# Equilibrium constant and free energy relationship

### Free Energy and Equilibrium - Chemistry LibreTexts

Learn the concepts of Relationship Between Free Energy And Equilibrium Constant with the help of study material for IIT JEE by askIITians. A very brief introduction to Gibbs free energy and its relationship with equilibrium constants. Calculating an Equilibrium Constant from the Free Energy Change constant for the process at that temperature using the relationship between Delta Go and K.

Free Energy and the Equilibrium Constant

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.

## 19.7: Free Energy 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. The straight diagonal line shows the free energy of all possible compositions if the two gases were prevented from mixing.

The red curved line show the free energy of the actual reaction mixture. It corresponds to the free energy change for a process that never really happens: Isomerization of butane The standard molar free energy change for this very simple reaction is —2. The green curve adds the free energy of mixing to the above sum; its minimum defines the equilibrium composition.

### Gibbs Free Energy

The answer is that no matter how low the free energy of the products, the free energy of the system can be reduced even more by allowing some of the products to be "contaminated" i. 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. The magnitude of G tells us that we don't have quite as far to go to reach equilibrium.

### Free Energy and the Equilibrium Constant - Chemistry LibreTexts

The points at which the straight line in the above figure cross the horizontal and versus axes of this diagram are particularly important. The straight line crosses the vertical axis when the reaction quotient for the system is equal to 1.

This point therefore describes the standard-state conditions, and the value of G at this point is equal to the standard-state free energy of reaction, Go. Because there is no driving force behind the reaction, the system must be at equilibrium.

• Free Energy and Equilibrium

The relationship between the free energy of reaction at any moment in time G and the standard-state free energy of reaction Go is described by the following equation. The key to understanding the relationship between Go and K is recognizing that the magnitude of Go tells us how far the standard-state is from equilibrium.

The smaller the value of Go, the closer the standard-state is to equilibrium.