Gibbs free energy, often referred to simply as Gibbs energy, is a fundamental thermodynamic state function that quantifies the energy available for performing work within a thermodynamic system. This critical concept is defined as the difference between the system's enthalpy and the product of its temperature and entropy. Essentially, Gibbs energy serves as a gauge for assessing the potential of a chemical reaction to occur, with negative values indicating spontaneous reactions.
The change in Gibbs energy during a chemical reaction, known as Gibbs energy change, reflects the difference in Gibbs free energy from the reaction's initial state to its final state. This change is influenced by both the enthalpy and entropy variations associated with the reaction. By evaluating Gibbs energy change, we can determine the spontaneity of a reaction: a positive change signals that the reaction is non-spontaneous and requires energy input, while a negative change indicates that the reaction is spontaneous and releases energy.
Gibbs energy change is not only pivotal in assessing spontaneity but also plays a vital role in calculating equilibrium constants and determining the energy dynamics—whether energy is absorbed or released—during a reaction. Furthermore, it assists in evaluating reaction mechanisms and establishing the thermodynamic feasibility of various reactions.
In summary, Gibbs energy change is an essential aspect of thermodynamics, providing valuable insights into the behavior of thermodynamic systems. It serves as a critical tool for scientists studying chemical processes and developing new materials.
In an electrochemical cell, the Gibbs free energy change (ΔG) is directly related to the cell's EMF (E) through the equation:
ΔG = -nFE
Where:
This equation indicates that a spontaneous reaction (ΔG < 0) corresponds to a positive EMF, meaning the cell can perform electrical work. Conversely, a non-spontaneous reaction (ΔG > 0) has a negative EMF, requiring external energy to proceed.
| Parameter | Symbol | Relationship with ΔG |
| Electromotive Force (EMF) | E | ΔG = -nFE |
| Standard EMF | E° | ΔG° = -nF E° |
| Equilibrium Constant | K | ΔG° = -RT ln K |
| Reaction Quotient | Q | ΔG = ΔG° + RT ln Q |
| Number of Electrons Transferred | n | Directly proportional to ΔG |
| Faraday's Constant | F | F ≈ 96,485 C/mol |
| Universal Gas Constant | R | R = 8.314 J/(mol·K) |
The derivation of the relationship between Gibbs free energy change and EMF involves considering the work done by the electrochemical cell. The maximum work obtainable from a galvanic cell is equal to the decrease in Gibbs free energy of the cell reaction. This is expressed as:
ΔG = -nFE
Under standard conditions (1 M concentration, 1 atm pressure, 25°C), the standard Gibbs free energy change (ΔG°) and the standard EMF (E°) are related by:
ΔG° = -nF E°
For non-standard conditions, the Nernst equation is used to determine the EMF of the cell:
E = E° - (RT/nF) ln Q
Where:
At equilibrium, the Gibbs free energy change (ΔG) is zero, and the reaction quotient (Q) equals the equilibrium constant (K). The relationship between the standard Gibbs free energy change (ΔG°) and the equilibrium constant is given by:
ΔG° = -RT ln K
This equation shows that a large equilibrium constant (K > 1) corresponds to a negative ΔG°, indicating a spontaneous reaction under standard conditions.
The EMF of a cell is a measure of the cell's ability to perform electrical work. Since ΔG represents the maximum reversible work that can be performed by the system, the relationship ΔG = -nFE directly links the EMF to the free energy change.
The reduction potential of a half-cell is a measure of its tendency to gain electrons (be reduced). The standard reduction potential (E°) is related to the standard Gibbs free energy change (ΔG°) by:
ΔG° = -nF E°
The maximum work obtainable from a galvanic cell is equal to the decrease in Gibbs free energy of the cell reaction. This maximum work is achieved under reversible conditions, where the process occurs infinitely slowly, allowing the system to remain in equilibrium throughout the reaction.
In an electrochemical cell, the Gibbs free energy change of the reaction determines the cell's ability to perform electrical work. A negative ΔG indicates a spontaneous reaction, allowing the cell to generate electrical energy.
The cell potential is the potential difference between the two electrodes of a galvanic cell, and it is measured in volts,, whereas the emf is the difference among the electrode potentials of the cathode and anode.
Magnetic resonance imaging (MRI), radiofrequency ablation (RFA) used in cardiology and tumor therapy, and localized dielectric heating (short wave diathermy) used in physiotherapy are the three main EMF applications in medicine.
The maximum amount of work that can be extracted from a closed system is characterized as Gibbs free energy.
