MIESSLERquimica inorgânica, Manuais, Projetos, Pesquisas de Química

Baixe MIESSLERquimica inorgânica e outras Manuais, Projetos, Pesquisas em PDF para Química, somente na Docsity! AEice RS id Gary L. Miessler * Donald A. Tarr  Inorganic Third Edition GARY L. MIESSLER = DONALDA. TARR | — St. Olaf College Northfield, Minnesota PEARSON e Prentice Esc] Pearson Education Intemational vi Contents 4 SYMMETRY AND GROUP THEORY 76 4-1 Symmetry Elements and Operations 76 4-2 Point Groups 82 4-2-1 Groups of Low and High Symmetry 84 4-2-2 Other Groups 86 4-3 Properties and Representations of Groups 43] Matrices 92 43-27 Representarions of Point Groups 94 4-3-3 Character Tables 97 4-4 Examples and Applications of Symmetry 102 4-4-1 Chirality 102 4-4-2 Molecular Vibrations 103 5 MOLECULAR ORBITALS 116 5-1 Formation of Molecular Orbitals from Atomic Orbitals 5-1-1 Molecular Orbitals from s Orbitals 117 5-12 Molecular Orbitals from p Orbitals 119 5.1.3 Molecular Orbitals from d Orbitais 120 514 Nonhonding Orbitals and Other Factors 122 5-2 HomonuclearDiatemic Molecules 122 5-2-1 Molecular Orbitals 122 22 Orbital Mixing 124 5.23 First and Second Row Molecules 125 52.4 Photoelectron Spectroscopy 130 525 Correlation Diagrams 132 5-3 Heteronuclear Diatomic Molecules 134 5-3-1 Polar Bonds 134 5.3.2 Ionic Compounds end Moleculur Orbitals 138 5-4 Molecular Orbitals for Larger Molecules 139 5.4.1 EHET 440 54.2 CO 143 54-3 HO 148 5.44 NH: 151 545 BF; 154 4. Molecuh hapes 15 547 Hybrid Orbitals 157 -5 Expanded Shells and Molecular Orbitals 161 116 6 —ACID-BASE AND DONOR-ACCEPTOR CHEMISTRY 165 6-1 Acid-Base Concepts as Organizing Concepts 165 6-1-1 History 165 6-2 Major Acid-Base Concepts 166 6-2-1 Arrhenius Concept 166 6-2-2 Brónsted-Lowry Concept 167 6-2-3 Solvent System Concept 168 6-2-4 Lewis Concept 170 6-2-5 Frontier Orbitals and Acid-Base Reactions 171 6-2-6 Hydrogen Bonding 174 6-2-7 Electronic Spectra (including Charge Transfer) 178 Contents vii 6-3 Hard and Soft Acids and Bases 179 6-3-1 Theory of Hard and Sofi Acids und Bases 183 6-3-2 Quuntitative Measures 187 6-4 Acid and Base Strengih 192 1-Meastrement of Acid-Base Interaction 192 6-4-2 Thermodynamic Measurements 193 6-4.3 Proton Affiniry 194 6-4-4 Acidity and Basicity of Binary Hydrogen Compounds 194 69-45 Inductive Effects 196 6-4-6 StrengthofOxyacids 196 647 Acidity of Cations in Aqueous Solution 197 6-4-8 Steric Effects 199 649 Solvation and Acid-Base Strength 200 6-4-10 Nonaqueous Solvents and Acid-Base Strength 201 6-4-11 Superacids 203 7 THE CRYSTALLINE SOLID STATE 207 7-1 Formufas and Structures 207 7-1-1 Simple Structures 207 2 Structures of Binary Compounds —214 7-1-3 More Complex Compounds 218 7-1-4 Radius Ratio 218 7-2. Thermodynamies of Ionic Crystal Formation 220 7-2-1 Lattice Energy and Madelung Constant 220 722 Solubility Jon Size (Large-Large and Small-Smatl), and HSAB. 222 7-3 Molecular Orbitals and Band Swucture 223 7-3-1 Diodes. The Photovoltaic Effect, and Light-Emitting Diodes 226 7-4 Superconductivity 228 741 LowTemperature Superconducting Alloys 228 The Theory of Supercondactivity (Cooper Puirs) 229 7-4-3 High-Temperature Superconduciors (YBazCu 307 and Related Compounds) 230 7-5 Bonding in lonic Crystals 231 7-6 Imperfections in Solids 231 7-7 Silicates 232 8 CHEMISTRY OF THE MAIN GROUP ELEMENTS 240 8-1 General Trends in Main Group Chemistry 241 84.1! Physical Properiies 241 8-1-2 Electronegativity 243 8-4-:3 To ion Energy 244 8-1-4 Chemical Properties 244 =2— Hydrogen 24 8-2-1 Chemical Properties 248 8-3 Group | (IA): The Alkali Metals 249 8-3-1 The Elements 249 8-3-2 Chemical Properties 250 8-4. Group 2 (A The Alkaline Earihs 253 841 The Elements 253 842 Chemical Properties 254 viii Contents 8-5 Group 13-(HtA) -—256 8-5-4 The Elements 256 gs Other Chemistry of the Group 13 (THA) Elements 260 8-6 Group l4(IVA) 261 8-6-] The Elements 261 8-6-2 Compounds 267 8-7 Ciroup IS(VA) 272 8-7-1 The Elements 272 8-7-2 Compounds 274 8-8 Group ló (VIA) 279 8-8-/ The Elements 279 -9 Group I7(VIIA): The Halogens 8-9-1 The Elements 285 8:10 Group 18 (VIENA): The Noble Gases —291 8-10-1 The Elemenis 291 8-10-2 Chemistry 292 9 €OORDINATIONCHEMISTRY | STRUCTURESAND 10 ISOMERS 299 9.1 History 299 9-2 Nomenclature 304 9-3 Isomerism 309 9-3.! Stereoisomers 310 Four-Coordinate Complexes 310 Chirality 37! Six-Coordinate Complexes 311 Combinations of Chelate Rings 375 Ligand Ring Conformation 318 Constitutional Isomers 319 9.3.8 Experimental Separation and Identification of Isomers 322 9-4 Coordination Numbers and Structures 323 94.1 Low Coordination Numbers (CN = 1,2, and3) 325 9-4-2 Coordination Number 4 327 9-4-3 Coordination Number 5 328 Coordination Number 6 329 Coordination Number 7. 33! Coordination Number 8 332 Larger Coordination Numbers 333 COORDINATION CHEMISTRY |l: BONDING 337 10-1 Experimenta! Evidence for Electronic Structures 337 10-1-1 Thermodynamic Data 337 10-1-2 Magnetic Susceptibility 339 10.1-3 Electronic Spe 342 10-1-4 Coordination Nembers and Molecular Shapes 342 10-2 Theories of Electronic Structure 342 10-2-4 Terminology 342 10-2-2 Historical Background 343 10-3 Ligand Field Theory 345 10-3-] Molecular Orbitals for Ociahedra! Complexes 345 10-3-2 Orbital Splitting and Electron Spin 346 10-3-3 Ligand Field Stabilization Energy 350  Contents XÍ 14-3-6 Olefin Metathesis 344 14-4 Heterogeneous Catalysts 548 14-4-1 Zicgler-Natia Polymerizations 548 14-4-2 Water Gas Reaction 549 ORGANOMETALLIC CHEMISTRY 556 15-1 Main Group Paralleis with Binary Carbony] Complexes 556 15-2 The Isolobal Analogy 558 15-2-1 Extensions of the Analogy 561 15-2-2 Examples of Applications of the Analogy 565 15-3 Metal-Metal Bonds 566 15-3-1 Multiple Metal-Metal Bonds 568 15-4 Cluster Compounds 572 15-4-1 Boranes 572 15-4-2 Heteroboranes 577 15-4-3 Metalluboranes and Metallacarboranes 579 15-4-4 Carbonyl Clusters 582 15-4-5 Carbide Clusters 587 15-4-6 Additional Comments on Clusters 588 16 BIOINORGANIC AND ENVIRONMENTAL CHEMISTRY 594 16-1 Porphyrins and Related Complexes 596 J6-1-1 tron Porphyrins 597 16-1-2 Similar Ring Compounds 600 16-2 Other Tron Compounds 604 16-3 Zinc and Copper Enzymes 606 16-4 Nitrogen Fixation 611 16-5 Nitric Oxide 616 16-6 Inorganic Medicinal Compounds 618 16-6-1 Cisplatin and Related Complexes 618 16-6-2 Auranofin and Arthritis Treatment 622 16-6-3 Vanadium Complexes in Medicine 622 +6- Study ft DNA Usine Em ganic Ag: pt 622 