Gibbs Energy Change in Chemical Thermodynamics

Gibbs energy change refers to the thermodynamic potential that is used to evaluate the highest reversible work done by a thermodynamic system at constant pressure and temperature. It is the highest amount of non-expansion work which can be drawn out from a thermodynamically closed system (exchange of work and heat takes place with its surroundings but not with matter). This maximum work can be only achieved in an entirely reversible process.

When a system changes from its initial state to final state, reduction in Gibbs energy change is equivalent to the system’s work done to its surroundings, and minus the work done by pressure forces.

Gibbs energy represented by symbol G is also the minimised thermodynamic potential when a system attains a state of chemical equilibrium at constant temperature and pressure. Its derivative with regards to the system’s reaction coordinate disappears at the point of equilibrium. For this reason, the decrease in G is essential for a spontaneous reaction at fixed temperature and pressure.

In the 1870s, American scientist Josiah Willard Gibbs developed Gibbs free energy, which was originally known as available energy. He, in the year 1873, illustrated this “available energy” as something like:

“The greatest amount of mechanical work that can be attained from a given amount of a specific substance in a given original state, without increasing its total capacity or letting heat to pass to or from external bodies, except such as at the end of the processes are left in their original condition.”

The Gibbs energy change is explained concerning three state functions like:

• Enthalpy

• Temperature

• Entropy

Since this energy is a mixture of state functions, it is also called a state function.

ΔG = ΔH – TΔS

Here, all the thermodynamic quantities belong to the system. So, under standard conditions, the above Gibbs free energy change equation can be expressed as:

ΔG° = ΔH° – TΔS°

As G is considered a state function, ΔGo can be achieved from “standard free energy change of formation” values in standard thermodynamic quantities or extended thermodynamic properties of substances through the same relationship utilised to evaluate ΔH° and ΔS°.

Standard Free Energy Change of Formation

A compound’s standard energy change of formation is the Gibbs energy change that goes along with the formation of one mole of that same substance from its constituent elements at standard rates (the maximum stable form at 25 degree Celsius and 100 kilo Pascal). The symbol is ΔfG˚.

The standard Gibbs free energy of all the elements in their standard states (graphite, diatomic oxygen gas, etc.) is zero because there is no involvement of any change.

ΔfG = ΔfG˚ + RT ln Qf

Here, Qf is reaction quotient.

At the state of equilibrium,

ΔfG = 0, and Qf = K, so the expression becomes

ΔfG˚ = −RT ln K,

where K = equilibrium constant.

The following Table Shows ΔfG˚ of Some Selected Substances.

Gibbs Energy Change and Equilibrium

Let’s take a homogeneous chemical reaction as the following:

A + B ⇌ C + D

In this reaction, all the substances are in gaseous form at a temperature of interest. If the total sum of the products’ standard free energies is smaller than the reactants, delta G° will be –ve for the reaction, and it will proceed towards the right. 

If the reactants get entirely converted to products, equilibrium constant will be infinity. The equilibrium constants which are observed hold finite values, which implies that although the products hold lesser free energy as compared to the reactants, few of the latter will always remain when the process reaches a state of equilibrium.

Note: A homogeneous reaction is a reaction where everything occurs in a single liquid or gas phase.

To comprehend how equilibrium constants are related to values of delta G°, you need to assume that all the reactants are gases, such that for example, gas A’s free energy is given by:

GA = G°A + RTlnPA ............(1)

The free energy change is equivalent to the sum of products’ free energies minus the sum of reactants’ free energies. 

ΔG = GC + GD – GA – GB............(2)

GC and GD are products, and GA and GB are reactants.

Utilising equation number (2) to expand every term of equation number (3):

ΔG = (G°C + RTlnPC) + (G°D + RTlnPD) – (G°B + RTlnPB) – (G°A + RTlnP + A)

Now, G∘ can be expressed as delta G∘, and logarithmic pressures can be combined into a single fraction:

ΔG = ΔG° + RTln ( PCPD / PAPB )

The above equation can be further expressed conveniently through reaction quotient Q:

ΔG = ΔG° + RTlnQ

The quantity of free energy (G) gradually becomes more -ve during any natural process. Therefore, when a chemical reaction occurs, G falls and never becomes more +ve. In due course, a certain point is achieved where further conversion of reactants into products will make G to rise. At this point, free energy (G) is minimum, and no further change can occur; then the reaction is at equilibrium.

When the reaction proceeds towards equilibrium, ΔG value becomes less –ve and reaches zero. At the state of equilibrium, ΔG is 0 and Q = K so that it can be written as:

ΔG° = –RT ln K, where K is equilibrium constant; special value of Q corresponding to equilibrium composition.

To understand better, take a look at the following example:

Dissociation of Dinitrogen Tetroxide

The necessary gas-phase reaction is N204 🡪 2NO2

This is a very easy example of a homogeneous reaction’s free energy relationships.

Image will be uploaded soon

One mole of N2O4 (1) free energy is lesser than two moles of NO2 (2) by 5.3 kJ, which means ΔG∘ = + 5.3 kJ for the entire conversion of reactants into products. According to the image above, the diagonal line represents the free energy of all conceivable compositions, if N2O4 and NO2 were restricted from getting mixed. Free energy of the actual reaction is shown by the curved red line. This line proceeds through a lowest at (3) where 0.814 moles of dinitrogen tetroxide are in equilibrium with 0.372 moles of nitrogen dioxide. Free energy of mixing of products and reactants corresponds to (4) that will always be an equilibrium mixture whose G is less than pure reactants or pure products. Hence, some quantity of reaction will take place even if ΔG° is +ve.

What is the Difference Between ΔG° and ΔG?

You must know the dissimilarity between these two quantities as the ∘ (degree) symbol makes a huge difference. ΔG° holds a single value for a specific reason at given pressure and temperature, and the difference is:

Σ G°f,products - Σ G°f,reactants

Whereas, ΔG shows the sum of free energies of all the elements involved in a reaction mixture at any specific system composition. ΔG continuously varies as the composition changes and finally reaches zero at equilibrium. 

Solved Numerical on Gibbs Free Energy

Question. Calculate the change in standard free energy for the given reaction at a temperature of 25 degree Celsius.

N2 + 3H2 🡪 2NH3

Delta H and S are -81.5 KJ and -189.0 J/K, respectively.

Solution.

By putting the values in equation ΔG = ΔH – TΔS:

ΔG = -81.5KJ – (298 K) (-0.1890KJ/K)

ΔG = -24.7KJ

The above discussion on what is Gibbs energy and the criteria for equilibrium must have cleared your concept regarding the same. For more related topics of Chemistry, you can download the Vedantu app and get access to hundreds of study materials and online tutorials.