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

Gibbs Free Energy is a thermodynamic quantity that measures the amount of usable energy in a system to perform work at a constant temperature and pressure. It helps predict the spontaneity of a reaction; if the Gibbs Free Energy is negative, the process can occur spontaneously, indicating it’s energetically favorable.

Dive into the world of thermodynamics where Gibbs Free Energy stands as a pivotal concept, bridging the gap between physics and chemistry. It’s the key to understanding how and why chemical reactions occur, offering insights into the spontaneity of processes and the balance of energetic transformations in our universe.

## 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. Suppose there’s a change in Gibbs’s free energy, a negative change, or a downhill direction for Gibbs’s free energy. In that case, 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.

## What is Gibbs free energy in thermodynamics?

In thermodynamics, Gibbs Free Energy (G) is a state function that measures the usable energy, or free energy, available to perform work in a thermodynamic system at a constant temperature and pressure. It is named after Josiah Willard Gibbs, who introduced the concept in the late 19th century. Gibbs Free Energy is central to chemical thermodynamics for predicting the direction of chemical reactions and determining whether a process is spontaneous.

Definition and Formula

The equation defines the Gibbs Free Energy of a system:

G = H − TS

where:

G is the Gibbs Free Energy,

H is the enthalpy of the system,

T is the temperature in Kelvin,

S is the entropy of the system.

The change in Gibbs Free Energy (ΔG) during a process is given by:

ΔG = ΔH−TΔS

where ΔH is the change in enthalpy, ΔS is the change in entropy, and T is the absolute temperature at which the process occurs.

Spontaneity and Equilibrium

Spontaneous Processes: A process is spontaneous if it occurs without needing to be driven by an external force. For a reaction at constant temperature and pressure, spontaneity is determined by the sign of ΔG:

If ΔG<0, the process is exergonic (releases energy) and occurs spontaneously.

If ΔG>0, the process is endergonic (absorbs energy) and is non-spontaneous under the given conditions.

If ΔG=0, the system is in a state of equilibrium, where the forward and reverse reactions occur simultaneously.

Equilibrium: At equilibrium, the Gibbs Free Energy of the system is at a minimum, and there is no net change in the system’s composition over time. The condition ΔG=0 derives the equilibrium constant for chemical reactions, linking thermodynamics with chemical kinetics.

Importance in Chemical Reactions

The concept of Gibbs Free Energy is crucial for understanding and predicting the behavior of chemical reactions, including:

The direction in which a chemical reaction will proceed.
The extent to which reactants are converted into products.
How changes in conditions (like temperature and pressure) affect the spontaneity of reactions.

Application in Biological Systems

In biochemistry, Gibbs Free Energy explains how cells harness energy from exergonic reactions (e.g., the breakdown of glucose during cellular respiration) to drive endergonic processes necessary for life, such as muscle contraction, active transport across cell membranes, and the synthesis of biomolecules.

Environmental and Industrial Applications

Gibbs Free Energy is also applied in environmental science and engineering to assess the feasibility of reactions in processes like forming mineral deposits, corrosion, and developing renewable energy technologies.

In summary, Gibbs Free Energy is a fundamental thermodynamic quantity that serves as a criterion for spontaneity and equilibrium in chemical and physical processes, underpinning the theoretical and practical understanding of virtually all chemical reactions and energy transformations.

## What is Gibbs free energy in Electrochemistry?

In electrochemistry, Gibbs Free Energy plays a crucial role in understanding and predicting the behavior of electrochemical reactions, which are the basis of batteries, fuel cells, and electrolysis processes. The change in Gibbs Free Energy (ΔG) in an electrochemical reaction provides insight into the feasibility of the reaction and the electrical work that can be obtained from or required by an electrochemical cell.

Relationship between Gibbs Free Energy and Electrochemical Cells

The change in Gibbs Free Energy for an electrochemical reaction is related to the electrical work done by the cell, which is given by the equation:

ΔG = −nFE cell

where:

ΔG is the change in Gibbs Free Energy,

n is the number of moles of electrons transferred in the reaction,

F is the Faraday constant (96, 485 C mol−1), representing the charge per mole of electrons,

Ecell is the electrochemical cell’s electromotive force (EMF) or cell potential in volts.

Spontaneity of Electrochemical Reactions

The sign of ΔG and the value of Ecell determine the spontaneity of the electrochemical reaction:

If ΔG < 0 and Ecell > 0, the reaction is spontaneous, indicating that the electrochemical cell can function as a galvanic (voltaic) cell, generating electrical energy from a chemical reaction.

If ΔG > 0 and Ecell < 0, the reaction is non-spontaneous as written, meaning that external electrical energy is required for the reaction to proceed, characteristic of an electrolytic cell.

Electrochemical Cell Potential and Gibbs Free Energy

The cell potential (Ecell) measures the driving force behind an electrochemical reaction. The difference in the reduction potentials of the cathode and anode determines it. The relationship between ΔG and Ecell reflects how the thermodynamics of a reaction (energy changes) directly translates into electrical work potential.

As we wrap up our journey through the realm of Gibbs Free Energy, we emerge with a deeper appreciation for the elegant principles that govern the natural world. This concept not only illuminates the path of reactions in the microscopic realm but also sheds light on the broader implications for biological systems and technological advancements, highlighting the intricate dance of energy that powers life itself.