16-8 Environmental Chemistry 624 16-8-1 Metals 624 16-8-2 Nonmetals 629 APPENDIX A ANSWERS TO EXERCISES 637 APPENDIX B-1 APPENDIX B-2 IONIC RADII 668 JONIZATION ENERGY 671 — APPENDIX B-3 ELECTRONAFFINITY 672 APPENDIX B-4 APPENDIX B-5 APPENDIX B-6 APPENDIX B-7 APPENDIX C APPENDIX D ELECFRONEGATIVITY 673 ABSOLUTE HARDNESS PARAMETERS 674 Ca, Eu, Cp, AND Ep VALUES 675 LATIMER DIAGRAMS FOR SELECTED ELEMENTS 676 CHARACTER TABLES 681 ELECTRON-DOT DIAGRAMS AND FORMAL CHARGE 691 INDEX 697  11 WHAT IS INORGANIC CHEMISTRY? CONTRASTS WITH ORGANIC CHEMISTRY I£ organic chemistry is defined as the chemistry of hydrocarbon compounds and their derivatives, inorganic chemistry can be described broadly as the chemistry of “every- thing else” This includes all the remaining elements in the periodic table, as well as car- bon, which plays a major role in many inorganic compounds. Organometallic chemistry, a very large and rapidly growing ficld, bridges both areas by considering compounds containing direct melal-carbon bonds, and includes catalysis of many or- game reactions. Bioinorganic chemistry bridges biochemistry and inorganic chemistry, Y includes the study of both inorganic and organic com- pounds. As can be imagine thc inorganie rcalm is extremely broad, providing essen- lially limitless areas for investigation. areas, single, double, and triple covalent bonds are found, as shown in Figure 1-1; [or inorganic compounds, these include direct metal-metal bonds and metal-carbon bonds. However, although the maximum number of bonds between two carbon atoms is three, there are many compounds containing quadruple bonds betwcen metal atomis. kn addition to lhe sigma and pi bonds common in organie chemistry, quadruply bonded metal atoms contain a delta (8) bond (Figure 1-2); a combination of onc sigma bond, two pi bonds, and onc delta bond makes up the quadruple bond. The delta bond is possible in these cases because metal atoms have d orbitals to use in bonding, whercas carbon has only-s and p orbitals available. In organic compounds, hydrogen is nearly always bonded to a single carbon. In inorganic compounds. especially of the Group 13 (IA) clements, hydrogen is fre- quently encoumtered as a bridging atom between two or more other atoms. Bridging hy- drogen atoms can also occur in metal cluster compounds. In these clusters. hydrogen atoms form bridges across edges or faces of polyhedra of metal atoms. Alkyl groups may also act as bridges in inorganic compounds, a function rarely encountered in or- ganic chemistry (exceptin reaction intermediates). Examples of terminal and bridging hydrogen atoms and alkyl groups in inorganic compounds are shown in Figure 1-3. 2 Chapter 1 Introduction to Inorganic Chemistry Organic Inorganic OxganometalLic o co F—F [Hg—HgP+ [4 0C—Mn—CH, cf c “Ss o H H “ee” 0—0 ç É em; TN o 2 oc A H H . Sc OCHs ó NR; ci qa Cl ” H—C=C—H N=N 08=05 17 “el ci e P- Cl: ai R efa FIGURE 1-1 Single and Multiple Bonds in Organic and Inorganic Molecutes. Deita FIGURE 1-2 Examples of Bondimg interactions: Some of the most striking differences between the chemistry of carbon and that of many other elements are in coordination number and geometry. Although carbon is usu- ally limited to a maximum coordination number of four (a maximum of four atoms bonded to carbon, as in CH4), inorganie compounds having coordination numbers of tive, six, seven, and more are very common; the most common coordination geometry is an oetahedral arrangement around a central atom, as shown for [TiFG]”" in Figure 1-4.  1-3 Genesis of the Elements (the Big Bang) and Formation ofthe Earth 5 and solubility relations, also interest analytical chemists. Subjects related to structure determination, spectra, and theories of bonding appeal to physical chemists. Finally, the use of organometaltic catalysts provides a connection to petroleum and polymer chem- 1.3 istry, and the presence of coordination compounds such as hemoglobin and metal-con- taining enzymes provides a similar tie to biochemistry. This list is not intended to describe a fragmented field of study, but rather to show some of the interconnections between inorganic chemistry and other fields of chemistry. The remainder of this chapter is devoted to the origins of imorganic chemistry, from the creation of the elements to the present. K is a short history, intended only to provide the reader with a sense of connection to the past and with a means of putting some of the topics of inorganic chemistry into the context of larger historical events. Tn many later chapters, a brief history of each topic is given, with the same intention. Al- though time and space do not allow for much attention to history, we want to avoid the impression that any part of chemistry has sprung full-blown from any one person's work or has appeared suddenty. Although certain events, such as a new thcory or a new type of compound or reaction, can later be identitied as marking a dramatic change of direction in inorganie chemistry, all new ideas are built on past achievements. In some cases, experimental observations from the past become understandable in the light of new theoretical developments. In others, the theory is already in place, ready for the new compounds or phenomena that it will explain. We begin our study of inorganic chemistry with the genesis of the elements and the GENESIS OF THE ELEMENTS (THE BIG BANG) AND FORMATION OF THE EARTH creation of the universe. Among the difficult tasks facing anyone who attempts to explain the origin of the universe are the inevitable questions: “What about the time just before the creation? Where did the starting material, whether energy or matter, come from?” The whole idea of an origin at a specific time means that there was nothing before that instant. By its very nature, no theory attempimg to explain the origin of the universe can be expected to extend infinitely far back in time. Current opinion favors the big bang theory! over other creation theories, although many controversial points are yet to be explained. Other theories, such as the steady- state or oscillating fheories, have their advocates, and the creation of the universe is cer- taim to remain a source of controversy and study. According to the big bang theory, the universe began about 1.8 X 101º years ago with an extreme concentration of energy in a very small space. In fact, extrapolation