1. General characteristics of solid state

Chapter 1
solid state

Solids are characterised by the state of matter in which particles are closely packed and held together by strong inter molecular attractive force.

General Characteristics / Properties of Solids

(a) In solid state the particles are not able to move randomly.

(b) They have definite shape and volume.

(c) Solids have high density.

(d) Solids have high and sharp melting point which is depend on the strength or value of binding energy.

(e) They are very low compressible.

(f) They show very slow diffusion.

2. Amorphous and crystalline solids

Types of Solids (Amorphous/Crystalline)

Crystalline solids :

(a)  In this type of solids the atoms or molecule are arranged in a regular pattern in the three dimensional network.

(b)  They have well defined geometrical pattern, sharp melting point, definite heat of fusion and anisotropic nature.

(c)  Anisotropic means they exhibit different physical properties in all directions.

e.g. The electrical and thermal conductivities are different directions.

(d) They are generally incompressible.

(e) The general examples of crystalline solids are as Quartz, diamond etc.

Amorphous Solids :

(a) In this type of solids, the arrangement of building constituents is not regular.

(b) They are regarded as super cooled liquids with high viscosity in which the force of attraction holding the molecules together are so great, that the material becomes rigid but there is no regularity in structure.

(c) They do not have sharp melting points.

(d)  They are isotropic as they exhibit same physical properties in all the directions.

(e) The general examples of this solids are as glass, Rubber, plastics etc.

Difference between crystalline and amorphous solids :

3. Classification of crystalline solids

Classification of crystalline solids


Crystal : A crystal is a homogeneous portion of a solid substance made by regular pattern of structural units bonded by plane surface making definite angles with each other.

Space lattice : The arrangement of constituents like atom, ions and molecules in different sites in three dimensional space is called space lattice.

Unit cell : The smallest repeating unit in space lattice which when repeats over and over again, results in a crystal of the given substance called unit cell.   

Properties of a cube : 

Face : The plane surface of the crystal are called faces.

Edge : An edge is formed by the intersection of two adjacent faces.   

Interfacial angles : The angle between the perpendiculars two intersecting faces called interfacial angles.

Unit Cell in two dimensions :

Now in order to uniquely explain a regular arrangement in two dimensions we need the help of three parameters, two distance parameters and one angular parameter. Based upon their different relationships we can define different cases

Case ‘A’ (a = b) angle = 90º

The unit cell in such a case is a squaresuch square side by side we will obtain the entire two dimensional arrangement.

Case ‘B’(a ¹ b) angle = 90º

Placing The unit cell formed in this case is a rectangle.

Unit cell in three dimensions :

It has six parameters, 3-distance parameters and 3-angular parameter.

a, b, c are lengths of unit cell (also known as the  crystallographic axes). a, b, g  are known as the crystallographic angles.

4. Different Classes of Crystals


Based on different permutations of a, b, c and a, b, g we define different crystal classes.

Seven Crystal System

Table : 4

Hint for memorise : CaTORacHMT

Note : In 3-D 14 different types of unit cell are found and these are also known as 14 Bravais lattice.

Types of unit cell :

In every crystal class, the positioning of the lattice points may be different. Based upon these different positions occupied by the lattice points, we have different types of unit cells.

1. Simple / primitive type of unit cell : If lattice points or the particles of the solid are present only at the corners of the unit cell.

2. Body centred unit cell : lattice point are at the corners as well as at the body centre.

3. Face centred unit cell : lattice points are at corners as well as at each of the face centres.

4. End centred unit cell : lattice points are at the corners as well as at centre of any of two opposite faces.

Each of these arrangements corresponds to a unique and different type of arrangement.These 14 different arrangements are called the 14  Bravais lattices.

In any lattice, the surrounding of each and every lattice point is exactly identical

5. Mathematical Calculations of Cubic System



Simplest crystal is to be studied in cubic system.  Three types of cubic systems are following.

(a) Simple Cubic (SC) : Atoms are arranged at the corners of the cube.

(b) Body Centered Cubic (BCC) : Atoms are arranged at the corners and at the centre of the cube.

(c) Face Centered Cubic (FCC) : Atoms are arranged at the corners and at centered of the each faces.

Contribution of different Lattice point in one Cubical unit cell :

 (i) Contribution from one corner lattice point = th.  

(shared in 8 identical cubes)

 (ii) Contribution from one face centered lattice point =.     

(shared in 2 identical cubes)

(iii) Contribution from edge centered lattice point = th.       

(shared in 4 identical cubes)

 (iv) Contribution from body centered lattice point = 1.  

(it is present inside or at the centre of cube)

Number of atoms per unit cell / unit cell contents :

The total number of atoms contained with in the unit cell for a simple cubic called the unit cell content.

(a) Simple cubic structure (sc) :

Each corner atom is shared by eight surrounding cubes.  Therefore, it contributes for  of an atom.


(b) Body centered cubic structure (bcc) :

(i) Eight Corner atoms contribute one atom per unit cell.

(ii) Centre atom contribute one atom per unit cell.

(iii) So, total 1 + 1 = 2 atoms per unit cell.

(c) Face centered cubic structure (fcc) :

(i) The eight corners atoms contribute for  of an atom and thus one atom per unit cell.

(ii) Each of six face centered atoms is shared by two adjacent unit cells and therefore one face centred  atom contribute half of its share.  Means

 atom per unit cell.  

(iii)    So, total Z = 3 + 1 = 4 atoms per unit cell.

Atomic radius :

It is defined as the half of the distance between nearest neighbouring atoms in a crystal.  It is expressed in terms of length of the edge (a) of the unit cell of the crystal.

(a) Simple cubic structure [S.C.] 

Radius of atom ‘r’ =    

(b) Face centered cubic structure (FCC) ‘r’ = 

(c) Body centered cubic structure (BCC) ‘r’ =               

 a = b = c

a = b = g = 90º

6. Arrangement of the atom / particles of the solids in three dimensions

Arrangement of the atom / particles of the solids in three dimensions

Now having gained a knowledge of some of the terms, let us study how the different arrangements in space are brought about.

Firstly we will focus our attention on the solids containing only one type of lattice points.

The solids which contain only one type of lattice points are:

  • metallic solids (eg. Iron)
  • molecular solids (eg. dry ice)
  • covalent network solids (eg. diamond)

(Ionic solids do not fall into this category as they contain more than one type of particles,they will be studied in the later parts of the chapter)

All the atoms or particles of the solids will be represented by solid spheres, each of radius ‘r’.

We will be taking these spheres of radius ‘r’ and explore how we can arrange these in three dimensions.Firstly we will begin with arrangement in one dimension.

Arrangement in 1-D : In one dimension it is possible to arrange the spheres in two possible ways.


Not Stable [because the potential energy of the system is not minimum]

2.          a = 2r

          Coordination number = 2

1-D close packing stable arrangement

This is the predominant way of packing in one dimension and as such most of the space lattices will  show such an arrangement in one dimension along the planes of close packing.

Arrangement in two dimension :  

In two dimensions also there are two ways of packing the spheres(in moving from one dimension to two dimensions it can be imagined that the two dimensional array will be made up of 1-D closed pack arrays / lines  which are stacked one on top of other.

1. Square packing : If the one dimensional arrays are placed on top of one another, we get the square packing in two dimensions.

One sphere will be in contact with 4 other spheres.

 area of square = a2 = 4r2                               

area of atoms in the square =

 fraction of area occupied by spheres =  = 78%

2. Hexagonal close packing : (in 2-D) If in a two dimensional arrangement,every one dimensional array is placed in the cavity of the just preceding array, we get the hexagonal packing in two dimensions.

 area of hexagon =   

area of atoms =  

fraction of area occupied = 91%

As is evident from the above calculations, the spheres are in closer contact in the hexagonal arrangement, hence the hexagonal arrangement is considered to be a better way of packing as compared to the  square packing.

Arrangement in three Dimensions :

1. Simple cubical arrangement in three dimensions :

(will be made up of 2-D sheets arranged one over other)

The simple cubical packing is obtained by arranging the square pack sheets of two dimension one over the other such that spheres of the second sheet are exactly (vertically) above the spheres of first sheet.

(Note that , hence crystal thus formed will belong to the cubic crystal class, and as the lattice points are only at the corners, hence the unit cell will be simple, therefore what we get is the simple cubic)

(i) Relation between ‘a’ and ‘r’

 a = 2r (because atoms along the edge are touching each other)

(ii) Effective no. of atoms per unit cell :

 (Z) =  × 8 = 1

(iii) Packing fraction :

Packing efficiency =

   =  = 0.52  (or 52%)

(Note : This is not a very efficient way of packing as the packing fraction is very low)

(iv)  Coordination Number :

It is defined as the number of atoms touching any one particular atom. For simple cubic, coordination number = 6.

(v)  Density of unit cell : It is the ratio of mass of the spheres present in unit cell and total volume of unit cell.

 Density of the unit cell =


Where Z = no. of atoms in a unit cell

M/NA = mass of a single  atom

M = molar mass

NA = Avogadro number (6.023 × 1023)

2. Body centred cubic :

The body centred cubic is a unique way of packing, as the 2D-arrays that can be imagined to constitute the space lattice are themselves formed in a unique way. The lattice points in the 2D array do not touch each other. The spheres start touching each other only upon moving from  2D to 3D, i.e when the 2D arrays are placed on top of each other in such a fashion that the spheres of the next plane are into the cavities of the first plane of spheres.The third plane of spheres is then exactly identical to the first plane of spheres.

(i)  a  ¹ 2r (as atoms along the edge are not touching each other)

they touch along  the body diagonal, hence a = 4r.

(ii) Effective number of atoms (Z) = 1 +  × 8 = 2.

(iii) Packing fraction =  =  0.68 = 68%

(iv) Coordination No.= 8

 (the sphere at the body centre will be touching the spheres at the eight corners)

(v) Density =  =   (Q Z = 2)

3.  Close packing in three dimensions :

(These are made up of two dimensional hexagonally packed sheets) In second layer we have two kinds of voids.                            

(i) Voids of second layer below which there are spheres of first layer (all voids of type ‘a’).

(ii) Voids of second layer below which there are voids of first layer (all voids of type ‘b’).

For third layer, we have two possibilities.

 (A) If spheres of IIIrd layer are placed in voids of IInd layer below which there are spheres of Ist layer (voids of type ’a’) then Ist layer and  IIIrd layer are identical so this is called AB–AB pattern repeat or hexagonal close packing)

Hcp unit cell : a = 2r = b

(i)  Calculation of ‘c’ :

For the estimation of ‘c’, consider the spheres marked 1,2,3,4 in the unit cell as shown.These four spheres form a regular tetrahedron. The length of the perpendicular from ‘4’ to the equilateral triangle 1-2-3 will be equal to c/2.

  cos 30º =

Apply pythagoras theorem.

x2 + (c/2)2 = a2   Þ   c =  4r

Volume of the hexagon = Area of base x Height.

(ii)  Effective no. of atoms per unit cell :

Z =  × (no. of atoms at corner) +  × (no. of atoms at face centres) + 1 × (no. of atoms inside the body)

          =  × 12  +  × 2 + 1 × 3 = 2 + 1 + 3 = 6

Packing fraction : = 0.74 = 74%

Coordination No. : C.N. = 12

Density (Q Z = 6)

(B) ABC-ABC arrangement :

If the third  layer spheres are placed in those  voids of second layer under which there are voids of the first layer of spheres (voids of type ‘b’), then the first and the third layer of spheres will not be identical.Such an arrangement will lead to an ABC-ABC type of arrangement.It is also known as the cubical close packing (ccp) or also as the Face Centred Cubic structure (FCC).

(a = tetrahedral voids)

(b = octahedral voids)

In the ABC – ABC pattern, the spheres of 4th layer are vertically above the spheres of Ist layer then these consecutive layers are different from each other, fourth layer will be idential to first layer so it will be called ABC – ABC repeat pattern.It is also called the ccp (cubical close packing) because a cubical type of unit cell is used for the study of this arrangement.

