# Gibbs Free Energy Calculator

Created by Dominika Śmiałek, MD, PhD candidate
Reviewed by Dominik Czernia, PhD and Jack Bowater
Last updated: Aug 03, 2022

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 – Change in Gibbs free energy;
• ΔH – Change in enthalpy;
• ΔS – Change in entropy; and
• T – Temperature in Kelvin.

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

## Enthalpy vs. entropy

Enthalpy, here noted as H, is a kind of energy – the sum of the molecules' internal energies and the flow of energy. Entropy, on the other hand, noted as 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), change in entropy (ΔS), temperature (T), or change in Gibbs free energy (ΔS). As the formula can be read backward 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 Gibbs energy is 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:

$\small \rm N_2 + 3H_2 = 2NH_3$
• 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 = 20 °C = 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

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

💡 Double check if the Gibbs free energy units seem reasonable in relation to enthalpy and entropy units.

## FAQ

### How do I calculate Gibbs free energy?

To calculate Gibbs free energy:

1. Determine the temperature at which the reaction occurs.

2. Subtract the initial entropy from its final value to find the change in entropy.

3. Calculate the change in enthalpy in the same way.

4. Multiply the change in entropy by the temperature.

5. Subtract the product from the change in enthalpy to obtain the Gibbs free energy.

### Why is Gibbs free energy 0 at equilibrium?

Gibbs free energy is zero for systems at the equilibrium because there is no net change in any of the quantities it depends on. Since everything is constant, no energy is available to do any work (unless the process is disturbed!).

### What information does Gibbs free energy give about a reaction?

Gibbs free energy tells us about the maximum energy available in the system to do work. It's typically used to determine whether the reaction is spontaneous, nonspontaneous, or at equilibrium.

### What happens when Gibbs free energy is zero?

When Gibbs free energy is equal to zero, the forward and backward processes occur at the same rates. It means that the system is at equilibrium, and the concentrations of the reactants and products don't change.

### How to determine if a reaction is spontaneous or nonspontaneous?

To work out the spontaneity of a chemical reaction, calculate its Gibbs free energy.

If it's positive, the process is spontaneous (exergonic).

A negative value means it's nonspontaneous (endergonic).

Dominika Śmiałek, MD, 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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