Witten accoding to the New Text book (2012-2013) published by the ahaashta State Boad of Seconday and Highe Seconday Education, Pune. Std. XII Sci. Chemisty Numeicals Pof. Santosh B. Yadav (. Sc., SET, NET) Depatment of Chemisty R. Jhunjunwala College, Ghatkopa Salient Featues: Completely exam oiented solved poblems. Fomulae bank fo evey topic. Pactice poblems with hints fo evey subtopic. Poblems fom vaious competitive exams. 236 Solved poblems, 637 Poblems fo pactice and 10 ultiple Choice Questions. Self evaluative in natue. Taget PUBLICATIONS PVT. LTD. umbai, ahaashta Tel: 022 6551 6551 Website: www.tagetpublications.in www.tagetpublications.og email : mail@tagetpublications.in
Std. XII Sci. Chemisty Numeicals Taget Publications Pvt Ltd. Sixth Edition: Novembe 2012 Pice: ` 120/- Pinted at: India Pinting Woks 2, G.D. Ambeka ag, Wadala, umbai 00 031 Published by Taget PUBLICATIONS PVT. LTD. Shiv andi Sabhagiha, hate Naga, Nea LIC Colony, ithaga Road, ulund (E), umbai - 00 081 Off.Tel: 022 6551 6551 email: mail@tagetpublications.in
PREFACE The desie to lean Chemisty emains diminished unless and until the student mastes Physical chemisty. Physical chemisty is a field of science which mainly consists of poblems and hence it calls fo a deep knowledge of fomulas and ability to solve numeical poblems quickly and efficiently. Hence to ease this task we bing to you Std. XII Sci. Chemisty Numeicals a book containing adequate solved poblems fo evey chapte classified into subtopics that povides an indepth knowledge of the pocedue to tackle the poblems. At the end of each topic and sub-topic pactice poblems ae povided to test the student s pepaation and incease his confidence. Additional and multiple choice questions ae also povided to incease the knowledge and ability of the student. Boad poblems and vaious competitive exams poblems of the last many yeas have been included to povide the impotance of questions. To end on a candid note, I would like to make a humble equest to each and evey student: Peseve this book as a Holy Gail as it helps you in the complete and thoough pepaation fom the examination point of view. Thee is always a oom fo impovement, hence I welcome all suggestions and eget any eos that may have occued in the making of this book. Best of luck to all the aspiants! You s faithfully Publishe
Contents No. Topic Name Page No. 1. Solid State 1 2. Solutions and Colligative Popeties 20 3. Chemical Themodynamics and Enegetics 62. Electochemisty 116 5. Chemical Kinetics 163 6. IUPAC Name and Nomenclatue 23
TARGET Publications 01 Solid state Fomulae 1. Density of unit cell: z. d 3 a. whee, a is edge of unit cell N A Avogado numbe (6.023 10 23 ) ola mass z numbe of atoms pe unit cell Fo fcc, z fo bcc, z 2 fo simple cubic, z 1 Std. XII Sci.: Chemisty Numeicals 2. Radius ule and coodination numbe fo ionic cystals: In simple ionic cystals, the cations commonly occupy the voids o holes. The voids ae empty spaces left between anionic sphees. i. Radius Ratio : The citical adius atio of the void (cation) and sphee (anion), is calculated by solid geomety. Radius atio Cation adius Anion adius ii. Coodination Numbe (CN) : The numbe of sphees (atoms, molecules o ions) diectly suounding a single sphee in a cystal, is called coodination numbe. 3. Cystal stuctues of some elements and thei coodination numbe s (CN): Cystal stuctue Example Coodination No. bcc Li, Na, K, Rb, Cs, Ba 8 fcc o ccp Ni, Cu, Ag, Au, Pt 12 hcp (Hexagonal closed packed) Zn, o, Cd, V, Be, g 21. Relation between adius atio, coodination numbe and geomety : Coodination Geomety Examples Radius atio numbe 0.155 to 0.225 3 Plana tiangula B 2 O 3 0.225 to 0.1 Tetahedal ZnS 0.1 to 0.732 6 Octahedal NaCl 0.732 to 1.0 8 Cubic CsCl Solid State 1
Std. XII Sci.: Chemisty Numeicals 5. Chaacteistics of some typical cystal stuctue : Cystal Type of unit Examples Radius CN cell atio Cation Anion CsCl bcc CsCl, CsB, TiCl 0.93 8 8 NaCl fcc AgCl, go 0.52 6 6 ZnS fcc ZnS 0.0 CaF 2 fcc CaF 2, SF 2, CdF 2 0.73 8 TARGET Publications 2 Solved Examples Type 1: Radius Ratio of ionic compound/ The Fomula of compound Example 1.1 Baium has a adius of 22 pm and cystallizes in a body-cented cubic stuctue. What is the edge length of the unit cell? Given: Radius () 22 pm To find: Edge length of unit cell (a)? Fomula: Fo BCC Fom fomula, a 3 3a 22 517.3 pm 1.7320 Example 1.2 Aluminium cystallizes in cubic close packed stuctue. Its metallic adius is 125 pm. What is the edge length of unit cell? Given: Radius () 125 pm To find: Edge length of unit cell (a)? a Fomula: 2 2 Since Al cystallizes in Face cented cubic (FCC) stuctue Fom fomula, a 2 2 125 2 1.12 a 353.5 pm Example 1.3 In silicates the oxygen atom foms a tetahedal void. The limiting adius atio fo tetahedal void is 0.22. The adius of oxide is 1. Å. Find out the adius of cation. Given: Radius of oxide ( ) 1. Å Radius atio 0.22 To find: Radius of cation ( )? Fomula: Radiusof thecation Radius atio Radiusof theanion Fom fomula, Radius atio 0.22 1. 