# 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 theÂ concentration of the reactants and the products for a reversible reaction at any time. Here, we will learn about the relationship betweenÂ 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 (Î”G), is negative. The reaction is considered as non-spontaneous when Î”G is positive. In theÂ case of a reversible reaction, the backward reaction is spontaneous when the value of Î”G is negative. When the value of Î”G is zero, the reaction is said to be at equilibrium, as at this point no free energy is left for driving the reaction.

Mathematically,

WhereÂ  Î”G0Â is the standard Gibbs energy.

At equilibrium, we know thatÂ the value of Î”G0Â is 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, weÂ get

It is important to note that, on the basis of the value of Î”G0, we can interpret the spontaneity of any given reaction.

When Î”G0Â <0, the reaction is spontaneous.

When Î”G0< 0 then the value o f â€“Î”G0/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 Î”G0> 0

When Î”G0> 0, then the value of â€“Î”G0/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

For the reaction A + B  C + D the equilibrium constant is