Important Topic Of Chemistry: Gibbs Energy

Gibbs free energy, often referred to as Gibbs energy, is a cornerstone concept in chemistry and thermodynamics. It provides a quantitative measure of a reaction’s spontaneity under constant temperature and pressure. With wide-ranging applications in predicting reaction feasibility and equilibrium states, Gibbs free energy plays an integral role in science and engineering.

In this article, we’ll explore the definition, formula, and applications of Gibbs free energy, along with its significance in determining the spontaneity of chemical reactions.

What is Gibbs Free Energy?

Gibbs free energy is a thermodynamic potential that quantifies the maximum reversible work a system can perform at constant temperature and pressure. Represented by the symbol G, it measures the energy available for a process after accounting for energy losses due to entropy.

The concept is critical for understanding the direction and feasibility of chemical reactions. A negative Gibbs energy (ΔG<0) indicates a spontaneous process, while a positive value (ΔG>0) implies non-spontaneity.

Gibbs Free Energy: Historical Background & Its Role in Thermodynamics

• The concept of Gibbs free energy was introduced by Josiah Willard Gibbs in 1876. Gibbs developed this property to predict the spontaneity and equilibrium of reactions. Initially termed "available energy," the idea revolutionized thermodynamic studies and remains a foundational principle in modern chemistry.
• At constant temperature and pressure, Gibbs Energy is the maximum (or reversible) work that a thermodynamic system can perform. In thermodynamics, reversible work denotes a special method of carrying out work in such a way that the system remains in perfect equilibrium with all of its surroundings.
• Gibbs free energy is referred to as a thermodynamic potential in thermodynamics. Furthermore, this potential is used to compute the maximum amount of reversible work that a single thermodynamic system can perform at constant pressure and temperature.
• Furthermore, the SI unit for measuring Gibb’s free energy is Joules. Furthermore, when a thermodynamic system undergoes a reversible transformation from its initial to the final state, the decrease in Gibbs energy is proportional to the work done by this system and its surroundings.
• However, the work of pressure forces is not taken into account here. Furthermore, when a system reaches chemical equilibrium at constant temperature and pressure, its thermodynamic potential is minimized. Furthermore, at this equilibrium point, the derivative of this system with respect to its reaction coordinate vanishes.

Gibbs Free Energy: Formula, Spontaneity, and Thermodynamic Equilibrium

The Gibbs free energy (or Gibbs energy) is a thermodynamic potential that can be used to calculate the maximum reversible work that a thermodynamic system can perform at constant temperature and pressure. 

• The Gibbs free energy (∆G=∆H-T∆S measured in joules in SI) is the maximum amount of non-expansion work that can be extracted from a thermodynamically closed system (one that can exchange heat and work with its surroundings, but no matter). This maximum can only be reached through a completely reversible process.
• When a system undergoes a reversible transformation from an initial to a final state, the decrease in Gibbs free energy equals the work done by the system to its surroundings, minus the work of the pressure forces.
• The Gibbs energy (G) is the thermodynamic potential that is minimized when a system reaches chemical equilibrium at constant pressure and temperature. At the equilibrium point, its derivative with respect to the system’s reaction coordinate vanishes. As a result, lowering G is required for a reaction to being spontaneous at constant pressure and temperature.
• According to the second law of thermodynamics, there is a general natural tendency for systems reacting at standard conditions for temperature and pressure (or any other fixed temperature and pressure) to achieve a minimum of the Gibbs free energy.
• The change G (sometimes written “delta G” or “dG”) in Gibbs free energy that is (or would be) caused by the reaction is a quantitative measure of its favorability at constant temperature and pressure. As a prerequisite for the reaction to occur at constant temperature and pressure, G must be less than the non-pressure-volume (non-PV, e.g. electrical) work, which is frequently equal to zero (hence G must be negative).
• In the case of a reversible process, G equals the maximum amount of non-PV work that can be performed as a result of the chemical reaction. When two chemical reactions are coupled, an otherwise endergonic reaction (one with positive G) can occur.
• The incorporation of heat into an inherently endergonic reaction, such as the elimination of cyclohexanol to cyclohexene, can be viewed as coupling an unfavorable reaction (elimination) to a favorable one (coal combustion or another source of heat) such that the total entropy change of the universe is greater than or equal to zero, resulting in a negative total Gibbs free energy difference of the coupled reactions.