0.22 1. 0.308 Å Example 1. The adius of Be 2 cation is 59 pm and that of S 2 is 170 pm. Find out the coodination numbe and stuctue of BeS. Given: Radius of cation Be 2 ( ) 59 pm Radius of anion S 2 ( ) 170 pm To find: i. The coodination numbe of Be 2 S 2? ii. Stuctue of BeS? Fomula: Radius atio Radiusof thecation Radiusof theanion Solid State
TARGET Publications Fom fomula, Radius atio Be 2 S 2 59 170 0.37 Since the adius atio lies in between 0.225 0.1 The coodination numbe of Be 2 S 2 is And the stuctue of BeS is tetahedal. Example 1.5 If the adius of cation is 96 pm and that of anion is 618 pm. Detemine the coodination numbe and stuctue of the cystal lattice. Given: Radius of cation ( ) 96 pm Radius of anion ( ) 618 pm To find: i. Coodination numbe? ii. Stuctue of the cystal lattice? Fomula: Radiusof thecation Radius atio Radiusof theanion Fom fomula, Radius atio 96 618 0.1553 Since the adius atio lies in between 0.155 0.225 The coodination numbe of cystal is 3 And the stuctue of cystal lattice is Tigonal plana. Example 1.6 The adius of calcium ion is 9 pm and that of an oxide ion is 16 pm. Find the coodination numbe of calcium. Given: Radius of cation ( ) 9 pm Radius of anion ( ) 16pm To find: The coodination numbe of calcium? Std. XII Sci.: Chemisty Numeicals Fomula: Radiusof thecation Radius atio Radiusof theanion Fom fomula, Radius atio 9 16 0.638 Since the adius atio lies in between 0.1 0.732 The coodination numbe of calcium is 6. Example 1.7 Sodium metal cystallizes in body centeed cubic lattice with cell edge.29 Å. What is the adius of sodium atom? Given: Edge length of unit cell (a).29 Å To find: Radius ()? Fomula: Radius () Fo BCC Fom fomula, 3a Radius () Solid State 3 3a 1.7320.29 1.86 Å Example 1.8 B ion foms a close packed stuctue. If the adius of B ions is 195 pm. Calculate the adius of the cation that just fits into the tetahedal hole. Can a cation A having a adius of 82 pm be slipped into the octahedal hole of the cystal A B -? Given: Radius of anion B ( ) 195 pm Radius of cation ( A ) 82 pm To find: i. The adius of the cation that just fits into the tetahedal hole ( )? ii. Whethe the cation A having a adius of 82 pm can be slipped into the octahedal hole of the cystal (A B )?
Std. XII Sci.: Chemisty Numeicals Fomula: Radius atio i. Fo, ii. Radiusof thecation Radiusof theanion Limiting value fo fo tetahedal hole is 0.225 0.1 Fom fomula, Radius of the tetahedal hole ( A ) Radius atio 0.225 195 3.875 pm Fo cation A with adius 82 pm Fom fomula, Radius atio 82 195 0.205 As it lies in the ange 0.1 0.732, hence the cation A can be slipped into the octahedal hole of the cystal A B. Example 1.9 A solid AB has ZnS type stuctue. If the adius of cation is 50 pm, calculate the maximum possible value of the adius of anion B. Given: Radius of cation ( ) 50 pm To find: Radius of anion ( )? Radius of thecation Fomula: Radius atio Radius of the anion ZnS has tetahedal aangement. The ange of fo stable fou fold coodination is 0.225 to 0.1 Hence the adius of anion can be calculated by taking 0.225 50 0.225 0.225 222.22 pm TARGET Publications Example 1.10 Detemine the stuctue and coodination numbe of gs on the basis of adius atio in which adius of g 2 and S 2 is 65 pm and 18 pm espectively. Given: Radius of cation g 2 ( ) 65 pm Radius of anion S 2 ( ) 18 pm To find: i. The coodination numbe of gs? ii. Stuctue of gs? Fomula: Radiusof thecation Radius atio Radiusof theanion Fom fomula, Radius atio g 2 S 2 65 18 0.3533 Since the adius atio lies in between 0.225 0.1 The coodination numbe of gs is. And the stuctue of gs is Tetahedal. Type 2: Density of the unit cell Example 2.1 Al cystallizes in FCC stuctue. Calculate the mola mass of Al atoms, if length of the unit cell is 0 pm and density of Al is 2.7 g/cm 3. Given: Density (d) 2.7 g/cm 3 Length of unit cell (a) 0 pm.0 10 8 cm z (FCC) To find: Atomic mass of element ()? Fomula: i. V a 3 ii. Density (d) N A Solid State
