# Equilibrium Class 11 Notes Chemistry Chapter 7

Introduction, Physical and Chemical Equilibrium, Homogeneous and Heterogeneous Equilibria, Le Chatelier's Principle, pH Scale, Common Ion Effect

## Introduction

Equilibrium is the most important characteristic property of reversible reactions. These reactions for which the forward reaction occurs to a much greater extent are considered to be unidirectional in nature and whenever the rate of forward reaction is equal to rate of backward reaction, equilibrium is attained, not to forget that equilibrium exists only in closed system.

It is the state of system at which temperature, pressure, volume and composition have fixed value and does not vary with time. Chemical Reactions can be divided into two categories:

1. Irreversible Reactions: The reactions which proceed to completion and the products fail to recombine to give back reactants. For example

AgNO3 + NaCl ⟶ AgCl + NaNO3

2. Reversible Reactions: The reactions which never go to completion and products recombine to give back reactants. For example

PCl5(g) ⇌ PCl3(g) + Cl2(g)

N2(g) + 3H2(g) ⇌ 2NH3(g)

## Physical Equilibrium

We know that solid, liquid and gas are the three states of substance. Therefore, three types of physical equilibrium are possible. These are

Solid(s) ⇌ liquid (l)

Liquid(l) ⇌ gas(g)

Solid(s) ⇌ gas(g)

Here the sign double half arrows ( ⇌ ) pointing in the opposite directions is both for the reversible change as well as for the equilibrium state.

1. Solid(s) – liquid(l) equilibrium: At equilibrium two processes takes place at the same rate i.e.,

Ice(s) ⇌ water(l)

H2O(s) ⇌ H2O(l)

At equilibrium,

Rate of melting of ice = Rate of freezing of water

The temperature at which the solid and liquid states of a pure substance are in equilibrium at the atmospheric pressure is called the normal freezing point or melting point of that substance.

2. Liquid(l) – gas(g) equilibrium:

H2O(l) ⇌ H2O(g)

In such type of equilibrium,

Rate of vaporisation of water = Rate of condensation of water vapour

3. Solid(s) – gas(g) equilibrium: Such type of equilibrium is attained in case of volatile solids.

Example : If solid iodine is placed in a closed vessel, violet vapours starts appearing in the vessel. The intensity of violet vapour increases with time and ultimately it becomes constant.

I2(s) ⇌ I2(g)

In this equilibrium,

Rate of sublimation = Rate of condensation

### Solids in liquids:

Suppose sugar is added continuously into a fixed volume of water at room temperature and stirred thoroughly with a glass rod. First the sugar will keep on dissolving but then a stage will come when no more sugar dissolves. Instead it settles down at the bottom. The solution is now said to be saturated and in a state of equilibrium. In this state

Rate of dissolution = Rate of precipitation

Sugar(s) ⇌ Sugar (in solution)

The amount of the solid in grams that dissolves in 100 g of the solvent to form a saturated solution at a particular temperature is called the solubility of that solid in the given solvent at that temperature.

### Gases in liquids

Such type of equilibrium is present in soda water bottle in which CO2 gas is dissolved in water under high pressure. There is a state of dynamic equilibrium between the CO2 present in the solution and the vapours of the gas above the liquid surface at a given temperature.

CO2(g) ⇌ CO2(aq)

### Henry’s law

It states that, The mass of gas that dissolved in a given mass of a solvent at any temperature is proportional to the pressure of the gas above the surface of the solvent.

m ∝ p

m = kp

where k is Henry’s constant and its value depends upon the nature of the gas, nature of liquid and temperature.

### General Characteristics of Physical Equilibrium

1. Equilibrium is possible only in a closed system at a given temperature.

2. Both the opposing processes occur at the same rate and there is a dynamic but stable condition.

3. All measurable properties of the system remain constant.

4. When equilibrium is attained for a physical process, it is characterised by constant value of one of its parameters at a given temperature.

5. The magnitude of such quantities at any stage indicates the extent to which the physical process has proceeded before reaching equilibrium.

