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1 SOLIDE STATE Introduction : Five states of matter – solid, liquid, gas, plasma and BEC (Bose-Einstein condensate) Solid states chemistry – study of structure of solids and their properties Solid substance – Definite shape-mass-volume. If we study variation in properties of solids by carrying out changes in it, we can have many uses of solids. E.g. substance used in super conductors and plastics for packing can be prepared by this way. Solids differ from liquid and gas in one aspect that is fluidity. Hence liquid and gases are called fluids. But in solids, the ions, molecules are in some definite form and arranged in a systematic manner. Hence, they have definite shape and so it is not a fluid. Solids are of two types – Crystalline and Amorphous. In a crystalline solids, arrangement of atoms or ions is systematic or regular; while in amorphous solids arrangement of constituent particles is irregular. We will study in this unit, the arrangement of atoms or ions and their relationship with their properties and what changes we can make in these properties ( i.e. in arrangement ) so that innumerable solid substances with desired and useful properties can be obtained. Crystalline and Amorphous Solid Substances : 1 Solids can be classified as crystalline or amorphous on the basis of the nature of order of arrangement present in the arrangement of their constituent particles. Crystalline solid – Usually consist of large number of small crystals. Each small crystal units have a definite characteristic geometrical shape. In a crystal, arrangement of constituent particles (atoms, molecules, ions) is ordered. It has long range ordered structure i.e. regular pattern of arrangement of particles which repeats itself periodically over the entire crystal. E.g. NaCl, Quartz etc. Amorphous solid – Usually consists of particles of irregular shape. The arrangement of constituent particles (atoms, molecules or ions) in such a solid has only short range order. In such an arrangement, a regular and periodically repeating pattern is observed for short distance only. Such short range ordered arrangements are scattered and disordered. For example… Glass, rubber and plastic are typical examples of amorphous solids. Quartz and Quartz glass are the two structures of same substance where Quartz is crystalline (fig - a) and Quartz glass is amorphous (fig – b). Both have identical composition, yet in the case of quartz glass (b) there is no long range order (i.e. amorphous). Due to the difference in the arrangement of the constituent particles, the two types of (a) (b) solids differ in their properties. e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 Differences between Crystalline and Amorphous Solids : 1. 2. 3. 4. 5. 6. 7. 8. Shape : Definite shape and possessing characteristics geometry Irregular shape Melting point : Definite and sharp melting point which is the characteristic of the crystal of the solid Becomes soft gradually during the small temperature range i.e. have no definite and sharp melting point Fusion enthalpy : Definite and characteristic fusion enthalpy No definite and characteristic fusion enthalpy Cleavage Property : Divided into two parts by cutting the crystal with sharp cutting tool like knife. The surface of the new part obtained is plain and soft i.e. it is an original one Divided into two parts by cutting the crystal with sharp cutting tool like knife; but the surface of new part obtained is not as the original one. i.e. it is irregular Nature : True solid Pseudo solid or super cooled liquids(Highly viscous liquid) Order of arrangement of constituent particles : The order is maintained till a long range The order is maintained in a short range Effect of Temperature The graph (temperature → time) obtained on cooling after heating is not a curvature. The temperature remains definite during crystallization The graph (temperature → time) obtained on cooling after heating is a curvature. Temperature range is obtained during crystallization. Properties: Their properties like electrical conductivity, thermal conductivity, mechanical strength and refractive index are different in different direction – Anisotropic in nature. Their properties like electrical conductivity, thermal conductivity, mechanical strength and refractive index are same in all direction – Isotropic in nature. Classification on the basis of Binding Forces : (1) 2 Most of the solid substances are crystalline viz. metals like copper, iron, silver, etc., non metals like phosphorus, sulphur, Ionic solids like sodium chloride, potassium chloride and molecular solids like naphthalene. The classification of crystalline solids on the basis of intermolecular attraction forces involved in them, can be made into following four types… Molecular solids : Non-polar molecular solids : Polar molecular solids : Molecular solids containing H-bond : e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 (2) (3) (4) Ionic Solids : Metallic Solids : Covalent Solids : (1) Molecular solids : In molecular solids the constituent particle present in them is molecule. Non-polar Molecular Solids : This type of solids includes elements like Ar, He or molecules formed by non-polar covalent bonds like dihydrogen, dichlorine, dibromine, diiodine etc. Possess weak Dispersion forces or London forces and hence low melting points Soft - non conductor of electricity They are in liquid or gaseous state at normal temperature and pressure. Polar Molecular Solids : These solids generally possess polar covalent bond. E.g. SO2, NH3, CS2 and CHCl3 etc. Molecules are bound by strong polar-polar interactions Soft and non conductor of electricity Melting points are higher than those of non-polar molecular solids Exist in liquid or gaseous state at normal temperature and pressure e.g. solid SO2 and solid NH3 Molecular Solids Containing Hydrogen Bond : Atoms like H form polar covalent bond by combining with electronegative atoms like F, O or N e.g. ice Non conductor of electricity Volatile liquids or soft solids at room temperature and pressure In molecule of ice, 4 molecules of water are attracted by H-bond It gets separated from the hydrides of other elements of the same group because of H bond (2) Ionic Solids : Constituent particles are ions. Such solids are formed by three dimensional arrangements of cations and anions bound by strong columbic (electrostatic) forces. Hard and brittle Melting points and boiling points are higher Since ions are not free to move in solid state, they are non conductor of heat and electricity