Chemistry Class 11 Chapter 8: Chemical Equilibrium Notes

Chemical equilibrium describes the state reached by a reversible reaction, one that proceeds in both the forward and reverse directions rather than going to completion, when it is carried out in a closed container: the concentrations of reactants and products stop changing, and the rate of the forward reaction becomes exactly equal to the rate of the reverse reaction. Although the system appears static from the outside, at the molecular level both reactions continue indefinitely at equal rates, which is why this state is called a dynamic, rather than a static, equilibrium; the same idea applies to purely physical changes, such as the equilibrium between a liquid and its vapour in a closed container.

The chapter introduces the equilibrium constant, Kc, which measures the position of an equilibrium under a given set of conditions and depends only on temperature, and shows how it can equivalently be expressed in terms of partial pressures (Kp), moles (Kn), or mole fractions (Kx). It then applies Le Chatelier's principle, that a system at equilibrium responds to any imposed change by shifting to counteract that change, to predict how altering concentration, pressure, volume, or temperature shifts the position of an equilibrium, and closes by using these ideas to explain how industrial processes such as the Haber process and the contact process are optimized to maximize product yield.

Learning Objectives

• Distinguish between macroscopic events, observable with the naked eye, and microscopic events, occurring at the molecular level, in a chemical system approaching equilibrium
• Describe a reversible reaction and define dynamic chemical equilibrium in terms of equal forward and reverse rates and constant reactant/product concentrations
• Define dynamic equilibrium between two physical states, such as a liquid and its vapour, or a solid and its liquid
• State the necessary conditions for chemical equilibrium and describe the characteristic features by which it can be recognized
• Deduce the equilibrium constant expression, Kc, for a homogeneous reaction from its balanced chemical equation
• Write equilibrium expressions in terms of concentration (Kc), partial pressure (Kp), number of moles (Kn), and mole fraction (Kx), and relate these constants to one another
• Distinguish between homogeneous equilibria, where all species share one phase, and heterogeneous equilibria, where more than one phase is present
• State Le Chatelier's principle and apply it to predict the effect of changes in concentration, pressure, volume, temperature, or catalyst on a system at equilibrium
• Determine whether Kc increases or decreases with a change in temperature, given whether a reaction is exothermic or endothermic
• Explain how Le Chatelier's principle is applied industrially in the Haber process and the contact process to maximize product yield

Key Concepts

8.1 Reversible Reactions and Chemical Equilibrium

Reactions in which the reactants are completely consumed and converted into products are called irreversible reactions; such reactions stop once the limiting reactant is used up. Reversible reactions, by contrast, proceed continuously in both the forward and reverse directions without the concentrations of reactants and products ever falling to zero, and are written with a double arrow, such as N2(g) + 3H2(g) <=> 2NH3(g), 2NO2(g) <=> N2O4(g), and PCl5(g) <=> PCl3(g) + Cl2(g). When a reversible reaction takes place in a closed container, so that none of the reacting substances can escape, the reaction eventually reaches a stage called chemical equilibrium, at which the concentrations of all reactants and products become constant and the rates of the forward and reverse reactions become equal.

8.2 Macroscopic and Microscopic Events; Dynamic Equilibrium

Macroscopic events are phenomena that can be observed with the naked eye without considering individual particles, such as a change in colour, the evolution or absorption of heat, the formation of a precipitate, the evolution of a gas, or a change in volume, pressure, or composition. Microscopic events, by contrast, cannot be observed directly and include collisions between molecules, the breaking and forming of bonds, the rearrangement of atoms, and the loss or gain of electrons; macroscopic changes are simply the combined, observable result of huge numbers of simultaneous microscopic events.

