Gibbs free energy of formation

Gibbs Free Energy of Formation is a thermodynamic property that quantifies the energy change associated with the formation of a compound from its constituent elements in their standard states. The concept is named after Josiah Willard Gibbs, an American scientist who made significant contributions to the field of thermodynamics in the late 19th century. The Gibbs free energy of formation is a crucial parameter in chemical thermodynamics, physical chemistry, and materials science, providing insights into the spontaneity of chemical reactions and the stability of compounds.

Definition

The Gibbs free energy of formation (\( \Delta G_f^\circ \)) of a compound is defined as the change in Gibbs free energy (\( \Delta G \)) when one mole of the compound is formed from its elements in their most stable forms at standard conditions (1 bar pressure and 298.15 K temperature, unless specified otherwise). Mathematically, it can be expressed as:

\[ \Delta G_f^\circ = G_{products}^\circ - G_{reactants}^\circ \]

where \( G_{products}^\circ \) and \( G_{reactants}^\circ \) are the Gibbs free energies of the products and reactants, respectively, under standard conditions.

Significance

The Gibbs free energy of formation is a fundamental parameter in predicting the direction of chemical reactions. A negative \( \Delta G_f^\circ \) indicates that the formation of the compound from its elements is spontaneous under standard conditions, while a positive value suggests that the reaction is non-spontaneous. Compounds with a very negative \( \Delta G_f^\circ \) are typically more stable and less reactive.

Calculation

The Gibbs free energy of formation can be calculated using the following relation:

\[ \Delta G_f^\circ = \Delta H_f^\circ - T\Delta S^\circ \]

where:

• \( \Delta H_f^\circ \) is the enthalpy of formation of the compound,
• \( T \) is the temperature in Kelvin,
• \( \Delta S^\circ \) is the change in entropy of the system.

This equation highlights the interplay between enthalpy and entropy changes in determining the spontaneity of a reaction.

Applications

The Gibbs free energy of formation is widely used in various fields such as:

• Chemical engineering: In the design and analysis of chemical processes.
• Environmental science: In assessing the environmental impact of chemical reactions.
• Materials science: In predicting the stability of materials and their reactions.
• Biochemistry: In understanding the energetics of biochemical reactions.

See Also

• Thermodynamics
• Chemical reaction
• Enthalpy
• Entropy