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CHEMISTRY NOTES www gneet com,CLASSIFICATION OF CRYSTALLINE SOLIDS. Crystalline solids can be classified on the basis of nature of intermolecular forces operating. between them in to following four categories,i Molecular ii Ionic iii metallic iv covalent. i Molecular solids,Further divided in into three categories. a Non polar molecular solids,i Constituent particles Non polar molecules. Ii Bonding force Dispersion forces or London forces. iii Binding energy in kJ mol 0 05 40,iv Melting point Very low about 84. v Physical nature Soft,vi Electrical conductivity Insulator. Examples H2 N2 O2 He NA Ar Kr,b Polar molecular solids. i Constituent particles Polar molecules,Ii Bonding force Dipole dipole interaction. iii Binding energy in kJ mol 5 25,iv Melting point low about 158. v Physical nature Soft,vi Electrical conductivity Insulator. Examples HCl HBr SO2 SO3 etc,c H bonded molecular solids. i Constituent particles Polar molecules containing O N F and H. Ii Bonding force Hydrogen bonding and Dipole dipole interaction. iii Binding energy in kJ mol 10 40,iv Melting point low about 273. v Physical nature Hard,vi Electrical conductivity Insulator. Examples H2O ice,ii Ionic solids,i Constituent particles Ions. Ii Bonding force Electrostatic force of attraction. iii Binding energy in kJ mol 400 4000,iv Melting point High 1500. v Physical nature Hard but brittle, vi Electrical conductivity Insulator in solid state but conductor in molten and. in aqueous state,Examples NaCl KCl CuSO4 CaF2 CsCl etc. www gneet com,CHEMISTRY NOTES www gneet com,iii Metallic solids. i Constituent particles Positively charged ions kernels in a sea of mobile. Ii Bonding force Metallic bonding,iii Binding energy in kJ mol 70 1000. iv Melting point 800 1000, v Physical nature Hard but malleable and ductile except Na K Li etc. vi Electrical conductivity conductor,Examples Fr Cu Zn Ni Co Al Au Pt etc. iv Covalent or Network solids,i Constituent particles Atoms. Ii Bonding force Covalent bonds,iii Binding energy in kJ mol 150 500. iv Melting point High 4000,v Physical nature Hard, vi Electrical conductivity Insulator except graphite. Examples SIO2 diamond graphite SiC carborundum,CRYSTAL LATTICE AND UNIT CELL. Crystal lattice, The regular arrangement of an infinite set of points which describes the three dimensional. arrangement of constituent particles atom ions molecules in space is called a crystal. lattice or space lattice The space lattice may be one two or three dimensional depending. upon the number of parameters required to define it. There are only 14 possible three dimensional lattices They are called Bravais Lattice. Following are the characteristics of a crystal lattice. i Each point in a lattice is called lattice point or lattice site. ii Each point in a crystal lattice represents one constituent particle which may be atom. ion or molecule, ii Lattice points are joined by straight line to bring out the geometry of the lattice. The smallest repeating units of space lattice which when repeated over and over again in. three dimensions result into whole of the space lattice of crystal is called unit cell The. crystal may therefore be considered to consists of infinite number of unit cells. A unit cell is characterized by, i its dimensions along the three edges a b c These edges may or. may not be perpendicular to each other, ii angle between edges between b and c between a and c. and between a and b,Thus unit cell is characterized by six parameters. www gneet com,CHEMISTRY NOTES www gneet com,Types of unit cells. i Simple or primitive, The unit cells in which particles i e atoms ions or molecules are present only at the. corners of the unit cell are called simple or primitive cells. ii Face centered, In this type of unit cells points are represented at the corners as well as centers of each. ii Body centered, These are the unit cells in which points are present at the corners and an additional point. is present at the centre of the unit cell,iv End centered. The unit cell in which points are present at the corners and at the centre of the two ends. Number of atoms in unit cell,It should be noted that. i An atom present at the corner is equally shared by eight unit cells Therefore. contribution of an present at the corner to each unit cell is 1 8. ii An atom present at the face centre is equally shared between two unit cells Therefore. contribution of an atom present at the face centre towards each unit cell is. iii An atom present within the body of the unit cell body centre is shared by no other. unit cell Hence contribution of an atom present within body of unit cell is 1. iv An atom present at the edge centre of unit cell is equally shared by four unit cells. Therefore contribution of an atom present at the edge centre towards each unit cell is. www gneet com,CHEMISTRY NOTES www gneet com, The point representing the atoms molecules or ions in a unit cells are known as lattice. point and is denoted by Z also called as Rank of a crystal. The number of lattice point or number of atoms per unit cell in the above four types of. unit cells may be calculated as follows,a Simple or Primitive 1. b Face centered 1 1,c Body centered 1,d End centered 1 1. Unit cells of 14 types of Bravais Lattices,System Axial Axial angles Unit cells Examples. 