Le-chatelier's principle and its application

Le-chatelier's principle

The state of equilibrium in any system depends upon factors present in the system, such as temperature, pressure and concentration of various species. These factors are called reaction variables or parameters. A change in any one of the parameters may affect the position of the equilibrium. The general rule that can explain the effect of changes in these parameters on the state of equilibrium was formulated by H. Le Chatelier (1885), and F. Braun (1886) and is commonly called as Le Chatelier's principle.

The principle may be stated as, 'if a system at equilibrium is subjected to a change in one or more variables such as, pressure, temperature, and/or concentration, then the equilibrium shifts in such a way so as to undo the effect of the change'.

The Le Chatelier's principle is also called the 'principle of mobile equilibrium'. It is very useful in predicting qualitatively, the effect of change in the reaction variables on a system at equilibrium.Factors-affecting-equilibrium">

Factors affecting equilibrium

Effect of concentration on equilibrium

If a system is at equilibrium and the concentration of one of the species involved in the reaction is increased, the system will readjust so as to decrease the concentration of that species. Thus, the reaction will proceed in such a manner so as to consume some of the increased concentration. Similarly if the concentration of some substance is decreased, the reaction will proceed so as to make up the loss in the concentration.

To illustrate this, let us consider the reaction,

At equilibrium, the concentrations of A, B, C and D are constant. If at equilibrium a small amount of the substance 'A' is added to this reaction, then according to the Le Chatelier' principle, the equilibrium shifts in a direction so as to undo the effect of the increased concentration of 'A'. In other words the reaction proceeds in the direction, which decreases the concentration of 'A'. Thus, with an increase in the concentration of any one of the reactants such as 'A', the equilibrium will shift towards right, (products side) by making more 'A' to react with B, to form more products.

On the other hand, when the concentration of C (or any other product) is increased, the reaction will shift towards left (reactant side).

Thus, according to Le Chatelier's principle in general, an increase in the concentration of any of the substances on one side of the equilibrium shifts the equilibrium to produce more of the substances on the other side of it.

Effect of temperature on equilibrium

According to the Le Chatelier's principle, when the temperature or heat supplied to a system at equilibrium is increased, the system should move in a direction so that the added heat is absorbed. Thus, an increase in the temperature of a chemical system at equilibrium, favours an endothermic reaction i.e., a reaction that proceeds with the absorption of heat.

On the other hand, if temperature of the system is decreased under constant pressure and volume conditions, the equilibrium will shift in such a way so as to produce some heat. A decrease in the temperature of a system at equilibrium, favours an exothermic reaction i.e., the reaction, which proceeds with the evolution of heat.

For example in the following,

the reaction is exothermic in the forward direction and endothermic in the backward direction.

If the temperature of the system at equilibrium is increased, then, according to the Le Chatelier's principle, the equilibrium will shift in the direction where heat is absorbed i.e. endothermic direction. The increasing temperature results in a shift of the reaction towards left (reactant side). This will result in the formation of lesser amount of ammonia.

On the other hand, when the temperature of this system is lowered, it will favour the exothermic direction of the equilibrium i.e. where heat is evolved. The equilibrium will shift in the forward direction, and more ammonia will be produced. Thus, according to Le Chatelier's principle,

Effect of pressure on equilibrium

Change of pressure has no significant effect on the following equilibrium.

• The equilibrium involving only solids are not affected by a change of pressure. Virtually no change in volume results due to change in pressure in solids.

• The equilibrium involving liquids and/or gases, where the number of molecules before and after the attainment of equilibrium remain the same, (where n = 0), the reactions are not affected by a change of pressure For example, in the reactions,

There is no change in the number of molecules in going from reactants to products i.e. the reactions and the equilibrium are not affected by a change of pressure. (n = 0).

• However, in gaseous reactions where there is a change in the number of molecules in going from reactants to products or vice-versa, pressure plays an important role. For example, the equilibrium in the following reactions are greatly influenced by any change in the pressure of the system.