in solid state. Their aqueous solution or molten state can conduct electricity. (3) Metallic Solids : Possess solid state and constituent atoms are arranged in systematic way. Metals are orderly collection of positive ions (positively charge kernels) surrounded by and held together by a sea of free electrons. Electron sea model of metal Hard and brittle Freely moving delocalized electrons are mobile and are evenly spread out throughout the crystal – hence metals are good conductors of heat and electricity Metals have luster and in some cases have colours Ductile and malleable 3 e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 (4) Covalent or Network Solids : Crystalline solids. Giant molecules – due to formation of covalent bonds between adjacent atoms throughout the crystal Covalent bonds are strong and directional in nature, therefore atoms are held very strongly at their position. Hard and brittle. Extremely high melting points – may decompose before melting. Non conductor of electricity (generally) For example… Diamond, graphite, silicon carbide etc. Graphite is soft & good conductor of electricity. Structure of graphite – sp2 hybridized carbon, free electron, layered structure and good solid lubricants Diamond is hard and non conductor of electricity. Structure of diamond – sp3 hybridized carbon, no free electron, tetrahedral structure and extremely hard. Thus, it can be concluded that in the two allotropes of the same element, if intermolecular forces and hybridization formed are different, there is a great change in their properties. Thus, as a summary… Different types and Properties of Crystalline solids Type of Solid Constituen Attraction Example Physical Meltin Electrical t Particles Forces Mature g Point Conductivity Molecular Solid Molecules Dispersion Ar,CCl4, Soft Very Non-conductor Non Polar or London H2,I2,CO2 low Polar forces Molecules DipoleHCl,SO2, Soft Low Non-conductor Hydrogen Dipole inter NH3 bondPossessing attraction Molecules Hydrogen H2O(ice) Hard Low Non-conductor bond Ionic Solid Ions Coulombic NaCl, Hard but High Solid state, nonor MgO, brittle conducting but molten or aqueous Electrostatic ZnS, solution conductor CaF2 Positive Compa Hard but ion in sea r-Metallic Fe, Ca, ductile Conductors in solid of atively Metallic Solid bond Mg, Ag and and molten states delocalized very malleable electrons high SiO2 Non Conductor (Quartz) Covalent or Covalent Very SiC(Carboru Atoms Hard Network Solid bond high -ndum) C(Diamond) Conductor C(Graphite) (Exception) 4 e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 Crystal Lattice : The smallest particle of a substance is known as atom or molecule. Similarly, the smallest portion which describe crystal of solid is called the unit cell. This smallest portion possessing the chief characteristics of a crystalline solid. Such unit cells when arranged with each other in three dimensional directions, the formation of crystal results. This type of arrangement is called crystal lattice. If constituent particles of solid crystal are assumed to be spherical then in crystal formation this particles are arranged as under. In crystalline solid, each type of crystal is described by crystal lattice OR space lattice. (network OR pattern) A crystal lattice is defined as a pattern of points which describe the arrangement of constituent particle (atoms, molecules, ions) in a crystal. Each point represents the position of centre of the constituent particle. What is unit cell ? A crystal is made up of many small repeat units, stacked together in three dimensions. These units are called unit cells. The unit cell shows all the characteristics as well as geometrical shape of crystal. There are 14 kinds of unit cell. Out of 14 types of unit cells, three unit cells have cubic symmetry. Thus, the systematic three dimensional arrangement of points in space is called crystal lattice or space lattice. There are seven different crystal systems and in which there are 14 different possibilities of such three dimensional lattices (arrangement); which are known as Bravais lattice. (i.e. 14 kinds of unit cell) 3. Some of the Characteristics of Crystal lattice are… Each point in a lattice is called lattice point or lattice site. Each point in a crystal lattice represents one constituent particle which may be an atom, a molecule (group of atoms) or an ion. Lattice points are joined by straight lines to bring out the geometry of the lattice. 5 e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 1. 2. (1) (2) The Characteristics of Unit cell are… Its dimensions along the three edges, a, b and c. These edges may or may not be mutually perpendicular. Angles between the edges, α (i.e. between edges a b and c), β (i.e. between edges a and c) and γ (i.e. between edges a and b). Thus, a unit cell is characterized by six b parameters… i.e. edges a, b and c; angles α, β and γ Types of Unit cell : Unit cells are broadly divided into two categories… Primitive Unit Cells Centered Unit Cells Body – Centered Unit Cells Face – Centered Unit Cells End – Centered Unit Cells Primitive Unit Cells : When constituent particles are present only on the corner positions of a unit cell, it is called as primitive unit cell. c (1) (2) (a) (b) (c) (1) (2) (a) (c) (a) (b) (c) 6 a Centred Unit Cells : When a unit cell contains one or more constituent particles present at positions other than corners in addition to those at corners, it is called a centred unit cell. Centered unit cells are of three types… Body – Centered Unit Cells (b) Face – Centered Unit Cells End – Centered Unit Cells Body-Centered Unit Cells : Such a unit cell contains one constituent particle (atom, molecule or ion) at its body-center besides the ones that are at its corners. Face-Centered Unit Cells : Such a unit cell contains one constituent particle present at the center of each face, besides the ones that are at its corners. End-Centered Unit Cells : In such a unit cell, one constituent particle is present at the center of any two opposite faces besides the ones present at its corners. End-centred e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 b g Seven Primitive Unit Cells and their Possible Variations as Centered Unit Cells : Crystal System Possible Variations Primitive Body centred Face centred Axial Distance or Distance of Edge Axial Angle Example a=b=c α = β = γ = 90° NaCl, ZnS (zinc blende), Cu Primitive a=b=c α = β = γ ≠ 90° Calcite (CaCO3), Cinnabar (HgS) Possible Variations Primitive Body centred Face centred End centred Primitive End centred Axial Distance or Distance of Edge Axial Angle Example a≠b≠c α = β = γ = 90° Rhombic sulphur, KNO3 BaSO4 a≠b≠c α = γ = 90° β ≠ 120° Triclinic Primitive a≠b≠c α ≠ β ≠ γ ≠ 90° Crystal System Possible Variations Axial Distance or Distance of Edge Axial Angle Tetragonal Primitive Body centred a=b≠c α = β = γ = 90° Hexagonal Primitive a=b≠c α = β = 90° γ = 120° Cubic Rhombohedral Or Trigonal Crystal System Orthorhombic Monoclinic Monoclinic sulphur, Na2SO4.10H2O K2Cr2O7, CuSO4.5H2O, H3BO3 Example White tin, SnO2, TiO2, CaSO4 Graphite, ZnO, CdS What is Close Packing ? If constituent particles of solid crystal are assumed to be spherical then in crystal formation this particles are closely packed together. This is known as closed packing structure. The empty spaces in this structure are known as voids OR holes. 