TARGET Publications V (.0 10 8 cm) 3 6.59 10 23 cm 3 d z 23 23 6.023 10 6.59 10 2.7 26.81 amu Example 2.2 If the adius of palladium is 28 pm and the lattice type is body centeed cubic, what is the theoetical density of palladium? Given: Radius () 28 pm 2.8 10 8 cm z 2 (BCC) Atomic mass of Pd 106 To find: Density (d)? Fomula: i. Atomic Radius () ii. V a 3 iii. Density (d) Fo BCC 2.8 10 8 cm 1.732 a 8 2.8 10 cm a 1.732 5.727 10 8 cm V (5.727 10 8 cm) 3 18.78 10 23 cm 3 Fom fomula (iii), 2 106 d 23 23 6.023 10 18.78 10 1.87 g/cm 3 N A 3a Std. XII Sci.: Chemisty Numeicals Example 2.3 Polonium exist as a simple cube. The edge of its unit cell is 33.7 pm. Calculate its density. Given: Edge length (a) 33.7 3.37 10 8 cm Atomic mass of Po () 210 z 1 (Simple cube) Avogado s numbe N A 6.023 10 23 To find: Density (d)? Fomula: i. V a 3 ii. Density (d) V (3.37 10 8 cm) 3 3.79 10 23 cm 3 1 210 d 23 23 6.023 10 3.79 10 9.30 g/cm 3 Example 2. Gallium cystallizes in a simple cubic lattice. The density of gallium is 5.90 g/cm 3. Detemine a value fo atomic adius of gallium. Given: Density (d) 5.90 g/cm 3 Atomic mass of Ga () 69.7 z 1 (Simple cube) Avogado s numbe (N A ) 6.023 10 23 To find: Atomic adius ()? Fomula: i. Density (d) ii. V a 3 iii. a 2 Solid State 5
6 Std. XII Sci.: Chemisty Numeicals 1 69.7 5.90 23 6.023 10 V 1.96 10 23 a 3 1.96 10 23 2.7 10 8 Fo Simple cube stuctue Fom fomula (iii), 8 2.7 10 2 1.35 10 8 cm 135 pm Example 2.5 You ae given a small ba of an unknown metal. You find the density of the metal to be 11.5 g/cm 3. An X-ay diffaction expeiment measues the edge of the face-cented cubic unit cell as.06 10 10 m. Find the gam-atomic mass of this metal and tentatively identify it. Given: Density (d) 11.5 g/cm 3 z (FCC) Edge Length (a).06 10 10 m.06 10 8 cm To find: Atomic mass ()? Fomula: i. V a 3 ii. Density (d) V (.06 10-8 cm) 3 6.6923 10 23 cm 3 d z 23 23 11.5 6.023 10 6.6923 10 115.88 amu This weight is close to that of Indium. TARGET Publications Example 2.6 The edge length of the unit cell of Ta, is 330.6 pm; the unit cell is body-cented cubic. Tantalum has a density of16.69 g/cm 3 i. Calculate the mass of a tantalum atom. ii. Given: Calculate the atomic mass of tantalum in g/mol. Edge length of the unit cell (a) 330.6 pm 330.6 10 10 cm 3.306 10 8 cm Density (d) 16.69 g/cm 3 z 2 (FCC) To Find: i. ass of a tantalum atom? ii. Atomic mass of tantalum in g/mol? Fomula: i. V a 3 ii. ass Density Volume ii. Density (d) N V (3.306 10 8 cm) 3 3.6133 10 23 cm 3 i. ass of the 2 tantalum atoms in the bodycenteed cubic unit cell ass Density olume 16.69 3.6133 10 23 6.0307 10 22 g The mass of one atom of Ta 22 6.0307 10 2 3.015 10 22 g ii. Atomic mass of tantalum in g/mol Fom fomula (iii), d z 23 23 6.023 10 3.6133 10 16.69 2 Atomic mass of Ta 181.6 g/mol A Solid State
TARGET Publications Example 2.7 Nickel cystallizes in a face-cented cubic lattice. If the density of the metal is 8.908 g/cm 3, what is the unit cell edge length in pm? Given: Density (d) 8.908 g/cm 3 z (FCC Lattice) Atomic mass of Ni () 58.693 N A 6.023 10 23 To find: Edge length of unit cell (a)? Fomula: i. Density (d) ii. V a 3 58.693 58.693 V 23 d 6.023 10 8.908.376 10 23 cm 3 a.376 10 23 3.52 10 8 cm 352. pm Example 2.8 A metal cystallizes in a face-cented cubic lattice. The adius of the atom is 0.197 nm. The density of the element is 1.5 g/cm 3. What is this metal? Given: Radius of atom () 0.197 nm 1.97 10 8 cm Density (d) 1.5 g/cm 3 z (FCC Lattice) N A 6.023 10 23 atoms To Find: Name of metal? Fomula: i. a 2 2 ii. V a 3 iii. Density (d) N A Std. XII Sci.: Chemisty Numeicals Fo FCC Lattice 1.97 10 8 a 2 2 a 5.572 10 8 cm V (5.572 10 8 cm) 3 1.72995 10 22 cm 3 Fom fomula (iii), d z 23 22 6.023 10 1.72995 10 1.5 0.11 g/mol The metal is calcium. Example 2.9 etallic ion cystallizes in a type of cubic unit cell. The unit cell edge length is 287 pm. The density of ion is 7.87 g/cm 3. How many ion atoms ae thee within one unit cell? Given: Edge length of unit cell (a) 287 pm 287 10 10 cm 2.87 10 8 cm Density of ion (d) 7.87 g/cm 3 N A 6.023 10 23 atoms mol 1 Atomic mass of ion () 55.85 To find: Numbe of ion atoms (z)? Fomula: i. V a 3 ii. Density (d) N V (2.87 10 8 cm) 3 2.36 10 23 cm 3 d z 7.87 6.023 10 2.36 10 Solid State 7 A 23 23 55.85 z 2.006 z 2 atoms pe unit cell. Hence it is Face cented cubic stuctue (FCC)