(i) Relation between ‘a’ and ‘r’ :

  a  ¹ 2r

   (as the spheres touch along the face diagonal)

(ii) Effective no. of atoms :


(iii) Packing fraction :  =  = 0.74 = 74%        

(iv) Coordination number : 12      

(v) Density

Note : In close packings, whenever two consecutive layers are of different kinds(FCC, HCP) then packing efficiency will always be 74%

7. Types of voids found in close packing


1. Tetrahedral void (3-Dimensional 4 co-ordinate) :                                   

The tetrahedral void is formed whenever a sphere is placed on top of the triangular arrangement as in case of the triangular void.         

    r = 0.225 R

Location of tetrahedral voids in FCC unit cell :

The FCC unit cell has eight tetrahedral voids per unit cell. Just below every cornerof the unit cell, there is one. As there are eight corners, there are eight tetrahedral voids.

The spheres 1, 2, 3, 4 form a tetrahedral void. 

2. Octahedral void (3-Dimensional 6 coordinate void) The octahedral void is formed whenever two spheres are placed, one on top and the other below a square arrangement of spheres

r = 0.414 R      

Location of octahedral voids in a FCC unit cell :

In a FCC unit cell, there are four octahedral voids. They are present at all the edge centres and at the body centre. The contribution of the edge centre void per unit cell is     .

Hence, total number of octahedral voids = +  (1)  = 4

edge centres           body centre

Note : Let the no. of close packed spheres be N then the no. of octahedral void gemetrated = N and the number of tetrahedral void generated = 2N

3. Cubical void (3-Dimensional 8-coordinate void)

The cubical void is generally not found in closed packed structures, but is generated as a result of distortions arising from the occupancy of voids by larger particles.

Along body diagonal

 r = 0.732 R 


Ionic solids are characterised by the presence of atleast two types of particles,viz: the cation and the anion,even the simplest of ionic solids contains one cation and one anion.

The Cations are generally found to be of smaller size, and the anions of larger sizes. The anions thus form the lattice by occupying the lattice positions and the cations are found inside the voids in such structures.

The types of void occupied by the cation would depend upon the the ratio of its radius to that of the anion, popularly termed as the radius ratio. Hence, radius ratio = r+ / r

   Examples of ionic crystals :

(a) Rock Salt (NaCl) Coordination number (6 : 6) NaCl crystallizes in the face centred cubic structure. The chloride ions are present at all the lattice position and the sodium ions occupy all the octahedral voids.

Rock salt (NaCI) structure.       

Every sodium is in contact with four chloride ions, and every chloride is in contact with four sodium ions

(b) CsCl  C.No. (8 : 8)

Caesium chloride (CsCI) structure.     

The cesium ion is at the body centre and the chloride ions are at the corners.         

(c) Zinc Blend (ZnS) C.No. (4 : 4)

(d) Fluorite structure (CaF2) C.No. (8 : 4)

8. Crystals defects (Point Defects)


Imperfection can be because of :

– Conditions under which crystals have been developed.

– Impurities

– Temp (because of thermal conductivity some atoms/ions can get displaced

These imperfections can be

(a) Point defects – defects will be only at certain lattice positions.

(b) Line defects – If atoms/ions are misplaced/missing/replaced by some other ions along a line

(c) Plane (screw) defects – If atoms/ions are misplaced/missing/replaced by some other ions along a line in a plane.

Types of point defects

Point defect can be classified into three types :

(a) stoichiometric defects

(b) impurity defects

c) non-stoichiometric defect

(a) Stoichiometric defect

These are the point defects that do not distrub the stoichiometry of the solid. They are also called intrinsic ot thermodynamic defects. basically these are two types. Vacancy defecs and interstitial defects.

(i) Vacancy defect : When some of the lattice site are vacant, the crystal is said to have vacancy defect. This results in decrease in density of the substance. This defect can also develop when a substance is heated.

(ii) Interstitial defect : When some constituent particles (atoms or molecules) 

occupy an interstitial site. the crystal is said to have interstitial defect. This defect increases the density of the substance.

Vacancy and interstitial defects as explained above can be shown by non ionic solids. Ionic solids must always maintain electrical neutrality.

Rather than simple vacancy or interstitial defects, they show these defects as Frenkel and schottky defects.

(iii) Frenkel defect : This defect is shown by ionic solids. The smaller ion    

(usually cation) is dislocated from its normal site to an interstitial site. It creates a vacancy defect at its original site and an interstitial defect at  its new location.

Frenkel defect is also called dislocation defect. It does not change the density of the solid. Frenkel defect is shown by ionic substance in which there is a large difference in the size of ions, for example, ZnS, AgCl,AgBr and AgI due to small size of Zn2+ and Ag+ ions.

Eg. ZnS, AgCl, AgBr, AgI etc.

(iv) Schottky defect : It is basically a vacancy defect in ionic solids. In order         

to maintain electrical netrality. The number of missing cations and anions are equal.

 Like simple vacancy defect, schottky defect also decreases the density of the substance, Number of such defects in ionic solids is quite significant. For example, in NaCl there are approximately 106 schottky pairs per cm3 at room temperature. In 1 cm3 there are about 1022 ions. Thus, there is one schottky defect per 1016 ions. Schottky defect is shown by ionic substance in which the cation and anion are of almost similar sizes. For example,NaCl, KCl, CsCl and AgBr.

Note : It may be noted that AgBr shows both, Frenkel as well as schottky defects.

(b) Impurity defects 

If molten NaCl containing a little amount of SrCl2 is crystallised, some of          

the sites of Na+ ions are occupied by Sr2+. Each Sr2+ replaces two Na+ ions. It occupies the site of one ion and the other site remains vacant. The cationic vacancies thus produced are equal in number is the solid solution of CdCl2 and AgCl.

(c) Non-stoichiometric defect

The defects discussed so far do not disturb the stoichiometry of the crystalline substance. However a large number of non-stoichiometric inorganic solids are known which contain the constituent elements in non-stoichiometric ratio due to defects  in their crystal structures. These defects are of two types :

(i) metal excess defect and (ii) metal deficiency defect.

(i) metal excess defect                                                            

(a) metal excess defect due to anionic vacancies : Alkali halides like NaCl and KCl show this type of defect. When crystals of NaCl are heated in an atmosphere of sodium vapours, the sodium atoms are deposited on the surface of the crystal. The Cl ions diffuse to the surface of the crystal and combine with Na atoms to  give NaCl. This happens by loss of electron by sodium atoms to form Na+ ions. The released electrons diffuse into the crystal and occupy anionic site. As a result the crystal and now has an excess of sodium. The anionc sites occupied by unpaired electrons are called F-centres (from german word farbenzenter for colour centre). They impart yellow colour to the

crystals of NaCl. The colour results by excitation of these electrons when they absorb energy from the visible light falling on the crystals.     

Eg. :

*  The excess sodium in NaCl makes the crystal appears yellow.

*    Excess potassium in KCl makes it violet.

*  Excess lithium in LiCl makes it pink.

Greater the number of F-centres greater is the intensity of colour.  This type of defects are found in crystal which are likely to possess schottky Defects.

(b) metal deficiency defect due to the presence of extra cations at interstitial sites : Zinc oxideis white in colour at room temperature. On heating it loses oxygen and turns yellow.

Now there is excess of zinc in the crystal and its formula becomes Zn1+xO. The excess Zn2+ ions move to interstitial sites and the electrons to neghbouring interstitial sites.

(ii) metal deficiency defect : There are many solids which are difficult to prepare in the stoichiometric composition and contain less amount of the metal as compared to the stoichiometric proportion. A typical example of this type is FeO which is mostly found with a composition of Fe0.95O. it may actually range from Fe0.93O to Fe0.96O. In crystals of FeO some Fe2+ cations are missing and the loss of positive charge is made up by the presence of required number of Fe3+ ions.

9. Properties of Solids


1. Electric Properties :

On the basis of electrical conductivity the solids can be broadly classified into the three types:

(a) Metals (conductors) 

(b) Insulators 

(c)  Semi-conductors.

Following are salient features of electrical conductance in solids.

(i) The electrical conductivity of metallic conductors is due to the motion of electrons or positive holes (electronic conductivity) or through the motion of ions (ionic conductivity)

(ii) The conductance through electrons is called n-type conduction and through positive holes is called p-type conduction.

(iii) The conductance in insulators and semiconductors is mainly due to the presence of interstitial electrons and positive holes in the solids due to imperfections.

(iv) The conductivity of semiconductors and insulators increases with increase in temperature while that of metals decreases.

(v) Electrical conductivity of metal is in the order of 106–108 ohm–1 cm–1 while that of inculator is of the order of 10–12 ohm–1 cm–1. Semiconductors have intermediate value in the range 10–9 ohm–1 cm–1.

2. Magnetic Properties :

Based on the behaviour of substances when placed in the magnetic field, they are classified into five classes.

1. Types of solutions

Chapter 2:


1.Introduction : A solution is a homogeneous mixture of two or more substances which are chemically non-reacting. We come across many types of solutions in our daily life. e.g., solid-liquid, liquid-liquid, gas-gas. In this chapter we will learn several properties of solutions and their applications.

Solution: A homogeneous mixture of two or more substances is known as solution

Solute: The substance present in smaller amount in a solution is called solute.

Solvent: The substance present in larger amount in a solution is called solvent.

Types of Solutions

The concentration of a solution can be expressed by different concentration terms which are described as follows.

1. Electrochemical cells

Chapter 3


Batteries are everywhere in modern societies. They provide the electric current to start our autombiles and to power a host of products such as pocket caculators, digital watches, heart pacemaker, radio, and tape recorders.

Electrochemistry is the area of chemistry concerned with the interconversion of chemical and electrical.A battery is a an electrochemical cell, a device for interconverting chemical and electrical energy. A battery takes the energy relased by a spontaneous chemical reaction and uses it to produce electricity.

Electrochemical cell

It is device for converting chemical energy in to electrical energy.

The two types of cells are therefore reverse of each other   

Construction/ Working principle   

When ever an metal strip is put in an electrolyte the process of oxidation and reduction takes place simultaneously within the system. Due to this there is a potential difference between the metal phase and the liquid phase.

On joining the metal strips through a wire (of negligible resistence)  the current flows as long as the potential difference exists between the metal phase and the liquid phase.

I   Anode :

Some metals (which are reactive) are found to have tendency to go into the solution phase when these are placed in contact  with their ions or their salt solutions.

For example :  Zn rod is placed in ZnSO4solution .

The Zn atom or metal atoms will move in the solution to form Zn+2. After some time following equilibrium will be established.  

Zn(s)   Zn2+ +2e

There will be accumulation of sufficient negative charge on the rod which will not allow extra zinc ions to move in the solution. i.e. solution will be saturated with Zn+2 ions. 

The positive charge will be more concentrated nearly the rod.

The extra positive charge of the solution will be more concentrated around the negatively charged rod.  An electrical double layer is developed in the system and hence a potential difference is created between the rod and the solution which is known as electrode potential

This particular electrode is known as anode :

  • On anode oxidation will take place. (release of electron).
  • To act as source of electrons.
  • It is of negative polarity.
  • The electrode potential is represented by EZn(s) / Zn2+ (aq) 

II Cathode :

Some metals(Cu, Ag, Au etc.,) are found to have the opposite tendency i.e. when placed in contact with their aqueous ions, the ions from the solution will get deposited on the metal rod.

The following equilibrium will be established :  

Cu2+ +2e  Cu(s).

So rod will have deficiency of electron (positive charge).Extra negative charge will surround this positively charged rod and form double layer. An electrical double layer is developed in the system and hence a potential difference is created between the rod and the solution which is known as electrode potential. This will be known as cathode.

  • At cathode reduction will take place.(gain of e will take place)
  • To act as sink of electron.
  • Positive polarity will be developed.
  • Their electrode potential can be represented by : ECu2+(aq)/Cu(s)

Anode :

Cathode :

Construction of Cell :

It has  two half–cells,each having a beaker containing a metal strip that dips in its aqueous solution.

The metal strips are  called electrodes and are connected by an conducting wire.

Two solutions are connected by a salt bridge.

The oxidation and reduction half reactions occur at a separate electrodes and electric current flows   through the wire.

Selection of electrolyte for Salt Bridge :

The electrolyte in salt bridge should be such that speed of it's cation equals speed of it's anion in electrical field.

For that charge and sign of the ions should be almost equal.

Transport number of cation = Transport number of anion


Mobility of cation = Mobility of anion

KCl is generally preffered but KNO3 or NH4NO3 can also be used.

If Ag+, Hg2+, Pb2+, Tl+ ions are present in a cell then in salt bridge KCl is not used because there can be formation of  precipitate of AgCl, Hg2Cl2, PbCl2 or TlCl at mouth of tube which will prevent the migration of ions and its functioning will stop.