7 e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 What is co-ordination number ? The co-ordination number of each sphere (atom, molecule, ion) is the number of nearest neighbours immediately surrounding each such sphere. “Co-ordination number of an atom is the number of other atoms or groups directly linked to that atom.” Different types of three dimensional closed packing of constituent particles in (metallic) crystal : In three dimensional closed packing, there are four possibilities of arrangement if particles are assumed to be uniformly sized spheres. 1) Simple cubic packing 2) Body centered cubic packing (BCC) 3) Hexagonal close packed arrangement (HCP) Cubic close packed arrangement (FCC) 4) (1) Simple Cubic Packing : In simple cubic packing each sphere is touched by six neighbours− four in its own layer, one above and one below. The stacking (packing) pattern is thus a−a−a−a. Each sphere has co-ordination number 6 − four neighbours in one plane, one above and one below. 52% of the available volume is occupied by the spheres in simple cubic packing. 8 In simple cubic unit cell 8 atoms are present at the 8 corners of the cubic unit cell. Each atom is shared by 8 cubes. So atom present at each corner contributes 1/8 to each cube. Now there are 8 corners or atoms. Therefore, Number of atoms present in each unit cell of Simple cube… = 8 corner atoms × (1/8) atom per unit cell = 1 atom Thus, Simple cubic unit cell has one atom per unit cell. 52% of the available volume is occupied by the spheres in simple cubic packing. e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 In simple cubic lattice, the atoms are only at the corners. The particles touch each other along the edges. (as shown in figure) ∴ Relation between edge length of a cube ‘a’ and radius of each particle ‘r’ will be … a=2r 3 ∴ Volume of unit cell (cube) a = (2 r)3 = 8 r3 Each unit cell possess only one atom. 4 ∴ Volume occupied by one atom = πr 3 3 Volume of one atom ∴ Packing efficiency = × 100 Volume of unit cell 4 3 πr 3 = × 100 8 r3 π = × 100 6 (2) 9 = 52.36 % Body Centered Cubic Packing : In body centered cubic packing the spheres in the first layer ‘a’ remains slightly away from one another. The spheres in ‘b’ layer fit into the depression between spheres in a−layer. The third layer is arranged on second layer ‘b’ exactly the same way as layer − a. The stacking (packing) pattern is thus a−b−a−b. Each sphere has co-ordination number 8 − four A A A A A neighbours above and four below. B B B B 68% of the available volume is occupied by the A A A A A B B B B spheres in body centered cubic packing. A A A A A Iron , Sodium and 14 other metals crystallize in this way. This structure is also known as Body centered cubic (BCC) packing. e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 In Body centered cubic unit cell 8 atoms are present at the 8 corners of the cubic unit cell. Each corner atom is shared by 8 cubes. So atom present at each corner contributes 1/8 to each cube. In addition, one atom is located at the center of the unit cell, which is not shared by any other cube. Therefore, Number of atoms present in each unit cell of Body centered cube = ( 8 corner atoms × (1/8) atom per unit cell ) + 1 center atom = 2 atom. Thus, Body centered cubic unit cell has two atom per unit cell. 68% of the available volume is occupied by the spheres in body centered cubic packing. As shown in figure, the atom in the centre of body touches two other atoms diagonally present at the corner of body diagonal. ∴ For, ∆ AFD, ∠ ADF is right angle… AF2 = AD2 + FD2 Where, AF = c = Body diagonal FD = b = Face diagonal AD = a = Edge length ∴ c2 = a2 + b2 But, as derived in FCC unit cell… b2 = 2a2 ∴ c2 = a2 + 2 a2 ∴ c2 = 3 a2 Now, as shown in figure…Body diagonal c = 4 r ∴ c= 3a=4r 4 r 3 4 ∴ Volume of unit cell (cube) a 3 = ( r)3 3 ∴ a= 10 e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 Each bcc unit cell possess only two atoms. 4 ∴ Volume occupied by two atoms = 2 × πr 3 3 Volume of two atoms ∴ Packing efficiency = × 100 Volume of unit cell 4 2 × πr 3 3 = × 100 4 3 ( r) 3 π 3 × 100 8 = 68 % Hexagonal Close Packed Arrangement : In Hexagonal close packed arrangement there are two alternating hexagonal layers a−b−a−b. The a−b layers offset from each other so that the spheres in one layer fit in the small triangular depression of neighbouring layer. The stacking pattern is thus a−b−a−b . Each sphere has co-ordination number 12 − six neighbours in the same plane, three above and three below . 74% of the available volume is occupied by the spheres in hexagonal close packed arrangement. Zinc, Magnesium and 19 other metals crystallize in this way. = (3) Unit cell of Hexagonal close pack structure is not in syllabus. Only cubic unit cells are in the syllabus. 11 e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 (4) Cubic Close Packed Arrangement : In Cubic close packed arrangement there are three alternating hexagonal layers a−b−c−a− b−c. The a−b layers offset from each other so that the spheres in one layer fit in the small triangular depression of neighbouring layer. The third layer is offset from both a & b layers. The stacking pattern is thus a−b−c−a−b−c. Each sphere has co-ordination number 12 − six neighbours in the same plane, three above and three below. 