Last updated: July 3, 2026
Gibbs Free Energy Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
Gibbs free energy is calculated as ΔG = ΔH − TΔS, with entropy converted from J/(mol·K) to kJ/(mol·K) when enthalpy is in kJ/mol. Standard Gibbs free energy is calculated from equilibrium with ΔG° = −RT ln K. Negative ΔG means spontaneous, positive means non-spontaneous, and zero means equilibrium.
Gibbs free energy equals enthalpy change minus temperature times entropy change. A negative value means the reaction is spontaneous as written, a positive value is non-spontaneous, and zero means equilibrium.
Key Takeaways
- Gibbs free energy predicts thermodynamic spontaneity at constant temperature and pressure.
- Use ΔG = ΔH − TΔS with ΔH in kJ/mol, T in K, and ΔS converted from J/(mol·K) to kJ/(mol·K).
- ΔG < 0 is spontaneous, ΔG > 0 is non-spontaneous, and ΔG = 0 is equilibrium.
- Standard free energy and equilibrium are linked by ΔG° = −RT ln K.
- A favorable ΔG does not guarantee a fast reaction; kinetics depends on activation energy.
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
ΔG = ΔH − TΔS; ΔG° = −RT ln K
Where:
- ΔG=Gibbs free energy change(kJ/mol)
- ΔH=Enthalpy change(kJ/mol)
- T=Absolute temperature(K)
- ΔS=Entropy change(J/(mol·K))
- R=Gas constant(8.314 J/(mol·K))
- K=Equilibrium constant(dimensionless)
Worked Examples
Strongly spontaneous reaction
A negative enthalpy and positive entropy make ΔG very negative at room temperature.
- 1Convert entropy to kJ units: 200 J/(mol·K) = 0.200 kJ/(mol·K).
- 2Multiply TΔS: 298 K × 0.200 kJ/(mol·K) = 59.6 kJ/mol.
- 3Subtract: ΔG = −100 − 59.6 = −159.6 kJ/mol, so the reaction is spontaneous as written.
Temperature offsets positive enthalpy
A positive entropy term partly offsets an endothermic enthalpy change.
- 1Convert entropy: 100 J/(mol·K) = 0.100 kJ/(mol·K).
- 2Compute TΔS = 300 × 0.100 = 30 kJ/mol.
- 3Calculate ΔG = 50 − 30 = 20 kJ/mol, which is non-spontaneous under these conditions.
Standard free energy from K = 10
Use the equilibrium constant form to find ΔG° at 298 K.
- 1Use ΔG° = −RT ln K with R = 8.314 J/(mol·K).
- 2Substitute: ΔG° = −8.314 × 298 × ln(10) = −5708 J/mol.
- 3Convert to kJ/mol: −5708 J/mol = −5.71 kJ/mol; K > 1 gives negative ΔG°.
Introduction
Gibbs free energy links heat, entropy, temperature, and chemical equilibrium in one practical spontaneity test. This calculator evaluates ΔG = ΔH − TΔS using ΔH in kJ/mol and ΔS in J/(mol·K), converting entropy to kJ before subtraction. It can also calculate standard Gibbs free energy from an equilibrium constant with ΔG° = −RT ln K. Use it with the entropy calculator, equilibrium constant calculator, and authoritative definitions from the IUPAC Gold Book.
What Gibbs free energy means
Gibbs free energy, G, is the thermodynamic potential that predicts whether a process can do non-expansion work at constant temperature and pressure. For a reaction, ΔG compares the free energy of products and reactants. The sign is the key: negative ΔG favors the reaction as written, positive ΔG disfavors it, and zero ΔG corresponds to equilibrium.
- ΔG < 0:
spontaneous as written under the specified conditions.
- ΔG > 0:
non-spontaneous as written; the reverse direction is favored.
- ΔG = 0:
the system is at equilibrium.
The magnitude indicates driving force, not reaction speed; use the activation energy calculator for kinetics.
Using ΔG = ΔH − TΔS
The calculator expects ΔH in kJ/mol, T in kelvin, and ΔS in J/(mol·K). Because ΔH is usually tabulated in kJ/mol while entropy is usually tabulated in J/(mol·K), ΔS is divided by 1000 before multiplying by temperature. The working equation is therefore ΔG(kJ/mol) = ΔH(kJ/mol) − T × ΔS(J/mol·K) / 1000.