Functions of Salt Bridge :

A salt bridge is a U–shaped inverted tube that contains a gel permeated with an inert electrolyte.

It connects the solution of two half cell to complete the circuit.

It minimise the liquid junction potential. The potential difference between the junction of two liquids.

It maintains the electhical neutrality of the solution in order to give continious flow or generation of current.

" The simultaneous electrical neutrality of the anodic oxidation chamber and cathodic reduction chamber is due to same mobility or velocity of K+ and NO3 ions taken into salt bridge.

If the salt bridge is removed then voltage drops to zero.

The ions of the inert electrolyte do not react with other ion in the solution and the ions are not oxidised or reduced at the electrodes.

Generally tube is filled with a paste of agar-agar powder with a natural electrolyte/generally not common to anionic/cathodic compartment with porous plugs at each mouth of tube.

It prevents mechanical mixing of two electrolytic solution.

Electrode Potential :

The driving force that pushes the negative charge electrons away from the anode and pulls them towards the cathode is an electrical potential called electromotive force also known as cell potential or the cell voltage. Its unit is volt 

The potential difference devepoled between metal electrode and its ions in solution in known as electrode potential.

Electrode potential depends upon :

  • Concentration of the solution.
  • Nature of the metal.
  • Nature of the electrolyte.
  • Pressure temperature coditions.

The potential difference developed between metal electrodes and the solution of its ions at 1 M concentration at 1 bar pressure and 298 K is known as standard electrode potential.

Reference electrode  :

The potential of a singal electode cannot be determined what were the potential difference between two electrodes can be accurately measured using a reference electrode.

An electrode is chosen as a reference with respect to which all other electrodes are valued. 

Standard Hydrogen Electrode (SHE) is taken as standard reference electrode. Its electrode potential is arbitrarily assumed to be 0.00 volt.    

Standard Hydrogen Electrode (SHE)  consists of a platinum electrode in contact with H2 gas and aqueous H+ ions at standard state conditions (1 atm H2 gas, 1 M H+ (aq), 25°C).

  2H+ (aq, 1M) + 2e →  H2 (g, 1 atm)  [E° = 0V]

H2(g, 1atm) →  2H+ (aq, 1M) + 2e    [E° = 0V]

Cell potential :  

The difference in electrode potentials of the two half cell reactions (oxidation half cell and reduction half cell) is known as emf of the cell or cell potential.

The emf of the cell or cell potential can be calculated from the values of electrode potential of the two half cell constituning the cell. The following three methode are in use :

When oxidation potential of anode and reduction potential of cathode are taken into account :

cell = oxidation potential of anode + reduction potential of cathode

ox (anode) + E°red(cathode)

When reduction potential of both electrodes are taken into account :

cell = Reduction potential of cathode – Reduction potential of anode

 = E°cathode – E°anode  C both are reduction potential.

When oxidation potential of both electrodes are taken into account :

 E°cell = oxidation potential of anode – Oxidation potential of cathode

  = E°ox (anode) – E°ox (cathode)

The standard cell potential E° is the cell potential when both reactants and products are in their standard  states – solutes at 1 M concentration, gases at a potential pressure of 1 atm, solids and liquids in pure from, with all at a specified temperature, usually 25° C. 

cell is intensive property so on multiplying/Dividing cell reaction reaction by any number, the E°cell value would not change.

Free energy changes for cell reaction :

The free energy changeDG (a thermochemical quantity) and the cell potential E(an electrochemical quantity) both measure the  driving force of a chemical reaction.

The values ofDG and E are directly proportional and are related by the equation.

 DG = –nFE


n = Number of moles of electron transfered in the reaction.

 F = Faraday constant = 96485 C/mole e  96500  C/mole e

Shorthand Notation for Galvanic Cells

We require two half cells to produce an electrochemical cell, which can be represented by follwing few rules;

The anode half-cell is always written on the left followed on the right by cathode half cell.

The separation of two phases (state of matter) is shown by a vertical line.

The various materials present in the same phase are shown together using commas.

The salt bridge is represented by a double slash (||).

The significant features of the substance viz. pressure of a gas, concentration of ions etc. are indicated in brackets immediately after writing the substance.

For a gas electrode, the gas is indicated after the electrode for anode and before the electrode in case of cathode. (i.e  Pt H2 / H+ or H+ /H2 Pt)

For SHE reference potential is taken to be zero at all temperature.

SOP = – SRP = 0 for SHE.

To calculate standard potential of any other electrode a cell is coupled with standard hydrogen electrode (SHE) and it's potential is measured that gives the value of electrode potential of that electrode.

Anode  :  Zinc electrode                                                

Cathode :  SHE 

Cell :   Zinc electrode || SHE                  

Cell potential  :

Ecell =  – E°Zn2+/Zn      

  = 0.76 V (at 298 K experimentaly)                   

So, E0Zn2+/Zn = – 0.76 V (SRP) 

 E0 Zn/Zn2+(aq) = 0.76 V(SOP)

So, w.r.t. H2, Zn has greater

tendency to get oxidised. In similar manner reduction potentials (SRP) at 298 K for many other electrodes are calculated and are arranged in a series increasing order known as electro chemical series. 

Electrochemical Series :

Calculation of Electrode Potential of unknown electrode with the help of given (two) electrode.

Obtain the reaction of the 3rd electrode with the help of some algebraic operations on reactions of the given electrodes.

Then calculate DG of the 3rd reaction with the help of some algebaric operations of DG0 of 1st and 2nd reactions.

Use  DG0 = –nF E0elec. to calculate unknown  E.P.

is intensive property so if we multiply/Devide electrode reaction by any number the  value would not changed

i.e.    Zn2+ + 2e ®  Zn(s)   [E° = – 0.76 V[

Multiply by 2

2Zn2+ + 4e ®  2Zn(s)  [E° = – 0.76 V (remain same)]

1. Rate of a chemical reaction

Chapter 4

chemical kinetics

Introduction :

In the thermodynamics, we have studied whether a reaction will take place or not and if it does then upto what extent (chemical equiibrium), In this chapter we will study about how fast a chemical  reaction takes place and what are the different factors affecting this rate of chemical reaction. How to optimise the conditions as to maximse the output in optimum time. The last part of chapter will be dealing with the mechanism of a chemical reaction and catalysis.

Rate/Velocity of chemical reaction

The rate of change of concentration with time of different chemical species taking part in a chemical reaction is known as rate of reaction of that species.

Rate =  =  = mol lit–1 time–1  = mol dm–3 time–1 

Rate is always defined in such a manner so that it is always a positive quantity.

Types of Rates of chemical reaction :

For a reaction R  P

Average rate


Instantaneous rate : rate of reaction at a particular instant.


Instantaneous rate can be determined by drawing a tangent at time t on curve drawn for concentration versus time.

Initial Rate : Instantaneous rate at ‘t = 0’ is called initial rate [slope of tangent at t = 0].

Relation between reaction rates of different species involved in a reaction :

For the reaction :  N2 + 3H2  2NH3

Rate of reaction of N2 =

Rate of reaction of H2 =

Rate of reaction of NH3 =

These rates are not all equal. Therefore by convention the rate of a reaction is defined as

Rate of reaction 

Note : Rate of reaction value is dependent on the stoichiometric coefficients used in the reaction while rate of any species will be fixed value under given conditions.

2. Expressing concentration of solutions

Expressing concentration of solutions 

Concentration Terms :

% Concentration

Mass percentage. :It is the amount of solute in grams dissolved per 100 g of solution. e.g., 10% solution of sodium chloride means 10 g of solid sodium chloride present in 100 g of solution

% w/w =  × 100

Ex.     10% w/w urea solution = 10 g of urea is present in 100 g of solution.

= 10 g of urea is present in 90 g of water.

Mass by volume percentage (% w/v) : It is defined as mass of solute dissolved per 100 ml of solution. It is commonly used in medicine and pharmacy.

% wt/vol. (w/v)

% w/v = wt. of solute/100 mL of solution

 % w/v =


10%  (w/v) urea solution. = 10 g of urea is present in 100 mL of solution.

 But not 10 g of urea present in 90 ml of water  for dilute solution  :  volume solution = volume solvent.

Volume percentage (% v/v) : It is defined as volume of a solute dissolved per 100 ml of solution.

% v/v =  × 100

Strength of solution in g/L : Weight of solute (in gram) per litre (1000 mL) of solution.


10%  (w/v) sucrose solution, then specify its concentration in g/L

100 mL .......... 10 g

1000 mL ....... = 100 g/L

Molarity (M) : It is expressed as the number of moles of solute per litre of solution.

Molarity = No. of moles of solute per litre of solution.

Let     n =  No. of moles of solute ; N = No. of moles of solvent ;  V = volume of solution

no. of moles of solute = molarity x volume ( in L)

no. of m. moles of solute = molarity x volume ( in mL)

If V1 mL of C1 molarity solution is mixed with V2 mL of C2 molarity solution (same substance or solute)

Cf (V1+V2) = C1V1 + C2V2

 Cf =  =  where Cf = molarity of final solution

Molality (m) : It is defined as number of moles of solute per 1000 g or 1 kg of solvent.

Molality = No. of moles of solute per kg(1000 g) of solvent.

Let w gram of solute (Molar mass = Mg/mole) is dissolved in 'W' gram of solvent.

molality =   molality =

Molality not depends on temperature.

Normality : It is defined as number of gram equivalents of solute dissolved per litre of solution.

No. of equivalents per litre of solution =  = n-factor molarity

No. of equivalents = normality × volume (in L)

Equivalent mass =

No. of equivalent= =

'n' - factor

(i) For oxidizing/reducing agents : no. of e involved in oxidation/reduction half reaction per mole of oxidising agent /reducing agent.

e.g.  : 5e + 8H+ + MnO4 =Mn2+ + H2O         n- factor  = 5

(ii) For acid/ base reactions : no. of H+ ions displaced/ OH ions displaced per mole of acid/ base.

e.g.  : NaOH    n - factor = 1        H2SO4      n - factor = 2

(iii) For salt :   n = Total charge on cations.


total charge on anions              

 e.g.  : Al2(SO4)3                    n - factor = charge on the cation = 2 x 3 = 6

Mole-fraction (x) : It is the ratio of number of moles of a particular component to the total number of moles of all the components. e.g., mole-fraction of component A, xA = , where nA is the number of moles of component 'A' and nB is the number of moles of component 'B'.

For binary mixture.

Xsolute =  = ; XSolvent  =  =

Xsolute  + XSolvent = 1

 Parts per million (ppm) : The number of parts of solute present in 1 million parts of solution are called its ppm. When a solute is present in small quantities (very minute amounts), it is easier to express the concentration in parts per million.

(a) ppm (w/w) =  × 106

(b) ppm (w/v) =  × 106

(c) ppm (moles/moles) =  × 106

Table : 1

 Note : All volume related concentration terms are temperature dependent.

3. Colligative properties & constitutional properties

colligaive properties & constitutional properties

Constitutional Properties : Properties which are dependent on nature of particles are constitutional properties like electrical conductance.

Colligative properties  : The properties of the solution which are dependent only on the total no. of particles relative to solvent/solution or total concentration of particles in the solution and are not dependent on the nature of particle i.e. shape, size, neutral /charge etc. of the particles.

There are 4 colligative properties of solution

Osmotic pressure

Relative lowering in vapour pressure

Elevation in b.p. (Tb)

Depression in freezing pt. (Tf)

(i) Osmosis & Osmotic pressure :

Osmosis:  The spontaneous flow of solvent particles from solvent side to solution side or from solution of low concentration side to solution of high concentration side through a semipermeable membrane (SPM) is known as osmosis.



Conclusion : After some time in (A) grape or egg will shrink and in (B) grape or egg will swell.

e.g. (i) A raw mango placed in concentrated salt solution loses water & shrivel into pickle.

(ii) People taking lot of salt, experience water retention in tissue cells. This results in puffiness or swelling called edema.

Biological Importance of Osmosis

The cell walls of plants and animals are semipermeable in nature and thus are responsible for the osmosis. When a cell comes in contact with water a tendency of flow of water into the cell is developed. The pressure developed inside the cell due to the inflow of water is called turgor.

If the cell comes in contact with a concentrated solution, cell would shrink, which is called plasmolysis. Cell walls are able to permit the flow of selected ions and molecules also along with water.