Consider steam and carbon monoxide reacting to form hydrogen and carbon dioxide, H2O(g) + CO(g) -> H2(g) + CO2(g): when the gases are first mixed, the maximum possible number of collisions between H2O and CO molecules occurs, so the forward reaction proceeds at its fastest rate, and this rate gradually slows as the reactants are consumed. At the same time, as H2 and CO2 molecules accumulate, collisions between them become more frequent, and the reverse reaction, which starts at a low rate, gradually speeds up. Eventually the forward and reverse rates become equal, and the reaction reaches chemical equilibrium; although the concentrations of reactants and products then stay constant, and the reaction may appear to have stopped, at the microscopic level both the forward and reverse reactions continue indefinitely at equal rates, making this a dynamic equilibrium rather than a static one.

8.3 Dynamic Equilibrium Between Two Physical States

Dynamic equilibrium also applies to purely physical changes: when a reversible phase change occurs, such as ice and water coexisting at 0 degrees C, water converts to ice at exactly the same rate that ice converts back to water, so no net change occurs even though both processes continue. A similar dynamic equilibrium exists between a liquid and its vapour in a closed container: molecules near the liquid's surface with enough energy escape into the gas phase, a process called evaporation, while gas-phase molecules that collide with the liquid surface are recaptured, a process called condensation.

As evaporation and condensation continue, their rates eventually become equal, establishing a dynamic equilibrium at which the vapour pressure remains constant at a given temperature as long as the system is undisturbed. Raising the temperature increases the average kinetic energy of the liquid's molecules, increasing both the rate of evaporation and, once more vapour is present, the rate of condensation, until a new dynamic equilibrium is reached at a higher equilibrium vapour pressure.

8.4 Conditions and Characteristics of Chemical Equilibrium

Chemical equilibrium can only be studied when two conditions are satisfied: the state of equilibrium applies only to reversible reactions, and equilibrium can only be established in a closed system, one from which no reactant or product is allowed to escape; a reversible reaction carried out in an open container never reaches equilibrium, since escaping gas continuously shifts the system in one direction. Several important characteristics follow from this: at equilibrium, the concentrations of reactants and products remain constant; the equilibrium state can be approached from either direction, starting from pure reactants or from pure products; a catalyst does not change the position of equilibrium or the value of the equilibrium constant, it only helps the system reach equilibrium more quickly; and the value of the equilibrium constant does not depend on the initial concentrations used, but depends only on temperature.

If pure solids or pure liquids take part in an equilibrium system, their concentrations are not included in the equilibrium constant expression, because the concentration of a pure solid or liquid, essentially its density, does not change and therefore has no effect on the value of the equilibrium constant.

8.5 Types of Equilibrium: Homogeneous and Heterogeneous

With respect to the physical states of the species involved, equilibria are classified into two types. A homogeneous equilibrium is one in which all reactants and products exist in the same phase, as in the synthesis of ammonia, N2(g) + 3H2(g) <=> 2NH3(g), the formation of sulfur trioxide, 2SO2(g) + O2(g) <=> 2SO3(g), or the esterification of ethanoic acid with ethanol, in which every species is a liquid. A heterogeneous equilibrium is one in which the reactants and products exist in more than one phase, as in the thermal decomposition of calcium carbonate, CaCO3(s) <=> CaO(s) + CO2(g), the reaction of carbon with steam, C(s) + H2O(g) <=> CO(g) + H2(g), or the reaction of iron with steam, 3Fe(s) + 4H2O(g) <=> Fe3O4(s) + 4H2(g).

8.6 The Equilibrium Constant (Kc) and the Law of Mass Action

In 1864, the chemists Guldberg and Waage measured the compositions of many reaction systems at equilibrium and found that, for any reversible reaction, the ratio of the product of the equilibrium concentrations of the products, each raised to its coefficient in the balanced equation, to the equivalent product of reactant concentrations, is always constant under a given set of conditions. For the general reaction aA + bB <=> cC + dD, this equilibrium constant expression is written Kc = [C]^c[D]^d / ([A]^a[B]^b), where square brackets denote molar concentration in mol dm-3.