When the pressure on a reaction involving gases (where n 0) is changed, the equilibrium will shift in a direction so as to undo the effect of change in pressure. As an increase of pressure will cause a decrease in volume so, an increase of pressure on a gaseous system will shift the equilibrium in a direction of decrease in volume, and vice-versa. Therefore,increase in pressure will favour a reaction, which proceeds towards decrease in volume (n = - ve), the equilibrium will shift in such a way that it decreases the pressure by shifting in the forward direction. On the other hand, in a reaction which proceeds towards an increase in volume (n = + ve), the decrease in pressure will shift the equilibrium towards right by increasing the pressure. Thus, according to Le Chatelier's principle,

Effect of catalyst on equilibrium

Catalyst has no effect upon the equilibrium concentration of the reactants and products. In fact, a catalyst accelerates the forward and backward reactions to the same extent and therefore simply helps in the attainment of the equilibrium state faster.

Effect of the inert gas on equilibrium

The effect produced due to the addition of an inert gas (which does not react with any of the reactants and products) on the equilibrium of a reaction, can be predicted qualitatively as follows:

Inert gas added keeping pressure of the system constant

The addition of an an inert gas increases the volume of the system, which in turn, causes the equilibrium position of the system to move in the direction of larger number of gaseous molecules. Thus, we will have

Inert gas added keeping volume of the system constant

Addition of an inert gas into a system at equilibrium under constant volume causes,

• an increase in the pressure of the system,

• an increase in the total number of moles in the system.

Total pressure of a system is then given by, P_totalV = n_total RT or

Under constant volume, at any temperature, the ratio n_total / P_total remains constant even on the addition of an inert gas i.e., the equilibrium position of the reaction remains unaffected. As a result, there is no change in any of the variable and the amount of the substances at equilibrium by the addition of inert gas.

Application of Le-chatelier's principle

The Le Chatelier's principle has a great practical significance for all physical and chemical systems. Applicability of this principle to some of the systems is described below:

Liquid - vapour system

Equilibrium between a liquid and its vapours can be represented by the equation.

The effect of change in temperature and pressure on this equilibrium are as follows.

An increase in pressure on a system where a liquid-vapour equilibrium exists

According to the Le Chatelier's principle, this will make the system move in a direction of lower volume. An increase in pressure on the system will result in the condensation of vapours to give liquid, since, liquids have lower volume as compared to vapours. The equilibrium will shift towards left. On the other hand, if the pressure is decreased, more and more liquid will get converted into vapours.

The effect of increase in temperature where a liquid-vapour equilibrium exists

According to the Le Chatelier's principle, this will make the reaction move in a direction which absorbs heat i.e., the endothermic process will be favoured. As vaporization (liquid g vapours) is an endothermic process, a rise in temperature will favour the process of vaporization i.e. more liquid would get converted into vapours.

As a result of these effects an increase in temperature and decrease in pressure, shall favour this process Liquid Vapour to proceed in the forward direction.

For example, during the preparation of carbonated drinks such as Cola or beer, a large amount of CO₂is dissolved in the solution under high pressure. When these bottles are opened, the pressure decreases and the dissolved carbon dioxide escapes out.

Manufacture of ammonia (Haber's Process)

Ammonia can be synthesized from nitrogen and hydrogen in accordance with the reaction.

The equilibrium constant of this reaction may be written as,

The characteristics of the reaction are:

Firstly, the reaction proceeds with a decrease in volume. Therefore, an increase in pressure should favour the forward reaction. The equilibrium between nitrogen, hydrogen and ammonia at 200C has been studied at different pressures and the following data has been obtained.

Pressure/atom	1	100	300	1000
NH3 (%)	15.3	81.5	90.0	99.3

The most favourable pressure range for the production of ammonia is found to be 152000 - 684000 mm of Hg pressure.

Secondly, the reaction is exothermic, therefore the Le Chatelier's principle predicts lower temperature to be favourable for the forward reaction.

Temp./oC	200	400	600	700
NH3 (%)	90.0	47.7	13.8	7.3

Since at low temperature, the reactions tend to be slow due to kinetic effects, an optimum temperature (450C) should give the most favourable results.