Various processes taking place due to osmosis are :

(a) Absorption of water from soil through the cell walls of roots.

(b) Movement of water from roots to the upper parts of plants & trees.

(c) Various types of locomotion in plants like stretching of leaves, opening of flowers, etc., are also based on osmosis.

(d) Germination is also caused due to osmosis as water moves into the seeds through cell walls. 

The phenomenon of osmosis : A solution inside the bulb is separated from pure solvent in the beaker by a semipermeable membrane, Net passage of solvent from the beaker through the memberane occurs, and the liquid in the tube rises untill equilibrium is reached. At equilibrium, the osmotic pressure exerted by the column liquid in the tube is sufficient to prevent further net passage of solvent.

Although the passage of solvent through the membrane takes place in both direction, passage from the pure solvent side to the solution side is more favoured and occurs faster. As a result, the amount of liquid on the pure solvent side decreases, the amount of liquid on the solution side increases, and the concentration of the solution decreases. 

Osmotic Pressure : The equilibrium hydrostatic pressure developed by solution column when it is seperated from solvent by semipermeable membrane is called O.P. of the solution.

  = gh     ;   = density of soln.

g = acceleration due to gravity   ; h = eq. height

1 atm  = 1.013 x 105 N/m2




Definition  : The external pressure which must be applied on solution side to stop the process of osmosis is called osmotic pressure of the solution.

If two solutions of concentration C1 and C2 are kept separated by SPM, and C1 > C2 then particle movement take place from lower to higher concentration. So, extra pressure is applied on higher concentration side to stop osmosis. And Pext. = (1 – 2)

Reverse Osmosis : If the pressure applied on the solution side is more than osmotic pressure of the solution then the solvent particles will move from solution to solvent side. This process is known as reverse osmosis.

Berkely : Hartely device/method uses the above pressure to measure osmotic pressure.

e.g. used in desalination of sea-water.

Vant – Hoff Formula (For calculation of osmotic pressure)


     concentration (molarity)


             = CST

            S = ideal solution constant                    = atm. 

            = 8.314 J mol–1 K–1 (exp value)

            = R (ideal gas) constant

             = CRT =  RT (just like ideal gas equation)      

In ideal solution solute particles can be assumed to be moving randomly without any interactions.

 C = total concentration of all types of particles.

 = C1 + C2 + C3 + s.................


Type of solutions :

(a) Isotonic solution : Two solutions having same osmotic pressure are consider as isotonic solution.

                        1 = 2 (at same temperature)

(b) Hypotonic & Hypertonic solutions : If two solutions 1 and 2 are such that 2 > 1 , then 2 is called hypertonic solution and 1 is called hypotonic solution.


Fig ure 


Conclusion :Pressure is applied on the hypertonic solution to stop the flow of solvent partices, this pressure become equal to (2 – 1) and if hypotonic solution is replaced by pure solvent then pressure becomes equal to 2.

4. Solution containing volatile solute / solvents

Solution containing volatile solute / solvents

Mixture of 2 volatile liquids

Raoult's law ( for volatile Liq. Mixture )

Statement of Raoult's law ( for volatile liq. mixture ): In solution of volatile liquids, the partial vapour pressure of each component is directly proportional to its mole fraction.

pA µ xA   =>   pA = xAPAº

pA = Partial vapour pressure of component A

xA = Mole fraction of component ‘A’ in solution.

PAº = Vapour pressure of pure component ‘A’ at given temperature

Derivation of total pressure over solution using Raoult’s law and Dalton’s law:

Let A, B be to two volatite liquids in a closed container as shown.

  pA = xAPAº

Similarly, for liquid B we have,

  pB = xBPBº

Total pressure over the solution PT , according to Dalton's law is

PT = pA + pB = xAPA0 + xBPB0

Determining composition of vapour phase:       


yA = mole fraction of A in vapour phase above the solution and

yB = mole fraction of B in vapour phase above the solution

Now, we have, pA = yA PT     .....Dalton's law of partial pressure for a gaseous mixture     

 pA = xAPAº         ...........Raoult's law

  Thus,    pA =  yA PT  = xA PAº

  Also,    pB =  yBPT  =  xBPBº

xA + xB = 1 =  ; Thus

Graphical Representation of Raoult's Law:

pA= xAPAº   &   pB  = xB PBº

PT = xAPAº + xB PBº

PT =  ( PAº – PBº ) xA + PB0                                            

PT =  ( PBº – PAº ) xB + PA0         

This represents equation of straight line. PT v.s. x

Note:  If PAº > PBº , A is more volatile than B. B.P. of A < B.P. of B. 

Limitations of Raoult’s Law: Raoult's Law only works for ideal solutions. Very dilute solutions obey Raoult's Law to a reasonable approximation.

5. Ideal and non-ideal solutions

Ideal and Non-ideal Solution

Ideal Solutions : Those solutions which obey Raoult's law over the entire range of conc. are called ideal solutions. When the forces of attraction between A—A, B—B is similar to A—B, then A and B will form ideal solution.

  Properties of ideal solution :

(i) Raoult's law is obeyed         

(ii) DHmix = 0, i.e., there should not be enthalpy change when components of ideal solutions are mixed.

(iii) DVmix = 0, (1L + 1L = 2L) i.e., there should not be change in volume on mixing. e.g.; n-hexane and n-heptane; ethyl bromide and ethyl iodide; benzene and toluene; chlorobenzene and bromobenzene form ideal solutions.

(iii) DSmix = +ve  

(iv) DGmix = –ve

Non_Ideal Solutions :

Those solutions which do not obey Raoult's over the entire range of concentration are called non-ideal solutions.

When the forces of attraction between A—A, B—B is different from A—B then 'A' and 'B' form non-ideal solutions. For these solutions :

(i) Raoult's law is not obeyed. 

(ii) DHmix ¹ 0 ;  

(iii) DVmix ¹ 0.

Types of Non-Ideal Solutions : Non-ideal solution can be two types.

  •  Non ideal solutions showing positive deviation
  • Non ideal solutions showing negative deviation          

6. Azeotropic Mixtures

Azeotropic Mixtures

Very large deviations from ideality lead to a special class of mixtures known as azeotropes, azeotropic mixtures, or constant-boiling mixtures.

Azeotropes : Liquid mixtures which distill over without changes in composition are called constant boiling mixtures or Azeotropes or Azeotropic mixtures.

A boiling liquid mixture at the azeotropic composition produces a vapour of exactly the same composition, and the liquid does not change its composition as it evaporates. Two types of azeotropes are known.

Minimum Boiling Azeotropes : Non-ideal solutions showing large positive deviation from Raoult's law form minimum boiling azeotropes which boil at temperature lower than boiling point of its components 'A' and 'B', e.g., water and benzene, chloroform and methanol.

Maximum Boiling Azeotropes : Non-ideal solutions showing large negative deviation from Raoult's law form maximum boiling azeotropes which boil at temperature higher than the boiling point of its components A and B respectively, e.g., a mixture of HCl and H2O containing 20.2% HCl by weight boils at 108.5ºC higher than either pure HCI (– 85°C) or water (100°C).

7. Solubility of gases in liquids

Solubility of gases in liquids

Factors Affecting Solubility of Gas In Liquid :

(i) Nature of gas

(ii) Nature of liquid 

(iii) Temperature

(iv) Pressure

Henry's Law (effect of pressure on solubility of gases in liquids) :

Statement : The solubility of a gas in a liquid at a given temperature is directly proportional to its partial pressure at which it is dissolved.

 Let  x = Mole fraction of unreacted gas in solution at a given temperature as a measure of its solubility.

 p = Partial pressure of gas in equilibrium with the solution.

 By Henry's law:   x µ p     or   p µ x

That is;    p = KHx   or    x = ,    

where KH = Henry's law constant.

Characteristics of Henry's Law constant (KH).

(i) Unit same as those of pressure: torr or bar.         

(ii) Different gases have different value of KH  for the same solvent.

(iii) The KH value of a gas is different in different solvents and it increase with the increase in temperature.

(iv) Higher the value of KH of a gas, lower will be its solubility. Since, x = .

Plot of p Vs x is a straight line passing through the origin with slope equal to KH .

Plot of p Vs x for solution of HCl in cyclohexane.

Note : If a mixture of gases is brought in contact with solvent each constituent gas dissolves in proportion to its partial pressure. It means Henry's law applies to each gas independent of the pressure of other gas.

Effect of temperature : Solubility of gases in liquids decreases with rise in temperature.

Explanation : When dissolved, the gas molecules are present in liquid phase and the process of dissolution can be considered similar to condensation and heat is evolved in this process. We have learnt that dissolution process involves dynamic equilibrium and thus must follow Le Chatelier's principle. As dissolution of gases in liquids is an exothermic process, the solubility should decrease with increase of temperature.

Note : KH values for both N2 and O2 increase with increase of temperature indicating that the solubility of gases increases with decrease of temperature. It is due to this reason that aquatic spcies are more comfortable in cold water rather than warm water.

Applications of Henry's law : It has several applications in biological and industrial phenomena.

(i) To increase the solubility of CO2 in soft drinks and soda water the bottle is sealed under high pressure.

(ii) Scuba divers must cope with high concentrations of dissolved gases while breathing air at high pressure underwater. Increased pressure increases the solubility of atmosphere gases in blood. When the divers come towards surface, the pressure is gradually decreased. This releases the dissolved gases and leads to the formation of bubbles of nitrogen in the blood. This blocks capillaries and creates a medical condition known as bends, which are painful and dangerous to life. To avoid bends, as well as, the toxic effects of high concentrations of nitrogen in the blood, the tanks used by scuba divers are filled with air diluted with helium (11.7% helium, 56.2% nitrogen and 32.1% oxygen).

(iii) At high altitudes the partial pressure of oxygen is less than that at the ground level. This leads to low concentrations of oxygen in the blood and tissues of people living at high altitudes or climbers. Low blood oxygen causes climbers to become weak and unable to think clearly, symptoms of a condition known as anoxia.


2. Nernst equation

Nernst Equation

Cell potentials depend on temperature and on the composition of the reaction mixtures.

It depends upon the concentration of the solute and the partial pressure of the gas, if any.

The dependence upon the concentration can be derived from thermodynamics.

From thermodynamics

 DG = DG° + RT ln Q

– nFE = – nFE° + 2.303 R T log Q

E = E° –   log Q


T = 298 K , 

R = 8.314 J/mol K , 

F = 96500 C

Now we get,        

E = E° –   log Q


n = number of transfered electron ,

Q = reaction quotient

Nernst equation can be used to calculate cell potentials for non standard conditions also.

Nernst equations can be applied to half cell reactions also.

 Applications of Nerst equation 

Nernst Equation for Electrode Potential 

Hydrogen Electrode

    H2(g)  2H+(aq) + 2e

    E = E0 – log

 Metal–metal soluble salt electrode.     

Zn2+ + 2e  Zn(s)

Gas – electrode Hydrogen electrode.

Redox electrode

Nernst Equation for cell Potential :

aA + bB   CC + dD

Ecell  =  lnQ

n – no. of electrons which gets cancelled out while making cell reaction.

Equilibrium in electrochemical cell

G0 = – nF Eºcell

G = – nF Ecell

From thermo dynamics

Concentration cells :

A concentration cell consists of two electrodes of the same material, each electrode dipping in a solution of its own ions and the solution being at different concentrations.

 The two solutions are separated by a salt bridge.

e.g.    Ag(s) | Ag+ (a1) || Ag+ (a2) | Ag(s)     (a1 < a2)  a1 , a2  are concentrations of each half cell

At LHS electrode   Anode :      Ag (s)   Ag+(a1) + e

At RHS electrode Cathode :     Ag+(a2) + e  Ag(s)

The net cell reaction is :     Ag+ (a2)  Ag+ (a1)

The nernst eq. is

 Ecell = –  log             (Here n = 1, Temp, 298 K)

Likewise, the e.m.f. of the cell consisting of two hydrogen electrodes operating at different pressure P1 and P2 (P1 > P2 ) and dipping into a solution HCl is :

Ecell log         (at 298 K)   

Solubility product and EMF (Metal Metal Insoluble Salt Electrode) :

A half cell containing metal M and its sparingly soluble salt MA in a saturated solution.

 i.e  M(s)  | MA (satd) or a metal, its sparingly soluble salt in contact with a solution of a soluble salt NaA of the same anion, i.e. M(s) | MA(s) | NaA is set up. 