74% of the available volume is occupied by the spheres in cubic close packed arrangement. Silver, Copper and 16 other metals crystallize in this way. This structure is also known as Face centered cubic (FCC) packing. In Face centered cubic unit cell 8 atoms are present at the 8 corners of the cubic unit cell. Each atom is shared by 8 cubes. So atom present at each corner contributes 1/8 to each cube. In addition there are six atoms at the faces of the cube and each is shared by two unit cells. So atom present at each face contributes ½ to each unit cell. 12 e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 Therefore, Number of atoms present in each unit cell of Face centered cube… = ( 8 corner atoms × (1/8) atom per unit cell ) + ( 6 atoms at faces × ½ atom per unit cell) = 4 atom. Thus, Face centered cubic unit cell has four atom per unit cell. 74% of the available volume is occupied by the spheres in cubic close packed arrangement. As shown in figure, the atom in the centre of body touches two other atoms diagonally present at the corner of face diagonal. ∴ In ∆ ABC, ∠ ABC is right angle… AC2 = AB2 + BC2 Where, AC = b = Face diagonal AB = BC = a = Edge length 2 2 2 b =a +a ∴ ∴ b = 2a Now, as shown in figure…Face diagonal ‘b’ = 4 r ∴ b= 2a=4r ∴ a=2 2 r ∴ Volume of unit cell (cube) a 3 = (2 2r)3 Each FCC unit cell possess four atoms. 4 3 πr 3 Volume of four atoms ∴ Packing efficiency = × 100 Volume of unit cell 4 4 × πr 3 3 = × 100 4 3 ( r) 3 ∴ Volume occupied by four atoms = 4 × = π 2 × 100 6 = 74 % 13 e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 NOTE : In hcp & ccp both arrangements coordination number of sphere is 12. Hence close packing is equally efficient in both these types. Therefore, in hcp also… ∴ Packing efficiency = Volume of four atoms × 100 Volume of unit cell π 2 × 100 6 = 74 % = Density of Unit Cell : Suppose, edge length of a unit cell of a cubic crystal determined by X-ray diffraction is ‘a’; ‘d’ is the density of the solid substance and ‘M’ is the molar mass then… In case of cubic crystal… Volume of unit cell = a3 Mass of the unit cell = no. of atoms in the unit cell × mass of each atom =z×m (Here ‘z’ is the number of atoms present in one unit cell and ‘m’ is the mass of a single atom) Mass of an atom present in the unit cell (m) = M/NA Where, M is molar mass and NA is Avogadro constant. Therefore density of the unit cell is… Density of unit cell Mass of unit cell Volume of unit cell z×m a3 z×M a3 × NA = = ∴ d = Thus, as a summary… Structure Simple cubic Body centered cubic Hexagonal close packed Cubic close packed Stacking Co-ordination Space used % Unit cell pattern Number 6 52 Primitive cubic a− a− a− a 8 68 Body centered cubic a−b−a−b 12 74 Non-cubic a−b−a−b 12 74 Face centered cubic a−b−c−a−b−c Type of Cell Simple Cubic Body Centered Cubic (BCC) Face Centered Cubic (FCC) End Centered Cubic 14 No. of Atoms at Corners 8 × (1/8) = 1 8 × (1/8) = 1 8 × (1/8) = 1 8 × (1/8) = 1 No. of Atoms in Faces 0 0 6 × (1/2) = 3 2 × (1/2) = 1 No. of Atoms in Total Center of Cube 0 1 1 2 0 4 2 e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 Tetrahedral hole and Octahedral hole : In cubic closed packed arrangement there are two types of holes. Tetrahedral holes : Holes which are directly beneath second layer of spheres and are surrounded by 4 spheres are called tetrahedral voids. OR The hole produced when a sphere is placed on the three spheres in one plane giving tetrahedral arrangement is called tetrahedral hole OR void. Octahedral holes : The holes which are not covered by second layer and are surrounded by six spheres are called octahedral holes OR voids. OR The hole produced when two spheres are placed one above and other below the central hole of the four spheres in a plane and in mutual contact is called octahedral void OR hole. 15 e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 CRYSTAL STRUCTURE OF IONIC SOLIDS Relation between Size of ions and Co-ordination number and Stability of Ionic crystal : The number of spheres that can be arranged around a central sphere depends on the size of the central sphere. Cations are generally smaller than anions. In a packing arrangement of anions, holes are produced in which cation will fit. As the size of cation increases, more anions having same size can be accommodated around cation. i.e. co-ordination number of cation increases. Hence stability of ionic crystal increases. Relationship between co-ordination number, radius ratio and crystal lattice structure : The co-ordination number of each sphere (atom, molecule, ion) is the number of nearest neighbors immediately surrounding each such sphere. In ionic solids each ion is surrounded by definite number of oppositely charged ions which is called co-ordination number of that ion. Co-ordination number generally depends on the size of cation. (Which is present in the hole) It is also related to the radius ratio. The ratio of radius of cation to radius of anion is known as radius ratio. radius of cation r+ Radius Ratio = radius of anion r− As the size of cation decreases (i.e. as the radius ratio decreases) the space around the central cation also decreases hence less anion can be accommodated around it. Thus, coordination number of cation decreases. For example, in CsCl, NaCl and ZnS the size of cation decreases in following order… Cs+ > Na+ > Zn2+. Therefore radius ratio also decreases in following order. CsCl > NaCl > ZnS. (Hence their co-ordination number decreases… i.e. 8 > 6 > 4 ) Note : Radius ratio in CsCl – 0.92; in NaCl – 0.525; in ZnS – 0.407 16 Geometry of crystal lattice also changes as radius ratio changes. Radius ratio rc / ra Co-ordination Arrangement of anions around cations number of cation i.e. r+ / r− 3 0.15 to 0.22 Triangular 4 0.22 to 0.41 Tetrahedral (ZnS) 6 0.41 to 0.73 Octahedral, Face centered cube (FCC), NaCl 8 0.73 and above Octahedral, Body centered cube (BCC), CsCl e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 Sodium Chloride (NaCl) : Coordination number : Na+ - 6 and Cl− - 6 No. of formula unit in one unit cell : 4 For NaCl type arrangement : 2r+ + 2r− = a = Edge length Cesium Chloride (CsCl) : Coordination number : Cs+ - 8 and Cl− - 8 No. of formula unit in one unit cell : 1 For CsCl type arrangement : 2r+ + 2r− = c = Body diagonal Zinc Blend (ZnS) : Coordination number : Zn2+ - 4 and S2− - 4 No. of formula unit in one unit cell : 4 Fluorite Structure (CaF2) : Coordination number : Ca2+ - 8 and F− - 4 Ca2+ ions forms ccp lattice and F− in tetrahedral hole No. of formula unit in one unit cell : 4 Antifluorite Structure (Na2O) : Coordination number : Na+ - 4 and O2− - 8 O2− ions forms ccp lattice and Na+ in tetrahedral hole No. of formula unit in one unit cell : 17 e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 Imperfections OR Defects in Solids : All crystalline solids have short range as well as long range order in the arrangement of their constituent particles, yet crystals are not perfect. Any kind of irregularities from perfectly ordered arrangement of constituent particles in crystals is called “imperfection” or “defect”. Usually a solid consists