This expression can be derived from the law of mass action, which states that the rate of a reaction is proportional to the active masses (concentrations) of the reacting substances: for A + B <=> C + D, the forward rate is kf[A][B] and the reverse rate is kr[C][D], and since these two rates are equal at equilibrium, kf[A][B] = kr[C][D], so kf/kr = [C][D]/[A][B] = Kc, a new constant called the equilibrium constant. Applying this to real reactions gives, for example, Kc = [NH3]^2 / ([N2][H2]^3) for the synthesis of ammonia, and Kc = [NO2]^4[O2] / [N2O5]^2 for the decomposition of dinitrogen pentoxide; a worked example using equilibrium concentrations of 0.470 mol dm-3 ethanoic acid, 0.070 mol dm-3 ethanol, and 0.364 mol dm-3 each of ethyl ethanoate and water gives Kc = 4.03 for the esterification reaction, while a propanone-hydrogen cyanide addition reaction with equilibrium concentrations of 0.0267 mol dm-3 for each reactant and 0.0233 mol dm-3 for the product gives Kc = 32.7 dm3 mol-1.

8.7 Units of Kc and Relationships Between Equilibrium Constants

When the total number of moles of reactants and products in the balanced equation are equal, the concentration units in the Kc expression cancel completely, leaving Kc with no units, as in the ester formation reaction; when the number of moles are unequal, as in ammonia synthesis, the units do not cancel, giving Kc units such as dm6 mol-2 that depend on the specific reaction. Four different quantities can be used to express an equilibrium constant: Kc, based on molar concentrations; Kp, based on the partial pressures of gaseous species; Kn, based on numbers of moles; and Kx, based on mole fractions.

These four constants are related by Kp = Kc(RT)^Delta n, Kp = Kx(P)^Delta n, and Kp = Kn(N)^Delta n, where R is the gas constant, T is the absolute temperature, P is the total pressure, N is the total number of moles present, and Delta n is the difference between the number of moles of gaseous products and gaseous reactants in the balanced equation. If Delta n = 0, meaning the balanced equation has equal moles of gaseous reactants and products, then Kp = Kc = Kx = Kn, and the value of the equilibrium constant is the same regardless of which concentration units are used; a worked example converts Kc = 6.0 x 10^-2 at 500 degrees C for ammonia synthesis (Delta n = -2) into Kp = 1.4 x 10^-5, showing that Kp is smaller than Kc for this reaction.

8.8 Le Chatelier's Principle

The position of equilibrium refers to the relative amounts of reactants and products present in an equilibrium mixture; if a system at equilibrium is disturbed so that the position shifts toward more product, the equilibrium is said to have shifted to the right, and if it shifts toward more reactant, it is said to have shifted to the left. Le Chatelier's principle, proposed by the French chemist Henry-Louis Le Chatelier, states that if a system at equilibrium is disturbed, it responds in such a way as to counteract, or partially nullify, the effect of that disturbance. This principle is most commonly applied to four types of disturbance: a change in concentration, a change in pressure or volume, a change in temperature, and the addition of a catalyst.

8.9 Effects of Concentration, Pressure/Volume and Catalyst on Equilibrium

Adding or removing a reactant or product disturbs an equilibrium, and the system shifts to partially counteract the change. This is illustrated by the reversible hydrolysis of bismuth(III) chloride, BiCl3 + H2O <=> BiOCl + 2HCl: adding more BiCl3 or water pushes the reaction forward, producing more BiOCl and HCl, while adding more BiOCl or HCl pushes the reaction in reverse, producing more BiCl3; conversely, removing BiCl3 shifts the reaction in reverse, and removing BiOCl or HCl shifts it forward. In every case, the equilibrium position changes, but the value of Kc itself remains constant, since Kc depends only on temperature.

