CBSE NOTES CLASS 12 CHEMISTRY CHAPTER 1

THE SOLID STATE

Solids

Solids are the chemical substances which are characterised by definite shape and volume, rigidity, high density, low compressibility. The constituent particles (atoms, molecules or ions) are closely packed and held together by strong inter particle forces.

1. They have definite mass, volume and shape.

2. Inter molecular distances are short.

3. Inter molecular forces are strong.

4. Their constituent particles (atoms, molecules or ions) have fixed positions and can only oscillate about their mean positions.

5. They are incompressible and rigid.

Types of solids

The solids are of two types: Crystalline solids and amorphous solids.

Crystalline solids are anisotropic in nature.

Anisotropic solids are those in which some of the physical properties like electrical resistance or refractive index show different values when measured along different directions in the same crystals. This arises from different arrangement of particles in different directions. They have long order arrangement of particles.

Amorphous solids are isotropic in nature.

Isotropic solids are those, in which there is no long range order in arrangement of particles and arrangement is irregular along all the directions. Therefore, value of any physical property would be same along any direction.

DISTINCTION BETWEEN CRYSTALLINE AND AMORPHOUS SOLIDS

 S. No. Property Crystalline Amorphous 1. Shape Definite characteristic geometrical shape Irregular shape 2. Melting point Melt at a sharp and characteristic temperature Gradually soften over a range of temperature 3. Cleavage property When cut with a sharp edged tool, they split into two pieces and the newly generated surfaces are plain and smooth When cut with a sharp edged tool, they cut into two pieces with irregular surfaces 4. Heat of fusion They have a definite and characteristic heat of fusion They do not have definite heat of fusion. 5. Anisotropy Anisotropic in nature Isotropic in nature 6. Nature True solids Pseudo solids or super cooled liquids 7. Order in arrangement of constituent Long range order Only short range order.

DIFFERENT TYPES OF CRYSTALLINE SOLIDS

 Type of Solid Constituent Particles Bonding/ Attractive Forces Examples Physical Nature Electrical Conductivity Melting Point (1) Molecular Molecules (i) Non-Polar Dispersion or London forces Ar, CCl4, H2, I2, CO2 Soft Insulator Very low (ii) Polar Dipole-dipole interactions HCl, SO2 Soft Insulator Low (iii) Hydrogen Bonded Hydrogen Bonding H2O (ice) Hard Insulator Low (2) Ionic solids Ions Coulombic or Electrostatic NaCl, MgO, ZnS, CaF2 Hard but brittle Insulators in solid state but conductors in molten state and in aqueous solutions High (3) Metallic solids Positive ions in a sea of delocalised electrons Metallic bonding Fe, Cu, Ag, Mg Hard but malleable and ductile Conductors in solid state as well as in molten state Fairly high (4) Covalent or network solids Atoms Covalent SiO2, SiC, C-diamond, AlN Hard Insulators Very High C(graphite) Soft Conductor (exception)

Crystal lattice

If the three dimensional arrangement of constituent particles in a crystal is represented diagrammatically, in which each particle is depicted as a point, the arrangement is called crystal lattice. A regular three dimensional arrangement of points in space is called a crystal lattice.

Unit cell

The smallest geometrical portion of the crystal lattice which can be used as repetitive unit to build up the whole crystal is called unit cell.

1. Each point in a lattice is called lattice point or lattice site.

2. Each point in a crystal lattice represents one constituent particle which may be an atom, a molecule (group of atoms) or an ion.

3. Lattice points are joined by straight lines to bring out the geometry of the lattice

Parameters of a unit cell

A unit cell is characterised by six parameters, a, b, c, α, β and γ.

1. its dimensions along the three edges, a, b and c. These edges may or may not be mutually perpendicular.

2. angles between the edges, α (between b and c) β (between a and c) and γ (between a and b).

Types of unit cells

(i) Simple or primitive unit cell - In which the particles are present at the corners only.

(ii) Face centred unit cell - In which the particles are present at the corners as well as at the centre of each of six faces

(iii) Body centred unit cell - In which the particles are present at the corners as well as at the centre of the unit cell.