of an aggregate of large number of small crystals. These small crystals have defects or imperfection in them. This happens when crystallisation process occurs at fast or moderate rate. Single crystals are formed when the process of crystallisation occurs at extremely slow rate (which is quite impossible). Even these crystals are not free from defects. Thus, defects are basically irregularities in the arrangement of constituent particles. The perfectly pure crystalline state is observed only at 0 K (i.e. at −273 °C). The defects may also arise due to the heat absorbed by the crystals from the surroundings (i.e. due to increase in temperature) or due to the presence of impurities in the crystals. It is not possible to explain many properties of solids such as the mechanical strength or electrical conductivity etc. in terms of pure structure alone. Imperfections not only modify the properties but also sometimes impart new properties to the solids. Broadly speaking, the defects are of two types… (1) point defects and (2) line defects. Point defects are the irregularities or deviations from ideal arrangement around a point or an atom in a crystalline substance. Whereas the line defects are the irregularities or deviations from ideal arrangement in entire rows of lattice points. These irregularities are called crystal defects. We shall confine our discussion to point defects only. Types of Point Defects : (C) Point defects can be classified into three types… Stoichiometric Defects : (1) Vacancy Defect - Schottky Defects (2) Interstitial Defect - Frenkel Defects Non-stoichiometric defects (1) Metal Excess Defect (a) Metal excess defect due to anionic vacancies (b) Metal excess defect due to the presence of extra cations (2) Metal Deficiency Defect (a) Metal deficiency defect due to cationic vacancies (b) Metal deficiency defect due to the presence of extra anions Impurity Defects (A) Stoichiometric Defects : These are the point defects that do not disturb the stoichiometry of the solid. If imperfections in the crystal are such that the ratio between the cations and anions remains the same as represented by the molecular formula, i.e. stoichiometry of the solid is not disturbed, the defects are called “Stoichiometric defects”. They are also called intrinsic or thermodynamic defects. 18 e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 (A) (B) (1) Basically these are of two types, vacancy defects and interstitial defects. Vacancy Defect : 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. This type of vacancy defects is generally shown by non-ionic solids. Whereas, Ionic solids must always maintain electrical neutrality. Hence, rather than simple vacancy defect, this type of defect in Ionic solids known as Schottky defects. Schottky Defect : It is basically a vacancy defect in ionic solids. In order to maintain electrical neutrality, the number of missing cations and anions are equal. Schottky defect is shown by ionic substances in which the cation and anion are of almost similar sizes and having high coordination number. e.g. NaCl, KCl, CsCl and AgBr. 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. Effect on density : As the number of ions decreases as a result of this defect, the mass decreases whereas the volume remains the same. Hence, like vacancy defect, the density of the solid decreases. (2) Interstitial Defect : When some constituent particles (atoms or molecules) occupy an interstitial site, the crystal is said to have interstitial defect. This defect results in the increase in the density of the substance (because mass increases but volume remains the same). This type of interstitial defects is generally shown by non-ionic solids. In ionic solids interstitial defect is known as Frenkel defect. Frenkel Defect : This defect is shown by ionic solids. The smaller ion (usually cation) is dislocated from its normal site and it occupies 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 and having low coordination number, for example, ZnS, AgCl, AgBr and AgI due to small size of Zn2+ and Ag+ ions. It is important to note that AgBr shows both, Frenkel as well as Schottky defects. 19 e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 Some other consequences of Schottky and Frenkel defects : Density of the crystals, having Schottky defect, decreases. Solids having these defects conduct electricity to a small extent by an ionic mechanism. Crystals having these defects have ‘holes’ due to the absence of ions in certain lattice points. When electric current is applied, a nearby ion moves from its lattice site to occupy a ‘hole’. This creates a new ‘hole’ and another nearby ion moves into it and so on. This process continues and a ‘hole’, thereby migrates from one end to the other end. Thus, it conducts electricity. Due to presence of holes, the stability (or the lattice energy) of the crystal decreases. In Frenkel defect, similar charges come closer. This results in the increase of dielectric constant of the crystals. Difference between Schottky and Frenkel Defect : SCHOTTKY DEFECT FRENKEL DEFECT 1) It is due to equal number of cations and anions missing from the lattice sites. 2) This results in the decrease in the density of the crystal. This type of defect is found in ionic compounds (like alkali halides) having high coordination number; and cations and anions of similar sizes, e.g. NaCl, CsCl etc. 1) 2) 3) 3) It is due to the missing of cations from the lattice sites and these occupy the interstitial sites. It has no effect on the density of the crystal. This type of defect is found in crystals with low coordination number and in which the difference in the size of cations and anions is very large, e.g. silver halides. (B) Non-Stoichiometric Defects : (1) (2) If imperfections in the crystal are such that the ratio between the cations and anions becomes different from that represented by the molecular formula, i.e. stoichiometry of the solid is disturbed, the defects are called “non-stoichiometric defects”. 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… Metal Excess Defect Metal Deficiency Defect (1) Metal Excess Defect : 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 vapour, 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 sites. 