back to the time of origin requires zero volume and infinite temperature, Whether this is true or not is still a source of argument. What is abmost universally agreed on is that the universe is expanding rapidky, from an initial event during which neutrons were formed and decayed quickly (half-life = 11.3 min) into protons, electrons, and antineutrinos: n—>> pre +» or n—> H- Sfe+z In this and subsequent equations, 1H = p = a proton of charge +1 and mass 1,007 atomic mass unit (amu)? Y = a gamma ray (high-energy photon) with zero mass Ip A Cox, The Elements, Their Origin, Abundance and Distribution, Oxford University Press, Ox- ford, 1990, pp. 66-92: T. Selbin, J. Chem. Edue., 1973, 50, 306, 380; A. A. Penzias, Science, 1979, 105, 549. “More accurate masses are given inside the back cover of this t 6 Chapter 1 Introduction to Inorganic Chemistry Se=e" = am electron of charge —1 and mass ma amu (also known as a B particle) Je =: e! = a positron with charge +1 and mass aa amm a neutrino with no charge and a very small mass Ve = an antineutrino with no charge and a very small mass dn = a nentron with no charge and a mass of 1.009 amu Nuclei are described by the conventiou mass number. SS mb symbol or Proto plus neutrons nholear charge SY INDO! After about | second, the universe was made up of a plasma of protons, neutrons, electrons, neutrinos, and photons, but the temperature was too high to allow the forma- tion of atoms. This plasma and the extremely high energy caused fast nuclear reactions. As the temperature dropped to about 10º K, the following reactions occurred within a matter of minutes: H+n—= H+Hy 2H + 2H + ly 1 f T “1 MH +3H —> 3He + do He + — jHe + Y The first is the Himiting reaction because the reverse reaction is also fast. The in- terplay of the rates of these reactions gives an atomic ratio of He/H = 1/10, which is the abundance observed in young stars. By this time, the temperature had dropped enough to allow the positive particles to capture electrons to form atoms. Because atoms interact Jess strongly with electromag- netic radiation than do the individua! subatomic particles, the atoms could now interact with each other more or less independent!y from the radiation, The atoras began to con- dense into stars, and the radiation moved with the expanding universe. This expansion caused a red shift, leaving the background radiation with wavelengths in the millimeter range, which is characteristic of a temperature of 2.7 K. This radiation was observed im 1965 by Penzias and Wilson and is supporting evidence for the big bang theory. Within one half-life of the neutron (11.3 min), half the matter of the universe con- sisted of protons and the temperature was near 5 X 108 K. The nnetei formed in the first 30 to 60 minutes were those of deuterium CH), He, “He, and “He. (Helium 5 has a very short half-life of 2 X 1072! seconds and decays back to helium 4, effectively limiting the mass number of the nuclei formed by these reactions to 4.) The following reactions show how these nuclei can be formed in a process called Aydrogen burning: maria > JH +92 + me WH+HlH— JHe + 9 He + jHe —> 3He + 24H The expanding material from these first reactions began to gather together into galactic clusters and then into more dense stars, where the pressure of gravity kept the  1.3 Genesis of the Elements (the Big Bang) and Formation ofthe Earth 7 temperature high and promoted further reactions. The combination of hydrogen and he- lium with many protons and neutrons led rapidly to the formation of heavier elements. In stars with internal temperatures of 10” to 108 K, the reactions forming 2H, “He, and “He continued, along with reactions that produced heavier nuclei, The following hetium-burning reactions are among those known to take place under these conditions: 23He —> Be + y He + Be — MC + y te+iH—> JN — Bor tferm In more massive stars (temperatures of 6 X 108 K or higher), the carbon-nitrogen cycle is possible: Ee+H—S EN +y BN — liC+fe+ ve CHiH = !N ty nN+ia > Ro +y Ú Ro —> BN + fe + UN + da ——> die + e The net result of this cycle is the formation of helium from hydrogen, with gamma rays, positrons, and neutrinos as byproducts. In addition, even heavier elements are formed: Rc + RC — Ne + He 2 o —> si + lhe 2 o — ils + bn At still higher temperatures, further reactions take place: : i i É É y+ Us — Mg + iHe Bs; + He — BS + ts + dHe — Bar + q Even heavier elements can be formed, with the actual amounts depending on a complex relationship among their inherent stability, the temperature of the star, and the Nifetime of the star, The curve of inherent stability of nuclei has a maximum at JéFe, ac- e mo o . «e reactions con- tinued indefinitely, the result should be nearly complete dominance of elements near iron over the other elements. However, as parts of the universe cooled, the reactions slowed or stopped. Conseguently, both lighter and heavier elements are common. For- mation of elements of higher atomic number takes place by the addition of neutrons to anuclens, followed by electron emission decay. In environments of low neutron densi- ty, this addition of neutrons is relatively slow, one neutron at a time; in the high neutron density environment of a nova, 10) to 15 neutrons may be added in a very short time, and the resulting nucleus is then neutron rich: Xre + 134 —» GFe — fico + Se 10 Chapter 7 Introduction to inorganic Chemistry explanation of geology. There is also general agreement that the Earth has a core of iron and nickel, which is solid at the center and liquid above that, The outer half of the Earth's radius is composed of silicate mincrals im the mantle, siticate, oxide, and sulfide minerals in the crust; and a wide variety of materials at thc surface, including abundant water and the gascs of the atmosphere. The different types of forces apparent in the early planet Earth can now be scen indircety in lhe distribution of minerals and elements. In locations whcrc liquid magma brokce through the crust, compounds that are readily solubte in such molten rock werc carried along and deposited as ores. Fractionation of the mincrals then depended on their melting points and solubilitics in the magma. In other locations, water was the sourec of the formation of ore bodies. At lhese sites, water leached mincrais from the nding nd later evaporated, leaving the minerals behind, The solubilities