# Relationship of gibbs free energy and equilibrium constant

### Standard change in free energy and the equilibrium constant (video) | Khan Academy

Sep 20, For any reaction that is taking place, the change in Gibbs Free Energy is related to the reaction quotient as: [math]\Delta G= \Delta G^0 + RT ln. A very brief introduction to Gibbs free energy and its relationship with equilibrium constants. The equilibrium constants we actually of the free energy relationships in a.

The free energies of solid and liquid components are constants that do not change with composition. 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.

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.

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.

### Relationship Between Free Energy And Equilibrium Constant - Study Material for IIT JEE | askIITians

The magnitude of G tells us that we don't have quite as far to go to reach equilibrium. 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. 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.

## 19.7: Free Energy and the Equilibrium Constant

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. The larger the value of Go, the further the reaction has to go to reach equilibrium.