Gibbs Free Energy Preview

Physics Thermodynamics • Advanced Applications and Extensions in Thermodynamics

Written by STEM Calculators Team Published January 8, 2026 Updated February 24, 2026

6. Gibbs Free Energy Preview

Compute Gibbs free energy $$ G = H - T S $$ and for reactions $\Delta G = \Delta H - T\,\Delta S$ with equilibrium $K=\exp\!\big(-\Delta G/(RT)\big)$ . Includes a standard reaction library and a temperature-dependence preview plot.

Inputs support: pi, e, sqrt(), sin, cos, exp, log. Use * for multiplication.

Mode + Inputs

Mode: Temperature $T$ (K): Gas constant $R$ (J/mol·K): Standard reaction library: Reaction $\Delta H^\circ$ (kJ/mol-rxn): Reaction $\Delta S^\circ$ (J/mol·K-rxn): System enthalpy $H$ (kJ): System entropy $S$ (J/K): Temperature preview plot: Plot variable: Plot span (K): Progress $\tau\in[0,1]$ (dot): Play speed:

Reaction mode assumes $\Delta H^\circ$ and $\Delta S^\circ$ are approximately constant over the plotted temperature window (a “preview”).

Ready

Steps

Enter values and click Solve.

Temperature dependence preview

Preview curve with pan/zoom

Hover: (T, y)=…

Dot position is controlled by $\tau$ across the plotted temperature window. Double-click the plot to reset.

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Gibbs Free Energy Preview — Theory

Gibbs free energy helps predict whether a process can be thermodynamically favored at a given temperature (especially at constant $T$ and $P$). The calculator supports both a single-state computation $G=H-TS$ and a reaction preview using $\Delta G=\Delta H-T\Delta S$ along with the equilibrium constant $K$.

1) Definition: $G = H - TS$

\[ G = H - TS. \]

$H$ is enthalpy (often in kJ, kJ/mol, etc.).
$S$ is entropy (often in J/K, J/(mol·K), etc.).
$TS$ has energy units; be consistent with conversions.

2) Reactions: $\Delta G(T) = \Delta H - T\Delta S$

For a reaction written in a specific direction, the “preview” model uses:

\[ \Delta G(T)=\Delta H - T\Delta S. \]

This is a simplified temperature dependence assuming $\Delta H$ and $\Delta S$ are roughly constant over a temperature window. For high-accuracy work, heat-capacity corrections may be needed.

3) Spontaneity tease: sign of $\Delta G$

$\Delta G<0$: thermodynamically favored as written (under the stated conditions).
$\Delta G>0$: not favored as written; the reverse direction is favored.
$\Delta G\approx 0$: near equilibrium.

4) Link to equilibrium: $K=\exp\!\left(-\Delta G/(RT)\right)$

\[ K = \exp\!\left(-\frac{\Delta G}{RT}\right), \qquad \ln K = -\frac{\Delta G}{RT}. \]

$R$ is the gas constant (commonly $8.314\ \mathrm{J/(mol\cdot K)}$).
Use $\Delta G$ in joules per mole when combined with $R$ in J/(mol·K).
Large negative $\Delta G$ implies very large $K$ (products strongly favored).

5) Sample (library): $\mathrm{H_2 + \tfrac{1}{2}O_2 \rightarrow H_2O}$ at 298 K

Using standard values (example):

\[ \Delta G^\circ(T) = \Delta H^\circ - T\Delta S^\circ \quad\Rightarrow\quad \Delta G^\circ(298\ \mathrm{K}) \approx -237\ \mathrm{kJ/mol}, \] \[ K = \exp\!\left(-\frac{\Delta G^\circ}{RT}\right)\ \ \text{(very large)}. \]

6) Plot interpretation

$\Delta G(T)$ is typically a roughly linear function of $T$ if $\Delta H,\Delta S$ are treated constant.
$\log_{10}K(T)$ changes rapidly because $K$ depends exponentially on $\Delta G/(RT)$.
Pan/zoom lets you examine specific temperature ranges without losing readability.

Limitations

“Standard” reaction values are typically defined at 1 bar and 298 K; conditions matter.
Real systems may require non-ideal activities/fugacities and heat-capacity corrections.
$\Delta G$ predicts thermodynamic favorability, not reaction speed (kinetics).