The solubility product of a sparingly doubles salt is a kind of equilibrium constant.

Work done by a cell :

(i)     Let 'n' faraday charge be taken out of a cell of EMF 'E' ; then work done by the cell will be calculated as : work = Charge × Potential = nFE

(ii)    Work done by cell = Decrease in free energy

 so  –DG = nFE

or   Wmax = + nFEº where Eº is standard EMF of the cell

3. Conductance of electrolytic solutions

Conductance of electrolytic solutions

Electrolytic Conductance :

Factors Affecting Conductance & Resistance :

1.   Solute – Solute interactions (Inter – Ionic force of attraction) Greater the force of  attraction, greater will be the resistance.

 Force Charge

2.Solute – Solvent Interaction (Hydration/Solvation of Ions) Greater the solvation
Solvation Charge   greater will be resistance Li+ (Hydrated largest)        Cs+ (Hydrated smallest)

 resistance of LiCl > resistance of CsCl

3. Solvent solvent interaction (Viscosity) : greater the viscosity greater will be resistance

4.  Temperature

        T        R

5.  Nature of electrolyte

 Weak electrolyte – high resistance strong electrolyte – Low resistance

Resistance :

R =  (Ohm's law ( )

R =

 – resistivity/specific resistance

     – resistance of unit length wire of unit area of cross section = constant = ( m)

Resistivity of a solution is defined as the resistance of the solution between two electrodes of 1 cm2 area of cross section and 1 cm apart.


Resistance of 1 cm3 of solution will be it's resistivity.

Conductance :

        = S (Siemens)

Conductivity/specific conductance

unit –1 cm–1

= conductivity of 1 cm3 of solution

a  concentration of ions

K =       G =

K  ( no. of ions) no. of charge carries

Since conductivity or resistivity of the solution is dependent on it's concentration, so two more type of conductivities are defined for the solution. 

Molar conductivity/molar conductance ((lm) :

Conductance of a solution containing 1 mole of an electrolyte between 2 electrodes which are 1cm apart.

Let the molarity of the solution 'C'

 C moles of electrolyte are present in 1 Lt. of solution.

so molar conductance = K

Its units are Ohm–1 cm2 mol–1

Equivalent conductance : Conductivity of a solution containing 1 g equivalent of the electrolyte.

leq – equivalent conductivity/conduction.

leq = 

Its units are Ohm–1 cm2 eq–1

Variation of conductivity and molar conductivity with concentration

Conductivity always decreases with the decrease in concentration both for weak and strong electrolytes. 

The number of ions per unit volume that carry the current in a solution decreases on dilution.

Molar conductivity increases with decreases in concentration. This is because the total volume, V of solution containing one mole of electrolyte also increases.

Molar conductivity is the conductance of solution.

When concentration approaches zero, the molar conductivity is known as limiting molar conductivity and is represented by the symbol .

Strong Electrolytes :

For strong electrolytes. increses slowly with dilution and can be represented by the equation

The value of the constant 'A' for a given slovent and temperature depends on the type of electrolyte i.e. the charges on the cations and anion produced on the dissociation of the electrolyte in the solution.

Example : Thus NaCl, CaCl2, MgSO4 are known as 1-1 , 2-1 and 2-2 electrolyte respectively. 

All electrolytes of a particular type have the same value for 'A'.

Weak electrolytes

Weak electrolytes like acetic acid have lower degree of dissociation at higher concentration and hence for such electrolytes, the change in with dilution is due to increases in the number of ions in total volume of solution that contains 1 mol of electrolyte.

At infinite dilution (i.e. concentration c zero) electrolyte dissociates completely (a= 1),but at such low concentration the conductivity of the solution is so low that it connot be measured accurately.

Molar conductivity versus c1/2 for acetic acid  (weak electrolyte) and potassium chloride   

(strong electrolyte in aqueous solutions. 


Kohlarausch's Law : 

"At infinite dilution, when dissociation is complete, each ion makes a definite contribution towards equivalent conductance of the electrolyte irrespective of the nature of the ion with which it is associated and the value of equivalent conductance at infinite dilution for any electrolyte is the sum of contribution of its constituent ions."


i.e.,  l¥ = l+  + l 

At infinite dilution  or near zero concentration when dissociation is 100%, each ion makes a definite contribution towards molar conductivity of electrolyte irrespective of the nature of the other ion. (because interionic forces of attraction are zero)


 V+= no. of cation in one formula unit of electrolyte,  = no. of anions in one formula unit of electrolyte

For NaCl  = 1 v- = 1

For Al2(SO4)3  = 2 v- = 3

Applications of Kohlaraushch's law

Calculate  for any electrolyte from the  of individual ions.

etermine the value of its dissociation constant once we known the  and  at a given concentration c.

 Degree of dissociation : At greater dilution the ionization become 100%, therefore called infinite dilution.

At lower dilution the ionization (dissociation into ions) is less than 100% and equivalent conductance become lower,

 i.e.,   leq < l°eq 

 degree of dissociation

Dissociation constant of weak electrolyte :

KC =   

a = degree of dissociation

C = concentration 

The degree of dissociation then it can be approximated to the ratio of molar conductivity at the concentration c to limiting molar conductivity, , Thus we have :

But we known that for a weak electrolyte like acetic acid.

Solubility(s) and KSP of any sparingly soluble salt.

Sparingly soluble salt = Very small solubility

 Solubility = molarity = 0

so, solution can be considered to be of zero conc or infinite dilution.

Variation of K, lm & leq  of solutions with Dilution

  Kconc. of ions in the solution. In case of both strong and weak electrolytes on dilution the concentration of ions will decrease hence K will decrease.      

4. Electrolytic cells and electrolysis

Electrolytic cells and electrolysis

Electrolysis :

Electrolyte  is a combination of cations and anions which in fused state can conduct electricity.

This is possible due to the movement of ions from which it is made of and electrolyte.

The process of using an electric current to bring about chemical change is called electrolysis.

Electrolysis is a process of oxidation and readuction due to current in the electrolyte.

The product obtained during electrolysis depends on following factors.

The nature of the electrolyte

The concentration of electrolyte

The charge density flowing during electrolysis.

The nature of the electrode

 Active vs Inactive electrodes :

The electrodes in the cell that are active because the metals themselves are components of the half reactions.

As the cell operates, the mass of the zinc electrode gradually decreases, and the [Zn2+]  in the anode half – cell increases. At the same time, the mass of the copper electrode increases and the [Cu2+] in the cathode half – cell decreases; we say that the Cu2+ "plates out" on the electrode.

For many redox reactions, however, there are no reactants or products capable of serving as electrodes. Inactive electrodes are used, most commonly rods of graphite or platinum, materials that conduct electrons into or out of the cell but cannot take part in the half -reactions.

In a voltaic cell based on the following half reactions, for instance, the species cannot act as electrodes

2I(aq) I2(s) +2e [anode ; oxidation]

MnO4 (aq) + 8H+ (aq) + 5e Mn2+ (aq) + 4H2O(λ) [cathode ; reduction]

Therefore, each half – cell consists of inactive electrodes immersed in an electrolyte solution that contains all the species involved in that half -reaction. In the anode half-cell, I ions are oxidized to solid I2. The electrons released flow into the graphite anode, through the wire, and into the graphite cathode. From there, the electrons are consumed by MnO4 ions as they are reduced to Mn2+  ions.

Examples of Electrolysis      

Using inert (pt/graphite) electrodes.

Cathode (red) : Pb2+ + 2e  Pb(s)    E0 = 0.126V

Anode :     2Br- Br2 + 2e- E0 = – 1.08 V

Ecell = – 0.126 – (0.108) x 10 = – 1.206 V

Eext > 1.206 V

Electrolysis of CuSO4 molten

Cathode : Cu2+ + 2e Cu     [E0 = +0.34 V]

Anode :      [E0 = – 2.05 V]

H2S2O8 – marchall's acid peroxy disulphuric acid.

Ecell = 0.34 – (2.05) = – 1.71 V (negative  not feasible)


Electrolysis of aq CuSO4

Electrolysis of aq NaBr solution (initially PH = 7)

Electrolysis of aq NaCl

Rate of production of Cl2 is more than rate of production of O2 gas.

Note : According to thermodynamics, oxidation of H2O to produce O2 should take place on anode but experimentally (experiment from chemical kinetics) the rate of oxidation of water is found to be  very slow. To increase it's rate, the greater potential difference is applied called over voltage or over potential but because of this oxidation of Cl ions also become feasible and this takes place on anode.

Electrolysis using attackable (reactive) electrodes.

  • Electrolysis of aq. CuSO4 using Cu electrode.

electrolytic refining

  • AgNO3(aq) using Cu cathode & Ag anode.

Faraday's Law of Electrolysis : 

1st Law : The mass deposited/released/produced of any substance during electrolysis is proportional to the amount of charge passed into the electrolyte.


  W = ZQ

Z – electrochemical equivalent of the substance.

Unit of Z =  = Kg/C or g/C

Z = Mass deposited when 1 C of charge is passsed into the solution.

Equivalent mass (E) : mass of any substance produced when 1 mole of e are passed through the solution during electrolysis.

E =


2nd Law :  When equal charge is passed through 2 electrolytic cells and this cells are connected in series then mass deposited at electrode will be in the ratio of their electrochemical equivalents or in the ratio of their equivalent masses.      

Current Efficiency :

current efficiency  =  x 100

current efficiency =   x 100

5. Batteries


Battery :

A battery is a an electrochemical cell, a device for interconverting chemical and electrical energy. A battery takes the energy relased by a spontaneous chemical reaction and uses it to produce electricity.

Primary Batteries : In the primary batteries, the reaction occurs only once and after use over a period of time battery becomes dead and cannot be reused  again. The most familiar example of this type is the dry cell (known as Leclanche cell after its discoverer) which is used commonly in our transistors and clocks. All substances used are either pure solids or pure liquids.

Types of primary batteries :

(i) Dry cell %                            

   Anode  : Zn(s)

  Cathode : MnO2(s)

Electrolyte : Paste of NH4Cl + ZnCl2 in starch

  Cathode :

 MnO2 + NH4+ + e  MnO(OH) + NH3

(Oxidation state of Mn changes from +4 to +3)

 Anode :

  Zn  Zn2+ + 2e

(ii) Mercury cell :

Anode: HgO(s)

 Cathode : Zn(Hg)

 Electrolyte : Paste of KOH + ZnO 

Cathode :

Zn(Hg) + 2OH  ZnO(s) + H2O(l) + 2e 


Anode  :

HgO(s) + H2O(l) + 2e   Hg(l) + 2OH

Secondary Batteries : A secondary cell afer use can be recharged by passing current through  it in the opposite direction so that it can be used again. A good secondary cell can udnergo a large number of discharing and charging cycles. The most important secondary cell is the lead storage battery commonly used in automobiles and inverters.

  Anode          : Pb(s)

Cathode : PbO2(s)

Electrolyte : 38 % Conc. H2SO4 solution Ecell = 2.05 V. 


During the working of the cell discharge H2SO4 will be consumed so it's concentration in the solution hence density of the solution will decrease during charging of the cell PbSO4 will get converted into Pb(s) and, PbO2(s) and H2SO4 will be produced.

Nickel – cadmium battery.

Ecell = constant as cell reaction has pure solide/liquids only.

Anode : Cd(s)

Cathode : NiO2(s)

Electrolyte : KOH

Cd + 2OH Cd(OH)2 + 2e

2e + NiO2 + 2H2O Ni(OH)2(s) + 2OH

 Cd(s) + NiO2(s) + 2H2O(λ)Cd(OH)2(s) + Ni(OH)2(s)

6. Fuel cells

Fuel cell

Fuel cells (H2 – O2 cell) : Galvanic cells those are designed to convert the energy of combustion of fuels like hydrogen, methane, methanol etc. directly into electrical energy are called fuel cells.


7. Corrosion


It is a process of deterioration of a metal as a result of its reaction with air or water (environment) surrounding it.

In case of iron, corrosion is called rusting. Chemically, rust is hydrated form of ferric oxide, Fe2O3 .xH2O  Rusting of iron is generally caused by moisture, carbon dioxide and oxygen present in air.

