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# Gibbs Free Energy

By now, you have a brief idea of thermodynamics. You have learnt enough about its laws and arms. But, have you come across the concept of Gibbs free energy yet? If not, you are reading the right stuff! In this topic, we will study all about Gibbs Free energy and look at how it works.

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## What is Gibbs Free Energy?

Gibbs Energy is the maximum (or reversible) work that a thermodynamic system can perform at a constant temperature and pressure. The reversible work in thermodynamics implies a special method in which work is carried out such that the system remains in perfect equilibrium with all its surroundings.

In the language of chemical reactions, the word reversible signifies that the reaction can be carried out in either direction simultaneously and it always maintains a dynamic equilibrium. This also implies that the reactions in both the directions should proceed with a decrease in free energy. This might look impossible.

However, it is only possible if, at equilibrium, the Gibbs free energy of the system is at its minimum value. Without this, the system spontaneously changes to the configuration of lower free energy. We can mathematically define the Gibbs free energy by the equation:

G = HÂ –Â TS

Where H = heat content, S = entropy of the system, T = absolute temperature

### The Conditions of Equilibrium

A thermodynamic system is in equilibrium if both itâ€™s intensive properties and extensive properties are constant. By intensive properties, we mean temperature and pressure. Extensive properties imply the U, G, A.

In other words, we can say that the total change in any of the property is zero at equilibrium. Looking at the below equation we can assume if the reaction is reversible and the Gibbs free energy is zero. we can say that the system is in equilibrium.

AÂ +Â BÂ â‡ŒÂ CÂ +Â D; â–³rG = 0

The Gibbs energy for a reaction which is in the standard state, â–³rGá¶¿ is related to the equilibrium constant as follows:

0 = â–³rGá¶¿Â +Â RTÂ lnÂ K

or â–³rGá¶¿ = â€“RTÂ lnÂ K

or â–³rGá¶¿ = âˆ’2.303Â RTÂ logÂ K

It is also known that:

â–³rGá¶¿ =Â â–³rHá¶¿Â â€“Â Tâ–³rSá¶¿ =Â â€“RTÂ lnÂ K

## Solved Example for You

Q: Explain the concept of Gibbs energy in endothermic and exothermic reactions.

Ans:Â For endothermic reactions, the value of â–³rHá¶¿ is could be large and positive. However, if we see that the value of K is less than 1, it is highly unlikely that the reactants will form much of the product.

On the other hand, in case of exothermic reactions, the value of â–³rHá¶¿ are usually very large and negative. We must also note that even the value of â–³rGá¶¿ is likely to be large and negative. In these cases, we will see that the value of K will be much larger than 1. Thus, we can also say that strong exothermic reactions will have a larger value of K.

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