# Equilibrium Constant, Reaction Constant and Gibbs Free Energy

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  ΔGis the standard Gibbs energy.

At equilibrium, we know that the value of ΔGis zero and the value of Q is equal to Kc.

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 ΔG0 <0, the reaction is spontaneous.

When ΔG0< 0 then the value o f –ΔG0/RT 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 ΔG0> 0

When ΔG0> 0, then the value of –ΔG0/RT 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.

#### Practise This Question

Equilibrium constants K1 and K2 for the following equilibria are

NO(g) + 0.5O2(g)  K1 NO2(g) and
2NO2(g)  K2 2NO(g) + O2(g)