## Chemical Equilibrium

Every reversible reaction consists of one pair of reaction, one is forward and other is backward reaction. At one stage during reversible reactions, forward and backward reaction proceed at the same time with the same rate, the reaction is then said to be in equilibrium. If the opposing processes involve chemical reactions, the equilibrium is called Chemical equilibrium.

### (i). Law of Chemical Equilibrium

This law states that the rate of an elementary reaction is proportional to the product of the concentration of the reactants. At a constant temperature, the rate of a chemical reaction is directly proportional to the product of the molar concentrations of the reactants each raised to a power equal to the corresponding stoichiometric coefficients as represented by the balanced chemical equation. Let us consider the reaction,

A + B ⇌ C + D

rf = Kf[A][B]

rb = Kb[C][D]

At equilibrium rf = rb.

Kf[A][B] = Kb[C][D]

K_{c}=\frac{K_f}{K_b}=\frac{[C][D]}{[A][B]}

Kc is called the equilibrium constant, [ ] ⟶ denotes active masses.

For a general reversible reaction

aA + bB ⇌ cC+ dD

K_{c}=\frac{[C]^c[D]^d}{[A]^a[B]^b}

### (ii). Equilibrium constant of reverse reaction

Equilibrium constant for the reverse reaction is the inverse of the equilibrium constant for the reaction in the forward direction.

K'_c=\frac{1}{K_c}

### (iii). Relation between Kp and Kc

For a general reversible reaction

aA + bB ⇌ cC+ dD

K_{c}=\frac{[C_C]^c[C_D]^d}{[C_A]^a[C_B]^b} .....(1)

K_{p}=\frac{[P_C]^c[P_D]^d}{[P_A]^a[P_B]^b}

K_{p}=\frac{[C_C]^c\times[RT]^c.[C_D]^d\times[RT]^d}{[C_A]^a\times[RT]^a.[C_B]^b\times[RT]^b}

K_{p}=\frac{[C_C]^c[C_D]^d(RT)^(c+d)}{[C_A]^a[C_B]^b(RT)^(a+b)}

From eq. (1),

K_{p}=K_c(RT)^{(c+d)-(a+b)}

K_{p}=K_c(RT)^{Δn}

Where, Δn = difference of stoichiometric coefficients of gaseous products and reactants.

### (iv). Characteristics of Equilibrium

1. At the state of equilibrium, certain available properties like pressure, concentration and density becomes constant.
2. Chemical equilibrium can be established from either side.
3. A catalyst can cause the state of equilibrium to be reached faster, but does not alter the state of equilibrium.
4. Chemical equilibrium is dynamic in nature.
5. Any change in external stress (Pressure, temperature or concentration) causes disturbance in equilibrium state. The state of equilibrium being stable, is again reached by some adjustment.
6. If temperature is changed, a new equilibrium is achieved with a new value for relative concentration of products and reactants.
7. If temperature is kept constant, pressure and concentration of reactants / products is altered, system shifts in forward or backward direction in order to nullify the alteration (stress).

### (v). Factors Affecting Equilibria

1. Change in Concentration: When the concentration of any of the reactants or products in an equilibrium reaction is altered, the equilibrium mixture’s composition changes in order to minimize the effect of the concentration change.

2. Change in Temperature: According to Le-Chatelier’s principle if the temperature of an equilibrium system is increased, the equilibrium will move in the direction of the added heat.

3. Change in Pressure: The pressure has no effect on the equilibrium if the number of moles of gaseous reactants and products does not change. The change in pressure in both liquids and solids can be neglected in heterogeneous chemical equilibrium.

3. Change in Volume: When the volume of a gaseous mixture at equilibrium is increased, the equilibrium moves in the direction of a larger number of gaseous molecules.

4. Effect of a Catalyst: The equilibrium is unaffected by the catalyst. This is due to the fact that the catalyst favours both forward and backward reactions equally.

## Homogeneous Equilibria

When in an equilibrium reaction, all the reactants and the products are present in the same phase (i.e., gaseous or liquid) it is called a homogeneous equilibrium. For example,

N2(g) + 3H2(g) ⇌ 2NH3(g)

## Heterogeneous Equilibria

When in an equilibrium reaction, the reactants and the products are present in two or more than two phases, it is called a heterogeneous equilibrium.

