Gibbs Free Energy Equation Units and Calculator

This calculator finds the Gibbs free energy change, ΔG, from enthalpy change, ΔH, temperature, and entropy change, ΔS. Enter ΔH in kJ/mol, temperature in °C, and ΔS in J/(mol·K); the result is ΔG in kJ/mol, with the temperature also shown in kelvin.

Formula

The Gibbs free energy equation at constant temperature and pressure is ΔG = ΔH − TΔS. In this calculator, the entered enthalpy change ΔH is in kJ/mol, temperature T is entered in °C and converted to kelvin by adding 273.15, and entropy change ΔS is in J/(mol·K). Because the entropy term is then in J/mol while enthalpy is in kJ/mol, the calculator divides TΔS by 1000 to convert joules to kilojoules:

ΔG (kJ/mol) = ΔH (kJ/mol) − [(t (°C) + 273.15) × ΔS (J/(mol·K)) ÷ 1000]

The output ΔG is the Gibbs free energy change per mole of reaction as represented by the supplied quantities. A negative value indicates a thermodynamically favorable direction under the specified conditions; it does not say how quickly the reaction proceeds.

Worked Example

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

1. Convert temperature: T = 25 + 273.15 = 298.15 K.
2. Calculate the entropy term: TΔS = 298.15 K × 50 J/(mol·K) = 14907.5 J/mol = 14.9075 kJ/mol.
3. Calculate free energy: ΔG = −10 kJ/mol − 14.9075 kJ/mol = −24.9075 kJ/mol, which rounds to −24.9075 kJ/mol at four decimal places.

Assumptions

• The inputs are changes per mole of reaction, and all quantities use the same reaction direction and stoichiometric basis.
• Temperature is absolute temperature in the equation; the calculator accepts °C and converts it using the exact offset 273.15.
• ΔH and ΔS are treated as applicable at the entered temperature. If they vary significantly with temperature, use values or a model appropriate to that temperature.
• The equation describes the thermodynamic change under constant temperature and pressure. It does not account for kinetic barriers or establish a reaction rate.

What Units Does Gibbs Free Energy Use?

Gibbs free energy is an energy, so its SI unit is the joule (J). In chemistry, values are commonly reported per mole of reaction, usually as J/mol or kJ/mol. The equation’s terms must have matching units: ΔH and TΔS are both energy changes per mole. The temperature in TΔS must be in kelvin, not Celsius.

Entropy is energy divided by temperature, so molar entropy change is expressed in J/(mol·K). Multiplying by kelvin cancels the kelvin unit: K × J/(mol·K) = J/mol. If ΔH is entered in kJ/mol while ΔS is in J/(mol·K), convert one term before subtracting. This calculator uses joules for the entropy term and divides by 1000 to express it in kJ/mol.

• ΔG: J/mol or kJ/mol
• ΔH: the same energy-per-mole unit used for ΔG
• T: K
• ΔS: J/(mol·K) when energy is in joules, or kJ/(mol·K) when energy is in kilojoules

How to Interpret the Result

For a process at constant temperature and pressure, ΔG indicates the change in free energy for the stated direction. If ΔG is less than zero, that direction is thermodynamically favorable; if it is greater than zero, the reverse direction is favorable under those conditions. If ΔG is zero, the system is at equilibrium in the idealized thermodynamic sense, with no net driving force for change.

“Favorable” does not mean “fast” or “guaranteed to happen visibly.” A reaction can have a negative ΔG and still proceed slowly because it faces an activation-energy barrier. Nor does ΔG alone specify the final amount of product: equilibrium composition depends on the reaction and conditions. The sign is meaningful only with a clear reaction direction and consistent units.

Using ΔH and ΔS Across Temperatures

The equation helps explain how temperature can affect favorability. If ΔH and ΔS remain roughly constant over the temperature range of interest, increasing T increases the magnitude of the TΔS term. The balance between enthalpy and entropy can therefore change with temperature.

• If ΔH is negative and ΔS is positive, both terms favor negative ΔG at positive temperatures.
• If ΔH is positive and ΔS is negative, both contributions make ΔG positive.
• If ΔH and ΔS are both negative, the enthalpy contribution favors the forward direction while the −TΔS contribution becomes positive; lower temperatures may favor negative ΔG.
• If ΔH and ΔS are both positive, the entropy contribution becomes more negative as temperature rises; higher temperatures may favor negative ΔG.

These are qualitative patterns, not universal temperature thresholds. The values of ΔH and ΔS can change with temperature, and phase changes or other transitions can alter the appropriate thermodynamic description.

Common Unit Mistakes and Limits

The most frequent error is inserting Celsius directly into TΔS. For example, 25 °C corresponds to 298.15 K, not 25 K; using 25 would badly underestimate the entropy contribution. Another common error is subtracting a value in J/mol from one in kJ/mol without converting. The calculator handles these two conversions, but it cannot detect an incorrect sign, an entropy value reported under a different convention, or mismatched reaction stoichiometry.

Check whether source data are stated per mole of substance or per mole of reaction as written. Multiplying a balanced equation by a factor multiplies its ΔH, ΔS, and ΔG by the same factor. Also distinguish standard Gibbs energy change, often written ΔG°, from the actual ΔG under a particular composition. Standard-state values alone do not necessarily equal the free-energy change in a mixture away from standard conditions.

The simple equation is most directly useful when suitable ΔH and ΔS values are known at the temperature of interest. For a reacting mixture, the relation ΔG = ΔG° + RT ln Q accounts for composition through the reaction quotient Q; calculating that form requires the relevant standard free energy, temperature, and activities or a justified approximation for Q. This calculator does not calculate ΔG° or reaction-mixture activities.

Frequently Asked Questions

What is the SI unit of Gibbs free energy?
The SI unit of energy is the joule. Chemical free-energy changes are commonly given in J/mol or kJ/mol when expressed per mole of reaction.

Can Gibbs free energy be measured in kJ/mol?
Yes. kJ/mol is a standard chemistry unit. Ensure enthalpy and the TΔS term are both converted to kJ/mol before subtracting.

Why must temperature be in kelvin?
The equation uses absolute temperature. Kelvin begins at absolute zero, so it is the appropriate scale for multiplying temperature by entropy; convert Celsius by adding 273.15.

Is entropy measured in J/(mol·K)?
Molar entropy change is often reported in J/(mol·K). Multiplying it by temperature in kelvin gives J/mol, an energy change per mole.

Does negative ΔG mean a reaction happens quickly?
No. Negative ΔG indicates thermodynamic favorability in the stated direction under the conditions considered. Reaction speed depends on kinetics, including activation barriers.

What is the difference between ΔG and ΔG°?
ΔG is the free-energy change for the actual conditions and composition. ΔG° refers to a defined standard state; relating the two for a mixture requires a reaction-quotient term.

Related

• Empirical Formula Calculator and Calculation Table
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in dh | Enthalpy change | kJ/mol | -10 | -
in t | Temperature | °C | 25 | -273.15
in ds | Entropy change | J/(mol·K) | 50 | -
out dg | Gibbs free energy change | kJ/mol | dh - ((t + 273.15) * ds / 1000) | 4
out tk | Absolute temperature | K | t + 273.15 | 2