A change in pressure or volume only affects the position of a gas-phase equilibrium when the number of moles of gaseous reactants differs from the number of moles of gaseous products; if these numbers are equal, changing pressure or volume has no effect on the equilibrium position. In the synthesis of ammonia, N2(g) + 3H2(g) <=> 2NH3(g), four moles of gaseous reactants form two moles of gaseous product, so increasing the pressure, or decreasing the volume, shifts the equilibrium toward the side with fewer gas molecules, favouring the forward reaction and producing more ammonia; decreasing the pressure, or increasing the volume, shifts the equilibrium the other way, favouring the reactants.

A catalyst provides an alternative reaction pathway with a lower activation energy for both the forward and the reverse reaction equally, so it speeds up the rate at which equilibrium is reached without changing the equilibrium position or the value of the equilibrium constant; the overall yield of the reaction therefore stays the same, whether or not a catalyst is used, though a catalyst allows that same yield to be reached in far less time.

8.10 Effect of Temperature on Equilibrium

Temperature is the only factor that changes the actual numerical value of the equilibrium constant, Kc, rather than simply shifting the position of equilibrium while Kc stays fixed. For an exothermic reaction, such as 2SO2(g) + O2(g) <=> 2SO3(g), Delta H° = -198 kJ, increasing the temperature favours the reverse, heat-absorbing reaction, shifting the equilibrium to the left, decreasing the concentration of SO3, and decreasing the value of Kc, which falls from about 1 x 10^26 at 298 K to about 2.8 x 10^2 at 1000 K; decreasing the temperature has the opposite effect, favouring the forward reaction and increasing Kc, which is why SO3 production is favoured at lower temperature.

For an endothermic reaction, such as N2O4(g) <=> 2NO2(g), Delta H° = +57.2 kJ, increasing the temperature favours the forward, heat-absorbing reaction, shifting the equilibrium to the right, increasing the concentration of NO2, and increasing the value of Kc, which rises from about 7.7 x 10^-5 at 273 K to about 0.4 at 373 K; decreasing the temperature favours the reverse reaction and decreases Kc. In general, raising the temperature always favours whichever direction of a reaction is endothermic, regardless of whether that happens to be the forward or the reverse direction.

8.11 Industrial Applications: Haber's Process and the Contact Process

The synthesis of ammonia by the Haber process, N2(g) + 3H2(g) <=> 2NH3(g), Delta H = -46.11 kJ/mol, is exothermic and proceeds with a decrease in the number of gas moles, so Le Chatelier's principle predicts that maximum yield is favoured by continuously removing ammonia as it forms, by using high pressure, and by using low temperature. In practice, very low temperature makes the reaction far too slow to be economical, so industrial plants instead use a moderate temperature of around 673 K (400 degrees C) together with an iron catalyst, promoted with MgO, Al2O3 and SiO2, to speed up the approach to equilibrium, combined with a high pressure of 200 to 300 atmospheres; under these compromise conditions, useful yields of ammonia are obtained at a commercially practical rate, even though the very highest possible yield, up to 98.3 percent, would require far more extreme, and far less economical, conditions of very low temperature and very high (1000 atmosphere) pressure.

A similar compromise governs the production of sulfur trioxide in the contact process for making sulfuric acid, 2SO2(g) + O2(g) <=> 2SO3(g), Delta H = -97.9 kJ/mol: Le Chatelier's principle predicts that high pressure and low temperature favour the highest yield of SO3, but at low temperature the equilibrium is reached only very slowly. Industrially, a mixture of SO2 and O2 (as air) at about 1 atmosphere pressure is passed over a solid vanadium(V) oxide catalyst; because the reaction is exothermic, the gas temperature rises to around 600 degrees C as it reacts, so the mixture is cooled and recycled at the more favourable temperature of 400 to 500 degrees C to increase the final yield of SO3.

