# Gibbs Free Energy Calculator

By Dominika Miszewska, PhD candidate
Last updated: Sep 09, 2021

This Gibbs free energy calculator is just perfect if you're looking for a tool that estimates whether or not a reaction can happen spontaneously. The Gibbs free energy equation, A.K.A. the delta G equation, combines the enthalpy vs. entropy relation.

The upcoming paragraphs tell you how to calculate Gibbs free energy, provide the Gibbs free energy units, and give the uses of this delta G calculator.

## Gibbs free energy

What is Gibbs energy? In equations it is known as G, and it's a combination of enthalpy and entropy. The sign in front of Gibbs free energy indicates the direction of the chemical reaction, as long as two conditions are met:

In such a case, there are two possible options depending on what you get from the delta G formula:

1. If ΔG > 0, the reaction is nonspontaneous - external energy is crucial for the reaction to begin. This external energy can be heat, a photon, or any other source of energy.

2. If ΔG < 0, the reaction is spontaneous and happens without any external energy. You don't need to add anything, the atoms within the reaction will initialize it by themselves.

## Delta G equation

The delta G formula for how to calculate Gibbs free energy (the Gibbs free energy equation) is:

`ΔG = ΔH − T * ΔS`

where:

• ΔG is the change in Gibbs free energy;
• ΔH is the change in enthalpy;
• ΔS is the change in entropy; and
• T is the temperature in Kelvin.

Again, the answer to "What is Gibbs energy?" is that it combines are enthalpy vs. entropy and their relationship.

## Enthalpy vs. entropy

Enthalpy, here noted as H, is a kind of energy - the sum of of the molecules' internal energies and the flow of energy. Entropy, on the other hand, noted S, is a measurement of the randomness of molecules.

The system tries to reach minimum enthalpy and maximum entropy at all times.

Enthalpy's unit is `J * mol -1`, while entropy's is `J/K`.

Therefore, we can derive the Gibbs free energy units from the Gibbs free energy equation. These are simply units of energy, typically `J`.

## Gibbs free energy calculator

This tool applies the formula to real-life examples. All you need to know is three out of four variables: change in enthalpy (ΔH), entropy (ΔS), temperature (T), or Gibbs free energy (ΔS). As the formula can be read backwards or in any direction, just put in all the data you have and see the fourth number appear.

For the sake of completeness, here are all the formulas we use:

• `ΔG = ΔH − T * ΔS`;
• `ΔH = ΔG + T * ΔS`; and
• `ΔS = (ΔH − ΔG) / T`.

## Delta G calculator in practice

Knowing the theory behind what is Gibbs energy without knowing how to use it in practice is no use to anyone. That's why we prepared a simple example of how to calculate Gibbs free energy with this tool. Imagine you have a reaction and know its initial entropy, enthalpy and that it happens at 20°C. Moreover, there's also a note on the final entropy and enthalpy.

Now all you need to figure out is whether the reaction is spontaneous or if it needs external energy. In that case, let's calculate the Gibbs free energy!

Let's work it out with the following reaction:

`N2 + 3H2 = 2NH3`

• Initial enthalpy: H0 = 0;
• Final enthalpy: H1 = -92.22 kJ * mol -1;
• Initial entropy: S0 = 583.65 J/K;
• Final entropy: S1 = 384.9 J/K; and
• T = 20oC = 20 + 273.15 = 293.15 K.

Therefore,

• ΔH = -92.22 kJ * mol -1; and
• ΔS = -198.75 J/K = -0.19875 kJ/K.

From the delta G formula:

`ΔG = ΔH − T * ΔS`

`ΔG = -92.22 - (-0.19875 * 293.15)`

`ΔG = -33.96 kJ`

💡 Check twice if the Gibbs free energy units seem reasonable, in relation to enthalpy and entropy units.

The delta G equation result is below zero, which means that the reaction is spontaneous.

Dominika Miszewska, PhD candidate
ΔG = ΔH − T * ΔS
Enthalpy change (ΔH)
kJ
Entropy change (ΔS)
kJ
Temperature (T)
K
Gibbs free energy (ΔG)
kJ
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