of the mincrals in cither magma or water depend on the elements, their oxidation states, and the other clements with which they are combined. A rough division of the elements can be made according to their ease of reduction to the clement and their combination wilh oxygen and sulfur. Siderophiles (iron-loving ciements) concentrate in the metalhic core. Hithophiles (rock-loving clements) combine primarily with oxygen and the halides and are more abundamt in the crust, and chaleophiles (Greek, Ahalkos, coppcr) com- bine more readily with sulfur, selenium, and arsenic and are also found in the crust. Atmophiles are present as gases. These divisions are shown in the pertodic table in Figure 1-9. As an example of the action of water, we can explain the formation of bauxite (hydrated Aly0s) deposits by the leaching away of lhe more soluble salts from alumi- nosilicate deposits. The silicate portion is soluble enough in water that it can be Icachcd away, leaving a higher concentration of aluminum. This is shown in the reaction + aluminositicate higher concentration silicate of Al (leached away) 1 2 3 á 5 6 7 8 9 10 n 12 13 14 15 16 7 18 TA HA THB IVB VB VIB VIB VIIB IB FB IA IVA VA VIA VIA VIHA r=-—— emu igi Hei Both Tithophile | Atmophiles and chalcophile Lithophiles Siderophiles ; “| Chalcophiles & Including tanthauides Ce tbrough Tu * Enclading acrinides Th. LU FIGURE 1-9 Geochemical Classification of the Elements. (Adaptod with permission from PA Cox, The Elements. Their Origin, Abundunce, and Distribution. Oxford University Press, Oxford, 1990. p. 13) 1-6 The Histary of Inorganic Chemistry in which HySiO4 is a generic representatios for a number of soluble silicate species. This mechanism provides at least a partial explanation for the presence of bauxite de- posits m tropical areas or in areas that once were tropical, with large amounis of rainfall in the past. Further explanations of these geological processes must be left to more special- ized sonrces.º Such explanations are based on concepts treated later in this text. For example, modern acid-base theory helps explain the different solubilities of minerals in water or molten rock and their resulting deposits in specific locations. The divisions iltustrated in Figure 1-9 cam be partly explained by this theory, which is discussed in Chapter 6 and used im later chapters. E Fr a subj study; ical reactions were used THE HISTORY OF and the products apptied to daily life. For example, the first metais used were probabty INORGANIC gold and copper, which can be found in the metallic state, Copper can also be readily CHEMISTRY formed by the reduction of malachite—basic copper carbonate, Cu(CO;)(OH),—in charcoal fires. Silver, tin, antimony, and lead were also known as early as 3000 Rc. Iron appeared in classical Greece md in other areas around the Mediterranean Sea by 1500 pc. At about the same time, colored glasses and ceramic glazes, largely composed cf silicon dioxide (SiO,, the major component of sand) and other metallic oxides, which had been melted and allowed to cool to amorphous solids, were introduced. Alchemists were active in China, Egypt, and other centers of civilization early in als into gold, the treatises of these alchemists also described many other chemical reac- tions and operations. Distillation, sublimation, crystallization, and other techniques were developed and used in their studies. Becanse of the political and social changes of the time. alchemy shifted into the Arab world and later (about 1000 to 1500 ab) reap- peared in Europe. Gunpowder was used in Chinese fireworks as early as 1150, and alchemy was also widespread in China and India at that time. Alchemists appeared in art, literature, and science until at least 1600, by which time chemistry was beginning to take shape as a science. Roger Bacon (1214--1294), recognized as one of the first great experimental scientists, also wrote extensively about alchemy. By the 17th century, the common strong acids (nitric, sulfuric, and hydrochioric) k andem ystematie-deseriptions-of-common-salts-and-their -reactron: were being accumulated. The combination of acids and bases to form salts was appreci- ated by some chemists. As experimental techniques improved, the quantitative study of chemical reactions and the properties of gases became more common, atomic and mol- ecular weights were determined more accurately, and the groundwork was laid for what later became the periodic table. By 1869, the concepts of atoms and molecules were well] established, and it was possible for Mendeleev and Meyer to describe different forms of the periodic table. Figure 1-10 illustrates Mendeleev's original periodie table. The chemical industry, which had been in existence since very early times in the S amd refinimeg = panded as methods for the preparation of relatively pure materials became more com- mon. In 1896, Becquerel discovered radioactivity, and another area of study was opened. Studies of subatomic particles, spectra, and electricity finally led to the atomic theory of Bohr in 1913, which was soon modified by the quantum mechanics of Schrôdinger and Heisenberg in 1926 and 1927. $3, E. Ferguson. norganic Chemistry and he Earth, Pergamon Press, Tlmslord, NY. 1982; 1. E. Fer- gusson, The Heavy Elements. Pergamon Press, Elmsford, NY, 1990.  tr=90 Nb=94 Mo=96 186 Mn = Rh= 104,4 PL= 1974 Fe=56 Ru= 04.2 Tr= 198 Ni=Co=59 Pa =106.6 Os = 199 W=1 Cu=634 Ag=108 Hg =200 Mg=24 Zu=652 Có=n2 7=68 Ur= 16 Au= 197? 