We are already familiar with the concept of equilibrium in physical and chemical systems. We also know about the concept of reaction constant and how to calculate the concentration of the reactants and the products for a reversible reaction at any time. Here, we will learn about the relationship between equilibrium constant, reaction constant and Gibbs free energy.

Let us consider the chemical reaction given below.

We know, the reaction proceeds in the forward direction. It is termed as a spontaneous reaction when the value of Gibbs free energy (ΔG), is negative. The reaction is considered as non-spontaneous when ΔG is positive. In the case of a reversible reaction, the backward reaction is spontaneous when the value of ΔG is negative. When the value of ΔG is zero, the reaction is said to be at equilibrium, as at this point no free energy is left for driving the reaction.

Mathematically,

Where ΔG_{0 }is the standard Gibbs energy.

At equilibrium, we know that the value of ΔG_{0 }is zero and the value of Q is equal to K_{c}.

Hence, we can write,

We can also write it as,

Taking the antilog on both the sides of the equation, we get

It is important to note that, on the basis of the value of ΔG0, we can interpret the spontaneity of any given reaction.

When ΔG_{0} <0, the reaction is spontaneous.

When Δ*G*_{0}< 0 then the value o f –Δ*G*_{0}/R*T *can be seen as positive, and, thus the value of K >1. And we know that when the value of K > 1, the reaction is said to be a spontaneous reaction and it proceeds in the forward direction.

When Δ*G*_{0}> 0

When Δ*G*_{0}> 0, then the value of –Δ*G*_{0}/R*T *can be seen as negative and, thus the value of K <1. And we know that when the value of K < 1, the reaction is said to be a non-spontaneous reaction and it proceeds in the backward direction.

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