# What Is Gibbs Free Energy (Factors, Problems & Examples)

## Gibbs Free Energy

In this lecture, I will introduce Gibbs free energy. What is Gibbs free energy? Gibbs free energy, like enthalpy, is a human-made concept that cannot be measured.

So you cannot use an instrument to measure the Gibbs free energy of some object. Gibbs’s free energy can only be measured experimentally. That’s because a formula defines Gibbs free energy and this formula only holds under certain conditions. If these conditions aren’t met, Gibbs’s free energy breaks down.

## What Is Gibbs Free Energy?

Josiah Gibbs was an American mathematician who came up with working out. We call free energy, and free energy is calculated by taking the enthalpy change of the reaction and taking it away from the temperature multiplied by the entropy. Delta G (∆G) is the symbol that symbolizes the Gibbs free energy.

The Gibbs function is the enthalpy minus the temperature times the entropy. If there’s a change in Gibbs free energy, a negative change, or a downhill direction for Gibbs free energy, that’s the favored direction for a chemical process or a physical strategy.

This equation is,

ΔG = ΔH − TΔS

Delta H (ΔH) is the enthalpy change in kilojoules per mole (KJ/mole), the temperature is measured in Kelvin, and the entropy change is measured in joules per kelvin per mole.

### Factors Affecting Gibbs Free Energy

If you put all the products and reactants at one molar, if it’s a concentration, and one atmosphere, if it’s a gas, pure liquids, or pure solids, this standard free energy difference gives you the relative ordering of those standard states of reactants and standard state products.

Key Points

• If the standard state products are higher in energy than the standard state reactants, that’s a positive ΔG, which says that the reactants are favored. The reactants have stronger bonds than our products, and therefore, our reactants are more stable. If it becomes more positive, we have more freedom in our products than our reactants.
• If the products are lower in free energy in their standard states than the reactants, a negative free energy difference and the products are favored. Also, If we have an exothermic reaction, our products have stronger bonds with more stable bonds than our reactants. The reaction will be spontaneous.

So, you can talk about the various changes in enthalpy, entropy, and free energy. For a process to be spontaneous, to be favored by the universe. It could have a decrease in enthalpy. It could release energy, or it could absorb energy. Or the system could go towards a higher entropy state, with more microstates to disperse the energy. Or it could go to a lower entropy state, where the number of microstates is smaller.

Since free energy is a state function, I can calculate the free energy change for a reaction by taking the standard free energies of the formation of the products minus the standard free energies of the reactants’ formation. So this gives me a powerful tool to determine whether a reaction is favored or unfavored based on the products’ free energies and reactants’ formation.

Key Points

Let’s look at these conditions. These conditions are constant temperature and pressure. The reaction must be reversible, and there is no mechanical work done. Only PV work is allowed to be done.

• In an isolated system, the number of moles stays the same. That’s because there is no change in mass. So the number of moles stays the same, and the temperatures and pressure are constant. According to the ideal gas law, volume remains constant. So there is no volume change.

According to the formula for change in enthalpy, the PV work done is zero if there is no volume change. We can approximate the change in enthalpy to equal the internal energy or change in energy or heat.

### Significance of Gibbs free energy

Gibbs free energy, often denoted as ΔG, is a thermodynamic concept that provides valuable information about the spontaneity and equilibrium of a chemical reaction or physical process. It has significant implications in various scientific disciplines, including chemistry, biology, and physics. Here are some key significances of Gibbs free energy:

Spontaneity of Reactions: The sign of ΔG determines whether a reaction is spontaneous or non-spontaneous. A negative ΔG indicates a spontaneous reaction, which will proceed without requiring external energy input. On the other hand, a positive ΔG indicates a non-spontaneous reaction, requiring an input of energy to proceed.

Equilibrium Conditions: At equilibrium, the ΔG of a reaction is zero. This implies that the forward and reverse reactions occur at equal rates, and there is no net change in the concentration of reactants or products. Therefore, ΔG provides insights into the direction in which a reaction will proceed to achieve equilibrium.

Energy Availability and Work: Gibbs free energy is related to the maximum amount of work obtained from a system under constant temperature and pressure conditions. The difference between the initial and final values of ΔG determines the maximum non-expansion work that can be harnessed from the system.

Chemical Reactions and Biochemical Processes: In chemical reactions, the change in Gibbs free energy (ΔG) provides information about the energy changes associated with breaking and forming chemical bonds. In biochemical processes, ΔG helps determine the feasibility and energetics of metabolic pathways, such as ATP hydrolysis and enzyme-catalyzed reactions.

Thermodynamic Stability: The stability of a system can be assessed using Gibbs free energy. A lower ΔG corresponds to a more stable system, indicating a greater tendency for the system to remain in its current state. Conversely, a higher ΔG indicates less stability and a higher potential for change or spontaneous transformation.

Phase Transitions: Gibbs free energy is useful in understanding phase transitions, such as solidification, melting, vaporization, and condensation. By examining the changes in ΔG during these transitions, one can determine the conditions at which phase changes occur and the stability of different phases.

Overall, Gibbs free energy is a fundamental concept in thermodynamics that helps predict the spontaneity, equilibrium, and energetics of chemical reactions and physical processes.

### Unit of Gibbs Free Energy Equation

ΔG = Gibbs free energy, Unit: Joules per mole or J/Mol.
ΔH = Enthalpy change, Unit: Joules per mol or J/Mol.
T = Temperature, Unit: Kelvin (K). Temperature is always positive.
ΔS = Entropy change, Unit: Joules per kelvin per mole (J K⁻¹ mol⁻¹).

### Examples & Problems

Example: CH₄[gas] + 2O₂[gas] → CO₂[gas] + 2H₂O[steam] + Energy

Here Gibbs free energy problems:

Problem: 1

4KClO3(s) ⟶ 3KClO3(s) + KCl(s)
ΔG= ΔH−TΔS = −144KJ−298K (−0.036KJK) = −133KJ

Problem: 2

Cu2O(s) + C(s)⟶2Cu(s) + CO(g) ; Where, ΔH= 50, ΔS= 0.165
ΔG= 50 − 0.165T

### Conditions For Spontaneity

Gibbs free energy is an excellent indicator of whether we have a spontaneous or non-spontaneous reaction.

• If Gibbs Free Energy is negative or less than 0, it’s a spontaneous reaction. If enthalpy increases entropy, that’s going to be a spontaneous reaction. Here, ΔG < 0; Spontaneous & Exergonic reaction.
• If Gibbs Free Energy is ever positive or greater than 0, it’s not a spontaneous reaction. It’s not going to occur spontaneously. In other words, we’ll have to put some energy in for it to work.
Here, ΔG > 0; Spontaneous Backwards & Endergonic reaction.
• If Gibbs Free Energy is equal to zero, it will be in equilibrium.
Here, ΔG = 0; Equilibrium.

### Feasible Test

If Delta G is 0 or -1, the reaction is feasible at the state and temperature. But it might not be feasible depending on the temperature.

I hope you understand the Gibbs free energy properly. If you have any questions, then please comment down below.

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References:

Perrot, Pierre. A to Z of Thermodynamics. Oxford University Press. ISBN 0-19-856552-6.
Gibbs, Josiah Willard. “A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces.”
Peter Atkins; Loretta Jones. Chemical Principles: The Quest for Insight. W. H. Freeman.