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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.

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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 – TSWhere 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)Where deltaG is the change in Gibbs free energy, Gf is the final Gibbs free energy of the products of the reaction, Gi is the Gibbs free energy of the reactants, deltaH is the change of enthalpy, and deltaS is the change in entropy.

If a reaction leads to the formation of chemicals with less Gibbs free energy, the reaction occurs spontaneously. Here, deltaG is negative (Gf is less than Gi). If a reaction leads to the formation of chemicals with higher Gibbs free energy, the reaction does not occur spontaneously. Such a reaction would require some type of energy input.

In this case, deltaG is positive (Gf is higher than Gi). If the Gibbs free energy of the final and initial state of the chemicals is known, it is possible to predict whether a chemical transformation between the two states will happen spontaneously.For example, when we mix table salt (NaCl) with water, the salt dissociates in two ions (electrically charged atoms):NaCl —-> (Na+) + (Cl-)This is a spontaneous reaction because we do not need to do much except for adding the salt to the water and give it a bit of a stir.

We say that salt dissolves easily in water. Salt tends to dissociate because in the presence of water, the Gibbs free energy of the dissociated ions is less than Gibbs free energy of the two ions bonded together. The change of Gibbs free energy of this transformation would be:deltaG = Gf – GiBy replacing Gf with the Gibbs free energies of the dissociated ions (GNa and GCl) and Gi with the Gibbs free energy of salt (GNaCl), we have:deltaG = (GNa + GCl) – GNaClWhere (GNa + GCl) is less than GNaCl.

Lesson Summary

The Gibbs free energy is the available energy of a substance that can be used in a chemical transformation or reaction. Substances tend to transform into other substances that have less Gibbs free energy. The change of Gibbs free energy predicts whether a chemical reaction will occur spontaneously. Chemical reactions occur spontaneously if the change in Gibbs free energy between the products and initial reactants is negative (less than zero).

Learning Outcomes

When you are done, you should be able to:

  • Recall what Gibbs free energy is
  • Recite the equation for Gibbs free energy
  • Illustrate why and how spontaneous reactions occur
  • Explain how to determine if a chemical reaction will occur spontaneously

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