1=70 Sn=1I8 As=75 Sb=122 Bi=210? Se= 79,4 Te= 128? €1=355 Br=80 J=127 Hi= K=39 Rb=85.4 TL=204 Sr=876 Ba=137 Pb=207 FIGURE 1510 Mendeleev's 186 Ce=9" Periodic Table. Two years later, be La=94 revised his table into a Form similar Di=95 to a modem short-form periodic Ma=756 = 1182 table, wilh eight groups across. Inorganic chemistry as a field of study was extremely important during the carty years of the exploration and development of mineral resources. Qualitative analysis methods were developed to help identify mincrals and, combined with quantitative methods, to assess their purity and value. As the industrial revolution progressed, so did nitric acid, sulfuric acid, sodium hydroxide, and many other inorganic chemicals pro- duced on a large scale were common, Tn spite of the work of Werner and Jergensen on coordination chemistry near the beginning of the 20th century and the discovery of a number of organometallic com- pounds, the popularity of inorganic chemistry as a field of study gradually declined dur- ing most of the first half of the century. The need for inorganic chemists to work on military projects during World War TI rejuvenated interest in the field. As work was done on many projects (not least of which was lhe Manhattan Project, in which scien- tists developed the fission bomb that later led to the development of the fusion bomb), new areas of research appeared, old arcas were found to have missing information, and new theories were proposed that prompted further experimental work. À greaí expan- sion of inorganic chemistry started in the 1940s, sparked by the enthusiasm and ideas generated during World War EL in the 1950s, an carlier method used to describe lhe spectra of metal ions sur- rounded by negatively chargedions in crystals (crystalHield theory)? was extended by the use of molecular orbital theoryº to develop ligand field theory for use in coordina- tion compounds, in which metal ions are surrounded by ions or molecules that donate electron pais. This thcory, explained in Chapter 10, gave a more complete picture of the bonding in these compounds. The ficld developed rapidly as a result of this theoretical framework, the new instruments developed about this same time, and the generally reawakened interest in inorganic chemistry. 19 1955, Ziegler” and associatos and Natta!º discovered organometallic com- ponnds that could catalyze the polymerization of cthylene at lower temperatures and “H.A. Bethe, Ann. Physik, 1929, 3, 133. 37.8. Griffith and L. E. Orgel, Q. Rev Chem. Soc., 1957, XT. 381. PK. Ziegler, E. Holzkamp, H. Becil, and H. Martin, Angew Chem, 1958, 67, 54. “iG, Narta, J. Potym. Sci., 1955, 16. 143.  “HISTORICAL DEVELOPMENT OF ATOMIC THEORY The theories of atomic and molecular structure depend on quantum mechanics to de- mechanies require considerable mathematical sophistication, it is possible to under- stand the principles involved with only a moderate amount of mathemarics. This chap- ter presents the fundamentals needed to explain atomic and molecular structures in qualitative or semiquantitative terms. Although the Greek philosophers Democritus (460-370 Bc) and Epicurus (341270 Ec) presented views of nature that included atoms, many hundreds of years passed before experimental studies could establish the quantitative relationships needed for a coherent atomic theory. ln 1808, John Dalton published A New System of Chemical Philosophy, ! im which he proposed that . lhe ultimate particles of all homogeneous bodies are perfectly alike in weight, figure, etc. In other words, every particle of water is like every other particle of water, every parti- . 3 and that atoms combine in simple numerical ratios to form compounds. The terminolo- &y he used has since been modified, bnt he clearly presented the ideas of atoms and molecules, described many observations about hear (or caloric, as it was called), and form new compounds. Because of confusion about elemental molecules such as H> and O», which he assumed to be monatomic H and O, he did not find the correct formula for water. Dalton said that "Foha Dalton, À New System of Chemical Philosophy, 1808; reprinted with an TERÃO by Alexan- der Joscph, Peter Owen Limitod, London, 1965. Ibid, po 113 arco. a sas 15  T6 chapter? Atomicsiucture en HO Me: f gen a ixed; a - lric sparke, the whole is converted into steam, and if he pressure be great, Lhis stcam be- is the same number of particles in two measures of Tydrogen as in one of oxygen different gases: At the time T formed the thcory of mixed gases, Lhad a confused idea, as many have, I sup- pose, at this time, that the partícles of elastic fluids are all of lhe same size; thala given vol- ume of oxygcnous gas contains jusras many particies as the same votume of iydrogenous: vrií nol, that we had no data from which the question could be solved.... 1 |Iaterl became conyinc! i E i í lobular and all of à size; but that no two species agree in the size Ol Lheir arielos, the pressure and tempera- ture boing the same. 4 Only a few years later, Avogadro used data from Gay -Lussae to argue that equal E gas-atrequaHemperatares and-press raia th umber of mol olumes o! cules, but uncertainties about the nature of sulfur, phosphorus, arsenic, and mercury va- x : weights and molecutar “orimalas contributed to the delay-i in 1861, Kekulé gave 19 different possible formulas for acetic acid!é In the 18508, Cannizzaro revived the argument of Avogadro and argued that everyone should use the same set of atomic weights rather than the many different seis then being used. At à meeting in Karlsruhe in 1860, he distributed a pamphlet describing his views.” His proposal was eventually accepted, nd a consistent setof atomic weights and formulas gradually evolvi ed. In 1869, Mendeleev” and Meyer independently proposed periodic tables the development of atomic theory progressed rapidiy. 2-1-1 THE PERIODIC TABLE The idea of arranging the elements into a periodie table had been considered by many schemes were incomplete. Mendeleey and Meyer organized the elements im order of atomic weight and then identified families of elements with similar properties. By ar- ranging these families in rows or columns, and by considering similarities in chemicat behavior as well as atomie weight, Mendeleev found vacancies in the table and was able to predict the properties of several elements (gallium, scandium, germanium, polonium) that had not yet been discovered. When his predictions proved accurate, the concept of a periodic table was quickly established (soe Figure 1-10). The discovery of additional elements not known in Mendeleev's time and the synthesis of heavy elements have led In the modern periodie table, a horizontal row of elements is called a period, and United States difter from those used in Europe. The international Union of Pure and Applied Chemistry (IUPAC) has recommended that the groups be numbered | through 18, a recommendation that has generated considerable controversy. in this text, we will 2ybiel.. p. 133 “pie, pp. 144148. SIR. Partingion, 4 Shows Hiszory 0/ Chemistry. 