Formula for Gibbs Free Energy

The fundamental formula for Gibbs free energy is:

ΔG=ΔH−TΔS

Where:

ΔG: Change in Gibbs free energy (Joules)

ΔH: Change in enthalpy (Joules)

T: Temperature (Kelvin)

ΔS: Change in entropy (Joules per Kelvin)

or, more precisely, as;

G=U+PV-TS

Where,

U denotes internal energy (SI unit: joule)

P stands for pressure (SI unit: pascal)

V stands for volume (SI unit: m3 )

T is for temperature (SI unit: kelvin)

Entropy = S (SI unit: joule/kelvin)

Because Gibb’s free energy is a state function, it is independent of the path. So the change in Gibbs free energy is equal to the change in enthalpy minus the product of the system’s temperature and entropy change.

∆G=∆H-∆(TS)

This equation relates the thermodynamic properties of a system to its spontaneity.

Components of the Gibbs Free Energy Equation

a. Enthalpy (ΔH):

Enthalpy represents the total heat content of a system. A negative ΔH signifies an exothermic reaction, releasing energy into the surroundings.

b. Entropy (ΔS):

Entropy measures the system's disorder. Positive ΔS indicates increased randomness, favoring spontaneity.

c. Temperature (T):

Temperature influences the interplay between entropy and enthalpy. High temperatures magnify the impact of entropy on Gibbs energy.

Understanding Spontaneity Through ΔG

Spontaneity is determined by the sign of ΔG:

• ΔG<0: Reaction is spontaneous.
• ΔG>0: Reaction is non-spontaneous.
• ΔG=0: System is at equilibrium.

For instance, the transformation of diamond into graphite is a spontaneous reaction, though extremely slow under normal conditions.

Gibbs Energy in Reversible and Irreversible Processes

• Reversible Processes: Achieve maximum work efficiency, aligning with the decrease in Gibbs energy.
• Irreversible Processes: Involve energy dissipation, where the work done is less than the Gibbs energy change.

Relationship Between Gibbs Energy and Equilibrium

At chemical equilibrium, the Gibbs free energy of the system is minimized, and ΔG=0. This condition ensures that the forward and reverse reaction rates are equal, maintaining dynamic balance.

How Entropy and Enthalpy Affect Gibbs Energy

1. Exothermic Reactions (ΔH<0):

When coupled with positive ΔS, these reactions are always spontaneous.

2. Endothermic Reactions (ΔH>0):

Such reactions require significant entropy increases or high temperatures to achieve spontaneity.

Role of Temperature in Reaction Feasibility

The impact of temperature is evident in the term TΔS. For reactions with opposing ΔH and ΔS values:

• High temperatures favor entropy-driven reactions.
• Low temperatures favor enthalpy-driven reactions.

Gibbs Energy and Coupled Reactions

Reactions that are inherently non-spontaneous can proceed when coupled with spontaneous reactions. For example:

• The elimination of cyclohexanol to cyclohexene requires heat.
• Coupling this reaction with an exothermic process ensures overall spontaneity.

Applications of Gibbs Free Energy

• Chemical Engineering: Designing efficient reactions.
• Biochemistry: Understanding cellular energy transformations.
• Material Science: Predicting phase transitions.

Limitations of Gibbs Free Energy

• Does not provide information on reaction rates.
• Assumes constant temperature and pressure.

Examples of Spontaneous and Non-Spontaneous Processes

Spontaneous Processes:

• Ice melting at temperatures above 0°C.
• Diffusion of gas in a container.

Non-Spontaneous Processes:

• Electrolysis of water (requires energy input).

Conclusion

Gibbs free energy is a powerful tool for predicting the spontaneity and equilibrium of chemical processes. By linking thermodynamic properties like enthalpy and entropy, it offers invaluable insights into reaction feasibility across diverse scientific disciplines. Understanding ΔG enables researchers and engineers to design efficient systems and processes that align with nature's energy principles.