# Gibbs Free Energy Calculator

Created by Davide Borchia
Last updated: Dec 16, 2022

The Gibbs free energy is a fundamental quantity in chemistry: our Gibbs free energy calculator will uncover every secret of this fundamental thermodynamic concept.

Here we will not fear treading the notoriously treacherous ground of thermodynamics: we will guide you in an in-depth analysis of one of the chemists' most loved thermodynamic potentials: the Gibbs free energy. Keep reading to learn:

• What is the Gibbs free energy;
• What is the Gibbs free energy equation;
• Introducing variations: the delta G equation;
• A couple of words about enthalpy and entropy; and
• Free energy and spontaneity.

Our Gibbs free energy calculator will tell you the final answer: will this reaction go or not?

## What is the Gibbs free energy?

The Gibbs free energy is a thermodynamic potential (a scalar quantity that describes a thermodynamic state function, a function dependent only on the initial and final point of a process). The Gibbs free energy is defined if two conditions are satisfied:

• The temperature is constant (isotherm): processes like boiling water.
• The pressure is constant (isobar): any process conducted in an open container: excess or negative pressure would be quickly balanced by the environment.

## How to calculate the Gibbs free energy

The Gibbs free energy is defined in terms of other thermodynamic quantities, both thermodynamic potentials and mechanical or thermal variables.

The equation for the Gibbs free energy is:

$G=H-T\cdot S$

Where:

• $G$ is the Gibbs free energy;
• $H$ is the enthalpy;
• $T$ is the temperature; and
• $S$ is the entropy.

The enthalpy can be defined in terms of other quantities, somewhat completing the formula for the free energy:

$G = U + p\cdot V - T\cdot S$

Where we introduced:

• $U$, the free energy;
• $p$, the pressure; and
• $V$, the volume.

## The Gibbs free energy in a chemical reaction

In general, we exclude the mechanical work from the calculations (meaning that the variation of the volume is zero). Doing so, the value of a variation of the Gibbs free energy in a chemical reaction directly defines the spontaneity of the reaction itself.

We write the variation of the thermodynamic quantities from the end to the beginning of the reaction as:

$\Delta G = \Delta H - T\cdot\Delta S$

Where $\Delta$ indicates a finite change in the quantities. Notice how the temperature has no $\Delta$: we told you that to calculate the equation for the delta G we need to set that parameter constant.

## Entropy and enthalpy

Entropy and enthalpy are two fundamental quantities in the definition of the Gibbs free energy. The enthalpy is a thermodynamic potential that measures the internal energy of the system, or, in other words, the heath flow. Enthalpy is an energy, hence we measure it in joules.

Entropy is a thermal variable: a rather obscure concept of physics, entropy measures the disorder of a system and is linked to the fundamental physics of our Universe through the second law of thermodynamics, which states that in isolated systems, the entropy can only increase. A seemingly inoffensive sentence that hides the nature of time and seals the fate of the Universe. Entropy is not an energy and — at least in thermodynamics — has the dimensions of a ratio between energy and temperature: we measure it in joules per kelvin.

## The delta G equation as a way to define the spontaneity of a chemical reaction

The result of the formula for the free energy in a chemical reaction gives us fundamental information on the spontaneity of the reaction.

The value of the free energy calculated in the delta G equation corresponds to the available energy in a chemical reaction:

• If the mechanical work isn't zero, the variation of the free energy must take into account the product $p\Delta V$ to assess the spontaneity of the reaction. Subtract this term and follow the next points to proceed (you can find its value, for example, using the if you know the displacement and force of a piston).
• If the mechanical work is zero, we can directly use the Gibbs free energy equation with internal energy, which tells us that:
• If $\Delta G\text{\textless}0$, the reaction is spontaneous and proceeds while transferring energy towards the environment;
• If the calculated free energy variation is $\Delta G\text{\textgreater}0$, the reaction is non-spontaneous and requires us to input energy to proceed (chemists call this the activation energy).

Chemical reactions are categorized according to the variation of the calculated Gibbs free energy in:

• Endergonic reactions, for non-spontaneous processes; and
• Exergonic reactions for spontaneous processes.

Don't mistake the concept of end- and ex- ergonic with the emission or absorption of heat in the environment. The classification in endo- and exo- thermic reactions is due to the variation in enthalpy, and it slightly changes the distinction between spontaneous and non-spontaneous reactions.

🙋 Notice that in a reversible reaction, the variation of delta G tells us the direction of the reaction. In one direction, we would have free energy $\Delta G$, while in the other, with inverted final and starting point, we would have $-\Delta G$.

## How to use our Gibbs free energy calculator?

Our Gibbs free energy calculator is... spontaneous to use. Insert the value of the thermodynamic quantities you know (enthalpy, entropy, and temperature), and let us do the math: in the blink of an eye, you will see the value of $\Delta G$, and you will know if your reaction will run or no. But remember, as for everything in thermodynamics: be sure to understand the concept before launching yourself on the calculations. They may look easy, but they hide the complexity of the Universe.

Davide Borchia
ΔG = ΔH − T × ΔS
Enthalpy change (ΔH)
kJ
Entropy change (ΔS)
kJ
Temperature (T)
K
Gibbs free energy (ΔG)
kJ
People also viewed…

### Gay-Lussacs's law

Learn how to find the missing variable in an isochoric process with our Gay-Lussac's law calculator.

### Latent Heat

This latent heat calculator finds the latent and specific latent heat for many substances.