Equilibrium – Session 3

We already know that, at equilibrium, the rate of forward reaction is equal to the rate of reverse reaction. This is called equilibrium law. For example, the rate of evaporation and the rate of condensation of water are equal at equilibrium. Equilibrium law describes the relationship between the concentrations of reactants and the products in a reversible chemical reaction at equilibrium. We shall now understand the mathematical expression for the equilibrium law.

Let us take an example of a reversible reaction. The Reactant A and Reactant B react to form the products C and D. a, b, c and d represent reaction coefficients. The equilibrium law expression for this reversible reaction is shown here. Kc represents the equilibrium constant at a given temperature.

Let us derive this mathematical expression of the equilibrium law. For deriving this expression, we need to understand the law of mass action. Law of mass action states that the rate of a a chemical reaction is directly proportional to the product of the concentrations of the reactants. Each reactant is raised to the power of their respective stoichiometric coefficients.

Now we shall apply this law of mass action to a reversible reaction. At any given moment during the reaction, the rates of the forward reaction is directly proportional to the product of concentration of Reactant A and Reactant B. Reactant A and Reactant B are raised to the power of their coefficients. kբ represents the rate constant of forward reaction.

The rate of reverse reaction is directly proportional to the product of concentration of C and D. C and D are also raised to the power of their coefficients. kᵣ is the rate constant of reverse reaction.

At equilibrium, the forward and reverse reactions occur at the same rate. So in the given mathematical expression, the rate of forward reaction is equal to rate of reverse reaction. Now, we shall rearrange this equation to solve for the equilibrium constant. The term kբ divided by kᵣ is combined into a single constant, denoted as K꜀. K꜀ is called the equilibrium constant.

Let us apply the equilibrium Law to the Haber Bosch process. It is an industrial method used to synthesize the ammonia from the nitrogen gas and the hydrogen gas. The balanced chemical equation for this reaction is given. In this reaction, one molecule of the nitrogen gas reacts with three molecules of the hydrogen gas to produce two molecules of ammonia.

The equilibrium constant expression for the Haber Bosch process is illustrated. In this expression the nitrogen gas, hydrogen gas and the ammonia gas are in square brackets. Square brackets represent the concentration of these gases.

The value of the equilibrium constant tells us about the position of the equilibrium. It tells the relative concentrations of reactants and products at equilibrium. If the value of K꜀ is greater than one, the equilibrium favors the products. This means that there is a higher concentration of the ammonia at equilibrium compared to the nitrogen gas and hydrogen gas.

If the value of K꜀ is less than one, the equilibrium favors the reactants (reverse reaction predominates). This means that there are higher concentrations of the nitrogen gas and the hydrogen gas at equilibrium compared to the ammonia. If the value of K꜀ is equal to one, then the amounts of reactants and products are almost equal at equilibrium. This means that a significant amounts of the nitrogen gas, hydrogen gas and the ammonia gas is there at equilibrium.

The equilibrium in which all the reactants and products in a reversible reaction are in the same phase is called the homogeneous equilibrium. This means that all species involved are either in the gas phase, liquid phase, or aqueous solution. An example of the homogeneous equilibrium reaction is the formation of hydrogen iodide. In this reaction, the hydrogen, iodine and the hydrogen iodide are in the gaseous phase.

Heterogeneous equilibrium occurs when the reactants and the products are in different phases. It commonly involves at least one solid or liquid phase along with the gaseous or the aqueous species. An example of the heterogeneous equilibrium is the evaporation and the condensation of the water. Liquid water is in equilibrium with the gaseous water.

For heterogeneous equilibrium, the concentrations of pure solids and liquids remain constant. Only the concentrations of gases or solutes in the solutions can change. In the given example, the equilibrium constant expression includes only the concentration of gaseous specie. The concentrations of pure solids and pure liquids are not included in the equilibrium constant expression. This is because they do not change during the course of the reaction.

For reactions involving gases, the equilibrium constant can be expressed in terms of partial pressure. This is because gases are more conveniently measured in terms of pressure rather than concentration. The equilibrium constant expression in terms of partial pressure is represented as KP. KP represents the ratio of the partial pressure of the products to the partial pressure of the reactants. Each partial pressure term is raised to a power equal to the coefficient of the respective substance.

Consider the reversible gas phase reaction. According to the equilibrium law, the expression for KP is illustrated. PA, PB, PC, PD are the partial pressure of gases A, B, C, and D, respectively. a, b, c, and d are the stoichiometric coefficients of these gases.