Have you ever tried calculating the energy of a chemical reaction? If so, then you’ve probably already dealt with heat changes (enthalpy) and disorder of systems (entropy). Scientists usually use the Gibbs free energy equation to combine these two values into a single formula to be able to describe the formation of compounds from their constituent elements at the standard state.
In this article, we will learn all about the Gibbs free energy of formation: what it is, what is tells us, and how to calculate it.
This article is about the free energy of formation.
First, we’ll define the free energy of formation.
Then, we’ll relate it to Gibbs Free Energy and Enthalpy.
Next, we’ll look at a free energy formation chart and equation.
Lastly, we’ll go over examples of free energy of formation, featuring water and ammonia.
The Free Energy of Formation Definition
Free energy, G, is the energy available to do work.
The (standard) Gibbs free energy of formation (ΔGf°) refers to the free energy change when 1 mole of a substance is formed from its component elements in their reference states.
The reference state is the most thermodynamically stable state at standard temperature (1 bar) and standard temperature (25 °C). It is used as a reference point to calculate certain properties under a given set of conditions.
The formula for the Gibbs free energy of formation is:
$$\Delta G^\circ_f=\Sigma \Delta G^\circ_{f\,(products)}- \Sigma \Delta G^\circ_{f\,(reactants)}$$
The "Σ" symbol is called a summation symbol. What this means is that all the GIbbs free energy values for the products/reactants are added. For example, this would look like: $$\Sigma \Delta G^\circ_{f\,(products)}=\Delta G^\circ_{f\,a}+\Delta G^\circ_{f\,b}$$ Where a and b are products
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 (ΔHf°), 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 (ΔHf°), 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.
For more information regarding enthalpy and Gibbs free energy, please refer to our “Enthalpy” and “Gibbs Free Energy” articles.
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.
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