1 Cubic a b c 1 simple NaCl KCl ZnS Cu2O Pb Ag, regular all 90o 2 face centered Au Hg diamond Alums. 3 body centered,2 Tetragonal a b c 4 simple SnO2 ZnO2 TiO2 NiSO4. all 90o 5 Body centered ZrSiO4 PbWO4 White Sn,3 Hexagonal a b c 90 6 simple ZnO PBI2 CdS HgS. 120 Graphite Ice Beryl Mg Zn,4 Trigonal or a b c 7 simple NaNO3 CaSO4 Calcite. Rhombohedral 90 Quarts As Sb Bi, 5 Orthorhombic a b c 8 Simple KNO3 K2SO4 Calcite BaSO4. Rhombic all 90o 9 face centered Rhombic sulphure,10 Body MgSO4 7H2O. 11 end centered,6 Monoclinic a b c 90 12 Simple Na2SO4 10H2O. 90 13 End centered Na2B4O7 10H2O CaSO4 2H2O,Monoclinic sulphur. 7 Triclinic a b c 14 Simple CuSO4 5H2O K2Cr2O7 H3BO3. Solved example, Q A compound formed by the element X and Y crystallizes in cubic structure in which X. atoms are at the corners of the cube with Y atoms are at the centre of the face What is. the formula of the compound,www gneet com,CHEMISTRY NOTES www gneet com. The number of X atoms per unit cell 8 1,Number of Y atoms per unit cell 6 3. Thus chemical formula XY3,CLOSE PACKING OF CRYSTALLINE SOLIDS. Close packing refers to tight arrangement of spheres in a given space in such a way that. they occupy the maximum available space and hence the crystal has maximum density. The number of nearest neighbors of a particle is called coordination number. a Close packing in one dimension, There is only one way of arranging spheres in a one dimensional close packed structure. that is to arrange in row and touching each other Coordination number is 2. b Two dimensional close packing,1 Square close packing. Here spheres are arranged in such a way that every sphere is in contact with four other. spheres coordination number 4 since second row exactly below first such arrangement is. called AAA type arrangement,2 Hexagonal close packing. In this kind of packing spheres are arranged in such a way that every sphere is in contact. with six other spheres Coordination number 6, The second row may be placed above the first in a staggered manner such that its spheres. fit in the depressions of the first row If the arrangement of first row is called A type the. one in second row is different type and may be called B type When third row is placed are. line with first row then this row is also A And arrangement is known as ABAB type. C Three dimensional close packing, Two types of three dimensional close packing are obtained from hexagonal close packing. layers a Hexagonal close packing hcp b Cubic close packing ccp. While other two types of three dimensional close packing are obtained from square close. packed layers c Body Centered cubic arrangement bcc and d simple cubic arrangement. www gneet com,CHEMISTRY NOTES www gneet com,a Hexagonal Close packing hcp. In this arrangement atoms are located at the corners and centre of two hexagonal placed. parallel to each other three more atoms are placed in a parallel to midway between. these two planes,Characteristic features of hcp, i This type of packing is ABAB type of arrangement of the layers which indicates that. every alternate layers are alike,ii It has a 6 fold axis of symmetry. iii Each atom is surrounded by 12 another atoms 6 in own layer and 3 above and 3 blow. layers Coordination number 12, iv In hcp arrangement the atom occupy 74 of the available space and thus 26 of. space is empty, v It has only one set of parallel close packed layers Hence the chances for slipping of. one layer over the other is less,Example BE Cd Li Ca Cr Mo V Mg Zn Ce Zr OS Ru He. b Cubic closed packing ccp or face centered cubic fcc. In this type of close packing atoms are arranged at the corners and at the centers of all six. faces of a cube, If we start with hexagonal layers of spheres as shown in figure and second layer of spheres. is arranged placing the spheres over the holes in first layer one half of the holes can be. filled by these spheres Suppose that spheres in third layers are so arranged that they. cover holes in second layer the third layer neither resembles first layer or second layer. The fourth layer resembles first fifth resembles second and sixth resembles third