Mechanism of corrosion :

Oxidation :

Fe(s)  Fe2+ (aq) + 2e

Reduction :

2O2–(g) + 4H+ (aq)   2H2O(I)

Atomospheric  oxidation :

2Fe2+(aq) + 2H2O(l) + 1/2O2 Fe2O3(s) + 4H+(aq)

Factors which affect corrosion : The main factors which affect corrosion are

Rate of corrosion µ Rectivity of metal

                     µ Presence of impurities.

                     µ Presence of electrolytes.

                     µ temperature (with in a reason able limit)

Corrosion protection : Corrosion of metals can be prevented in many ways. Some commonly used methods are

(i) By surface coating

(a) By applying, oil, grease, paint or varnish on the surface.

(b) By sacrifical protection; coating/depositing a thin layer of any other metal which does not corrode. For example, iron surface can be protected from corrosion by depositing a thin layer of zinc, nickel or chromium on it.

(c) By Galvanization : Prevention of corrosion of iron by Zn coating.

(ii) cathodic protection : (By connecting metal to a more electropositive metal) In presence of the more electropositive metal, the given metal does not get corroded. For example, iron can be protected from corrosion by connecting it to a block/plate of zinc or magnesium.

(iii) By forming insoluble phosphate or chromate coating : Metal surfaces are treated with phosphoric acid to form an insoluble phosphate. Formation of a thin chromate layer also prevents the corrosion of metals.

(iv) Using anti – rust solutions : Solutions of alkaline phosphates and alkaline chromates are generally used as anti – rust solutions.

2. Factors influencing rate of a reaction

Factors affecting rate of chemical reaction :

1. Concentration

2. Temperature 

3. Nature of reactants & products

4.  Catalyst

5. pH of the solution

6. Dielectric constant of the medium.

7. Radiations/light

8. Pressure

9. Electrical & Magnetic field.

The first four factors generally affect rate of almost all reactions while other factors are specific to some reactions only. The common examples of these reactions are :

Concentration : We known from law of mass action that Rate is proportional to concentration of reactants. “ So, generally  rate of reaction decreases with passage of time, since concentration of reactants decreases.

Temperature :     

Nature of reactants & Products : 

(a) Physical state of reactants :

Gaseous state > Liquid state > Solid state

Decreasing order of rate of reaction.

(b) Physical size of reactants : As we decreases the particle size rate of reaction increases since surface area increases.

(c) Chemical nature of reactants :

If more bonds are to be broken, the rate of reaction will be slow.

Similarly bond strength is more, rate of reaction will be slow.

Catalyst :

Presence of positive catalyst lower down the activation energy hence increases the rate of reaction.

presence of negative catalyst increases activation energy hence decreases the rate of reaction.

Radiations/light : Radiation are useful for photochemical reaction.

Pressure :  Pressure is important factor for gaseous reaction.

Rate Law (Dependence of rate on concentration of reactants) : 

The representation of rate of reaction in terms of the concentration of the reactants is called the rate law.

It can only be established by experiments.

Generally rate law expressions are not simple and these may differ for the same reaction on conditions under which the reaction is being carried out.

But for large number of reactions starting with pure reactants we can obtain simple rate laws.

For these reactions :     

Rate µ (conc.)order 

Rate = K (conc.)order      – differential rate equation or rate expression

Where K = Rate constant = specific reaction rate = rate of reaction when concentration is unity

 unit of K = (conc)1– order time–1 

Note : Value of K is a constant for a given reaction, depends only on temperature

Order of reaction :

Let there be a reaction   m1A + m2¾® products.

Now, if on the basis of experiment, we find that

R µ [A]P [B]q    Where p may or may not be equal to m1 & similarly q may or may not be equal to m2.

p is order of reaction with respect to reactant A and q is order of reaction with respect to reactant B and (p + q) is overall order of the reaction.

Note : Order of a reaction can be ‘zero’ or any whole number, can be a fractional number and it can even be negative with respect to a particular reactant. But oveall order is not found to be negative for any reaction till observed.

   Examples showing different  values of order of reactions :  

  The reaction (2) does not take place in one single step. It is almost impossible for all the 12 molecules of the reactants to be in a state of encounter simultaneously. Such a reaction is called complex reaction and takes  places in a sequence of a number of elementary reactions. For an elementary reaction the sum of stoichiometric coefficients = order of the reactions. But for complex reactions order is to be experimentally calculated.

3. Integrated rate equations

Integrated rate laws

(a) Zero Order Reactions :

   For a zero order reaction

   General rate law is, Rate = k [conc.]º = constant

   If C0 is the initial concentration of a reactant and Ct is the

   concentration at time ‘t’ then

   Rate = k =    or   kt = C0 – Ct or  Ct = C0 – kt            

   Unit of K = same as that of Rate = mol lit–1 sec–1.

   Time for completion =

   t1/2 (half life period)   at t1/2 , Ct  = , so  kt1/2 = Þ t1/2 =

 t1/2  µ C0  

Examples of zero order reactions :

Generally decomposition of gases on metal surfaces at high concentrations follow zero order kinetics.


(b) First Order Reactions :


   If any substance is growing/increasing following first order kinetics then :


where a is initial concentration of the substance and x is the increment in its concentration after time t. 

Half life time (t1/2) 

Half life period for a 1st order reaction is a constant quantity.

Graphical Representation :


First order growth reaction :

For bacteria multiplication or virus growth use following concept Consider a growth reaction


Generation time :

At  ¾® t = generation time , x = a

  t =

Examples of 1st order reactions :

1. H2O2    ¾®    H2O + O2

2. NH4 NO2 ¾®   2H2O + N2

3. Radiactive decay       

All radioactive decays are always first order kinetics.


(c) Second order reaction :

2nd order Reactions

Two types

(d) Psuedo first order reaction :

A second order (or of higher order) reactions can be converted into a first order reaction if the other  reactant is taken in large excess. Such first order reactions are known as psuedo first order reactions.

 For A + B ¾® Products   [Rate = K [A]1 [B]1]


Now if ‘B’ is taken in large excess b > > a.


‘b’ is very large can be taken as constant

Þ  kb = log    Þ     k¢ =  log 

k¢ is psuedo first order rate constant

K’ will have units of first order.

K will have units of second order.

Examples of Pseudo 1st order reactions :

(a)    Hydrolysis of canesugar

C12H12O11   +   H2O  ¾¾®  C6H12O6 + C6H12O6

    sucrose            excess         

(b)    Hydrolysis of esters

CH3COOCH3  + H2O       CH3COOH + CH3OH


Table : Characterstics of First-and Second-Order Reactions of the Type A Products

Graphical comparison of different orders 

(A)     integrated rate law method :

It is method of hit and trial. By checking where the kinetic data (experimetal data) best fits into which integrated rate law ,  we determine the order. It can also be done graphically.

(B)  Method of half lives :

The half lives of each order is unique so by comparing half lives we can determine order

(C)  Ostwald’s isolation method : 

This method is useful for reaction which involve a large number of reactants. In this method, the concentration of all the reactants are taken in large excess exception that of one, so if

rate = k [A]a [B]b [C]c = k0 [A]a 

Then value of ‘a’ can be calculated by previous methods and similarly ‘b’ and ‘c’ can also be calculated

4. Methods to monitor the progress of the reaction

Methods to monitor the progress of the reaction :

(A)  Pressure measurement :

Progress of gaseous reaction can be monitored by measuring total pressure at a fixed volume & temperature.

This method can applied for those reaction also in which a gas is produced because of decomposition of a solid or liquid. We can get an idea about the concentration of reacting species at a particular time by measuring pressure.

 The pressure data can be given in terms of

 (i) Partial pressure  of the reactant

(ii) Total pressure of the reaction system

(iii)  Pressure at only some points of time  

(b)  Volume measurement :

(i)  By measuring the volume of product formed we can monitor the progress of reactions.   

(c) Optical rotation measurment :

It is used for optically  active sample. It is applicable if there is atleast one optically active species involved in chemical reaction.

The optically active species may be present in reactant or product.

It is found that    

(a = concentration , x = amount consumed)

where arer0, rt, r¥    are  angle of optical rotation at time    t = 0, t = t  and t = ¥

5. Effect of temperature on rate of reaction

Effect of temperature on rate of reaction 

In early days the effect of temperature on reaction rate was expressed in terms of temperature coefficient  which was defined as the ratio of rate of reaction at two different temperature differing by 100C(usually these temperatures were taken as 250C and 350 C) 

 T.C. = 2 to 3 ( for most of the reactions)

For some reactions temperature coefficient is also found to be less than unity. for example

2NO + O2 ® 2NO2   rate of reaction decreases on increasing temperature.

But the method of temperature coefficient was not exact and to explain the effect of temperature on reaction rate new theory was evolved

6. Arrhenius theory of reaction rate

Arrhenius theory of reaction rate

It was developed by max Trautz and William lewis.

It gives insight in to the energetics and mechanistic aspects of reactions.

It is based upon kinetic theory of gases.   

Arrhenius proposed a theory of reaction rate which states as follows :

A chemical reaction takes palce due to the collision among reactant molecules. The number of collisions taking place per second per unit volume of the reaction mixture is known as collision frequency (Z).

Every collision does not bring a chemical change. The collision that actually produce the products are effective collision. For a collision to be effective the following two barriers are to be effective the following two barriers are to be cleared.

Energy barrier :

The minimum amount of energy which the colliding molecules must posses as to make the chemical reaction to occur is known as threshold energy.

“The minimum amount of extra energy required by reactant molecules to pariticipate in a reaction is called activaiton energy (Ea)”

Orientation barrier :

Energy alone does not determine the effectiveness of the collision. The reacting molecules must collide in proper direction to make collision effective. Following diagrams can explain importance of suitable direction for collision.

Collision to be effective the colliding molecules must posses some certain minimum energy called threshold energy of the reaction.

Reactant molecules having energy equal or greater than the threshold are called active molecules and those having energy less than the threshold are called passive molecules.

Concept of energy of activation (Ea)

he extra amount of energy which the reactant molecules (having energy less than the threshold) must acquire so that their mutual collision may lead to the breaking of bond(s) and hence the energy is known as energy of activation of the reaction. It is denoted by the symbol Ea. Thus,

Ea = Threshold energy – Actual average energy,

Ea is expressed in kcals mole–1 or kJ mole–1.

The essence of Arrhenius Theory of reaction rate is that there exists an energy barrier in the reaction path between reactant(s) and product(s) and for reaction to occur the reactant molecules must climb over the top of the barrier which they do by collision. The existence of energy barrier and concept of Ea can be understood from the following diagram.

Collision frequency is the number of collisions per unit  

volume per unit time. It is denoted by the symbol Z. Z is directly proportional to . By 10ºC rise in temperature, so it is the fraction of the total number of effective collision that increases markedly resulting into marked increase in the reaction rate.

Arrhenius equation                        

Integrating equation 4 assuming Ea to be constant we get,

lnk = –         or       ln = –  or       k = 

This is integrated form of Arrhenius equation.

Where, Constant A = pre–exponential factor it is a constant for a given reaction.

From this equation it is evident that as T ® ¥, k ®  A. Thus, the constant A is the rate constant of reaction at infinity temperature. The rate constant goes on increasing with temperature.

So, when T approaches inifinty, k will be maximum. That is to say, A is the maximum rate constant of a reaction.

The expontential term i.e. e–Ea/RT measures the fraction of total number of molecules in the activated state or fraction of the total number of effective collisions.



nEa  =  no. of molecules of reactant in the activated state   

n = total no. of molecules of the reactant in the reaction

From Arrhenius Equation we have,     

log k = 

So from this it is evident that a plot of log k versus  will be a straight line of the slope equal to and intercept equal to log A as shown below :

Thus, from this plot Ea and A both can be determined accurately.

If k1 and k2 be the rate constant of a reaction at two different temperature T1 and T2 respectively, then we have

log k1 =    and

log k2 = 

Subtracting we get  

1. Adsorption

Chapter 5

surface chemistry

Introduction :

Surface chemistry is that branch of chemistry which deals with study of the phenomena occuring at the surface or interface, i.e. at the boundary separating two bulk phases. In this chapter our main emphasis will be on three important topics related to surface chemistry, viz., adsorption, colloids and emulsions.


The phenomenon of attracting and retaining the molecules of a substance on the surface of a liquid or a solid resulting into a higher concentration of the molecules on the surface is called adsorption. As a result of adsorption, there is a decrease of surface energy. The process of removal of an adsorbed substance from the surface on which it is adsorbed is called desorption. It is the reverse of adsorption and can be brought about by heating or by reducing the pressure.