(iv) End centred unit cell - In which the particles are present at the corners and at the centre of two opposite faces.

Number of particles per unit cell

 Unit cell type No of particles and their contribution Total Corner Face Centre Simple cubic 8 × $\frac{1}{8}$ = 1 - - 1 Face centred 8 × $\frac{1}{8}$ = 1 6 × $\frac{1}{2}$ = 3 - 4 Body centred 8 × $\frac{1}{8}$ = 1 - 1 2 End centred 8 × $\frac{1}{8}$ = 1 2 × $\frac{1}{2}$= 1 - 2

Coordination number

It is defined as the number of particles immediately adjacent to each particle in the crystal lattice.

• In simple cubic lattice, CN is 6,

• In body centred lattice, CN is 8

• In face centred cubic lattice CN is 12

• High pressure increases CN and high temperature decreases the CN

Seven crystal systems

There are about 230 crystal forms, which have been grouped into 14 types of space lattices, called Bravais lattices, on the basis of their symmetry.

These 14 latices have been grouped into seven different crystal systems on the basis of interfacial angles and axes.

SEVEN TYPES OF UNIT CELLS IN CRYSTALS

 Crystal System Possible Variations Axial distances Axial angles Examples Cubic Primitive, Face centred Body centred a = b = c α = β = γ = 90° NaCl, Zinc Blende, Cu Tetragonal Primitive, Body centred a = b ≠ c α = β = γ = 90° White tin, SnO2, TiO2, CaSO4 Orthorhombic Primitive Body centred Face centred End centred a ≠ b ≠ c α = β = γ = 90° Rhombic sulphur, KNO3, BaSO4 KNO3,BaSO4 Hexagonal Primitive a = b ≠ c α = β = 90°, γ = 120° Graphite, ZnO, CdS Rhombohedral or Trigonal Primitive a = b = c α = β = γ ≠ 90° Calcite (CaCO3), HgS (cinnabar) Monoclinic Primitive End centred a ≠ b ≠ c α = γ = 90°, β ≠ 90° Monoclinic sulphur, Na2SO4.10H2O Triclinic Primitive a ≠ b ≠ c α ≠ β ≠ γ ≠ 90° K2Cr2O7, CuSO4.5H2O, H3BO3

FOURTEEN BRAVISE LATTICES

Three cubic lattices, all sides are equal and all angles are 90o

Two types of tetragonal lattices, one side different, all angle are 90o

Four types of orthorhombic lattices, all sides unequal,all angles are 90o

Two types of monoclinic lattices, all sides unequal, one of the angles is not 90°

Close packing in crystals

Two dimensional packing of constituent particles

(i) Square close packing

The spheres of the two rows are aligned horizontally as well as vertically. If we call the first row as ‘A’ type row, the second row being exactly the same as the first one, is also of ‘A’ type. Similarly, we may place more rows to obtain AAA type of arrangement.

(ii) Hexagonal close packing

The second row is placed above the first one in a staggered manner such that its spheres fit in the depressions of the first row. If the arrangement of spheres in the first row is called ‘A’ type, the one in the second row is different and may be called ‘B’ type. When the third row is placed adjacent to the second in staggered manner, its spheres are aligned with those of the first layer. Hence this layer is also of ‘A’ type. The spheres of similarly placed fourth row will be aligned with those of the second row (‘B’ type). Hence this arrangement is of ABAB type.

Three dimensional packing of constituent particles

(i) Three dimensional close packing from two dimensional square close or AAA packing

The second layer is placed over the first layer such that the spheres of the upper layer are exactly above those of the first layer. This is called AAA structure. Simple cubic lattice, unit cell is primitive.

(ii) Three dimensional close packing from two dimensional hexagonal close packed layers

Placing the second layer

Let us take a two dimensional hexagonal close packed layer ‘A’ and place a similar layer above it such that the spheres of the second layer are placed in the depressions of the first layer. Since the spheres of the two layers are aligned differently, let us call the second layer as B.

Void or space or holes

Empty or vacant space present between spheres of a unit cell, is called void or space or hole or interstitial void. When particles are closed packed resulting in either cpp or hcp structure. Two types of voids are generated:

Tetrahedral voids are holes or voids surrounded by four spheres present at the corners of a tetrahedron.