Thirdly, since the reaction involved two gases, the use of a suitable catalyst should accelerate the reaction in the forward direction.

Manufacture of sulphur trioxide (Contact Process)

During the manufacture of sulphuric acid (Contact process), sulphur trioxide is prepared by the oxidation of sulphur dioxide in accordance with the reaction,

This reaction proceeds with a decrease in volume. Therefore, high pressure will favour the forward reaction.

Secondly, The reaction is exothermic, hence low temperature will be favourable for higher yield.

Thirdly, if the reaction is carried out under excess of oxygen, the equilibrium shifts in a direction so as to give larger amount of SO₃, due to the effect of increased concentration of one of the reactants. The optimum conditions for the reaction between SO_2(g) and O_2(g) are: a pressure of 1140 - 1292 mm of Hg and temperature 420°C - 450°C.

Formation of Nitric oxide (Birkland-Eyde process)

The endothermic reaction,

is one of the initial reactions in the Birkland - Eyde process for the manufacture of nitric acid.

The reaction is characterised by,

• No change in volume i.e. n = 0

• An endothermic reaction i.e., heat is absorbed during the reaction.

As a result of Le Chatelier's principle,

• The equilibrium state is not affected by any change in pressure.

• Due to endothermic nature of the reaction, an increase in temperature will favour the forward reaction i.e., more nitric oxide is formed at higher temperature.

• Formation of nitric oxide is favoured by taking any of the reactants, N₂ or O₂ in excess, (concentration effect).

Actually, nitrogen and oxygen are made to combine at 3000°C by means of an electric arc.

Problems

16. Predict the effect of changing pressure on the following physical equilibrium:

Solution

Solid water (ice) is in equilibrium with liquid water. The volume of a fixed mass of water is less than that of ice at its melting point. Therefore an increase in pressure will favour the forward reaction i.e., when pressure is applied to a system containing ice and water at equilibrium, more ice will melt.

17. What is the effect of changing pressure on the solubility of a gas in a liquid?

Solution

Dissolution of a gas in a liquid can be described by the equilibrium

Gas Liquid Solution

When the pressure on the gas is increased, according to Le Chatelier's principle, the equilibrium shifts in a direction so as to decrease the volume of the gas. As a result, more gas gets dissolved in the liquid i.e., equilibrium shifts to the right.

On the other hand, when the pressure on the gas is decreased, the equilibrium shifts in a direction so as to increase the volume of the gas. This is achieved by decreasing the solubility of the gas in liquid, i.e., the equilibrium shifts to the left.

18. For the exothermic formation of sulphur trioxide from sulphur dioxide and oxygen in the gas phase:

_(g)

K_p = 40.5 atm^-1 at 900 K and DH = -198 kJ

a) Write the expression of the equilibrium constant for the reaction.

b)At room temperature (300 K) will K_p be greater than, less than or equal to K_p at 900 K.

c) How will the equilibrium be affected if the volume of the vessel containing the three gases is reduced, keeping the temperature constant. Explain.

d)What is the effect of adding 1 mole of He_(g) to a flask containing SO_2, O₂ and SO₃ at equilibrium at constant temperature.

Solution

a) The equilibrium constant for this reaction is written in terms of the partial pressures of the reactants and products. So,

b) This reaction is exothermic. So, its equilibrium constant should increase with the lowering of temperature. Therefore, the value of K_p at 300 K will be greater than the value at 900 K.

c) When the volume of the vessel is reduced, the volume of the reaction mixture will decrease. As a result, the pressure of the gaseous mixture will increase. Le Chatelier's principle states that the system will move in a direction to undo the effect of the pressure increase. Therefore, a decrease in the volume of the reacting system will shift the equilibrium to the right, the system will move in a direction so as to decrease the number of moles in the system, by going from reactants to the product side. Thus, more SO_3(g) will be formed from the reactants.

d) Addition of helium to the reaction mixture at equilibrium under constant volume has no effect on the equilibrium.