Gibbs free energy

Core idea

Overview

Gibbs free energy quantifies the maximum amount of non-expansion work extractable from a thermodynamically closed system at constant pressure and temperature. It serves as a critical criterion for spontaneity, where a negative value indicates a reaction will proceed without external energy input by balancing enthalpy and entropy.

When to use: Use this equation to predict the spontaneity of chemical reactions or phase changes under conditions of constant temperature and pressure. It is particularly useful when determining the temperature at which a reaction shifts from being non-spontaneous to spontaneous.

Why it matters: This formula is the foundation of chemical energetics, allowing scientists to calculate equilibrium constants and design industrial chemical processes. In biology, it explains how cells couple unfavorable reactions with favorable ones to drive life-sustaining metabolic pathways.

Symbols

Variables

$Δ$ H = Enthalpy Change, $Δ$ S = Entropy Change, T = Temperature, $Δ$ G = Gibbs Free Energy

Δ H

Enthalpy Change

kJ/mol

Δ S

Entropy Change

kJ/molK

T

Temperature

K

Δ G

Gibbs Free Energy

kJ/mol

Walkthrough

Derivation

Formula: Gibbs Free Energy

Predicts feasibility of a process at constant temperature and pressure using enthalpy and entropy changes.

Temperature and pressure remain constant.

1

State the Gibbs Equation:

Gibbs free energy combines enthalpy ( $Δ$ H) and entropy ( $Δ$ S) effects at temperature T (K).

Δ G = Δ H - T Δ S

2

Interpret Feasibility:

A negative $Δ$ G indicates a feasible spontaneous direction under the stated conditions.

Δ G < 0 (spontaneous), Δ G = 0 (equilibrium)

Note: Watch units: $Δ$ H often in kJ mol^{-1}; $Δ$ S often in J $K^{- 1}$ mol^{-1}, so convert if needed.

Result

Δ G < 0 (spontaneous), Δ G = 0 (equilibrium)

Source: OCR A-Level Chemistry A — Thermodynamics

Free formulas

Rearrangements

Solve for $Δ H$

Make Delta H the subject

Δ H = Δ G + T Δ S

To make $Δ$ H the subject of the Gibbs free energy equation, add TΔ S to both sides of the equation.

Difficulty: 2/5

Solve for $Δ S$

Make Delta S the subject

Δ S = \frac{Δ H - Δ G}{T}

To make $Δ$ S the subject of the Gibbs free energy equation, first isolate the TΔ S term, then divide by T and adjust for the negative sign.

Difficulty: 2/5

Solve for $T$

Make T the subject

T = \frac{Δ H - Δ G}{Δ S}

To make T the subject of the Gibbs free energy equation, first subtract $Δ$ H, then multiply by -1, and finally divide by $Δ$ S.

Difficulty: 2/5

The static page shows the finished rearrangements. The app keeps the full worked algebra walkthrough.

Visual intuition

Graph

The graph displays a straight line where the y-intercept represents the enthalpy change and the slope is determined by the negative entropy change. For a chemistry student, this linear relationship means that as temperature increases, the spontaneity of the reaction changes at a constant rate depending on whether the entropy change is positive or negative. The most important feature of this curve is the x-intercept, which identifies the specific temperature where the Gibbs free energy reaches zero and the reaction transitions between being spontaneous and non-spontaneous.

Graph type: linear

Why it behaves this way

Intuition

Gibbs free energy represents a balance between a system's tendency to minimize its energy (enthalpy) and maximize its disorder (entropy), with temperature determining the relative weight of the disorder contribution.

Δ G

Change in Gibbs free energy. Represents the maximum non-PV work obtainable from a system at constant temperature and pressure.

The 'useful' energy available from a reaction. A negative value indicates a spontaneous process.

Δ H

Change in enthalpy. Represents the heat absorbed or released by a system at constant pressure.

Exothermic reactions (negative

Δ

H) release heat and tend to favor spontaneity.

T

Absolute temperature, typically in Kelvin.

Scales the importance of the entropy term. Higher temperatures amplify the effect of entropy on spontaneity.

Δ S

Change in entropy. A measure of the dispersal of energy or disorder within a system.

Reactions that increase disorder (positive

Δ

S) tend to favor spontaneity.

