8. Chemical equilibrium
🎯 Learning Outcomes
After completion of the chapter, students should be able to:
- Explain physical and chemical equilibrium in terms of a reversible reaction.
- Describe the meaning of the dynamic nature of equilibrium with an example.
- Explain and deduce the law of mass action.
- Write the equilibrium expression and the equilibrium constant with significance.
- Derive the relation between Kp and Kc.
- State Le Chatelier’s Principle and apply it to systems in equilibrium with changes in concentration, pressure, temperature, or the addition of a catalyst.
Introduction
Irreversible Reaction
- Chemical reactions that proceed to completion in one direction only are known as irreversible reactions.
- In irreversible reactions, reactants are completely converted into products in a certain interval of time. In these reactions, products do not form reactants again.
- It is represented by a full-headed arrow. (→)
- Fast reactions are generally irreversible.
- A dynamic equilibrium state is not possible.
- The law of mass action or Le Chatelier’s principle is not applicable.
Reversible Reaction
- Chemical reactions that proceed in both directions, forward and backwards simultaneously, are known as reversible reactions.
- These reactions never go to completion but always continue in both directions.
- Reversible reactions are represented by a double-headed arrow: (⇌)
- A dynamic equilibrium state is created.
- The law of mass action and Le Chatelier’s principle are applicable.
Static and Dynamic Equilibrium
Reversible reactions proceed in both (forward and backwards) directions simultaneously. In a reversible reaction, a state is achieved at which the rate of the forward reaction becomes equal to the rate of the backward reaction. This state is referred to as ‘chemical equilibrium’.
Consider a reversible reaction A + B ⇌ C + D, in which two reactants, A and B, are allowed to react together.
At the initial stage, the reaction proceeds in the forward direction only because no product is initially present.
As the reaction starts, A and B react to form C and D. Now C and D react with each other to produce A and B, and the reaction now proceeds in both forward and backward directions, but the rate of the forward reaction and the rate of the backward reaction are different.
Finally, a state is established at which the rate of backward reaction becomes equal to the rate of forward reaction. This state is called ‘chemical equilibrium’.
At the equilibrium state, the reaction does not stop. Reactants form products, and products again convert into reactants. This process always continues at constant conditions, but with the passage of time, there is no change in the concentration of reactants and products due to the same rate of reaction. At this point, it appears as if the reaction has stopped because we don’t see any change in the concentration of reactants and products with time.
Since chemical equilibrium continues and never stops, it is a dynamic equilibrium.
Physical Equilibrium
- Solid – liquid equilibrium
- Liquid – Vapour equilibrium, etc.
Characteristics of Chemical Equilibrium
Law of Mass Action
Based on many experimental observations, CM Guldberg and P Waage in 1863 proposed a generalisation applicable to chemical equilibrium.
At a constant temperature and pressure, the rate at which a substance reacts is proportional to its active mass (or concentrations) of all the reactants raised to the powers equal to their stoichiometric coefficients in the balanced chemical equation.
Active mass is the molar concentration of the substance. It is denoted by placing the formula of the substance in square brackets.
Let us consider a general reversible reaction
Here, A and B are reactants, C and D are products, and a, b, c, and d are their stoichiometric coefficients, respectively.
According to the law of mass action,
Similarly,
Here, [A], [B], [C], and [D] are the active masses of A, B, C, and D at the state of equilibrium of the reaction.
Now, at equilibrium,
The constant K_c or K_eq is called the equilibrium constant.
The equilibrium constant of a reversible reaction is defined as the ratio of the products of the active masses of the products to the products of the active masses of the reactants, all raised to the power of their stoichiometric coefficients.
Characteristics of the Equilibrium Constant
The equilibrium in any reversible reaction is characterised by the equilibrium constant. Its value depends upon the nature of the reaction, temperature, and pressure.
- The equilibrium constant does not depend upon the use of a catalyst.
- A change in concentration of reactants or products does not change the value of the equilibrium constant.
- The equilibrium constant for a particular reaction only depends upon the temperature, and if the involved species are gases, it depends upon pressure. It’s always constant at a given temperature and pressure.
Significance of the Equilibrium Constant
- If the value of the equilibrium constant is high, it indicates the reaction goes almost to completion in the forward direction. Because K_c is the ratio of K_f/K_b, a higher K_c means a higher value of K_f, or the rate of the forward reaction is higher.