The equilibrium between water vapour and liquid water in a closed container is an example of heterogeneous equilibrium.

H2O(l) ⇌ H2O(g)

## Le Chatelier's Principle

It states that if a stress is applied to a system in equilibrium, the equilibrium for the time being gets disturbed. As a result system moves in a direction which tends to relieve the external stress and finally a new equilibrium is attained.

## Ionic Equilibrium

### (i). Electrolyte

Electrolytes are the substances which conduct electricity in molten state or in solution. Example HCl, NaCl, KCl, CH3COOH etc.

### (ii). Arrhenius theory of Electrolytic dissociation

When an electrolyte is dissolved in a solvent it spontaneously dissociates into oppositely charged particles called ions, to a considerable extent. Electrolytic ionization or dissociation gives ions and unionized molecules in solution. For neutrality, the total charge on cations is equal to the total charge on the anions.

### (iii). Degree of Dissociation (α)

It is the fraction of one mole of the electrolyte that has dissociated under the given conditions. The value of α depends on temperature, dilution of electrolyte, nature of electrolyte and solvent.

α = No. of ionized moles / Total mo. moles

### (iv). Ostwald's Law of Dilution

According to this law, "The degree of ionization (or dissociation) of any weak electrolyte is inversely proportional to the square root of concentration."

α=sqrt{\frac{K}{C}}

Where, K = proportionality constant

## Concepts of Acids and Bases

### (i). Arrhenius Concept

Acid: Any substance when dissolved in water, increases the concentration of H+. e.g., HCl, H2SO4, HNO3 etc.

Base: Any substance when dissolved in water, increases the concentration of OH-. e.g., NaOH, KOH etc.

### (ii). Bronsted - Lowry Concept

Acid: Species (Molecule or ion) that donates a proton to another species.

Base: Species (Molecule or ion) that accepts a proton from another species.

HCl(Acid) + NH3(Base) ⟶ NH+4 + Cl-

### (iii). Lewis acids and bases

According to Lewis concept of acids and bases, a Lewis acid is an electron pair acceptor and a Lewis base is an electron pair donor.

Lewis acids: H+, Ag+, Fe2+, AlCl3, BF3, BCl3, BeCl2 etc.

Lewis Bases: Cl-, CN-, OH-, X-, NH-2, SH- etc.

An acid base reaction is the sharing of an electron pair with an acid by a base. This process is simply defined as coordination or neutralisation.

1. A strong acid is an acid that ionizes completely in water.

HCl(aq) + H2O (l) ⟶ H3O+ (aq) + Cl-(aq)

2. A weak acid is an acid that is only partially ionized in water.

CH3COOH(aq) + H2O(l) ⇌ CH2COO-(aq) + H3O+(aq)

3. A strong base is a base that ionizes completely in water.

KOH(aq) ⟶ K+(aq) + OH-(aq)

4. A weak base is a base which is partially ionized in water.

NH3(aq) + H2O(l) ⇌ NH+4(aq) + OH(aq)

## The pH Scale

pH of solution may be defined as negative logarithm of hydronium ion concentration.

pH = –log[H3O+]

pH=log\frac{1}{[H_3O^+]}

The pH range at 25°C is taken as 0 to 14.

pH = 7 Neutral
pH > 7 Basic
pH < 7 Acidic

## Common Ion Effect

The suppression in the dissociation of a weak electrolyte by the addition of a strong electrolyte having a common ion is called common ion effect.

For example: Ionisation of acetic acid (CH3COOH) and effect of addition of a small amount of acetate ion

CH3COOH(aq) ⟶ CH3COO-(aq) + H+(aq)

CH3COONa(aq) ⟶ CH3COO-(aq) + Na+(aq)

## Buffer Solution

A buffer solution is that solution which resists any change in its pH value on addition of small amount of acid or base. Although the pH of buffer changes on doing so, but the change in pH value will be less than the expected change. There are three types of buffer solution.

