh | Enthalpy change | kJ/mol | -10 | -
in ds | Entropy change | J/(mol·K) | 50 | -
in t | Temperature | °C | 25 | -273.15
out dg | Gibbs free energy change | kJ/mol | dh - ((t + 273.15) * ds / 1000) | 3