layer. then this type of arrangement is known as cubic closed packed ccp arrangement or face. centered cubic fcc arrangement The percentage of free space is 26 and coordination. number is 12,www gneet com,CHEMISTRY NOTES www gneet com. Characteristic features of ccp, i This type of packing has ABCABC type of arrangement of the layer i e the first three. layers are quite different from each other but this set of layer is repeated over and again. the addition of more layers, ii It has cubic symmetry the whole structure has four 3 fold axis of symmetry. iii As in hcp each atom in ccp arrangement has 12 nearest has 12 nearest neighbors i e. the coordinate number of each atom is 12, iv The ccp arrangement of atoms occupies 74 of the available space and thus 26 of the. space remains empty, v It has four sets of parallel close packed layers Hence the chances for slipping of one. layer over the other are more in the ccp arrangement than in the hcp arrangement Hence. metals having ccp structure, vi Example Cu Ag Au Pt Al Cr Co Cu Ag Fe PB Mn Ni Ca Sr Pt all noble gases. except He are found to posses cubic close packed structure Nearly 60 of the metals have. been found to possess either hcp or ccp structure,c Body Centered cubic structure bcc. Characteristic feature of body centered cubic arrangement. i In a body centered cubic arrangement the atoms occupy corners of a cube with an atom. at its centre, ii Each atom is in contact with eight other atoms four atoms in the layer just above and. four atoms in the layer just below and hence the coordination number in this type of. arrangement is only eight, iii This arrangement of atoms occupies only 68 of the total volume so this arrangement. is found in Na K Cs Rb W V Mo and Ba Only 20 of the metallic elements found to. posses bcc arrangement,www gneet com,CHEMISTRY NOTES www gneet com. d Simple cubic arrangement, The particles in the adjacent rows may show a horizontal as well as a vertical alignment. forming cubic A central sphere is surrounded by four other spheres in two dimension and. in three dimension surrounded by 6 spheres,VOIDES OR HOLES. A crystal is formed as result of close packing of its constituting particles which are. supposed to have spherical shape Since they are touching each other only at one point. there must remain some empty spaces are called voids or holes or interstitial site. a Tetrahedral voids, The voids which are surrounded by four spheres which lie at the vertices of a regular. tetrahedron are called tetrahedral void There are 8 tetrahedral voids around each sphere. If N are the number of close packed sphere than tetrahedra voids are 2N coordination. number of tetrahedral void is 4,If r radius of the spherical tetrahedral site. R radius of closely packed sphere,Size of the tetrahedral void 0 225R. b Octahedral voids, The void which are surrounded by six sphere which lie at the vertices of a regular. octahedron is known as octahedral void There are six octahedron void around each. sphere There is one void per atom in a crystal If N are the number of close packed. sphere than octahedral voids are N coordination number of octahedral void 6. If r radius of the spherical octahedral site,R radius of closely packed sphere. www gneet com,CHEMISTRY NOTES www gneet com,Size of the tetrahedral void 0 414R. c Trigonal void, The void enclosed by three sphere in contact is called a Trigonal void This void and the. spheres surrounding it are in same plane There are 24 void around each sphere There are. 8 Trigonal voids per atom in a crystal,If r radius of the spherical Trigonal site. R radius of closely packed sphere,Size of the tetrahedral void 0 155R. d Cubic void, This type of void is formed between 8 closely packed spheres which occupy all eight. corners of cube This site is surrounded by eight spheres which touches each other Size of. the cubical void is given as,If r radius of the spherical cubical site. R radius of closely packed sphere,Decreasing order of the size of the various voids. Cubic Octahedral Tetrahedral Trigonal, Number of tetrahedral void 2 Number of atoms or octahedral voids. www gneet com,CHEMISTRY NOTES www gneet com,PACKING EFFICIENCY OF ccp AND hcp STRUCTURE. Packing efficiency is the percentage of total space filled by the particles. a Packing efficiency of ccp and hcp structure, In figure let cell edge length be a and face diagonal AC b. AC2 BC2 AB2,b2 a2 a2 Thus b 2 a i,If radius of sphere is r we find b 4r. From eq i 2 a 4r Thus r, There are four spheres per unit cell in ccp structure. Volume of four spheres 4 3,Volume of the cube a 2 2 16 2 3. Percentage of packing efficiency,Thus efficiency 72. OR Packing factor 0 72,www gneet com,CHEMISTRY NOTES www gneet com. b Packing