Calculator Inputs
Plotly Graph
The chart shows how free energy changes with temperature across your selected range.
Example Data Table
| Case | Mode | ΔH (kJ/mol) | ΔS (J/mol·K) | T (K) | Q | ΔG° (kJ/mol) | ΔG (kJ/mol) | Interpretation |
|---|---|---|---|---|---|---|---|---|
| 1 | Standard | 65.00 | 180.00 | 298.15 | 1.000 | 11.333 | 11.333 | Nonspontaneous at room temperature |
| 2 | Standard | -40.00 | -95.00 | 298.15 | 1.000 | -11.676 | -11.676 | Spontaneous at room temperature |
| 3 | Nonstandard | 65.00 | 180.00 | 450.00 | 0.050 | -16.000 | -27.212 | Forward direction strongly favored |
Formula Used
Standard Gibbs Free Energy Change
ΔG° = ΔH − TΔS
Use this relation when enthalpy and entropy are known for a process under standard-state assumptions. Temperature must be in Kelvin. Units must remain consistent.
Nonstandard Gibbs Free Energy Change
ΔG = ΔG° + RT ln Q
This adds concentration or pressure effects through the reaction quotient. Here, R = 8.314462618 J/mol·K, T is Kelvin, and Q must be positive.
Equilibrium Constant Relationship
ΔG° = −RT ln K
Rearranging gives K = e−ΔG°/RT. Large K values suggest products are favored. Very small K values suggest reactants are favored.
Critical Temperature Estimate
T = ΔH / ΔS
This estimate applies when ΔG is set to zero in the simplified model. It is useful for identifying crossover behavior, but real systems can deviate from this approximation.
How to Use This Calculator
- Select standard mode for ΔG° only, or nonstandard mode for ΔG.
- Enter enthalpy and entropy values using the correct units.
- Provide the system temperature and choose its unit.
- Enter Q only when nonstandard conditions apply.
- Set the chart temperature range and point count.
- Press the calculation button to generate results.
- Review spontaneity, equilibrium behavior, and temperature crossover information.
- Use the CSV or PDF buttons to save the result summary.
Frequently Asked Questions
1. What does Gibbs free energy change tell me?
Gibbs free energy change predicts whether a process is thermodynamically favorable at a chosen temperature and state. Negative values suggest spontaneity, positive values suggest nonspontaneity, and values near zero indicate equilibrium conditions.
2. Why must temperature be in Kelvin?
The thermodynamic equations require an absolute temperature scale. Kelvin starts at absolute zero, so energy relationships remain physically meaningful and unit-consistent in expressions like TΔS and RT lnQ.
3. What is the difference between ΔG and ΔG°?
ΔG° applies to standard-state conditions. ΔG applies to actual conditions and includes the reaction quotient term. When Q equals 1, the nonstandard correction disappears and ΔG equals ΔG°.
4. What happens if Q is less than K?
When Q is below K, the forward direction is thermodynamically favored. The system tends to move toward products until the reaction quotient approaches the equilibrium constant.
5. Can this calculator handle negative entropy changes?
Yes. Negative entropy changes are valid and often make processes less favorable at higher temperatures because the TΔS term becomes more unfavorable in the ΔG equation.
6. Why does the graph change slope with entropy?
In the simplified relation ΔG° = ΔH − TΔS, the slope with respect to temperature is controlled by −ΔS. Positive entropy gives a downward trend, while negative entropy gives an upward trend.
7. Is a negative ΔH always enough for spontaneity?
No. Spontaneity depends on both enthalpy and entropy, plus temperature. A process with favorable enthalpy can still become nonspontaneous if the entropy contribution opposes it strongly enough.
8. Are these results exact for every real system?
They are accurate within the chosen thermodynamic model. Real systems may show temperature-dependent enthalpy, nonideal behavior, phase changes, or activity corrections that require more advanced data.