Free Energy of Formation

The Free Energy of Formation Definition

The formula for the Gibbs free energy of formation is:

$$\Delta G^\circ_f=\Sigma \Delta G^\circ_{f\,(products)}- \Sigma \Delta G^\circ_{f\,(reactants)}$$

For example, here is the Gibbs free energy of liquid water:

$$2H_{2\,(g)} + O_{2\,(g)} \rightarrow 2H_2O_{(l)}:\,\,\,\Delta G^\circ_f=-228.6\frac{kJ}{mol}$$

Meanwhile, the standard enthalpy, or heat of formation (ΔH_f°), is the heat absorbed or released when 1 mole of a substance is formed from its respective elements in their standard states (Standard elements in their reference form have a free energy of formation of zero).

Both the standard enthalpy of formation (ΔH_f°), and entropy of formation (S°), relate to Gibbs free energy, as we use the Gibbs free energy equation to calculate both entropy and enthalpy together.

Enthalpy is the total change in heat within a system when pressure is constant. While entropy is the randomness or disorder of a system.

The Free Energy of Formation Equation

Now that we understand each term in the free energy of formation equation, we can begin to understand the equation itself.

$$ \Delta G^\circ = \Delta H^\circ - T \Delta S^\circ $$

Where

• \( \Delta G^\circ \) is the change in free energy
• \( \Delta H^\circ \) is the change in enthalpy or heat
• \(T\)\( \Delta S^\circ \) is the change in entropy (S) and temperature (T)

The free energy of formation basically refers to the change in Gibbs Free Energy when 1 mole of product is formed.

An important question regarding this equation is:

What does \(\Delta G\)'s sign say about the equation?

\(\Delta G\) tells you the direction of a chemical reaction and if it's spontaneous or not.

\(\Delta G\) > 0 exergonic reaction = spontaneous

\(\Delta G\) = 0 the system is at equilibrium

\(\Delta G\) < 0 endergonic reaction = not spontaneous

At equilibrium, there is no net change in the concentration of products and reactants.

$$\Delta G^\circ=\Sigma \Delta G^\circ_{products}- \Sigma \Delta G^\circ_{reactants}$$

You find the free energy of formation in a reaction by subtracting the sum of the free energy of formation for each reactant from the sum of the free energy of formation for each product.

On top of knowing about the Gibbs free energy signs, we should also understand what exergonic and endergonic reactions are:

Fig. 1 - Exergonic vs. Endergonic reaction. Daniela Lin, StudySmarter Originals.

Exergonic means that energy is released to the surroundings, as the bonds being made are stronger than the ones being broken.

In contrast, endergonic signifies that the energy is absorbed from the surroundings since the bonds being broken are stronger than the ones being made.

The Free Energy of Formation Table and Chart

The free energy of formation table and chart is given to establish a better understanding of how the Gibbs free energy equation, the free energy of formation, and enthalpy play a role when it comes to chemical reactions.

The chart below contains some of the most common compounds and their free energies of formation. Later on, we’ll go over some examples utilizing this chart.

Fig. 2 - The Free Energy of Formation Table and Chart of the most common compounds. Daniela Lin, Study Smarter Originals.

Some common free energy data are displayed in alphabetical order above. Notice how the elements in their standard states have a free energy formation of zero.

Free Energy of Formation Examples

Free Energy of Formation of Water

Gibbs Free Energy of Formation of Ammonia

We’ve reached the end of the article. Now you should understand what the free energy of formation is, why it works, and how to apply it. For more practice, please head over to our flashcards section!