Important Definitions

Key Facts and Relations

Topic	Key Fact / Relation
General equilibrium constant expression	Kc = [C]^c[D]^d / ([A]^a[B]^b) for aA + bB <=> cC + dD
Equilibrium constant from rate constants	Kc = kf / kr
Partial pressure equilibrium constant	Kp = (pC^c . pD^d) / (pA^a . pB^b)
Relating Kp and Kc	Kp = Kc (RT)^Delta n
Relating Kp and Kx	Kp = Kx (P)^Delta n
Relating Kp and Kn	Kp = Kn (N)^Delta n
Special case when Delta n = 0	Kp = Kc = Kx = Kn
Le Chatelier's principle	A system at equilibrium shifts to counteract any imposed disturbance
Effect of pressure increase (unequal gas moles)	Equilibrium shifts toward the side with fewer moles of gas
Effect of temperature	Exothermic reaction: T up shifts equilibrium left, Kc decreases; Endothermic reaction: T up shifts equilibrium right, Kc increases

Diagrams

Concentration vs Time as a Reversible Reaction Approaches Equilibrium: A plot showing reactant concentration falling and product concentration rising as a reversible reaction proceeds, both becoming constant once the forward and reverse reaction rates become equal at equilibrium

Effect of a Catalyst on the Forward and Reverse Activation Energies: An energy profile diagram showing that a catalyst lowers the activation energy of both the forward and reverse reactions by the same amount, speeding up the approach to equilibrium without changing its position

Percent Yield of Ammonia vs Temperature at Different Pressures: A set of curves showing how the percentage yield of ammonia in the Haber process decreases with increasing temperature and increases with increasing pressure, with the industrial compromise conditions marked

Short Questions & Answers

Long Questions & Answers

Explain the difference between macroscopic and microscopic events in a reversible reaction, and describe how the concept of dynamic equilibrium follows from this distinction.

What is the difference between a macroscopic and a microscopic event in a chemical system?

A macroscopic event is a change that can be observed directly with the naked eye, such as a colour change or the evolution of a gas, while a microscopic event is a molecular-level occurrence, such as a collision between particles or the breaking of a bond, that cannot be observed directly but is what actually causes the macroscopic change.

How does the rate of the forward reaction change as steam and carbon monoxide are first mixed?

At the moment of mixing, the concentrations of both reactants are at their highest, so the frequency of effective collisions between H2O and CO molecules, and therefore the rate of the forward reaction, is at its maximum; as the reactants are gradually consumed, this rate steadily decreases.

How does the rate of the reverse reaction change as the forward reaction proceeds?

At the start, essentially no product molecules are present, so the reverse reaction proceeds extremely slowly; as H2 and CO2 accumulate from the forward reaction, collisions between them become more frequent, so the rate of the reverse reaction gradually increases.

What happens once the forward and reverse rates become equal?

Once the two rates are equal, the amount of reactant being converted to product each second exactly balances the amount of product being converted back to reactant, so the concentrations of every species stop changing; the system has reached chemical equilibrium.

Why is this equilibrium described as dynamic rather than as the reaction having stopped?

Even though the bulk concentrations no longer change, individual reactant and product molecules are still continuously colliding and reacting in both directions at the microscopic level; the system only appears unchanging because these two ongoing processes occur at exactly equal rates, which is the defining feature of a dynamic, rather than a static, equilibrium.

State Le Chatelier's principle and explain how it is used to predict the effect of changes in concentration, pressure, and temperature on a system at equilibrium.

What does Le Chatelier's principle state?

It states that if a system at equilibrium is disturbed by an external change, the system responds in a way that counteracts, or partially nullifies, the effect of that disturbance, shifting the position of equilibrium until a new balance is established.

How does adding more of a reactant affect the position of equilibrium?

Adding more reactant increases its concentration above the equilibrium value, so the system shifts in the forward direction, consuming some of the added reactant and producing more product, until a new equilibrium position is established at which the rates of the forward and reverse reactions are again equal.

How does increasing the pressure on a gaseous equilibrium affect its position?