20 e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 A negative ion missing from its lattice site, leaving a hole which is occupied by an electron, thereby maintaining the electrical neutrality. As a result the crystal now has an excess of sodium. The anionic sites occupied by unpaired electrons are called F-centers (from the German word Farbenzenter for colour centre). They impart yellow colour to the crystals of NaCl. The appearance of colour is due to excitation of these electrons (i.e. F-centers electrons) when they absorb energy from the visible light falling on the crystals. Similarly, excess of lithium makes LiCl crystals pink and excess of potassium makes KCl crystals violet (or lilac). This defect is similar to Schottky defect and is found in crystals having Schottky defects. Metal Excess Defect due to the Presence of Extra Cations at Interstitial sites : Metal excess defect may also be caused by an extra cation occupying the interstitial sites of crystal. For example, when zinc oxide (white in colour at room temperature) is heated, 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 to maintain electrical neutrality. This defect is similar to Frenkel defect and is found in crystals having Frenkel defects. ZnO(s) ï ï ï ï heating Zn 2+ + 2 eï + 1 O 2(g) 2 It is important to note that, crystals with either type of metal excess defects contain some free electrons. Hence such materials acts as semi conductors. (2) Metal Deficiency Defect : Metal Deficiency Defect due to Cationic Vacancies : There are many solids which are difficult to prepare in the stoichiometric proportion and contain less amount of the metal as compared to the stoichiometric composition. For example… FeO which is mostly found with a composition - Fe0.95O. It’s composition may vary 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. This defect occurs when the metal shows variable valency, i.e. in transition metals. The defect usually occurs due to the missing of a cation from its lattice site and the presence of the cation having higher charge (e.g., 3+ instead of 2+) in the adjacent lattice site. E.g. FeO, FeS and NiO 21 e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 Metal Deficiency Defect due to the Presence of Extra Anions : This type of defect involves the presence of an extra anion in an interstitial position, the electrical neutrality is maintained by an extra charge on a cation. No example of crystals possessing this defect is known at present because anions are usually larger in size, so it is improper to expect them to fit into the interstitial sites. (C) Impurity Defects : These defects arise when foreign atoms are present in the crystal.. If foreign atoms are present at the lattice site in place of host atoms then we get substitutional solid solution. If foreign atoms are present in the vacant interstitial sites then we get interstitial solid solutions. The formation of the substitutional solid solution depends upon the electronic structure of the impurity while the formation of the interstitial solid solution depends upon the size of the impurity. Addition of impurities changes the properties of the crystal. The process of adding impurities to a crystalline solid so as to change its properties is called doping. Impurity Defect in Ionic Solids : In ionic solids, the impurities are introduced by adding impurity of ions. If the valency of impurity ions are different than valency of the host ions, vacancies are created. For example, If molten NaCl containing a little amount of SrCl2 as impurity is crystallized, some of the sites of Na+ ions are occupied by Sr2+. (i.e. Na+ ions are substituted by Sr+2 ion) Each Sr2+ replaces two Na+ ions to maintain electrical neutrality. Sr2+ ions occupies the site of one ion and the other site remains vacant. The cationic vacancies thus produced are equal in number to that of Sr2+ ions. These vacancies result in the higher electrical conductivity of the solid. Similar defect and behaviour is observed when CdCl2 is added to AgCl. (1) (2) 22 Impurity Defects in Covalent Solids : In case of covalent solids such as silicon or germanium (i.e. Group 14 elements) have 4 valence electrons. The impurities added to such covalent solids (elements) may be… Of elements of group-15 (i.e. having more than 4 valence electrons, like P, As – which have 5 valence electrons ) OR Of elements of group-13 (having less than 4 valence electrons, like B, Al, Ga – which have 3 valence electrons) Thus, the impurities added may be electron rich or electron deficit. This type of (impurities) defects thus introduced in the crystals are called electronic defects. e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 (a) Doping with Electron Rich Impurities : Group 14 element like silicon or germanium has 4 electrons in the valence shell. Hence, it normally forms four covalent bonds with the four neighbouring atoms. When it is doped with Group 15 element like P or As, the silicon or germanium atoms at some lattice sites are substituted by atoms of P or As. Since, these atoms have 5 electrons in the valence shell, after forming four normal covalent bonds with the neighbouring atoms, the fifth extra electron is free and gets delocalized. These delocalized electrons increase the conductivity of silicon or germanium. As the increase in conductivity is due to negatively charged electrons, the silicon or germanium crystals doped with electron rich impurities are called n-type semiconductors. (b) 23 Doping with Electron Deficit Impurities : Group 14 element like silicon or germanium has 4 electrons in the valence shell. Hence, it normally forms four covalent bonds with the four neighbouring atoms. e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 24 When it is doped with Group 13 element like B or Al or Ga, the silicon or germanium atoms at some lattice sites are substituted by atoms of B or Al or Ga. Since, Group 13 elements have only three valence electrons, they can form only three covalent bonds with the neighbouring silicon atoms. Thus, a hole is created at the site where fourth electron is missing. This is called electron ‘hole’ or electron vacancy. An electron from the neighbouring atom can jump to fill up this electron ‘hole’ but then an electron hole is created at the site from where electron has jumped. As it continues, the electron holes will move in opposite direction to that of the flow of electrons. Now, when an electric field is applied, the electrons move towards the positively charged plate and while the electron holes move towards the negatively charged plate as if they carry positive charge. Hence, silicon and germanium doped with electron-deficit impurities are called p-type semiconductors. e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 Applications of n-type and p-type Semiconductors : Various combinations of n-type and p-type semiconductors are used for making electronic devices. 