Adsorbent and adsorbate :The substance on the surface of which adsorption occurs is known as adsorbent. The substances that get adsorbed on the solid surface due to intermolecular attractions are called adsorbate.Charcoal, silica, gel, alumina gel are good adsorbents because they have highly porous structures and have large surface area. Colloids on account of their extremely small dimensions possess enoromous surface area per unit mass and are, therefore, also good adsorbents.

Examples of adsorption :

Adsorption of a gas by charcoal :  Finely divided activated charcoal has a tendency to adsorb a number of gases like ammonia, sulphur dioxide, chlorine, phosgene, etc. In this case, charcoal acts as an adsorbent while gas molecules act as adsorbate.

Adsorption of a dye by charcoal :  Animal charcoal is used for decolourising a number of organic substances in the form of their solutions. The discharge of the colour is due to the fact that the coloured component (generally an organic dye) gets adsorbed on the surface of the adsorbent (animal charcoal).

Sorption :  When both adsorption and absorption take place simultaneously.

Eg :  Dyes get adsorbed as well as absorbed in the cotton fibre i.e. sorption takes place.

Difference between adsorption and absorption :

The terms adsorption and absorption are different. Adsorption is a phenomenon in which there is higher concentration of another substance on the surface than in the bulk. On the other hand, absorption is a phenomenon in which the molecules of a substance are uniformly distributed throughout the body of other substance. For example, when silica gel is placed in the environment of water, it adsorbs the water vapour. The water vapour are present in high concentration at the surface of silica gel. On the other hand, when calcium chloride is placed in the environment of water, it absorbs water. The water vapour uniformly get distributed throughout the body of calcium chloride. Thus, silica gel adsorbs water vapour while anhydrous calcium chloride absorbs water.

Thermodynamics of adsorption : Adsorption is an exothermic process. Therefore DH of adsorption is always negative. When a gas is adsorbed the entropy of the gas decreases i.e. DS is negative. Adsorption is thus accompanied by decrease in enthalpy as well as entropy of the system, for a process to be spontaneous requirement is that DG must be negative. On the basis of equation, DG = DH - TDS, DG can be negative if DH has sufficiently high negative value as - TDS is positive. Thus, in an adsorption process, which is spontaneous, DS is negative, and DH is also sufficiently negative and as a combination of these two factors, DG is negative.

H becomes less and less negative as adsorption proceeds further and further. Ultimately DH becomes equal to TDS and DG becomes zero. This is the state at which equilibrium is attained.

Enthalpy of adsorption DHadsorption : It is the amount of the heat released when 1 mole of an adsorbate gets adsorbed on a particular adsorbent at adsorption equilibrium. It depends upon the nature of both the adsorbate as well as adsorbent.

Types of adsorption : The adsorption is classified into two types :

(i) Physical adsorption (i.e. physisorption) : When the particles of the adsorbate are held to the surface of the adsorbent by the physical forces such as van der Waal’s forces, the adsorption is called physical adsorption or vanderwaals adsorption.

(ii) Chemical adsorption (i.e. chemisorption) :

When the molecules of the adsorbate are held to the surface of the adsorbent by the chemical forces, the adsorption is called chemical adsorption.

Difference between physical adsorption and chemical adsorption

Competitive adsorption : When an adsorbent is in contact with more than one species (adsorbate). There will be competition among them to get adsorbed on to the surface of the adsorbent. The one that is more strongly adsorbed gets deposited first in preference to the others. Further a strongly adsorbed substance may displace a weakly adsorbed substance.

Ex. NH3 can displace O2 or N2 from the surface of charcoal.

Adsorption of gases on solids :

The extent of adsorption of a gas on a solid surface is affected by the following factors:

The nature of the gas (i.e. nature of the adsorbate). The easily liquefiable gases such as HCl, NH3, Cl2 etc. are adsorbed more than the permanent gases such as H2, N2 and O2. The ease with which a gas can be liquefied is primarily determined by its critical temperature. Higher the critical temperature (Tc) of a gas, the more easily it will be liquefied and, therefore, more readily it will be adsorbed on the solid.

Gas    SO2      CH4     H2  

TC     330K   190 K   33 K

Nature of adsorbent. The extent of adsorption of a gas depends upon the nature of adsorbent. Activated charcoal (i.e. activated carbon), metal oxides (silica gel and aluminium oxide) and clay can adsorb gases which are easily liquified. Gases such as H2, N2 and O2 are generally adsorbed on finely divided transition metals Ni and Co.

Activation of adsorbent :

(a) Metallic adsorbents are activated by mechanical rubbing or by subjecting it to some chemical reactions.

(b) To increase the adsorbing power of adsorbents, they are sub-divided into smaller pieces. As a results, the surface area is increased and therefore, the adsorbing power increases.

Effect of temperature :Mostly the process of adsorption is exothermic and the reverse process or desorption is endothermic. If the above equilibrium is subjected to increase in temperature, then according to Le-Chaterlier’s principle, with increase in temperature, the desorption will be favoured. Physical adsorption decreases continuously with increase in temperature whereas chemisorption increases initially, shows a maximum in the curve and then it decreases continuously.

The initial increase in chemisorption with increase in temperature is because of activation energy required.

This is why the chemical adsorption is also known as “Activated adsorption”.

A graph between degree of adsorption (x/m) and temperature ‘t’ at a constant pressure of adsorbate gas is known as adsorption isobar.


Effect of pressure. The extent of adsorption of a gas per unit mass of adsorbent depends upon the pressure of the gas. The variation of extent of adsorption expressed as x/m (where x is the mass of adsorbate and m is the mass of the adsorbent) and the pressure is given as below. A graph between the amount of adsorption and gas pressure keeping the temperature constant is called an adsorption isotherm.  

It is clear from the figure-1 that extent of adsorption (x/m) increases with pressure and becomes maximum corresponding to pressure Ps called equilibrium pressure. Since adsorption is a reversible process, the desorption also takes place simultaneously. At this pressure (Ps) the amount of gas adsorbed becomes equal to the amount of gas desorbed.

Freundlich Adsorption isotherm :

The variation of extent of adsorption (x/m) with pressure (P) was given mathematically by Freundlich.

At low pressure the graph is almost straight line which indicates that x/m is directly proportional to the pressure. This may be expressed as :

(x/m) a p     or       (x/m) = kp   where k is constant.

At high pressure the graph becomes almost constant which means that x/m becomes independent of pressure. This may be expressed as :

(x/m) = constant    or     (x/m) a p0   (since p0 = 1)     or    (x/m) = kp0.

hus, in the intermediate range of pressure, x/m will depend upon the power of pressure which lies between 0 to 1, fractional power of pressure. This may be expressed as

 (x/m) a p1/n    or     (x/m) = kp1/n  

Where n can take any whole number value which depends upon the nature of adsorbate and adsorbent. The above relationship is also called Freundlich’s adsorption isotherm.

The constant k and n can be determined as explained below : Taking logarithms on both sides of

Eq. (x/m) = kp1/n            we get                                                                      

 log (x/m) = logk + (1/n) log p.

One of the drawbacks of Freundlich isotherm is that it fails at high pressure of the gas. 

This equation applicable only when adsorbate substance form unimolecular layer on adsorbent surface. i.e. chemical adsorption.

Adsorption from solutions : The process of adsorption can take place from solutions also. It is observed that solid adsorbents adsorb certain solutes from solution in preference to other solutes and solvents. For example, animal charcoal decolouries impure sugar solution by adsorbing colouring dye in preference to sugar molecules.

The extent of adsorption from solution depends upon the concentration of solute in the solution as given by Freundlich isotherm :

(x/m) = k(c)1/n     (n 1)

where c is the equilibrium concentration of the solute in solution.

Temperature dependence here also is similar to that for adsorption of gases and in place of equilibrium pressure, we use equilibrium concentrations of the adsorbates in the solution.

Applications of adsorption :

In gas masks :  Activated charcoal is generally used in gas masks to adsorb poisonous and toxic gases from air. These masks are commonly used by the miners because there are poisonous gases like CO, CH4 etc. in the atmosphere in coal mines.

In dyeing of cloths : Mordants such as alums are used in dyeing of cloths. They adsorb the dye particles which, otherwise, do not stick to the cloths.

In dehumidizers : Silica gel is commonly used to adsorb humidity or moisture from air.

Removal of colouring matter : Many substances such as sugar, juice and vegetable oils are coloured due to the presence of impurities. They can be decolourised by placing them in contact with adsorbents like activated charcoal or fuller’s earth.

Heterogeneous catalysis : The phenomenon of adsorption is useful in the heterogeneous catalysis. The metals such as Fe, Ni, Pt, Pd, etc, are used in the manufacturing processes such as Contact process, Haber process and the hydrogenation of oils. Their use is based upon the phenomenon of adsorption.

Refining Petroleum : Silica gel is used as adsorbent in petroleum refining.

Chromatography : It is a method for separation of component and is based on preferential adsorption column is very common device used.

Creating vacuum : High vacuum can be created by removing gas by adsorption.

Adsorption Indicators : In volumetric analysis, adsorption indicator is used Surface of certain precipitates such as silver halide have the property of adsorbing some dye like eosin, fluorescein, etc In the case of precipitation titration (AgNO3 vs NaCI) of the indicator is adsorbed at the end point producing a characteristic colour on the precipitate.

In froth floatation process : (in metallurgy).

Softening of hard water : Ion exchange resins used for softening of hard water is based upon selective and competive adsorption of ions on resins.

Na2Z + Ca+2  CaZ + 2Na+

The organic polymers containing groups like –COOH, –SO3H and –NH2 etc. possess the property of selective adsorption of ions from solution.  These are quite useful in the softening of water.

1. Occurrence of metals old

Chapter 6

General principles and processes of isolation of elements

Introduction :

The compound of a metal found in nature is called  a mineral. The minerals from which metal can be economically and conveniently extracted are called ores. An ore is usually contaminated with earthy or undesired materials known as gangue. So all minerals are not ores but all ores are minerals. Ores may be classified mainly into following four classes.

(a) Native ores : They contain the metal in free state. Silver, gold, platinum etc, occur as native ores.

 (b) Oxidised ores : These ores consist of oxides or oxysalts (e.g. carbonates, phosphates, sulphates and silicates ) of   metals.

 (c) Sulphurised ores : These ores consist of sulphides of metals like iron, lead, zinc, mercury etc.

 (d) Halide ores : These ores consist of halides of metals.

Important ore :

Note : Mg obtained from both sea water & earth crust.

Metallurgy :

 The scientific and technological process used for the extraction/isolation of the metal from its ore is called as metallurgy.

The isolation and extraction of metals from their ores involve the following major steps:

(A) Crushing of the ore.

(B) Dressing or concentration of the ore.

(C) Isolation of the crude metal from its ore

(D) Purification or refining of the metal.


Chart2: Steps involved in metallurgy.


1.  Physical Method :

(A) Crushing and Grinding  :  The ore is first crushed by jaw crushers and ground to a powder (pulverisation of the ore) in equipments like ball mills and stamp mills.

(B)    Concentration : The removal of  unwanted useless impurities from the ore is called dressing, concentration or benefaction of ore.

 It involves several steps and selection of these steps depends upon the difference in physical properties of the compound of metal and that of gangue. Some of the important procedures are described below.

(i) Hydrolytic washing :

Gravity separation or "Levigation". Based on the difference in the densities of the gangue and ore particle.

Generally used for the concentration of oxide & native ore.

(ii) Electromagnetic sepration :

Based on difference in magnetic properties of mineral and gangue particle.

(a) Chromite ore [FeO.Cr2O3] is seprated from non magnetic silicious impurities.

(b) Cassiterite ore [SnO2] is seprated from magnetic wolframite [FeWO4 + MnWO4]

(iii) Froth floatation process :         

Generally used for concentration of low grade sulphide ore PbS, ZnS, Cu2S, CuFeS2

Principle :

Based on fact that mineral & gangue particles have different wettability in water and oil (pine oil used)

Mineral particle ® are wetted by oil.

Gangue particle ® Wetted by water.

Reagents Used :

(i)     Frothers :

These form stable froth which rises to the top of the flotation cell.

Oil like pine oil, comphor oil are used in small quantities.

Main Function of :

Frother ® Stick to ore & then take it to rise upto the top.

Stabilizer ® To stabilize the froth, froth stabilizer like [cresol & aniline] are added.