### 1. Acidic Buffer

This consists of solution of a weak acid and its salt with strong base. Example; CH3COOH and CH3COONa.

### 2. Basic Buffer

This consists of solution of weak base and its salt with strong acid. e.g., NH4OH and NH4Cl

### 3. Salt Buffer

It is a solution of salt which itself can act as a buffer. Such a salt is the salt of weak acid and weak base. For example,

CH3COONH4 ⇌ NH4+ + CH3COO-

When an acid is added, it reacts with CH3COO- to produce CH3COOH and when a base is added, it react with NH4+ to produce NH4OH.

### Buffer Capacity

It is the number of moles of acid or base required by one litre of a buffer solution for changing its pH by one unit.

Buffer Capacity = No. of moles of acid or base adder per litre / Change in pH

## Solubility and Solubility Product

The number of moles of solute in one litre of a saturated solution (mole / L) is defined as solubility. Let us calculate solubility of salt AgCl.

AgCl ⇌ Ag+ + Cl-

Ksp = [Ag+][Cl-]

Ksp is called solubility product.

In pure water,

Ksp = [Ag+][Cl-]

Ksp = S2    { ∵ S = [Ag+] = [Cl-] }

S=sqrt{K_{sp}}

## Summary

1. Equilibrium : It represents the state of a process in which the properties like temperature, pressure, concentration of the system do not show any change with the passage of time.

2. Physical equilibrium : It is a state of equilibrium in which the two opposing processes involve changes in physical state only.

3. Chemical equilibrium : It is a state of equilibrium in which the two opposing processes involve change of chemical species.

4. Reversible reaction : A reversible reaction is one which proceeds in both the forward and backward directions.

5. Law of mass action : This law states that at constant temperature, the rate of chemical reaction is directly proportional to the product of molar concentrations of the reacting substances.

6. Equilibrium constant (K): It is the ratio of the product of the molar concentrations of the substances formed to that of the reacting substances raised to the powers equal to their stoichiometric coefficients in the chemical equation at a particular temperature.

7. Henry’s law : The mass of a gas dissolved in a given mass of a solvent at any temperature is directly proportional to the pressure of the gas above the solvent.

8. Le Chatelier’s Principle : When a system in dynamic equilibrium is subjected to a stress such as a change in concentration, pressure or temperature, the equilibrium shifts in a direction that opposes or reduces the stress.

9. Strong electrolytes : Electrolytes which are ionized almost completely in aqueous solution under similar conditions of concentration and temperature are called strong electrolytes.

10. Weak electrolytes : Electrolytes which are poorly ionized in aqueous solution under similar conditions of concentration and temperature are called weak electrolytes.

11. Solubility product : It is the product of concentration of ions in a saturated solution of a sparingly soluble salt at a given temperature.

12. Arrhenius acid-base concept : According to Arrhenious, an acid is a substance which gives hydrogen ions and base is a substance which gives hydroxyl ions in aqueous solutions.

13. Bronsted-Lowry acid-base concept : According to this concept, an acid is a proton donor and base is a proton acceptor.

14. Lewis acid-bases concept : According to this concept, an acid is an electron pair acceptor and base is an electron pair donor.

15. pH value : pH value of a solution is the negative logarithm of the hydrogen ion concentration (in moles per litre) present in it. Thus pH = -log[H+]

16. Irreversible reaction : If a reaction cannot take place in the reverse direction i.e., the products formed do not react to give back the reactants under the same conditions is called an irreversible reaction.

17. Homogeneous equilibria : When in an equilibrium reaction, all the reactants and the products are present in the same phase (i.e., gaseous or liquid), it is called a homogeneous equilibrium.

18. Heterogeneous equilibrium : When in an equilibrium reaction, the reactants and the products are present in two or more than two phases, it is called a heterogeneous equilibrium.

19. Buffer solution : It is defined as a solution which resists in its pH value even when small amounts of the acid or the base are added to it.

20. Conjugate base : A base formed by the loss of proton by an acid is called conjugate base of the acid.

21. Conjugate acid : An acid formed by the gain of a proton by the base is called conjugate acid of the base.