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. For example…‘npn’ and ‘pnp’ type of transistors are used to detect or amplify radio or audio signals. The solar cell is also an efficient photo-diode used for conversion of light energy into electrical energy. Germanium and silicon are group 14 elements and therefore, have a characteristic valence of four and form four bonds as in diamond. A large variety of solid state materials have been prepared by combination of groups 13 and 15 or 12 and 16 to simulate average valence of four as in Ge or Si. Typical compounds of groups 13 – 15 are InSb, AlP and GaAs. Gallium arsenide (GaAs) semiconductors have very fast response and have revolutionized the design of semiconductor devices. ZnS, CdS, CdSe and HgTe are examples of groups 12 – 16 compounds. In these compounds, the bonds are not perfectly covalent and the ionic character depends on the electronegativities of the two elements. Electrical Properties : (1) 25 Solids exhibit an amazing range of electrical conductivities, extending over 27 orders of magnitude ranging from 10–20 to 107 ohm–1 m–1. Solids can be classified into three types on the basis of their conductivities. Conductors : The solids with conductivities ranging between 104 to 107 ohm–1m–1 are called conductors. Metals have conductivities in the order of 107 ohm–1m–1 are good conductors. They are further classified as metallic conductors and electrolytic conductors. In the metallic conductors, the flow of electricity is due to flow of electrons (electronic conductors) without any chemical change occurring in the metal. The conductivity of metals depends upon the number of valence electrons available per atom. In case of electrolytic conductors like NaCl, KCl, etc., the flow of electricity takes place to a good extent only when they are taken in the molten state or in aqueous solution. e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 (2) (3) The flow of electricity is due to flow of ions. However, in the solid state, they conduct electricity only to a small extent which is due to the presence of defects (holes, electrons, etc.). Thus, metals conduct electricity in the solid as well as molten state, electrolytes conduct electricity only in aqueous solution or molten state. Insulators : These are the solids with very low conductivities ranging between 10–20 to 10–10 ohm–1m–1. Semiconductors : These are the solids with conductivities in the intermediate range from 10–6 to 104ohm– 1m–1. The Energy Band Model of Metal : It can be explained on the basis of molecular orbital theory. A metal lattice has an extremely large number of atoms. The atomic orbitals of these atoms with the same symmetry and same energy overlap, resulting in the formation of energy bands. Depending upon the different types of atomic orbitals which overlap, different energy bands are obtained. These energy bands can be joined together OR can also be separate. The highest occupied energy band is called the valence band while lowest unoccupied energy band is called conduction band. The energy gap between the top of the valence band and the bottom of the conduction band is called energy gap − Eg. 26 Sodium Magnesium In the case of metals, the valence band may be half filled OR there may be an overlapping between the valence bands and the conduction bands. This makes it possible for the electrons to go into the vacant conduction bands and hence is responsible for high electrical conductivity of metals. Thus, metals are good conductors. In case of Insulators, the energy gap is very large and therefore the vacant conduction band is not available to the electrons of completely filled valence band. For example…in diamond the energy gap is very large. Hence electrons cannot move from valence band into conduction band. This makes diamond as an insulator. In semi conductors like Si (Silicon) and Ge (Germanium), value of energy gap Eg between valence band and conduction band is small and increase in temperature gives thermal energy, hence some of the electrons of the valence band move into the conduction band. Thus, it shows electrical conductivity and it acts as a semiconductor. (like Si and Ge) e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 Distinction among (a) Metals (b) Insulators and (c) Semiconductors. In each case, an unshaded area represents a conduction band. Effect of Temperature on Electrical Conductivity : Electrical conductivity of metals decreases with increase of temperature because on heating, the positive ions of the metal atoms start vibrating and produce hindrance in the flow of electrons. The electrical conductivity of semiconductors increases with increase in temperature because more electrons can jump to the conduction band. Substances like silicon and germanium which show this type of behaviour are called intrinsic semiconductors. In fact, all pure substances that show conductivity similar to that of silicon and germanium are called intrinsic semiconductors. The conductivity of intrinsic semiconductors is so low that as such they have no practical use. The conductivity can be increased by doping, either by adding electron rich impurities or electron deficit impurities. The semiconductors thus obtained are called n-type and p-type semiconductors, as already discussed. Conductivity of Transition Metal Oxides : It is interesting to learn that transition metal oxides show marked differences in their electrical properties. For example…TiO, CrO2 and ReO3 behave like metals. Rhenium oxide, ReO3 is like metallic copper in its conductivity and appearance. Certain other oxides like VO, VO2, VO3 and TiO3 show metallic or insulating properties depending on temperature. It is interesting to point out that the variation in conductivity is very large even among similar compounds. 