8 Std. XII Sci.: Chemisty Numeicals Example 2.10 A metal cystallizes into two cubic system-face cented cubic (FCC) and body cented cubic (BCC) whose unit cell lengths ae 3.5 and 3.0Å espectively. Calculate the atio of densities of FCC and BCC. Given: FCC unit cell length 3.5Å BCC unit cell length 3.0Å z 1 fo FCC z 2 fo BCC 2 To Find: Ratio of densities of FCC and BCC d1 d? 2 Fomula: i. V a 3 ii. Density (d) FCC unit cell length 3.5 Å BCC unit cell length 3.0 Å V 1 (3.5 10 8 ) 3 V 2 a 3 (3.0 10 8 ) 3 z1 Density in FCC (d 1 ) 1 z2 Density in BCC (d 2 ) N d d 1 2 z 1 V 2 z2 V1 8 3 2 (3.0 10 ) 8 3 (3.5 10 ) 23 2.7 10 2 23.2875 10 2 0.6297 1.259 d d 1.259 1 2 A 2 Poblems fo Pactice TARGET Publications Type 1: Radius Ratio of ionic compound/ The Fomula of compound 1. A cubic solid is made of two elements P and Q. Atoms of Q ae at the cones of the cube and that of P ae at the bodycente. What is the fomula of the compound? What ae the coodination numbes of P and Q? 2. The two ions A and B have adius 58 and 210 pm espectively in closed packed cystal of compound AB. Pedict the coodination numbe of A. 3. The ionic adii of Rb, B ae 1.7 and 1.95 espectively. Pedict the most pobable type of geomety exhibited by RbB on the basis of adius atio ule.. A solid has NaCl stuctue. If adius of the cation is 150 pm. Calculate the maximum possible value of the adius of the anion. 5. Why is coodination numbe of 12 not found in ionic cystals? 6. Gold cystallizes in a FCC lattice, the obseved unit cell length is.070 Å. Calculate the adius of a gold atom. 7. A compound is fomed by two elements and N. The element N foms CCP and d 1 atoms of occupy of tetahedal 3 voids. What is the fomula of the compound? 8. Feic oxide cystallizes in a hexagonal close-packed aay of oxide ions with two out of evey thee octahedal holes occupied by feic ions. Deive the fomula of the feic oxide. 9. A compound foms hexagonal closepacked stuctue. What is the total numbe of voids in 0.5 mol of it? How many of these ae tetahedal voids? Solid State
TARGET Publications Type 2: Density of the unit cell 10. Thallium(I) chloide cystallizes in eithe a simple cubic lattice o FCC lattice of Cl ion. The density of a given sample of solid is 9.0 g cm 3 and edge of the unit cell is 3.95 10 8 cm. Pedict the categoy of unit cell. 11. Tungsten has a BCC lattice and each lattice point is occupied by one atom. Calculate the metallic adius of the tungsten atom if density of tungsten is 19.30 g/cm 3 and its atomic mass is 183.9. 12. Euopium cystallizes in a BCC lattice. The density of euopium is 5.26 g/cm 3. Calculate the unit cell edge length. (Atomic mass 152) 13. Al cystallizes in FCC stuctue. Its metallic adius is 125 pm. What is the edge length of unit cell? How many unit cells ae thee in 1 cm 3 of Al. 1. Coppe cystal has a face cented cubic stuctue. Atomic adius of coppe atom is 128 pm. What is the density of coppe metal? (Atomic mass of coppe is 63.5) 15. Kypton cystallizes with a face-centeed cubic unit cell of edge 559 pm. i. What is the density of solid kypton? ii. What is the atomic adius of kypton? iii. What is the volume of one kypton atom? iv. What pecentage of the unit cell is empty space if each atom is teated as a had sphee? 16. At a cetain tempeatue and pessue an element has a simple body-cented cubic unit cell. The coesponding density is.253 g/cm 3 and the atomic adius is 9.92 Å. Calculate the atomic mass fo this element. Std. XII Sci.: Chemisty Numeicals 17. Calculate the X ay density of Aluminium which foms FCC cystal lattice, if edge length of unit cell is.09 Å. (Atomic mass of Al 26.98 g/mol. Avogado s numbe 6.023 10 23 ) 18. Platinum cystallizes in FCC cystal with unit length of 3.9231 Å. Calculate the density and atomic adius of platinum. (Atomic mass of Pt 195.08) Additional Poblems fo Pactice 1. etallic uanium cystallizes in a body centeed cubic lattice, with one U atom pe lattice point. How many atoms ae thee pe unit cell? If the edge length of the unit cell is found to be 33 pm, what is the metallic adius of U in pm? 2. A solid is made up of two elements P and Q. Atoms Q ae in FCC aangement, while P occupy all the tetahedal sites. What is the fomula of the compound? 3. In FCC stuctue of mixed oxide, the lattice is made up of oxide ions, one eighth of tetahedal voids ae occupied by divalent ions (A 2 ) while one half of octahedal voids ae occupied by tivalent ions (B ). What is the fomula of the oxide?. Niobium is found to cystallize with BCC stuctue and found to have density of 8.55 g/cm 3. Detemine the edge length of unit cell. 5. A metallic cystal has FCC lattice stuctue. Its edge length is 360 pm. What is the distance of closest appoach fo two atoms? 6. Gold (atomic adius 0.1 nm) cystallizes in a face-cented unit cell. What is the length of a side of the cell? 7. Given that a solid cystallizes in a bodycented cubic stuctue that is 3.05 Å on each side. What is the volume of one unit cell in Å? Solid State 9
