# Gibbs free energy

## Introduction to Gibbs Free Energy

Gibbs Free Energy, also known as Gibbs Function, is a thermodynamic quantity introduced by J.W. Gibbs in the late 19th century. It is a measure of the maximum amount of energy that can be obtained from a chemical reaction or physical process under constant temperature and pressure conditions. Essentially, it is a way of predicting whether or not a reaction will occur spontaneously or require an input of energy to proceed.

The Gibbs Free Energy equation takes into account two key factors: the change in enthalpy (heat) of the system and the change in entropy (disorder) of the system. If the change in enthalpy is negative (exothermic), and the change in entropy is positive (more disorder), then the Gibbs Free Energy is negative, meaning that the reaction is spontaneous and can occur without an input of energy. If the Gibbs Free Energy is positive, the reaction is non-spontaneous and will require an input of energy to proceed.

Gibbs Free Energy is an important concept in the study of thermodynamics and is often used in chemistry and engineering applications to determine the feasibility of a reaction or process.

## Calculating Gibbs Free Energy

The Gibbs Free Energy equation is given as:

ΔG = ΔH – TΔS

where ΔG is the change in Gibbs Free Energy, ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy.

To calculate the Gibbs Free Energy of a reaction or process, the values for ΔH and ΔS must be determined experimentally or theoretically. These values are typically reported in units of kilojoules per mole (kJ/mol).

Once the values for ΔH and ΔS are known, the Gibbs Free Energy can be calculated using the equation above. A negative value for ΔG indicates that the reaction is spontaneous, while a positive value indicates that the reaction is non-spontaneous.

## Applications of Gibbs Free Energy

The concept of Gibbs Free Energy has many important applications in chemistry, engineering, and other fields. For example, it can be used to predict the behavior of chemical reactions, including the direction and rate of reaction. It can also be used to design and optimize industrial processes, such as the production of chemicals and fuels.

In addition, Gibbs Free Energy can be used to study the stability of materials and the formation of crystals. It is also an important concept in the study of biological systems, where it is used to understand the behavior of enzymes and other biomolecules.

Overall, the concept of Gibbs Free Energy is a fundamental part of thermodynamics and has many important applications in various fields of science and engineering.

## Example of Gibbs Free Energy Calculation

One example of calculating the Gibbs Free Energy involves the combustion of methane gas (CH4) to form carbon dioxide (CO2) and water (H2O).

The balanced chemical equation for this reaction is:

CH4 + 2O2 → CO2 + 2H2O

The values for ΔH and ΔS for this reaction have been determined experimentally and are -890.4 kJ/mol and -0.242 kJ/K/mol, respectively.

To calculate the Gibbs Free Energy for this reaction at 298 K, we can use the equation:

ΔG = ΔH – TΔS

ΔG = -890.4 kJ/mol – (298 K)(-0.242 kJ/K/mol)

ΔG = -890.4 kJ/mol + 72.116 kJ/mol

ΔG = -818.3 kJ/mol

Since the value of ΔG is negative, we can conclude that the reaction is spontaneous and will occur without an input of energy.

This example illustrates how the concept of Gibbs Free Energy can be used to predict the behavior of chemical reactions and determine their feasibility.