31d ed. Macmillan, London, 1957; Feprmted, T960, Harper & Row, New York, p. 255 Sid, pp 2564 *D. L Mendeleev, 1. Russ. Phys. Chem. Soc.. 1869, é, 60, SL. Meyer, Justus Licbigs Ann. Chet. 1870, Suppl vii. 354, 2-1 Historical Development of Atomic Theory 17 Groups (American wadition) la DA MB IVB VB VIB VUR VIIB lB NB TA IVA VA VIA VHA VIA Groups (European traditiom IA JA JA IVA VA VIAVIIA VEL IB JB WB IVB VB VIBVIIB O Groups (IUPAC) 1 2 3 4 5 & 7 8 9 10 dl 12 13 14/15 46 47/18 2 3 Transition metals 5 10 Ê " iêle = - Tr it E E|u zu a t30 [31 Ss] ê E g elstel a z ETÊ o|39 40 i Flag ia U E o ss | & + [72 z ss [57 n Em [e 86 87 89 | ++ [104 “ju T T T * | 58 | Lanthanides | n + , = FIGURE 2-1 Names for Parts of = [00 | Acúnidos toã the Periodic Table. Ds use the FUPAC group numbers, with the traditional American numbers in parentheses. Some sections of the periodic table have traditional names, as shown in Figure 2-1. 2-1.2 DISCOVERY OF SUBATOMIC PARTICLES AND THE BOHR ATOM During the 50 years after the periodie tables of Mendeleev and Meyer were proposed, experimental advances came rapidly. Some of these discoveries are shown in Table 2-1. Parallel discoveries in atomic spectra showed that each element emits light of specific energies when excited by an electric discharge or heat. In 1885, Balmer showed that the energies of visible light emitted by the hydrogen atom are given by the equation t 1 ERAS do q) TABLEZI so Discoveries in Atomic Structure :. : 1896 AH. Becquerel Discovered radionctivity of uranium 1897 J.J. thomson Shoswed that electrons have a nogative charge, with charge/mass = 1.76 x 10! C/kg 190) RA Million Meusured the electronic charge (60x 10-C3 therefore the mass of f 1836 J911 E Rutherlord Established lhe muclear model of the atom (very small, heavy nucleus sutrounded by mostly empty space) 1913 HG. 3 Moseley — Determined nuclear charges by X-ray emission, establishing atomic numbers as more fundamental than atomic masses the electron is 9.11 x 1073! kg, = of the mass of the H atom 20 chapter? Atomic Suucture Quantum Number 6 5 4 Paschen series UR) Balmer series (visible transitions shown) Lyman series (UV) FIGURE 2-2 Eydrogen Atom Fnergy Levels  2-2 THE SCHRÓDINGER EQUATION 2-2 The Schrôdinger Equation 21 between lhe inherent unceriainties in the location and momentum of an electron moving in lhe x direction: àx dp, = = where à« = uncertainty in the position of the electron àp, = uncertainty in the momentum of the electron The energy of spectral lines can be measured with great precision (as an example, the Rydberg constant is known to 11 significant figures), in turn allowing precise deter- mination of the energy of electrons in atoms. This precision in energy also implies preci- sion in momentum (Ap, is small); lherefore, according to Heisenberg, there is a large uncertainty in the location of the electron (Áx is large). These concepts mean thal we cannot treat electrons as simple particles with their motion described precisely, but we must instead consider the wave properties of electrons. characterized by a degree of un- certainty in their location. In other words, instead of being able to describe precise orbits af clectrons, as in the Bohr theory, we can only describe orbitais, regions that describe the probable location of etectrons. The probability of finding the electron at a particular point in space (also called the electron density) can be calculated, at least in principle. In 1926 and 1927, Schridinger!” and Heisenberg”? published papers on wave mechanics (descriptions ol the wave properties of electrons in atoms) that used very different malhematical techniques. In spite of the different approaches, it was soon shown that their lheories were equivalent. Schridinger's differential equations are more commonly used to introduce the theory, and we will follow that practice. The Schrôdinger equation describes lhe wave propertes of an electron in terms of its position, mass, total energy, and potential energy. The equation is based on lhe wave function, *P, which describes an electron wave in space; in olher words, it describes an atomic orbital. En its simplest notation, the equation is HF = EW where H = the Hamiltonian operator E = energy of the electron *P = the wave function The Hamiltonian operator (frequently just called the Hamiltonian) includes de- rivatives that operate on the wave function. When the Hamiltonian is carried out, the result is a constant (the energy) times “P, The operation can be performed on any wave function describing an atomic orbital. Different orbitals have different W functions and different values of E. This is another way of describing quantization in that each orbital, characterized by its own function "FP, has a characteristic energy. “E. Schródinger. Amp, Phys. (Leipzig), 1926, 79, 361, 489, 734: 1926, 80. 437: 1926. 87. 109; issenshafien, 1926, 14, 664; Phys. Rev, 1926. 28, 1049. !24m operator is an instruction or set of instructions lhat states what to do with Lhe function that fol- Jews it, Lay De a simple instruction such as “malhiply the following function by 6? or it may be much more vomplicated than the Hamiltonian. The Hamiltonian operator is sometimes written H, with the ” (hat) symbol designating am operator. Natur  22 Chapter 2 Atomic Structure Tn the form used for caleulating energy levels, the Hamikonian operator is . Ze? AJ fas 2 4meg Va + pó gr This part of the operator describes sh This part of the operator describes the kinetic energy of the electron potential energy of ihe electron, the result of electrostatic attraction between the clectron and the nueleus. Tt is commonty designated asF where A = Planck's constant s ! = mass of lhe particle (electron) charge of the electron distance from the nucleus mN H charge of the nucleus 4mep = permittivity of a vacuum When this operator is applied to a wave function “F, r 5 = eu | ô where V= =— 4meor I + Verne) pa 2) = EF (xyz) The potential energy V is a result of electrostatic attraction between the electron and the nucleus. Atractive forces, like those between a positive nucleus and a negative electron, are defined by convention to have a negative potential energy. An electron near fhe-nucleus (small) is-stronglsy atiracted to the nucleus and has a large negative poten- tial energy. Electrons farther from the nucieus have potential energies that are small and negative, For an electron at infinite distance from the nucleus (» = 90), the attraction between the nucleus and the electron is zero, and the potential energy is zero. Because every “E matches an atomic orbital, there is no limit to the number of so- lutions of the Schródinger equation for an atom. Each W describes the wave properties of a given electron in a particular orbital, The probability of finding an electron at a given point in space is proportional to W?. A number of conditions are required for a physicalky realistic solution for W: 1. The wave function Y mustbe sin- | There cannot be two probabilities for gle-valued. an electron at any position in space. 