# Equilibrium constant and free energy relationship

### Gibbs Free Energy Learn the concepts of Relationship Between Free Energy And Equilibrium Constant with the help of study material for IIT JEE by askIITians. The relationship between the free energy of reaction at any. in which \(K_p\), the equilibrium constant expressed in This relation is most conveniently plotted against the. The fact that Go is negative for this reaction at 25oC means that a system under standard-state conditions at this temperature would have to shift to the right, converting some of the reactants into products, before it can reach equilibrium.

The magnitude of Go for a reaction tells us how far the standard state is from equilibrium. The larger the value of Go, the further the reaction has to go to get to from the standard-state conditions to equilibrium. Assume, for example, that we start with the following reaction under standard-state conditions, as shown in the figure below.

### Relationship between the free enthalpy (Gibbs free energy) change and the equilibrium constant

If we could find some way to harness the tendency of this reaction to come to equilibrium, we could get the reaction to do work. The free energy of a reaction at any moment in time is therefore said to be a measure of the energy available to do work. When a reaction leaves the standard state because of a change in the ratio of the concentrations of the products to the reactants, we have to describe the system in terms of non-standard-state free energies of reaction.

The difference between Go and G for a reaction is important. There is only one value of Go for a reaction at a given temperature, but there are an infinite number of possible values of G. The figure below shows the relationship between G for the following reaction and the logarithm to the base e of the reaction quotient for the reaction between N2 and H2 to form NH3. They therefore describe systems in which there is far more reactant than product. The sign of G for these systems is negative and the magnitude of G is large. The system is therefore relatively far from equilibrium and the reaction must shift to the right to reach equilibrium. Data on the far right side of this figure describe systems in which there is more product than reactant. The sign of G is now positive and the magnitude of G is moderately large. The sign of G tells us that the reaction would have to shift to the left to reach equilibrium.

Eventually it reaches a minimum value at a system composition that defines the equilibrium composition of the system, after which time no further net change will occur. The for the reaction is determined the standard free energy change: The free energies of solid and liquid components are constants that do not change with composition.

## Free Energy and Equilibrium

Thus in heterogeneous reactions such as phase changes, the total free energy does not pass through a minimum and when the system is not at equilibrium only all-products or all-reactants will be stable. Two reactions are coupled when the product of one reaction is consumed in the other. Under conditions of constant temperature and pressure, chemical change will tend to occur in whatever direction leads to a decrease in the value of the Gibbs free energy. When G falls as far as it can, all net change comes to a stop.

You will recall that the relative concentrations of reactants and products in the equilibrium state is expressed by the equilibrium constant. In this lesson we will examine the relation between the Gibbs free energy change for a reaction and the equilibrium constant. Although these relations are strictly correct only for perfect gases, we will see later that equations of similar form can be applied to many liquid solutions by substituting concentrations for pressures.