Wherever a sphere of the second layer is above the void of the first layer (or vice versa) a tetrahedral void is formed. These voids are called tetrahedral voids because a tetrahedron is formed when the centres of these four spheres are joined.

• Coordination number of a tetrahedral void is 4.

Octahedral voids are holes surrounded by six spheres located on a regular tetrahedron.

At other places, the triangular voids in the second layer are above the triangular voids in the first layer, and the triangular shapes of these do not overlap. One of them has the apex of the triangle pointing upwards and the other downwards. Such voids are surrounded by six spheres and are called octahedral voids.

• Coordination number of octahedral void is 6.

Number of voids of different types

Let the number of close packed spheres be N, then,

The number of octahedral voids generated = N

The number of tetrahedral voids generated = 2N

Placing 3rd layer

(i) Covering Tetrahedral Voids ABAB arrangement gives hexagonal close packing (hcp).

(ii) Covering Octahedral Voids: ABCABC arrangement gives cubic close packing or face centred CUBIC packing (ccp or fcc).

• In both these arrangements 74% space is occupied

• Coordination number in hcp and ccp arrangement is 12 while in bcc arrangement, it is 8.

• Close packing of atoms in cubic structure is fcc > bcc > sc.

• Metals have hcp structures. All noble gases have ccp structure except He (hcp structure).

Locating tetrahedral voids

Let us consider a unit cell of ccp or fcc lattice. The unit cell is divided into eight small cubes. Each small cube has atoms at alternate corners. In all, each small cube has 4 atoms. When joined to each other, they make a regular tetrahedron. Thus, there is one tetrahedral void in each small cube and eight tetrahedral voids in total.

Each of the eight small cubes has one void in one unit cell of ccp structure. The ccp structure has 4 atoms per unit cell. Thus, the number of tetrahedral voids is twice the number of atoms.

Locating octahedral voids

The body centre of the cube, C is not occupied but it is surrounded by six atoms on face centres. If these face centres are joined, an octahedron is generated.

Thus, this unit cell has one octahedral void at the body centre of the cube.

Besides the body centre, there is one octahedral void at the centre of each of the 12 edges. It is surrounded by six atoms, four belonging to the same unit cell (2 on the corners and 2 on face centre) and two belonging to two adjacent unit cells. Since each edge of the cube is shared between four adjacent unit cells, so is the octahedral void located on it. Only $\frac{1}{4}$ th of each void belongs to a particular unit cell.

Thus in cubic close packed structure:

• Octahedral void at the body-centre of the cube = 1

• 12 octahedral voids located at each edge and shared between four unit cells = $\frac{12}{4}$ = 3

Total number of octahedral voids = 4

In ccp structure, each unit cell has 4 atoms. Thus, the number of octahedral voids is equal to this number.

Density of unit cell (d)

Volume of a unit cell = a3

Mass of the unit cell = number of atoms in unit cell × mass of each atom = Z × m

The density of the unit cell is same as the density of the substance. Here,

d = density of unit cell,

M = molecular weight,

Z = no. of atoms per unit cell,

a = edge length of unit cell.

Packing efficiency or packing fraction

It is defined as the ratio of the volume of the unit cell that is occupied by the spheres to the volume of the unit cell.

Packing efficiency of primitive cubic unit cell

Atoms touch each other along edges.

If r = radius of atom and a = edge length, then,

Therefore,

Packing efficiency of face centred cubic unit cell

Efficiency of FCC and HCP is same

Atoms touch each other along the face diagonal.

Hence, d = $\frac{\mathrm{a}}{\sqrt{2}}$, r = $\frac{\sqrt{2}\mathrm{a}}{4}$ ⇒ a = $2\sqrt{2}\mathrm{r}$

Therefore,

Packing efficiency of body centred cubic unit cell

Atoms touch each other along the body diagonal.

