Chemistry

Reaction Gibbs Free Energy

Combine reaction enthalpy and entropy at a fixed temperature.

Δ G = Δ H - T Δ S

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Source & review

Difficulty

Intermediate

Read time

3 min

Prerequisites

Algebra, logarithms, and molar quantities

Review statusNeeds review

Source

OpenStax, Chemistry 2e, §16.4

Adapted from Teng-Jui Lin’s CHEM 145 equation sheet. The linked textbook reference was used to check the equation and its physical context. Pending editorial review.

Adapted from Teng-Jui Lin, Equation Sheets, under CC BY 4.0.

FormuLab adapted notation and chemical symbols, added variable meanings, units, applicability conditions, and an original worked example.

Definition

Understanding the core concept

The Gibbs energy change combines the reaction’s enthalpy change with its temperature-weighted entropy change. At constant temperature and pressure, its sign indicates the favored direction for the specified composition.

Variables & Units

Understanding each component

Symbol	Meaning	Units
$Δ G$	Reaction Gibbs energy change per mole of reaction	$J mo l^{- 1}$
$Δ H$	Reaction enthalpy change on the same molar basis	$J mo l^{- 1}$
$T$	Absolute temperature	$K$
$Δ S$	Reaction entropy change on the same molar basis	$J mo l^{- 1} K^{- 1}$

Real-World Applications

Where this formula is used in practice

Reaction direction

Assess whether the forward reaction lowers Gibbs energy at the specified conditions.

Temperature effects

Compare enthalpic and entropic contributions at one temperature.

Worked Example

Step-by-step calculation with real numbers

Problem

A reaction has enthalpy change +40.0 kJ/mol and entropy change +150 J/(mol·K). Find its Gibbs energy change at 298 K.

Given

Δ H = 40.0 kJ mo l^{- 1} = 40000 J mo l^{- 1}

Δ S = 150 J mo l^{- 1} K^{- 1}

T = 298 K

Solution

Δ G = Δ H - T Δ S

Δ G = 40000 J mo l^{- 1} - (298 K) (150 J mo l^{- 1} K^{- 1})

Δ G \approx - 4700 J mo l^{- 1}

Final Answer

Δ G \approx - 4700 J mo l^{- 1}

Formula Guide

Info

DifficultyIntermediate

Read Time3 min

PrerequisitesAlgebra, logarithms, and molar quantities

Tools

Source & review

StatusNeeds review

Last reviewedPending

Source

OpenStax, Chemistry 2e, §16.4

Adapted from Teng-Jui Lin’s CHEM 145 equation sheet. The linked textbook reference was used to check the equation and its physical context. Pending editorial review.

Adapted from Teng-Jui Lin, Equation Sheets, under CC BY 4.0.

FormuLab adapted notation and chemical symbols, added variable meanings, units, applicability conditions, and an original worked example.

Assumptions

• The initial and final states are compared at the same temperature; use constant pressure for the reaction-direction criterion.
• Use a consistent reaction basis and matching energy units for enthalpy and T times entropy.

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