Std. XII Sci.: Chemisty Numeicals 8. any metals pack in cubic unit cells. The density of a metal and length of the unit cell can be used to detemine the type fo packing. Fo example, gold has a density of 19.32 g/cm 3 and a unit cell side length of.08 Å. (1 Å 1 10 8 cm.) i. How many gold atoms ae in exactly 1 cm 3? ii. How many unit cells ae in exactly 1 cm 3? iii. How many gold atoms ae thee pe unit cell? iv. The atoms/unit cell suggests that gold packs as a (a) simple, (b) body-centeed o (c) face-centeed unit cell. 9. Niobium with atomic mass 92.9 amu cystallizes in body centeed cubic stuctue. If density of Niobium is 85.5 g/cm 3. Calculate atomic adius of Niobium 10. If the length of body diagonal fo CsCl which into a cubic stuctue with Cl ions at the cones and Cs ions at cente of unit cell is 7Å and the adius is 1.69 Å What is the adius of Cl? 11. any metals pack in cubic unit cells. The density of a metal and length of the unit cell can be used to detemine the type fo packing. Fo example, sodium has a density of 0.968 g/cm 3 and a unit cell side length (a) of.29 i. How many sodium atoms ae in 1 cm 3? ii. How many unit cells ae in 1 cm 3? iii. How many sodium atoms ae thee pe unit cell? 12. Chomium cystallizes in a body-cented cubic stuctue. The unit cell volume is 2.583 10 23 cm 3. Detemine the atomic adius os C in pm. 10 TARGET Publications 13. Sodium has a density of 0.971 g/cm 3 and cystallizes with a body-cented cubic unit cell. i. What is the adius of a sodium atom? ii. What is the edge length of the cell? Give answes in picometes. 1. Calcium has a cubic closest packed stuctue as a solid. Assuming that calcium has an atomic adius of 197 pm, calculate the density of solid calcium. 15. Calculate the length of edge of unit cell fo α-ion belonging to BCC stuctue. Take the density of α-ion as 7.86 10 3 kg/m 3. (Atomic mass of ion 55.85) 16. etallic coppe cystallizes in BCC lattice. If the length of cubic unit cell is 362 pm then calculate the closest distance between two coppe atoms, also calculate the density of cystalline coppe. 17. Coppe has FCC stuctue and its atomic adius is 0.1278 nm. Calculate its density. (Atomic mass of coppe 63.5) 18. Vanadium has the ion (monoatomic FCC) stuctue. If the length of unit cell edge is 305 pm, calculate the density of vanadium. (Atomic mass of V 50.9 g/mol) Questions Fom Vaious Exams 1. The ionic adius of an anion is 2.11 Å. Find the adius of the smallest cation that can have stable eight fold coodination with the above anions. [GATE-1987] 2. The chloide ion has a adius of 0.181 nm. Calculate the adius of smallest cation which can be coodinated with eight neighbouing chloide ions. [GATE-1989] 3. A solid has NaCl stuctue. If the adius of the cation is 100 pm, what is the adius of the anion? [CBSE 1985] Solid State
TARGET Publications. Pedict the closed packed stuctue of an ionic compound A B in which the adius of cation 18 pm and adius of anion 195 pm. What is the coodination numbe of cation? [CBSE-1998] 5. Pedict the stuctue of go cystal and coodination numbe of its cation in which adii of cation and anion ae equal to 65 pm and 10 pm espectively. [CBSE 1998] 6. The two ions A and B have adius 88 and 200 pm espectively in closed packed cystal of compound AB. Pedict the coodination numbe of A [CBSE 1990] 7. An ionic compound has unit cell consisting of A ions at the cones of a cube and B ions on the centes of face afte cube. What would be the empiical fomula of this compound? [AIEEE 2005] 8. In a solid AB having the NaCl stuctue A atoms occupies the cones of the cubic unit cell. If all the face centeed atoms along one of the axes ae emoved then the esultant stoichiomety of the solid is [IIT 2001] 9. A metallic element cystallizes into lattice containing a sequence of layes of ABABAB. Any packing of sphees leaves out voids in the lattice. Then calculate the empty space in pecentage by volume in this lattice. [IIT 1996] 10. A substance A x B y cystallizes in FCC lattice in which atoms A occupy each cone of the cube and atom B occupy the centes of each face of the cube. Identify the composition of A x B y [IIT 2002] 11. Chomium metal cystallizes with BCC lattice. The length of the unit cell edge is found to be 287 pm. Calculate the atomic adius. What would be the density of chomium in g/cm 3. (Atomic mass of C 51.99) [IIT July 1997] Std. XII Sci.: Chemisty Numeicals 12. A unit cell of sodium chloide has fou fomula unit. The edge length of the unit cell is 0.56 nm. What is the density of sodium chloide? [IIT ay 1997] 13. The unit cell of an element of atomic mass 96 and density 10.3 g cm 3 is cube with edge length 31 pm. Find the stuctue of the cystal lattice. (Simple cubic, FCC, BCC) (Avogado constant 6.023 10 23 mol 1 ) [CBSE 1995] 1. The unit cell of an element of atomic mass 108 and density 10.5 g/cm 3 is a cube with edge length 09 pm. Find the stuctue