27 e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 1) 2) 3) Thus, 1) 2) 3) For example… monoxides of transition metals, all of which possess NaCl structure, show large variations in electrical properties. Similar variations are observed among other oxides too. TiO is metallic, MnO, FeO, CuO etc. are insulators whereas VO is metallic or insulating depending upon temperature. CrO2 is metallic, MnO2 is insulator whereas VO2 is metallic or insulating depending upon temperature. ReO3 is metallic whereas VO3 and TiO3 are metallic or insulating depending upon temperature. TiO, CrO2 and ReO3 are metallic. MnO, FeO and CuO are insulators. VO, VO2, VO3, and TiO3 change from metallic to insulator at a certain temperature. Similar variation is observed among the sulphides of transition elements. Magnetic Properties of Solids : Every substance has some magnetic properties associated with it. The origin of these properties lies in the electrons. Each electron in an atom behaves like a tiny magnet. Its magnetic moment originates from two types of motions (i) its orbital motion around the nucleus and (ii) its spin motion around its own axis. Electron being a charged particle and undergoing these motions can be considered as a small loop of current which possesses a magnetic moment. Thus, each electron has a permanent spin magnetic moment and an orbital magnetic moment associated with it. Thus, each electron may be considered as a small magnet having a resultant permanent magnetic moment (dipole). As magnetic moment is a vector quantity, the net magnetic moment of an electron may be represented by an arrow. Thus, a material may be considered to contain a number of magnetic moments (dipoles); where magnetic dipoles may be thought of small bar magnets composed of north and south poles. Magnetic dipoles are analogous to electric dipoles having positive and negative electric charges. Magnitude of this magnetic moment (dipole) is very small and is measured in the unit called Bohr Magneton (BM or µB). It is equal to 9.27 × 10–24 A m2. 1) 2) 3) Based on the behaviour in the external magnetic field, the substances are classified into five different categories … Paramagnetic Diamagnetic Ferromagnetic 28 e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 4) 5) Antiferromagnetic Ferrimagnetic Note : Properties possessed by above types of substances are known as Paramagnetism, Diamagnetism, Ferromagnetism, Antiferromagnetism and Ferrimagnetism respectively. Paramagnetism : Paramagnetic substances are weakly attracted by a magnetic field. They are magnetized in a magnetic field in the same direction. They lose their magnetism in the absence of magnetic field. These have permanent dipoles because of the presence of some species (atoms, ions or molecuels) having one or more unpaired electrons. O2, Cu2+, Fe3+, Cr3+, TiO, Ti2O3, VO, VO2, CuO are some examples of such substances. Diamagnetism : Diamagnetic substances are weakly repelled by a magnetic field. H2O, TiO2, NaCl and C6H6 are some examples of such substances. They are weakly magnetized in a magnetic field in opposite direction. Diamagnetism is shown by those substances in which all the electrons are paired and there are no unpaired electrons. Pairing of electrons cancels their magnetic moments and they lose their magnetic character. Ferromagnetism : A few substances like iron, cobalt, nickel, gadolinium and CrO2 are attracted very strongly by a magnetic field. These Substances show permanent magnetism even in the absence of the magnetic field. Such substances are called ferromagnetic substances. Such substances remain permanently magnetized, once they have been magnetised. These substances are very strongly attracted by a magnetic field. The reason for such a magnetic behaviour by these substances is that in the solid state, the metal ions of these substances are grouped together into small regions called domains. Thus, each domain acts as a tiny magnet (having definite magnetic moment). 29 e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 (1) (2) (3) (4) In an unmagnetized piece of any ferromagnetic substance, the domains are randomly oriented such that their magnetic moments cancel each other. However, when the substance is placed in a magnetic field, all the domains get oriented in the direction of the magnetic field and a strong magnetic effect is produced. This ordering of domains persist even when the magnetic field is removed and the ferromagnetic substance becomes a permanent magnet. In fact, ferromagnetism is a case of large amount of paramagnetism. The ferromagnetic material CrO2, is used to make magnetic tapes used for audio recording. Antiferromagnetism : Substances which are expected to possess paramagnetism or ferromagnetism on the basis of magnetic moments of the domains but actually they possess zero net magnetic moment are called anti-ferromagnetic substances. E.g. MnO In MnO domain structure is similar to ferromagnetic substance, but their domains are oppositely oriented and cancel out each other's magnetic moment. Ferrimagnetism : Substances which are expected to possess large magnetism on the basis of the magnetic moments of the domains but actually have small net magnetic moment are called ferrimagnetic substances. Ferrimagnetism is observed when the magnetic moments of the domains in the substance are aligned in parallel and anti-parallel directions in unequal numbers. They are weakly attracted by magnetic field as compared to ferromagnetic substances. Fe3O4 (magnetite) and ferrites like MgFe2O4 and ZnFe2O4 are examples of such substances. These substances lose ferrimagnetism on heating and become paramagnetic. 30 e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 (5) (1) (2) It may be noted that all magnetically ordered solids, i.e. ferromagnetic and antiferromagnetic solids change into paramagnetic at high temperature. This is due to randomization of domains (spins) on heating. Ferrimagnetic substance, Fe3O4 becomes paramagnetic at 850 K. It is important to note that each ferromagnetic substance has a characteristic temperature above which no ferromagnetism is observed. This is known as curie temperature. Like electrical conductivity, the magnetic behaviour of the compound of transition elements with similar structure may not be same. E.g. TiO, VO and CuO are paramagnetic whereas MnO, FeO, CoO and NiO are antiferromagnetic. TiO2 is diamagnetic, VO2 is paramagnetic, CrO2 is ferromagnetic whereas MnO2 is antiferromagnetic. Sem – IV – 2015 Prasham Sheth Alay Majmudar Pooja Patel Yash Patel Kirtana Prabhu Kathan Shah Nidhi Patel Dhruv Shah Meet Shah Rutu Nikhal Anusha Patel Esha Gor Siddhi Shah Freya Shah Rashmi Menon 31 99 96 94 93 91 91 90 90 90 89 87 87 87 86 80 Sem – II – 2015 Gresha Vora Vedant Shah Sanket Bhardwaj Aayushi Joshi Jugal Shah Mihir Chaudhary Dhairya Shah Aransha Shah Saloni Chudgar Abhi Shah Chahat Shah Rutvik Panchal Tapash Bhavsar Rutva Joshi Aditi Parmar Zeel Mehta Dwij Shah 98 98 97 96 93 93 91 90 89 85 85 85 84 83 82 82 80 e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433 JEE score CHEMISTRY PHYSICS MATHS Pooja Patel 158 68 41 49 DAIICT Prasham Sheth 152 70 29 53 Nirma Computer Alay Majmudar 146 69 33 45 Nirma Computer It doesn’t matter how many resources you have. If you don’t know how to use them, it will never be enough. 32 e-CHEMTEST / CHAPTER – 1/ Sem – III / Ph : 079 – 30004433