efficiency of Body Centered Cubic Structure. In figure let cell edge length be a and face diagonal FD b diagonal FD c. From EFD b2 a2 a2 Thus b 2 a i,From AFD c2 a2 b2,c2 a2 2a2 3a2. The length of the body digonal c is equal to 4r Here r is the radius of the sphere atom. From eq ii we get 3 a 4r,There are two spheres per unit cell in bcc. Volume of two sphere 2 3,Volume of cube a,Percentage of packing efficiency. Thus efficiency 68,OR Packing factor 0 68,c Packing efficiency in simple cubic lattice. In simple cubic lattice 8 lattice points are on the corners of the cube Since a simple cubic. has only one atom Let edge length be a then a 2r here r is the radius of sphere. www gneet com,CHEMISTRY NOTES www gneet com,Percentage of packing efficiency. Density of cubic crystal,Density of unit cell, Mass of unit cell number atoms in a unit cell X mass of one atom. here N0 Avogadro s number and M Molar mass,If length of edge a then volume a3. SUMMARY OF STRUCTURE OF METALS, Sr No Property Hexagonal close Cubic close Body centered. packed packed cubic,hcp ccp or fcc bcc, 1 Arrangement of packing Closed pack Closed pack Not closed pack. 2 Type of packing AB AB AB A ABC ABC AB AB AB AB A. 3 Packing efficiency 74 74 68,4 Coordination number 12 12 8. 5 Malleability and ductility Less malleable malleable and. hard and brittle ductile, 6 Examples BE Mg Ca Cr Cu Ag Au Pt Alkali metals Fe. www gneet com,CHEMISTRY NOTES www gneet com,Radius ratio. In ionic compounds the geometrical shape of ionic crystals as well as the coordinate. number depends on the relative size of the ions Positive ions are small in size thus occupy. positions in voids And negative ions are larger in size occupy positions in corners. The ratio of the radii of the cation to the anion in crystal lattice is called radius ratio. Relation ship between Radius ratio Coordinate Number and Geometrical Shape. Radius ratio Coordination Structural Structure type Example. number arrangement,0 155 3 Planer triangular B 2O 3. 0 225 0 414 4 Tetrahedral ZnS CuCl CuBr CuI BaS,0 414 6 Octahedral Sodium chloride NaBR KBr MgO. 0 732 MnO CaO CaS, 0 732 1 8 Body centred Cesium chloride CsI CsBR NH4Br. Solved examples, Example 1 Potassium metal crystallises in face centred cubic arrangement with rdge. length 574pm What is the shortest separation of any two potassium nuclei. Solution For fcc arrangement ditance of neighbour 2r 2 0 707a. 0 707X574 46pm, Example 2 The cubic unit cell of aluminium molar mass 27 0 g mole has an edge length. of 405 pm and density 2 70 g cm3 What tpe of unit cell is. Solution from formula for density 3,2 7 6 023 1023 405 10 10. i e number of atoms per unit cell is 4 Hence unt cell is face centred type. Example 3 Crystalline CsCl has density 3 988 g cc Caluclate the volume occupied by single. CsCl ion pair in the crystal CsCl 168 4, Solution CsCl has simple cubic arrangement hence Z 1. Thus volume of unit cell volume of single CsCl ion pair. From formula for density 3,www gneet com,CHEMISTRY NOTES www gneet com. 3 7 014X10 23 cc,0 6 023 1023 3 998, Example 4 A metal is found to have a specific gravity of 10 2 at 25OC It crystallises in a. body centred cubic lattice with a unit cell edge length of 3 0 Calculate the atomic. Solution From formula for density 3,for body centred Z 1. 0 3 10 2 6 023 1023 3 10 8, Example 5 If the anions B0 form hexagonal close packing and cation A occupy only 2 3. octahedral sites in it then what would be the general formula of the compound. Solution Number of anions B per unit cell 6 for hcp arragement. Total number of octahedral sires 6,Nuber of cations per unit cell 6 X 2 3 4. A B 4 6 or A B 2 3,Hence formula of compound is A2B3. Example 6 A metallic element has cubic lattice Each edge of unit cell is 3 the denity of. the metal is 8 5 g cc How many unit cells will be present in 50g of metal. Solution Volume of unit cell a3 3X10 8 3 cm3,Mass of unit cell density X volume 8 5 X 3X10 8 3. Number of unit cell Mass of sample mass of unit cell. Number of unit cell 24,2 178 X 1023, Example 7 Tungsten is arranged in face centred cube having unit cell volume of 31 699 3. Calculate the radius and atomic volume of tungsten. Solution Volme a3 31 699 3,Edege length a 3 165,For fcc arrangement. 2 1 414 3 165, Example 8 A substance has a face centred cubic crystal with density of 1 984g cm3 and. edgelength 630 pm Caluclate the molar mass of the substance. From the formula of density 3,for fcc Z 4,0 3 1 984 6 023 1023 630 10 10.
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E-Book for General Knowledge Notes for SSC CGL Welcome to SSCPORTAL.IN ... Tricks, Books, Syllabus, Free Downloads, and much more.... http://sscportal.in .
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