of the cystal lattice (Simple cubic, FCC, BCC) (Avogado constant(n A ) 6.023 10 23 mol 1 ) [CBSE 1995] 15. An element (Atomic mass 60) having FCC unit cell, has density of 6.23 g cm 3. What is the edge length of the unit cell? 16. The compound CuCl has ZnS stuctue and the edge length of the unit cell is 500 pm. Calculate the density. (Atomic mass of Cu 63, Cl 35.5 Avogado constant 6.023 10 23 mol 1 ) [CBSE 1997] 17. An element A (atomic mass 100) having BCC stuctue has unit cell edge 00 pm. Calculate the density of A and the numbe of unit cells fo 10 g of A. (Avogado Numbe 6.023 10 23 ) [CBSE 1990] 18. An element of atomic mass 98.5 g/mol occus in FCC stuctue. If its unit cell edge length is 500 pm and its density is 5.22 g/cm 3. What is the value of Avogado constant? [CBSC 1997] 19. A face cented cubic element (atomic mass 60) has a unit cell 00 pm. What is its density?(n 6.023 10 23 mol 1 ) [CBSE 1992] Solid State 11
12 Std. XII Sci.: Chemisty Numeicals 20. Coppe cystal has face cented cubic lattice stuctue. Its density is 8.93 g/cm 3.What is the length of the unit cell? (N A 6.023 10 23 mol 1 ; Atomic mass of Cu 63.5) [CBSE 1992] 21. A metal (At mass 50) has a BCC cystal stuctue. The density of the metal is 5.96 g/cm 3. Find the volume of unit cell. (N A 6.023 10 23 mol 1 ) [CBSE 1993] 22. The density of chomium metal is 7.2 cm 3. If unit cell is cubic with edge length of 289 pm, detemine the type of unit cell (Simple/BCC/FCC) At mass of C 52 amu [CBSE 1997] 23. An element cystallizes in a stuctue having FCC unit cell of an edge of 200 pm. Calculate its density if 200 g of this element contains 2 10 23 atoms [CBSE 1991] 2. A metal has FCC cystal stuctue. The length of its unit cell is 0 pm. What is the mola mass of metal atoms if the density of the metal is 2.72 g/cm 3 (N A 6.023 10 23 ) [CBSE 1993] 25. The density of CsB which has CsCl (BCC) stuctue is. g/cm 3. The unit cell edge length is 00 pm. Calculate the inteionic distance in cystal of CsB. (N A 6.023 10 23. At mass of Cs 133, B 80) [CBSE 1993] 26. Potassium fluoide has the NaCl type stuctue. The density of KF is 2.8 g/cm 3 at 20 C. i. Calculate the unit cell length ii. Calculate the neaest neighbou distance in KF [CBSE 1999] TARGET Publications ultiple Choice Questions 1. The space occupied by b.c.c. aangement is appoximately (A) 50% (B) 68% (C) 7% (D) 56% 2. The maximum pecentage of available volume that can be filled in a face centeed cubic system by an atom is (A) 7% (B) 68% (C) 3% (D) 26% 3. In NaCl lattice, the adius atio is (A) 0.225 (B) 0.115 (C) 0.51 (D) 0.71 Na. Xenon cystallizes in face cente cubic lattice and the edge of the unit cell is 620 pm, then the adius of Xenon atom is (A) 219.20 pm (B) 38.5 pm (C) 265.5 pm (D) 536.9 pm 5. A metallic element cystallizes in simple cubic lattice. Each edge length of the unit cell is 3 Å. The density of the element is 8 g / cc. Numbe of unit cells in 108 g of the metal is (A) 1.33 10 20 (B) 2.7 10 22 (C) 5 10 23 (D) 2 10 2 6. The density of KB is 2.75 gm cm 3. Length of the unit cell is 65 pm. K 39, B 80. Then what is TRUE about the pedicted natue of the solid. (A) Solid has face centeed cubic system with z. (B) Solid has simple cubic system with z. (C) Solid has face centeed cubic system with z 1 (D) Solid has body centeed cubic system with z 2 Cl Solid State
TARGET Publications 7. A compound CuCl has face centeed cubic stuctue. Its density is 3. g cm 3. The length of unit cell is. (At mass of Cu 63.5 and Cl 35.5) (A) 5.783 Å (B) 6.783 Å (C) 7.783 Å (D) 8.783 Å 8. At oom tempeatue, sodium cystallizes in a body centeed cubic lattice with a.2 Å. The theoetical density of sodium (At. mass of Na 23) is (A) 1.002 g cm 3 (B) 2.002 g cm 3 (C) 3.002 g cm 3 (D).002 g cm 3 9. The edge length of the unit cell of NaCl cystal lattice is 552 pm. If ionic adius of sodium ion is 95 pm, what is the ionic adius of chloide ion? (A) 190 pm (B) 368 pm (C) 181 pm (D) 276 pm 10. The adius of the Na is 95 pm and that of Cl ion is 181 pm. Pedict the coodination numbe of Na. (A) (B) 6 (C) 8 (D) Unpedictable 11. A solid AB has ock salt stuctue. If the edge length is 520 pm and adius of A is 80 pm, the adius of anion B would be (A) 0 pm (B) 220 pm (C) 360 pm (D) 180 pm 12. NH Cl cystallizes in bcc lattice with edge length of unit cell equal to 387 pm. If adius of Cl is 181 pm, the adius of NH will be (A) 17 pm (B) 15 pm (C) 116 pm (D) 206 pm 13. What is the simplest fomula of a solid whose cubic unit cell has the atom A at each cone, the atom B at each face cente and C atom at the body cente (A) AB 2 C (B) A 2 BC (C) AB 3 C (D) ABC 3 Std. XII Sci.: Chemisty Numeicals 1. The packing efficiency of the two dimensional squae unit cell shown below is (A) 39.27 % (B) 68.02 % (C) 7.05 % (D) 78.5 % 15. If a stands fo the edge length of the cubic systems: simple cubic, body centeed cubic and face centeed cubic, then the atio of adii of the sphees in these systems will be espectively. 