(ii) Collector :

 K+ or Na+ ethyl xanthates (R = alkyl,M+ = Na+ , K+) are used as collectors. Which collect or attract mineral partical and make them water repellant.

Main Function : Make the ore hydrophobic.

(iii) Activating & Depressing agents :

In PbS + ZnS + FeS2 mixture NaCN + Na2CO3 is used to depress the floation properties of ZnS & FeS2.

ZnS + CN ¾® [Zn(CN)4]2– 

FeS2 + CN ¾® [Fe(CN)6]4– 

CuSO4 is then added which is activating for ZnS as Cu forms more stable complexing with CN than Zn2+ 

Froth floatation process

2.  Chemical Method :

(4) Leaching :

Used when ore is soluble in some suitable solvent like ® acid, base & suitable chemical reagent.

Ex. (a) Leaching of alumina from bauxite.

(b) Extraction of Ag & Au from their ores in the complex form by treatment with NaCN & KCN.

(c) Treatment of low grade Cu ores with conc. H2SO4.

(C)  Extraction of crude metal from concentrated ore :

The concentrated ore must be converted into a form which is suitable for reduction. Usually the sulphide ore is converted to oxide before reduction. Oxides are easier to reduce. Thus isolation of metals from concentrated ore involves two major steps as given below.

(i) Conversion to oxide

(ii) Reduction of the oxide to metal.

(i) Conversion to oxide :

Conversion of ore into oxide is carried out in two ways depending upon the nature of ore.  

Calcination. It is a process of heating the con­centrated ore strongly in a limited supply of air or in the absence of air. The process of calcination brings about the following changes :

 (a) The carbonate ore gets decomposed to form the oxide of the metal, e.g.,

FeCO3 (siderite)  FeO + CO2 

PbCO3 (cerrussite)   PbO + CO2

 CaCO3 (calcite ore / lime stone)  CaO + CO2 

 ZnCO3 (calamine)  ZnO + CO2 

CuCO3.Cu(OH)2 (malachite)  2CuO + H2O + CO2

MgCO3.CaCO3 (dolomite)  MgO + CaO + 2CO2

(b) Water of crystallisation present in the hydrated oxide ore gets lost as moisture, e.g.,

2Fe2O3.3H2O (limonite)   2Fe2O3(s) + 3H2O(g)  

Al2O3. 2H2O (bauxite)  Al2O3 (s) + 2H2O(g)      

c) Organic matter, if present in the ore, gets expelled and the ore becomes porous. Volatile impurities are removed.

Roasting :

Generally used for sulphide ore.

Process : Concentrated ore is strongly heated in excess of air or O2 below its metling point.

(a) Roasting at moderate temperature :

2PbS + 3O2  2PbO + 2SO2

2ZnS + 2O2  2ZnO + 2SO2

If temperature is low (500°C) & concentration of SO2 is high sulphate are produced.

  PbS + 2O2  PbSO4

ZnS + 2O2  ZnSO4

(b) Roasting at High temperature :

Self reduction / auto reduction / air reduction :

Sulphide ore of Cu, Pb, Hg & Sb when strongly heated in free supply of air, directly reduced to the metal this known as self reduction.

Cu2S (Copper glance) + O2 ¾® 2Cu + SO2

PbS (Gelena) + O2 ¾® Pb + SO2

HgS (Cinabar) + O2 ¾® Hg + SO2

Important Points

1.It remove impurities of As as As2O3, sulphur as SO2, P as P4O10 & Sb as Sb2O3

4M (M = As, Sb) + 3O2 ¾® 2M2O3

S + O2 ¾® SO2

P4 + 4O2 ¾® P4O10

2. Impurities of CuS & FeS in SnO2 converted to CuSO4 & FeSO4

 CuS + 2O2  CuSO4

FeS + 2O2  FeSO4

Note : Calcination & Roasting carried out in a reverberatory furnace.

Smelting :

Slag formation : In many extraction processes, an oxide is added deliberately to combine with other impurities and form a stable molten phase immiscible with molten metal called a slag. The process is termed smelting.

The principle of slag formation is essentially the following :

Nonmetal oxide (acidic oxide) + Metal oxide (basic oxide) ¾® Fusible (easily melted) slag

Removal of unwanted basic and acidic oxides: For example, FeO is the impurity in extraction of Cu from copper pyrite.

2CuFeS2 + 4O ¾®   Cu2S + 2FeO   +  3SO2

Cu2S    +   FeO      +   SiO¾®  FeSiO3 (Fusible slag)    +   Cu2S (matte)

                             (upper layer)                   (lower layer)

Matte also contains a very small amount of iron(II) sulphide.

To remove unwanted acidic impurities like sand and P4O10, smelting is done in the presence of limestone.

CaCO3 ¾® CaO + CO2

CaO + SiO2 ¾® CaSiO3 (fusible slag)

6CaO + P4O10 ¾® 2Ca3(PO4)2 (fusible slag - Thomas slag)

Properties of a slag :

 (i) Slag is a fusible mass.

 (ii) It has low melting point.

(iii) It is lighter than and  immiscible with the molten metal. It is due to these impurities that the slag floats as a separate layer on the molten metal and can thus be easily separated from the metal. The layer of the slag on the molten metal prevents the metal from being oxidised.

Type of flux : Fluxes are of two types viz., acidic flux and basic flux.

(a) Acidic flux : It is an acidic oxide (oxide of a non-metal) like SiO2, P2O5, B2O3 (from borax). It is used to remove the basic impurity like CaO, FeO, MgO etc. The acidic flux combines with the basic impurity and forms a slag.

(b) Basic flux : It is a basic oxide (i.e., oxide of a metal) like CaO (obtained from lime stone, CaCO3), MgO (from magnesite, MgCO3), haematite (Fe2O3) etc. It is used to remove the acidic impurity like SiO2, P2O5 etc. The basic flux combines with the acidic impurity and forms a slag.

Thus, slag can be  defined as a fusible mass, which is obtained when a flux reacts with an infusible acidic or basic impurity present in the oxide ore.

Reduction of a Metal Oxide

(1)    Reduction with Carbon :

         PbO + C ¾® Pb + CO

         2Fe2O3 + 3C ¾® 4Fe + 3CO2

***   ZnO + C  Zn + CO (Extraction of Zn)

***   SnO2 + 2C  Sn + 2CO

(2)    Reduction with CO :

         Fe2O3 + 3CO ¾® 2Fe + 3CO2

         Fe3O4 + 4CO ¾® 3Fe + 4CO2

         Reduction with C & CO is carried out in blast furnace.

(3)    Redution with Al :

GoldSchmidt or Aluminothermic process :

Metallic oxide of Cr & Mn reduced by Al & this reaction is known as thermite reaction.

  Mg + BaO2 ¾® BaO + MgO + Heat

         (i)       Cr2O3 + Al ¾® 2Cr(l) + Al2O3

***   (ii)     3Mn3O4 + 8Al ¾® 4Al2O3 + 9Mn

         (iii)    2Al + Fe2O3 ¾®Al2O3 + 2Fe

         (iv)     B2O3 + 2Al ¾® 2B + Al2O3

(4)    Redution by Mg & Na :

 (i)       TiCl4 + 2Mg  Ti + 2MgCl2

(ii)     TiCl4 + 4Na  Ti + 4NaCl

(5)  Self reduction or auto reduction or air reduction :

Sulphide ore of some of the metal like Hg, Cu, Pb & Sb, when heated in air some part of these ore change into oxide or sulphate, thenthat part react with remaing part of sulphide ore to give its metal & sulphur dioxide.

This process is known as self reduction.

Ex.    (i)(a) 2PbS + 3O2 ¾®2PbO + 2SO2

                   2PbO + PbS ¾®3Pb + SO2

         (b)      PbS + 2O¾®PbSO4

                   PbSO4 + PbS ¾®2Pb + 2SO2

         (ii)     2HgS + 3O2 ¾®2HgO + 2SO2

                   2HgO + HgS ¾®3Hg + SO2

(6)    Electrolytic Reduction :

Electrolytic reduction is an expensive method than chemical method, that's why generally we do not use this method.

But when very high pure metal is required then we use this method.

 This method is also used for highly reactive metal.

(i)  Electrolyric reduction in aqueous solution :

This method is used when product does not react with water.

Electrolytic reduction of Cu & Zn from their sulphates.

(ii) In other solvents : Flourine react with water so it is produced by electrolysis of KHF2 dissolved in anhydrous HF.

(iii) In fused metal : When produced metal react with water, then metal is extracted from fused melt of their ionic salt.

Eg.  (i) Al is extracted from electrolysis of fused mixture of Al2O3 and cryolite (Na3AlF6).

(ii) Extraction of Na by electrolysis of fused NaCl.

Note : In this electrolysis CaCl2 is added as impurity to lower the melting point from 800°C to 500°C.

(i)   Hydro Metallurgy :

 When metal can be extracted using solution without any heating or without any electrolysis then operation is known as hydrometallurgy.

  Basic Step

(i) Dissolution of the valuable metal in aqueous solution.

(ii) Purification of leach solution.

 (iii) Recovery of metal from purified solution.

Ex.    Extraction of Ag & Au :

 Metallic Ag dissolved in NaCN from ore of Ag & then precipitated with the help of Zn.

 AgS(s) + 4CN¯ ¾®  + S2–

2[Ag(CN)2]¯(aq) + Zn(s) ¾® [Zn(CN)4]2–(aq) + 2Ag(s)

(ii)    Pyrometallurgy :

 If furnace are used and ore are heated to extract metal then it is called pyrometallurgy.

Electrochemical principles of metallurgy :

Electrolytic reduction can be regarded as a technique for driving a reduction by coupling it through electrodes and external circuit to a reactive or a physical process with a more negative DG. The free energy available from the external source can be assessed from the potential it produces across the electrodes using the thermodynamic relation :

 DG = –nFE            ..........(i)

where n is the number of electrons transferred, F is Faraday’s constant (F = 96.5 kJ/mol) and Eº is electrode potential of the redox coupled formed in the system.

Hence, the total Gibb’s energy of the coupled internal and external process is

DG + DG (external) = DG – nFEext 

If the potential difference of the external source exceeds

Eext = – 

the reduction is thermodynamically feasible; thus, the overall process occurs with a  decrease in free energy.

More reactive metals have large negative values of the electrode potential. So their reduction is difficult. If the difference of two E0 values corresponds to a positive E0  and consequently negative G0  in equation (i), then the less reactive metal will come out of the solution and the more reactive metal will go to the solution, e.g.,

        Cu2+ (aq) + Fe(s) ® Cu(s) + Fe2+(aq)

In simple electrolysis, the Mn+  ions are discharged at negative electrodes (cathodes )and deposited there. Precautions are taken considering the reactivity of the metal produced and suitable materials are used as electrodes. Sometimes a flux is added for making the molten mass more conducting.

Hydrometallurgy : The processing of ores and minerals as well as metals and their compounds at relatively low, often ambient temperatures employing aqueous solution is known as hydrometallurgy. Occasionally, organic reagents are also used. This method of extraction is generally used for low grade ores. Copper is extracted by hydrometallurgy from low grade ore it is leached out using acid and bacteria. The solution containing Cu2+ is treated with scrap iron or H2.

  CuSO4 + Fe ® Cu(s) + FeSO4 

A hydrometallurgical process for the extraction of metals from ores, concentrates, or secondary materials essentially contains three basic steps—dissolution of the valuable metal in the aqueous solution (leaching) purification of leach solution and subsequent recovery of metal from the purified solutions either by electrolysis or by adding some electropositive metal to it.

Some of the metals obtained by hydrometallurgy are as follows :

(A) Extraction of Ag and Au : Metals like Au and Ag can be precipitated for their salt solution by electropositive metals for example, Zn.

Metallic Ag is dissolved from its ore in dilute NaCN solution, and the solute so obtained is treated with scrap Zn when Ag is precipitated. Air is blown into the solution oxidize Na2S. Leaching the metals like silver, gold with CN is an oxidation reaction (Ag ®  Ag+ or Au ® Au+)

Ag2S (s) +  4CN (aq) ® 2 [Ag(CN)2] (aq) + S2– (aq)

2[Ag(CN)2] (aq) + Zn (s) ® [Zn (CN)4]2– (aq) + 2Ag (s)

4Au (s) + 8 CN (aq) + O2 (g) + 2H2O (l)® 4 [Au(CN)2] (aq) + 4OH