The length of the body diagonal

$\mathrm{c}=\sqrt{3}\mathrm{a}=4\mathrm{r}$

Therefore,

The structure of ionic crystals

The ionic radius ratios of cation and anion play a very important role in giving a clue to the nature of the crystal structure of ionic substances. Larger ions (anions) occupy positions or lattice point in the unit cell, whereas the cations occupy the tetrahedral or octahedral voids depending upon the radius ratio of cation/anion.

Radius ratio of cation/anion and crystal structure

 S. No. Radius Ratio Cation/Anion Coordination number Shape Crystal structure Examples 1 < 0.225 2 or 3 Linear or triangular Linear or triangular B2O3 2 0.225-0.414 4 Tetrahedral ZnS type CuCl, CuBr, HgS, BaS 3 0.414-0.732 6 Octahedral NaCl type MgO, NaBr, CaS, KBr, Cao 4 0.732 or more 8 Cube CsCl type CsI, CsBr, NH4Br

Structure of ionic crystals

 Ionic Crystal Type Cation Occupy Anion Form Cooridnation NaCl (Rock Salt) type All octahedral voids FCC 6:6 CsCl type Body Centre FCC 8:8 ZnS (Sphalerite) type Alternate tetrahedral voids FCC 4:4 CaF2 (Fluorite) type Alternate body centre FCC 4:8 Na2O type All tetrahedral voids FCC 4:8
• On applying pressure, NaCl structure (6:6-coordination) changes into CsCl structure (8:8-coordination) and reverse of this occur at high temperature (760 K).

Imperfections in solids

In a crystalline solid, the atoms, ions and molecules are arranged in a definite repeating pattern, but some defects may occur in the pattern. Deviations from perfect arrangement may occur due to rapid cooling or presence of additional particles.

The defects are of two types, namely point defects and line defects.

Point defects are the irregularities or deviations from ideal arrangement around a point or an atom in a crystalline substance.

Line defects or crystal defects are the irregularities or deviations from ideal arrangement in entire rows of lattice points.

Point defects are of three types:

(i) Stoichiometric defects

(ii) Impurity defects

(iii) Non–stoichiometric defects

(i) Stoichiometric defect

These are point defects that do not disturb the stoichiometry of the solid. They are also called intrinsic or thermodynamic defects.

When some of the lattice sites 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.

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.

Ionic solids, exhibit vacancy defect as Frankel defect and Schottky defect.

Frankel Defect

In Frankel defect the smaller ion (usually cation) is dislocated from its normal site to an interstitial site and creates a vacancy defect at its original site and an interstitial defect at its new location. Frenkel defect is also called dislocation defect.

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.

Frenkel defects are not found in pure alkali metal halides because cations are of large size.

Schottky defect

Schottky defect is a vacancy defect in ionic solids. The number of missing cations and anions are equal. Schottky defect also decreases the density of the substance.

Schottky defect is shown by ionic substances in which the cation and anion are of almost similar sizes.

For example, NaCl, KCl, CsCl and AgBr.

AgBr shows both Schottky and Frenkel defects.

Difference between Schottky and Frenkel defects

 SNo Schottky defect Frenkel defect 1 It is due to equal number of cations and anions missing from the lattice site It is due to the missing of ions(usually cations) from the lattice sites and they occupy the interstitial sites 2 This results in decrease in density of crystal No effect on density 3 Found in highly ionic compounds with high coordination no, eg NaCl, CsCl. Found in crystals where the difference in size of cation and anion is very large. Eg, AgCl, ZnS.

(ii) Impurity defect

It arises when foreign atoms or ions are present in the lattice. In case of ionic compounds, the impurity is also ionic in nature.

When the impurity has the same charge as the host ion, it just substitutes some of the host ions.

Impurity defects can also be introduced by adding impurity ions having different charge than host ions, e.g. molten NaCl containing a little amount of SrCl2. In such cases,

Cationic vacancies produced = [Number of cations of higher valence × Difference in valence of the host cation and cation of higher valence]

(iii) Non-stoichiometric defect

Non-stoichiometric crystals are those which do not obey the law of constant proportions. The numbers of positive and negative ions present in such compounds are different from those expected from their ideal chemical formulae. However, the crystal as a whole is neutral.