1 (A) 2 a : 3 2 a : 3 2 a (B) 1a : 3 a : 2 a 1 (C) 2 a : 3 a : 1 2 2 a 1 (D) 2 a : 3 a : 1 2 a 16. CsB cystal has bcc stuctue. It has an edge length of.3 Å. The shotest inteionic distance between Cs and B ions is (A) 1.86 Å (B) 3.72 Å (C).3 Å (D) 7. Å 17. The numbe of atoms in 100 g of an fcc cystal with density d 10 g / cm 3 and cell edge equal to 100 pm, is equal to (A) 10 25 (B) 3 10 25 (C) 2 10 25 (D) 1 10 25 18. An element (atomic mass 100 g / mol ) having bcc stuctue has unit cell edge 00 pm. Then density of the element is (A) 10.376 g / cm 3 (B) 5.188 g / cm 3 (C) 7.289 g / cm 3 (D) 2.1 g / cm 3 Solid State 13 L
1 Std. XII Sci.: Chemisty Numeicals 19. Coppe cystallizes in fcc with a unit cell length of 361 pm. What is the adius of coppe atom? (A) 108 pm (B) 127 pm (C) 157 pm (D) 181 pm 20. AB cystallizes in a body centeed cubic lattice with edge length a equal to 387 pm. The distance between two oppositely chaged ions in the lattice is (A) 335 pm (B) 250 pm (C) 200 pm (D) 300 pm 21. A solid has a stuctue in which W atoms ae located at the cones of a cubic lattice, O atoms at the cente of edges and Na atoms at the cente of the cube. The fomula fo the compound is (A) NaWO 2 (B) NaWO 3 (C) Na 2 WO 3 (D) NaWO Answes to Additional Poblems fo Pactice 1. 2 atoms, 8.9 pm 2. P 2 Q 3. AB 2 O. 303.5 pm 5. 255 pm 6. 0.07 nm 7. 28.372 Å 8. i. 5.9058 10 22 atoms ii. 1.7238 10 22 unit cells iii. atom/unit cell iv. FCC 9. 1.3 10 2 pm 10. 181 pm 11. i. 2.5 10 22 atoms in 1 cm 3 ii. 1.27 10 22 unit cells iii. 2 atoms pe unit cell 12. 128 10 10 pm 13. i. 185.5 pm ii. 28. pm 1. 1.5 g/cm 3 15. 0.12 nm 16. 313 pm,.5 g/cm 3 17. 8.98 kg/m 3 18. 5.96 g/cm 3 TARGET Publications Answes to Questions fom Vaious Exams 1. 1.55 Å 2. 1.32 Å 3. 21.5 pm. Cubic, 8 5. Octahedal, 6 6. 6 7. AB 3 8. A 3 B 9. 26 % 10. AB 3 11. 12.27 pm, 7.30 g/ml 12. 2.16 g/cm 3 13. Body cented cubic (BCC) lattice. 1. Face cented cubic (FCC) lattice. 15. 00 pm 16. 5.22 g/cm 3 17. 5.188 g/cm 3, 3.0 10 22 unit cells 18. 6.03 10 23 mol 1 19. 6.226 g/cm 3 20. 361.5 pm 21. 2.7857 10 23 cm 3 22. Body cented cubic (BCC) lattice. 23. 1.7 g/cm 3 2. 27 g/mol 25. 36. pm 26. i. 537.7 pm ii. 268.9 pm Answe Key to ultiple Choice Questions 1. (B) 2. (A) 3. (C). (A) 5. (C) 6. (A) 7. (A) 8. (A) 9. (C) 10. (B) 11. (D) 12. (B) 13. (C) 1. (D) 15. (C) 16. (B) 17. (A) 18. (B) 19. (B) 20. (A) 21. (B) Solid State
TARGET Publications Hints to Poblems fo Pactice Poblem 1: Given : Atoms of P ae pesent at the bodycente Atoms of Q ae pesent at the cones of the cube To find: Fomula of the compound? Co-odination numbes of P and Q? It is given that the atoms of Q ae pesent at the cones of the cube. Numbe of atoms contibuted by a cone of atom Q pe unit cell 1 8 atoms Numbe of atoms contibuted by 8 cones of atom Q pe unit cell 1 8 8 1 atom It is also given that the atoms of P ae pesent at the body-cente. Theefoe, numbe of atoms of P in one unit cell 1 atom This means that the atio of the numbe of P atoms to the numbe of Q atoms, P:Q 1:1 Hence, the fomula of the compound is PQ. The coodination numbe of both P and Q is 8 Poblem 2: Given: Radius of Cation A ( ) 58 pm Radius of anion B ( ) 210 pm To find: The coodination numbe of AB? Fomula: Radiusof thecation Radius atio Radius of theanion Fom fomula, Radius atio A 58 210 0.276 B Since the adius atio lies in between 0.225 0.1 The coodination numbe of AB is And the stuctue of AB is Tetahedal Std. XII Sci.: Chemisty Numeicals Poblem 3: Given: Radius of Cation Rb ( ) 1.7Å Radius of anion B ( ) 1.95 Å To find: Stuctue of RbB? Fomula: Radiusof thecation Radius atio Radius of theanion Fom fomula, Radius atio Rb 1.7 1.95 0.7538 Solid State 15 B Since the adius atio lies in between 0.732 1.0 The coodination numbe of RbB is 8 And the stuctue of RbB is Cubic. Poblem : Given: Radius of cation Na ( ) 150 pm To find: Radius of anion Cl ( )? Fomula: Radiusof thecation Radius atio Radius of theanion NaCl has octahedal stuctual aangement The ange of fo stable six fold coodination is 0.1 to 0.732 Hence the adius of cation can be calculated by taking 0.1 Fom fomula, 0.1 0.1 150 362.32 pm 0.1 Poblem 5: aximum adius atio in ionic cystals lies in the ange 0.732 1 which coesponds to a coodination numbe of 8. Hence coodination numbe geate than 8 is not possible in ionic cystals.