If the numbers of moles of gas differ between the reactant and product sides, increasing pressure shifts the equilibrium toward whichever side has fewer moles of gas, since that side occupies less volume and partially relieves the increased pressure; if the moles of gas are equal on both sides, changing pressure has no effect on the equilibrium position.

How does increasing the temperature affect an exothermic equilibrium differently from an endothermic one?

Because raising temperature always favours whichever direction of a reaction absorbs heat, increasing temperature shifts an exothermic reaction's equilibrium toward the reactants, decreasing Kc, while it shifts an endothermic reaction's equilibrium toward the products, increasing Kc.

Why is temperature different from concentration and pressure in how it affects equilibrium?

Changing concentration or pressure shifts the position of equilibrium while leaving the numerical value of the equilibrium constant unchanged, since Kc depends only on temperature; changing temperature, however, actually changes the value of Kc itself, which is why temperature is described as the only factor that alters the equilibrium constant rather than simply shifting the equilibrium position around a fixed Kc.

Multiple Choice Questions (MCQs)

Quick Revision Summary

• Reversible reaction: proceeds in both directions, written with a double arrow (<=>); irreversible reaction: goes to completion
• Chemical equilibrium: reached in a closed system when forward and reverse rates become equal and concentrations become constant
• Macroscopic events (observable, e.g. colour change) result from countless microscopic events (molecular-level, e.g. collisions, bond breaking/forming)
• Dynamic equilibrium: both forward and reverse reactions continue indefinitely at equal rates; applies to chemical reactions and physical changes (e.g. liquid-vapour, ice-water)
• Conditions for equilibrium: reaction must be reversible; system must be closed
• Characteristics: constant concentrations; approachable from either direction; catalyst does not change position/Kc, only speeds attainment; Kc depends only on temperature
• Pure solids/liquids excluded from Kc expression (their concentration does not change)
• Homogeneous equilibrium: all species same phase; heterogeneous equilibrium: species in more than one phase
• Kc = [C]^c[D]^d / ([A]^a[B]^b) for aA+bB<=>cC+dD; derived from Kc = kf/kr using the law of mass action
• Four equilibrium constants: Kc (concentration), Kp (partial pressure), Kn (moles), Kx (mole fraction); Kp=Kc(RT)^Deltan, Kp=Kx(P)^Deltan, Kp=Kn(N)^Deltan; all equal when Delta n = 0
• Le Chatelier's principle: a system at equilibrium shifts to counteract any imposed disturbance
• Concentration change: shifts position to consume the addition/replace the removal; pressure/volume change: only matters if gas moles differ, shifts toward fewer gas moles side under higher pressure
• Temperature is the only factor that changes Kc itself: exothermic reaction, T up -> Kc down; endothermic reaction, T up -> Kc up
• Haber process (exothermic, moles decrease forward): industrial compromise of ~400°C, 200-300 atm, iron catalyst; Contact process (exothermic): ~1 atm, V2O5 catalyst, 400-500°C after cooling

Exam Tips

• Remember Kc depends only on temperature — changes in concentration, pressure, or volume shift the position of equilibrium but never change the numerical value of Kc itself
• Always leave pure solids and pure liquids out of an equilibrium constant expression — only include species whose concentration can actually change (gases and species in solution)
• When converting between Kp and Kc, calculate Delta n (moles of gaseous products minus moles of gaseous reactants) from the balanced equation first, and double check its sign before substituting into Kp = Kc(RT)^Delta n
• For pressure/volume questions, first check whether the total moles of gas differ between reactants and products — if they are equal, pressure and volume changes have no effect on the equilibrium position at all
• For temperature questions, first identify whether the given reaction is exothermic or endothermic from its Delta H sign, then apply the rule that raising temperature always favours whichever direction absorbs heat
• When explaining industrial conditions (Haber process, contact process), remember the answer is almost always a compromise between the yield favoured by Le Chatelier's principle and the reaction rate needed for the process to be economically practical