Standard Gibbs Energy of Reaction

General Chemistry • Spontaneous Change Entropy and Gibbs Energy

Written by STEM Calculators Team Published October 25, 2025 Updated February 24, 2026

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Standard Gibbs Energy of Reaction from Formation Values

This tool evaluates the standard Gibbs energy change of a reaction, \( \Delta_{r}G^\circ \), by combining tabulated standard Gibbs energies of formation, \( \Delta_{f}G^\circ \), of the species. It is a direct Hess-law sum that uses the stoichiometric coefficients of the balanced chemical equation and the usual standard state (pure substances at 1 bar, typically reported at 298.15 K).

\[ \begin{aligned} \Delta_{r}G^\circ &= \sum_{\text{products}} n\,\Delta_{f}G^\circ \;-\; \sum_{\text{reactants}} n\,\Delta_{f}G^\circ \\ &= \Big(c\,\Delta_{f}G^\circ(\mathrm{C}) + d\,\Delta_{f}G^\circ(\mathrm{D}) + \cdots\Big) \\ &\qquad - \Big(a\,\Delta_{f}G^\circ(\mathrm{A}) + b\,\Delta_{f}G^\circ(\mathrm{B}) + \cdots\Big) \end{aligned} \]

Units: enter all \( \Delta_{f}G^\circ \) in the same energy unit (the calculator uses kJ·mol⁻¹). For elements in their reference state (e.g., \( \mathrm{O_2(g)} \), \( \mathrm{H_2(g)} \), graphite \( \mathrm{C(s)} \)), \( \Delta_{f}G^\circ = 0 \).

Connection to \( \Delta_r H^\circ \) and \( \Delta_r S^\circ \)

When the standard temperature is specified, \( \Delta_{r}G^\circ \) may also be related to the enthalpy and entropy changes of reaction:

\[ \begin{aligned} \Delta_{r}G^\circ &= \Delta_{r}H^\circ - T\,\Delta_{r}S^\circ \end{aligned} \]

This calculator, however, computes \( \Delta_{r}G^\circ \) via the formation-sum formula above. If you need \( \Delta_{r}H^\circ \) or \( \Delta_{r}S^\circ \), use the corresponding tools.

Worked form (symbolic)

For the balanced reaction \( 2\,\mathrm{NO(g)} + \mathrm{O_2(g)} \rightarrow 2\,\mathrm{NO_2(g)} \),

\[ \begin{aligned} \Delta_{r}G^\circ &= 2\,\Delta_{f}G^\circ(\mathrm{NO_2}) \;-\;\Big(2\,\Delta_{f}G^\circ(\mathrm{NO}) + 1\,\Delta_{f}G^\circ(\mathrm{O_2})\Big) \\ &= 2\,\Delta_{f}G^\circ(\mathrm{NO_2}) \;-\; 2\,\Delta_{f}G^\circ(\mathrm{NO}) \qquad \big(\because \Delta_{f}G^\circ(\mathrm{O_2})=0\big) \end{aligned} \]

Interpreting the sign (spontaneity at standard conditions)

\( \Delta_{r}G^\circ < 0 \): reaction is spontaneous as written.
\( \Delta_{r}G^\circ > 0 \): reaction is nonspontaneous as written.
\( \Delta_{r}G^\circ = 0 \): reaction is reversible (at equilibrium).

Tips & common pitfalls

Balance the equation first; the coefficients \( n \) multiply each species’ \( \Delta_{f}G^\circ \).
Keep all energies in the same unit (kJ·mol⁻¹ here).
Use values tabulated at the same temperature (commonly 298.15 K).
Elements in their reference state have \( \Delta_{f}G^\circ=0 \); do not confuse this with entropy data, where elements usually have non-zero \( S^\circ \).
Optional: \( \Delta_{r}G^\circ \) is related to the equilibrium constant by \( \Delta_{r}G^\circ = -RT\ln K \) (with \( R \) in J·mol⁻¹·K⁻¹, \( T \) in K).

Frequently Asked Questions

How do you calculate the standard Gibbs energy of reaction from formation values?

Use the balanced reaction coefficients and apply ΔrG° = Σ(n·ΔfG° products) - Σ(n·ΔfG° reactants). Each ΔfG° must correspond to the correct species and phase and be in consistent units.

Why must the chemical equation be balanced before calculating ΔrG°?

Because the stoichiometric coefficients n multiply each species' ΔfG° contribution. If the equation is not balanced, the summed formation terms will not represent the reaction as written.

What value should I enter for ΔfG° of elements like O2(g) or H2(g)?

For an element in its reference (standard) state, ΔfG° is defined as 0. Enter 0 for those species when they appear in the reaction.

What does a negative or positive ΔrG° mean under standard conditions?

ΔrG° < 0 indicates the reaction is spontaneous as written under standard-state conditions, while ΔrG° > 0 indicates it is nonspontaneous as written. ΔrG° = 0 corresponds to equilibrium under standard conditions.

Can I include ionic charges, electrons, or state symbols in the reaction input?

State symbols may be ignored, but charges and electrons are not supported by this reaction-entry format. Enter the reaction as neutral species without explicit charge/electron notation.

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Frequently Asked Questions

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