- If the value of equilibrium is low, it indicates the reaction does not go towards completion, and the yield will be very low.
Unit of Equilibrium Constant
As the equilibrium constant is the ratio between the molar concentrations of products and reactants, if the molar concentrations of products and reactants are the same, it has no units. It varies from equation to equation.
Relation between Kp and Kc
For gaseous equilibrium systems, we can use the partial pressure of gases instead of molar concentration. Therefore,
“The equilibrium constant determined by using partial pressures of gases in a gaseous chemical equilibrium is denoted by Kp.”
Consider a general gaseous reversible reaction:
For the reaction, K_p is
Where P_A, P_B, P_C and P_D = partial pressures of gases A, B, C, and D, respectively.
Δn is the difference in the number of moles of products and reactants. or Δn = (c+d) − (a+b)
From the above relation, we conclude three results as follows.
1) Kp = Kc
In this case, there is no change in volume, and Δn will be equal to zero. For example:
In this example, the volume of products is equal to the volume of reactants.
2) Kp > Kc
In this case, the reaction occurs with an increase in volume, and the value of Δn is greater than zero. For example:
In this example, the volume of products is greater than the volume of reactants.
3) Kp < Kc
In this case, the reaction occurs with a decrease in volume, and the value of Δn is less than zero. For example:
In this example, the volume of products is less than the volume of reactants.
Le Chatelier’s Principle
If a system in equilibrium is subjected to a constraint (stress), the equilibrium shifts in such a direction as to reduce the effect of the applied constraint.
In other words, if a system at equilibrium is disturbed by some change, the system will shift in a direction to minimise or undo the effect of the change.
1) The Effect of a Change in Concentration
If at the equilibrium state, the concentration of one or more substances present in the equilibrium mixture is changed, the equilibrium system will no longer remain in the equilibrium state.
► On increasing the concentration of the reactant, the forward reaction will increase, and if the concentration of the product increases, the backward reaction proceeds.
► We can say that, if equilibrium is disturbed by increasing concentration, the system will shift in that direction where concentration is decreases. And if equilibrium is disturbed by decreasing concentration, the system will shift in that direction where concentration is increased.
2) The Effect of a Change in Temperature
The effect of a temperature change is related to the nature of the reaction, whether it is an endothermic reaction or an exothermic reaction.
- A. For an endothermic reaction, K_c increases with the increase in temperature.
- B. For an exothermic reaction, K_c decreases with the increase in temperature.
► If we disturb the equilibrium by an increase in temperature, the system will shift in the direction where heat is absorbed.
► It is important to note that the reverse of an exothermic reaction is endothermic, and the reverse of an endothermic reaction is exothermic.
► An Exothermic reaction is favoured by low temperature, and an endothermic reaction is favoured by high temperature.
3) The Effect of a Change in Pressure
Pressure only affects the equilibrium when a change in volume occurs.
► If we disturb the equilibrium by an increase in pressure, the system will shift in the direction in which volume decreases.
When the volumes of reactants and products are equal, there will be no effect of pressure. For example:
As the volume of products is greater than the reactants, the yield of ammonia will increase by increasing pressure. At low pressure, the reverse reaction will proceed.
An increase in pressure favours the backward direction.
4) Effect of the Catalyst
Catalysts affect the rate of forward and backward reactions simultaneously. Therefore, it does not affect the equilibrium; however, it reduces the time to reach equilibrium.
🗝️ Key Points to Remember
- Irreversible reactions go to completion in one direction (→); reversible reactions proceed in both directions simultaneously (⇌).
- Chemical equilibrium is a dynamic state where the rate of the forward reaction equals the rate of the backward reaction.
- Law of mass action: rate ∝ active mass raised to the power of stoichiometric coefficients.
- K_c = [C]^c[D]^d / [A]^a[B]^b for the reaction aA + bB ⇌ cC + dD.
- The equilibrium constant depends only on temperature (and pressure for gases), not on catalyst or initial concentration.
- K_p = K_c(RT)Δn, where Δn = (moles of gaseous products) − (moles of gaseous reactants).
- Le Chatelier’s Principle: a system at equilibrium shifts to counteract any applied change in concentration, temperature, or pressure.
- A catalyst speeds up the attainment of equilibrium but does not shift its position.
Test your understanding of reversible reactions, the law of mass action, Kp–Kc relation, and Le Chatelier’s Principle.