Signs and relationships

-TΔ S: The negative sign indicates that an increase in entropy (positive $Δ$ S) makes $Δ$ G more negative, thus favoring spontaneity. This term represents the energy 'lost' to increasing disorder, which is unavailable for the system being studied.

Free study cues

Insight

Canonical usage

This equation relates energy quantities (Gibbs free energy, enthalpy) and entropy at a given temperature, typically using SI units for consistency.

Common confusion

A common mistake is using temperature in Celsius (°C) instead of Kelvin (K). Another is mixing units (e.g., using kJ for ΔH and J for TΔS) without proper conversion, leading to incorrect energy calculations.

Unit systems

$Δ G$ J or kJ - Gibbs free energy change. Often expressed per mole (J/mol or kJ/mol) for chemical reactions.

$Δ H$ J or kJ - Enthalpy change. Often expressed per mole (J/mol or kJ/mol) for chemical reactions.

$T$ K - Absolute temperature. Must be in Kelvin (K); Celsius or Fahrenheit values must be converted.

$Δ S$ J K^-1 or kJ K^-1 - Entropy change. Often expressed per mole (J K^-1 mol^-1 or kJ K^-1 mol^-1) for chemical reactions.

Ballpark figures

Quantity:

One free problem

Practice Problem

A reaction has ΔH = -180 kJ/mol and ΔS = -0.15 kJ/(mol·K). Calculate ΔG at T = 500 K. Is the reaction spontaneous at this temperature?

Enthalpy Change-180 kJ/mol

Entropy Change-0.15 kJ/molK

Temperature500 K

Solve for: $G$

Hint: ΔG = ΔH - TΔS. Keep all units in kJ/mol.

The full worked solution stays in the interactive walkthrough.

Where it shows up

Real-World Context

When determining if a reaction is feasible at a given temperature, Gibbs free energy is used to calculate the G value from Enthalpy Change, Entropy Change, and Temperature. The result matters because it helps connect measured amounts to reaction yield, concentration, energy change, rate, or equilibrium.

Study smarter

Tips

Always convert temperature to Kelvin by adding 273.15 to the Celsius value.
Check that units for Enthalpy (usually kJ) and Entropy (usually J/K) are consistent by dividing Entropy by 1000.
A negative ΔG indicates a spontaneous process, while a positive ΔG indicates a non-spontaneous process.
When ΔG equals zero, the system has reached chemical equilibrium.

Avoid these traps

Common Mistakes

Mixing kJ and J
Using Celsius instead of Kelvin.

Keep going

Related Formulas

Common questions

Frequently Asked Questions

Predicts feasibility of a process at constant temperature and pressure using enthalpy and entropy changes.

Use this equation to predict the spontaneity of chemical reactions or phase changes under conditions of constant temperature and pressure. It is particularly useful when determining the temperature at which a reaction shifts from being non-spontaneous to spontaneous.

This formula is the foundation of chemical energetics, allowing scientists to calculate equilibrium constants and design industrial chemical processes. In biology, it explains how cells couple unfavorable reactions with favorable ones to drive life-sustaining metabolic pathways.

Mixing kJ and J Using Celsius instead of Kelvin.

When determining if a reaction is feasible at a given temperature, Gibbs free energy is used to calculate the G value from Enthalpy Change, Entropy Change, and Temperature. The result matters because it helps connect measured amounts to reaction yield, concentration, energy change, rate, or equilibrium.

Always convert temperature to Kelvin by adding 273.15 to the Celsius value. Check that units for Enthalpy (usually kJ) and Entropy (usually J/K) are consistent by dividing Entropy by 1000. A negative ΔG indicates a spontaneous process, while a positive ΔG indicates a non-spontaneous process. When ΔG equals zero, the system has reached chemical equilibrium.

References

Sources

Atkins' Physical Chemistry
IUPAC Gold Book: Gibbs energy
Wikipedia: Gibbs free energy
IUPAC Gold Book: Enthalpy
IUPAC Gold Book: Entropy
Callen, Herbert B. Thermodynamics and an Introduction to Thermostatistics
Callen's Thermodynamics and an Introduction to Thermostatistics
IUPAC Gold Book: Gibbs Free Energy

Overview

Variables

Derivation

State the Gibbs Equation:

Interpret Feasibility:

Rearrangements

Graph

Intuition

Insight

Practice Problem

Real-World Context

Tips

Common Mistakes

Related Formulas

Standard Gibbs free energy

Frequently Asked Questions

Sources