2. The wave function “VP andits first The probability must be defined at all derivatives must be continuous. positions in space and cannot change abraptly from one point to the next. 3. The ave function Y must ap- For large distances from the nuciens, smaller (the atom must be finite).  2-2 The Schrôdinger Equation 25 Particle in a box 24 y2 Wave function Y aa Partcie in box n=2 Wave function F ada Particle in a box n=] Wave function 'P E E FIGURE 2-4 wave Functions and Their Squares for the Particle in a Boxwithr = 1,2, and 3. The resulting wave functions and their squares for the first three states (the ground stare and first two excited states) are plotted im Figure 2-4. The squared wave functions are the probability densities and show the difference between classical and quantum mechanical behavior. Classical mechanics predicts that the electron has equat probability of being at any point in the box. The wave nature in the box, 2-2-2 QUANTUM NUMBERS AND ATOMIC WAVE FUNCTIONS The particle in a box example shows how a wave function operates in one dimension. Mathematicaliy, atomic orbitals are discrete solutions of the lhree-dimensional Schrôdinger equations. The same methods used for the one-dimensional box can be expanded to three dimensions for atoms. These orbital equations include three 26 Chapter 2 Atomic Structure guantum numbers, x, £ and my. A fourth quantum number, 42,, à result of relativistic corrections to the Schródinger equation, completes the description by accounting for the magnetic moment of the electron. The quantum numbers are summarized in Tables 2-2, 2-3, and 2-4. TABLE 2-2 Quantum Numbers and Their Properties Symbol Name Values Role n Principal Determines the major part of the energy 1 Angular momento O LZ sn! Deseribes angular dependence and cuntribuies to the energy m Magnetic 0,41, 42.044 Describes oxjentarion in space tangular momentum in the z ditection) 1 m, Spin E Describes orientation of the electron spin (magnetic momest) in space Orbitals with diflerent / values are known by the [oltowing labels, derived from early terias [or different families of spectroscopic lines: ! 9 1 2 a 4 8... Label s p d f K continuing alphabeticully TABLE 2-3 Hydrogen Atom Wave Functions: Angular Functions Angular factors Real wave functions Reluted 10 Functions In Polar in Caresian —— angular momentum afo coordinates coordinates Shapes Label 1 mos o Bd(a. 4) OB(x,9,2) l 1 05) O - , V2m va | - KB) o = — cos O vV2m Lo, 3 +1 = > Ssinê V2m + 3 + Ud) O > (3 cos? 6 — 1) 5 -1 cos O sin 6 vs S - > cosbsind =2 “DS ano J 5 : Source: Adapted from G. M. Burrow, Physical Chemistry, Sth ed., McGraw-Hill. New York, 1988, p. 450, with permission. ih — pib Norr: The relations (e 2) = sin d and (e + e “º)/2 = cos & can de used to convert (he exponential inaginary functions to real trigomomere functions, combining the ewa orbitals with 2mg = 1 10 give two onbitals vita sin d and cos q In a similar fashion, the orbitals with mm; = +2 resull in real functions with cos? 4 and sin? é. These functions have then been converted to Cactesian form by using the functions = rsinôcos dy = rsinBsind,andz = rcos A  2-2 The Schrôdinger Equation 27 TABLE 2-4 Hydrogen Atom Wave Functions: Radial Functions Radial Functions R(r). with o = Zrjay Orbital n t 15 1 o - 2 2 0 2» 1 35 3 2 3p t ad 2 Ryu = = [Eae vs 8INásL ao The fourth quantum number explains several experimental observations. Two of these observations are that lines in alkali metal emission spectra are doubled, and that a beam of alkali metal atoms splits into two parts if it passes through a magnetic field. Both of these can be explained by attrihuting a magnetic moment to the electron; it be- haves like a tiny bar magnet. This is usually described as Lhe spin of the electron b cause à spinning electrically charged particle also has a magnetic moment, but it should not be taken as an accurate description; it is a purely quantum mechanica] property. The quantum number « is primarily responsible for determíning the overall energy of an atomic orbital; the other quantum numbers have smaller effects on the energy, The quan- tum number ? determines the angular momentum of the orbital or shape of the orbital and has a smaller cffect on the energy. The quantum number 7x, determines the orientation of the angular momentum vector in a magnetic Geld, or the position of the orbital in space, as shown in Table 23, The quantum number 1 ni, determines the orientation of the electron e or opposed to iu(-: 5 When no feidi is pr esent, all my values (all three p orbitais or all five d orbitals) have te same energy and bolh m, values have the same encrgy. Together, the quantum numbers 2, |, and my define an atomic orbital; the quantum number 4, describes the electron spin wilhin the orbital. o One feature that should be mentioned is the appearance of i (= V=1) in the p and d orbital wave equations in Table 2-3, Because it is much more convenient to work with real functions than complex functions, we usually take advantage of another prop- erty of the wave equation. For differential equations of this type, any linear combination of solutions (sums or differences of the functions, with each multiplicd by any coefti- cient) to the equation is also a solution to the eguation. The combinations usually cho- sen for the p orbitals are the sum and difference of the p orbitals having mp = +1 and 1 —1, normatized by multiplying by the constants —= and —=, respectively: voo v2 ER(r)] sin 8 cos | LR(r) sin 0 sin & Ê Wopy = 5a = Wo) = 30 chapter 2 Atomic Structure FIGURE 2-6 Setected Atomic Orbitals, (Adapted with permission from G. O. Spessard and G.1. Miesster, Organomeraltic Chemistry, Premice Hall, Upper Saddle River. NI, 1997, p. 31, Fig.2-1) in order for Y = 0, either R(r) = 0 or Y(6,&) = 0. We can therefore determine nodal surfaces by determining under what conditions R = GorY = 0. Table 2-5 summarizes the nodes for several orbitals, Note that the total number of nodes in any orbital is n — 1 if the conical nodes of some d and f orbitals count as 2, 19 Angular nodes result when Y = 0 and are planar or conical, Angular nodes can be determined in terms of 6 and &, but may be easier to visualize if Y is expressed in UMaihematically, the nodal surface for the d2 orbital is one surface, but in this instance if fits me paltem better if lhought of as two nodes, ua -2 The Schródinger Equation 3 3 E 4 ? E so a nã ad a É 2 É gÊN é E g 5 má E dt Zoo 05 101520253 0 5 1015202530 ray Hay 2 sy 2 é go] E by Radial Wave Functions 2 as É os TI TP Zoo 05 15202530 O 5 101520 2530 ray Hay Is 5 0 É 0 5101520253 Hag 3s 3p 34 6 a 89 as .