Always use absolute temperature in kelvin. Celsius values make the TΔS term physically wrong.
Standard Gibbs free energy from an equilibrium constant
For standard-state thermodynamics, ΔG° and the equilibrium constant are connected by ΔG° = −RT ln K. R is 8.314 J/(mol·K), T is kelvin, and K must be dimensionless. A large K gives a negative ΔG° because products are favored at equilibrium; a small K gives a positive ΔG°. This relationship is the thermodynamic basis of many equilibrium calculations described by LibreTexts.
Spontaneity, equilibrium, and reaction quotient
ΔG under nonstandard conditions depends on composition through the reaction quotient Q: ΔG = ΔG° + RT ln Q. This calculator focuses on ΔG from ΔH and ΔS or ΔG° from K, but you can pair it with the reaction quotient calculator to reason about how changing concentrations pushes a reaction toward products or reactants.
When Q = K, ΔG = 0 and the reaction mixture is at equilibrium.
How temperature changes spontaneity
The entropy term TΔS grows with temperature, so temperature can change the sign of ΔG. If ΔH is positive and ΔS is positive, higher temperature can make a reaction spontaneous. If ΔH is negative and ΔS is negative, lower temperature favors spontaneity. If both signs favor or oppose the reaction, temperature changes the magnitude but usually not the sign.
| ΔH sign | ΔS sign | Spontaneity trend |
|---|---|---|
| Negative | Positive | Spontaneous at all temperatures in the simple model |
| Positive | Negative | Non-spontaneous at all temperatures in the simple model |
| Positive | Positive | Favored at high temperature |
| Negative | Negative | Favored at low temperature |
Units and data quality checks
Most errors come from mixing joules and kilojoules or using a temperature in degrees Celsius. Check that enthalpy and entropy data refer to the same balanced reaction and standard state. For precise work, use vetted thermodynamic tables such as the NIST Chemistry WebBook and report the temperature with the result.
Convert ΔS from J/(mol·K) to kJ/(mol·K) by dividing by 1000.
Use the natural logarithm, ln, not log base 10, in ΔG° = −RT ln K.
K must be positive and dimensionless.
Thermodynamic favorability does not guarantee a fast reaction rate; compare with the arrhenius equation calculator.
Quick Reference Card
Gibbs Free Energy — Quick Reference
Quick reference • Gibbs Free Energy Calculator
ΔG = ΔH − TΔS; ΔG° = −RT ln KValid range: T must be > 0 K; K must be positive and dimensionless; ΔH and ΔS may be positive or negative
Common Values
⚠ Watch Out
- •Use kelvin, not Celsius, for temperature.
- •Convert ΔS from J/(mol·K) to kJ/(mol·K) when ΔH is in kJ/mol.
- •Use natural logarithm ln(K), not log10(K).
- •Do not use zero or negative equilibrium constants.
Pro Tips
- →Check the sign convention for the reaction as written before interpreting ΔG.
- →Use consistent tabulated data for the same standard state and temperature.
- →Remember that ΔG predicts direction, while activation energy predicts speed.
- →At equilibrium, ΔG = 0 even though forward and reverse reactions continue microscopically.
FAQs
What does a negative Gibbs free energy mean?
A negative ΔG means the reaction is thermodynamically spontaneous as written under the specified conditions. It does not necessarily mean the reaction is fast.
Why is entropy divided by 1000 in this calculator?
ΔH is commonly entered in kJ/mol, while ΔS is commonly entered in J/(mol·K). Dividing ΔS by 1000 converts it to kJ/(mol·K) so TΔS and ΔH have matching units.
What is the difference between ΔG and ΔG°?
ΔG applies to the actual reaction conditions. ΔG° is the standard-state free energy change and is related to the equilibrium constant by ΔG° = −RT ln K.
What happens when ΔG equals zero?
When ΔG is zero, the system is at equilibrium. There is no net thermodynamic driving force toward products or reactants.
Can K be zero or negative in ΔG° = −RT ln K?
No. The equilibrium constant used in the logarithm must be positive and dimensionless. Zero or negative values are invalid for this equation.
Does a spontaneous reaction always occur quickly?
No. ΔG describes thermodynamic favorability, not rate. A reaction with negative ΔG can still be slow if its activation energy is high.