# Gibbs Free Energy: Definition & Significance

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• 0:00 Gibbs Free Energy
• 1:20 Spontaneity of Reactions
• 3:05 Gibbs Free Energy & Reactions
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Lesson Transcript
Instructor: Alfonso Reina
Have you ever wondered why some things just happen spontaneously? Have you ever asked yourself why salt dissolves in water? In this lesson, you will understand the meaning of the Gibbs free energy and how it helps us predict if a chemical reaction will happen spontaneously.

## The Gibbs Free Energy

When you pull a rock using a rope and a pulley, you raise the height of the rock. In mechanics, we would say that we increased the potential energy of the rock. This is because if we release it, the rock will gain speed as it falls. If the rock hits a nail that is partly inserted on the floor, the nail will penetrate the floor further. We would say that the rock did work on the nail because the original potential energy of the rock was used to insert the nail in the floor.

Similarly, the Gibbs free energy is the energy available in a substance to do work. However, this work does not involve mechanical work, meaning the substance does not expand or contract to push on something. It refers to the 'chemical work' involved in chemical reactions. One could think of chemical work as the energy involved in transforming one chemical into another. The Gibbs free energy is a chemical potential energy in a substance. It is defined by the equation:

G = H - TS

Where G is the Gibbs free energy, H is the enthalpy, T is the temperature, and S is the entropy. Enthalpy and entropy are thermodynamic properties of a system related to the system's internal energy and its degree of disorder.

## Spontaneity of Chemical Reactions

The mechanical potential energy of the rock is measured by the rock's height above the ground. On the ground, the rock has no potential energy. Similarly, the Gibbs free energy of a chemical is measured in reference to another chemical state that is assigned a Gibbs free energy of zero. Two different substances may have different Gibbs free energies. Also, the state of a substance may have higher Gibbs free energy than another state of the same substance.

On Earth, objects always want to fall and reduce their potential energy. In the world of chemical transformations, chemicals always want to minimize their Gibbs free energy. What this means is that chemicals will tend to transform to other states or chemicals that have less Gibbs free energy. The rock, if not supported by the rope, will always want to fall to the ground where it has less potential energy. A chemical with higher Gibbs free energy will always want to transform to a chemical with lower Gibbs free energy.

These types of chemical reactions are called spontaneous reactions because they happen without the need of any input energy, just like the rock falls without us doing anything. Ice will always convert to water when the temperature is above 0 degrees Celsius. At these temperatures, we never see water converting to ice. We would say that the conversion of ice to water occurs spontaneously. If we wanted to convert water to ice, we would need to extract heat. If we wanted to place the rock above the ground again, we would have to pull strongly on the rope. In this case, we would say that the conversion of water to ice and increasing the rock's height do not occur spontaneously.

## Gibbs Free Energy and Spontaneous Reactions

Whether a chemical transformation occurs spontaneously or not is determined by the change of Gibbs free energy:

deltaG = Gf - Gi = deltaH - T(deltaS)

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