16 Std. XII Sci.: Chemisty Numeicals Poblem 6: Given: Edge length of unit cell (a).070 Å To find: Radius ()? a Fomula: 2 2 Since Au cystallizes in face cented cubic (FCC) stuctue Fom fomula,.070 2 1.12 1. Å Poblem 7: d 1 Given: occupy of tetahedal voids 3 To find : Fomula of the compound? The CCP lattice is fomed by the atoms of the element N. Hee, the numbe of tetahedal voids geneated is equal to twice the numbe of atoms of the element N. d 1 The atoms of element occupy of the 3 tetahedal voids. Theefoe, the numbe of atoms of 2 1 3 2 of the numbe of atoms of N. 3 Theefoe, atio of the numbe of atoms of to that of N is : N 2 3 : 1 2:3 Thus, the fomula of the compound is 2 N 3 Poblem 8: Given: Feic oxide has hexagonal closepacked aay. Evey thee octahedal holes ae occupied by feic ions. To find: Fomula of the feic oxide? Let the numbe of oxide (O 2 ) ions be x. So, numbe of octahedal voids x TARGET Publications It is given that two out of evey thee octahedal holes ae occupied by feic ions. So, numbe of feic (Fe 3 ) ions 2 3 x Theefoe, atio of the numbe of Fe 3 ions to the numbe of O 2 ions, Fe 3 : O 2 2 3 x : x 2 3 : 1 2 : 3 Hence, the fomula of the feic oxide is Fe 2 O 3. Poblem 9: Given : Compound has hexagonal closepacked stuctue Avogado s Numbe N A 6.023 10 23 To find: Total numbe of voids? Numbe of tetahedal voids? Numbe of close-packed paticles 0.5 N A 0.5 6.023 10 23 3.011 10 23 Theefoe, numbe of octahedal voids 3.011 10 23 And, numbe of tetahedal voids 2 3.011 10 23 6.022 10 23 Theefoe, total numbe of voids (3.011 10 23 ) (6.023 10 23 ) 9.03 10 23 Poblem 10: Given: Density 9.0 g cm 3 Edge length (a) 3.95 10 8 cm Atomic mass of Th () 232 To find: Categoy of unit cell? Fomula: i. V a 3 ii. Density (d) V (3.95 10 8 cm) 3 6.163 10 23 cm 3 Solid State
TARGET Publications d z 23 23 9 6.023 10 6.163 10 232 1. 1 z 1 atom pe unit Hence it is Simple cubic stuctue (SC) Poblem 11: Given: Atomic mass of Tungsten () 183.9 Density (d) 19.30 g/cm 3 z 2 (Fo BCC) To find: etallic adius (a)? Fomula: i. Density (d) ii. V a 3 V N d A 2 183.9 23 6.023 10 19.30 3.160 10 23 cm 3 a 3 3.160 10 23 3.1628 10 8 cm Poblem 12: Given: Density of Euopium (d) 5.26 g/cm 3 Atomic mass () 152 To find: Edge length of unit cell (a)? Fomula: Atomic mass i. ass of 1 atom Avogado's numbe ii. ass Volume Density iii. Volume a 3 Std. XII Sci.: Chemisty Numeicals 152 Eu 23 6.023 10 152 V 23 6.023 10 5.26.7978 10 23 cm 3 Fom fomula (iii), a 3.7978 10 23 a 3.63 10 8 cm a 363 pm Poblem 13: Given: Radius () 125 pm 1.25 10 8 cm z (FCC) To find: Edge length of unit cell (a)? Numbe of unit cells in 1 cm 3 Al? Fomula: i. a 2 2 ii. V a 3 1.25 10-8 a 2 1.1 a 1.25 10 8 2 1.1 3.535 10 8 cm 353.5 pm V (3.535 10 8 ) 3.18 10 23 cm 3 Numbe of unit cells in 1 cm 3 of Al 1 cm 3 /V 1 23.18 10 2.266 10 2 unit cells Solid State 17 of
18 Std. XII Sci.: Chemisty Numeicals Poblem 1: Given: Atomic adius of Cu atom 128 pm 128 10 10 cm z (FCC) Atomic mass of Cu 63.5 To find: Density of Cu (d)? Fomula: i. Face diagonal 2 edge length ii. Volume (V) a 3 iii. Density (d) Fo FCC Lattice In face cented cubic aangement face diagonal is fou times the adius of atoms face diagonal 128 512 pm 512 10 10 cm Edge length (a) 512 2 362 10 10 cm V (3.62 10 8 cm) 3 7. 10 2 cm 3 Fom fomula (iii), 63.5 d 23 2 (6.023 10 7. 10 ) 8.897 g/cm 3 Poblem 15: Given: Edge length (a) 559 pm 5.59 10 8 cm z (FCC) Atomic mass of Kypton () 83.798 To find: i. Density of solid kypton? ii. Atomic adius of kypton? iii. Volume of one kypton atom? iv. % of the unit cell which is empty space? Fomula: i. V a 3 ii. Density (d) iii. iv. a 2 2 V 3 π3 TARGET Publications N V (5.59 10 8 cm) 3 1.768 10 22 cm 3 83.798 d 23 22 6.023 10 1.768 10 3.19 g/cm 3 Fo FCC Fom fomula (iii), 8 5.59 10 cm 2 2 1.98 10 8 cm Fom fomula (iv), 8 5.59 10 cm 2 1.1 V 3 3.12 (1.98 10 8 ) 3 3.12 7.762 10 2 3 23 9.756 10 3 V 3.25 10 23 cm 3 Volume of the atoms in the unit cell: 3.25 10 23 cm 3 1.292 10 22 cm 3 Volume of cell not filled with K: (1.768 10 22 ) (1.292 10 22 ).568 10 23 cm 3 % of empty space: 23.568 10 22 1.768 10 0.2615 26.15 % Poblem 16: Given: Density d.253 g/cm 3 Atomic adius (a) 9.92Å 9.92 10 8 cm z 2 (BCC) To Find: Atomic mass of element ()? A Solid State
TARGET Publications Fomula: i. 3a ii. Volume of the unit cell V a 3 iii. Density (d) 0 N Fo BCC 8 3 9.92 10.11 10 8 cm V (.11 10 8 cm) 3 6.9 10 23 cm 3 Fom fomula (iii), N 0 d z 23 23 6.023 10 6.9 10.253 2 88.89 amu Poblem 17: Given: Edge length (a).09 Å.09 10 8 cm Atomic mass of Al () 26.98 g/mol z (FCC) Avogado s numbe N A 6.023 10 23 To find: Density (d)? Fomula: i. V a 3 ii. Density (d) V (.09 10 8 cm) 3 6.6381 10 23 cm 3 26.98 d 23 23 6.023 10 6.6381 10 2.699 g/cm 3 Std. XII Sci.: Chemisty Numeicals Poblem 18: Given: Edge length (a) 3.9231 Å 3.9231 10 8 cm Atomic weight of Pt () 195.08 z (FCC) Avogado s numbe N A 6.023 10 23 To find: Density (d)? Atomic adius ()? Fomula: i. V a 3 ii. Density (d) iii. Atomic Radius () a 2 V (3.9231 10 8 cm) 3 6.038 10 23 cm 3 195.8 d 23 23 6.023 10 6.038 10 21.53 g/cm 3 Fom fomula (iii), 8 3.9231 10 2 138.7 pm Solid State 19