Types of non-stoichiometric defects

(a) Metal excess defect

Metal excess defect due to anionic vacancies

Alkyl halides like NaCl and KCl show this type of defect. Centres of the sites from where anions are missing are called F-centres, the vacant sites are occupied by electrons. F-centres contribute colour and paramagnetic nature of the crystal [F stands for German word Farbe meaning colour).

Metal excess defect due to presence of extra cations at interstitial sites, e.g., zinc oxide is white in colour at room temperature.

On beating, 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 neighbouring interstitial sites.

(b) Metal deficiency defect due to cation vacancy

It is due to the absence of a metal ion from its lattice site and charge is balanced by ion having higher positive charge. Transition metals exhibit this defect, e.g., FeO, which is found in the composition range from Fe0.93O to Fe0.96O. In crystal 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.

CLASSIFICATION OF SOLIDS ON THE BASIS OF ELECTRICAL CONDUCTIVITY

 Type of Solid Conductivity Reason for conductivity Example Conductors 104 to 107 (very high) Motion of electrons Metals Insulators 10-20 to 10-10 (very low) No conduction Wood, Rubber, Bakelite Semiconductors 10-6 to 104 (Moderate) Motion of interstitial electrons or holes or both Si, Ge etc

Band theory of conduction

Conduction band – The energy level; at which the electrons are free to conduct electricity,

Valence band – The energy level; at which the outermost cell electrons are found at normal temperature

Forbidden bone – The energy gap between the valence band and conduction band

Types of semiconductors

Electronic conductors having electrical conductivity in the range of 104 – 10-6 Ω-1 m-1 are known as semiconductors. Examples Si, GeSn (grey), Cu2O, SiC and GaAs

Intrinsic semiconductors

Pure substances that are semiconductors are known as Intrinsic Semiconductors e.g., Si, Ge

Extrinsic semiconductors

Their conductivity is due to the presence of impurities.

They are formed by doping. Doping can be defined as addition of impurities to a semiconductor to increase the conductivity. Doping of Si or Ge is carried out with P, As, Sb, B, Al or Ga.

(i) n·type semiconductors

Silicon doped with group 15 elements (electron rich impurities) like phosphorus is called n- type semiconductor.

Their conductivity is due to the presence of negative charge (electrons).

(ii) p·type semiconductors

Silicon doped with group 13 elements (electron deficient impurities) like gallium is called p-type semiconductor.

Their conductivity is due to the presence of positive holes.

Applications of n-type and p-type semiconductors

• Diode is a combination of n-type and p-type semiconductors and is used as a rectifier. Transistors are made by sandwiching a layer of one type of semiconductor between two layers of the other type of semiconductor. npn and pnp type of transistors are used to detect or amplify radio or audio signals.

• The solar cell is an efficient photo-diode used for conversion of light energy into electrical energy.

Magnetic Properties of Solids

Magnetic moment originates from two types of motions of electrons (i) its orbital motion around the nucleus and (ii) its spin around its own axis.

Each electron has a permanent spin and an orbital magnetic moment associated with it. Magnitude of this magnetic moment is very small and is measured in the unit called Bohr magneton, μB. It is equal to 9.27 × 10–24 A m2. Classfication on the basis of magnetic properties

Solids can be divided into different classes depending on their response to magnetic field.

1. Diamagnetic substances

These are weakly repelled by the magnetic field and do not have unpaired electrons, e.g., TiO2, V2O5, C6H6, NaCl etc.

2. Paramagnetic substances

These are attracted by the magnetic field and have unpaired electrons. They lose magnetism in the absence of magnetic field, e.g., O2, Cu2+, Fe3+, etc.

3. Ferromagnetic substances

These are attracted by the magnetic field and show permanent magnetism even in the absence of magnetic field e.g., Fe, Co and Ni.

1. Anti-ferromagnetic substances have net magnetic moment zero due to compensatory alignment of magnetic moments, e.g., MnO, MnO2, FeO, etc.

1. Ferrimagnetic substances

These substances have a net dipole moment due to unequal parallel and anti-parallel alignment of magnetic moments, e.g., Fe3O4, ferrites, etc.