á dos sos a > ad P4 3 » 3 2 zo 1 Bl 9 PATA TIETE rd TITO TA O 5 1015202530 5 1015 20 25 30 0 5 4015202530 Hay rag Has 25 2p a e Eu & 3 3 Radial Probability Functions 2 E Ê É a ; a TE TA É TOTO ; 5 1015 20 25 30 O 5 101520 25 30 Has rag + Is Probability agrêR? 5 10152025 30 Hay FIGURE 2-7 Radial Wave Functions and Radial Probability Functions  32 Chapter 2 Atomic Structure TABLE 2-5 Nodal Surfates - pherical nodes R(r) Examples (number of spherical nodes) z x Is o 2p o 3d 9 2s 1 3p 1 ad 1 3s 2 4p 2 5d 2 Angular nodes [Y (0,4) = 0] Examples (number of angular nodes) orhitals o p orbitais 1 plane for cach orbital d orbitais 2 planes for each orbital except d;> teonicaisuriace for dz a ap Cartesian (x. ) coordinates (see Table 2-3). In addition, the regions where the wave function is positive and where it is negative can be found. This information will be use- ful in working with molecular orbitals in later chapters. There are / angular nodes in any orbital, with the conical surface in the «2 and similar orbitals counted as two nodes. Radial nodes. or spherical nodes, result when R = 0, and give the atom a lay- ered appearance, shown in Figure 2-8 for the 3s and 3p; orbitals. These nodes occur when the radial function changes sign: they are depicted 1 m he radial function graphs by R(r) = O and in the radial probability graphs by 47/2R? = O. The Is, 2p, and 3d orbitals (the lowest energy orbitals of each shape) have no radial nodes and the number of nodes increuses as n increases. The number of radial nodes for a given orbital is al- ways equalton — 1 — 1, Nodal surtaces can be puzzling. For example, 4 p orbital has a nodal plane through the nucleus. How can an electron be on both sides of a node at the same time without ever having been at the node (at which the probability is zero)? One explanation is that the probability does not go quite to zero. Another explamation is that such a question really has no meaning for an electron thought of as a wave. Recall the parficle im a box example. Figure 2-4 shows nodes at x/a = 05forn = 2 andatx/a = 0.33 and 0.67 for n = 3, The same diagrams could represent the amplitudes of the motion of vibrating strings at the fundamental frequen- cy (n = 1) and multiples of 2 and 3. A plucked violin string vibrates at a specific fre- quency, and nodes at which the amplitude of vibration is zero are a natural result. Zero amplitude does not mem that the string does not exist at these points, but simply that the magnitude of the vibration is zero, An electron wave exists at the node as well as on both sides of a nodal surface, just as à violin string exists at the nodes and on both sides of points having zero amplitude. Still another explanation, in a lighter vein, was suggested by R. M. Fuoss to one of the authors (DAT) in a cl on bonding. Paraphrased from St. Thomas Aguinas, “Angels are not material beings. Therefore, they can be first in one place and later in another, without ever having been im between” Tf the word “electrons” replaces the word “angels” a semitheological interpretation of nodes could result. 20A, Szaho, 1 Chem. Educ., 1969, 46, 678, uses relaúvistic arguments to explain that the electron probablity at a nodal surface has a very small, but fimte, value.  2-2 The Schrôdinger Equation 35 2. The Pauli exclusion principle? requires that each electron in an atom have à unique set of quantum numbers. Aí least one quantum number must be different from those of every other electron. This principle does not come from the Schródinger equation, but from experimental determination of electronic structures. 3. Hund's rule of maximum multiplicity” requires that clectrons be placed in or- bitals so as to give the maximum total spin possible (or the maximum number of parallel spins). Two electrons ín the same orbital have a higher energy than two electrons in different orbitals, caused by electrostatic repulsion (electrons in the same orbital repel each other more than electrons in separate orbitals). Therefore, this rule is a consequence of the lowest possible energy rule (Rule 1). When there are one to six electrons in p orbitals, the required arrangements arc those given in Table 2-6. The multiphicity is the number of unpaired electrons plus |, ora + 1. “This is the number of possible energy levels that depend or the orientation of the net magnetic moment in a magnetic field, Any other arrangement of electrons re- sults in fewer unpaired electrons. This is only one of Hund's rules: others are de- seribed in Chapter 11. TABLE 2-6 Hund's Rule and Multiplicity Number of Electrons Arrangement Unpaired e Multiplicity ! A 1 2 2 E 2 3 3 AAA a 4 4 Ato 1 2 3 5 AS ts to 1 2 6 As ti ty 0 1 This rule is a consequence of the energy required for pairing electrons in the same orbital. When two electrons gecupy the same part of the space around an atom, they repel cach other because of their mutual negative charges with a Coutombie en- ergy of repulsion, IL, per pair of clectrons. As a result, this repulsive force [avors electrons in dilferent orbitals (different regions of space) over electrons in the same orbitals. In addition, there is an exchange energy, II. which arises from purely quantum mechanical considerations. This energy depends on the number of possible exchanges between two electrons with the same energy and the same spin. For example. the electron configuration of a carbon atom is 1522. arrangements of the 2p electrons can be considered: Pp. Three q 1h A + A t The first arrangement involves Coulombic energy, TI.., because it is the only one that pairs electrons in the same orbital. The energy ol this arrangement is higher than that of the other two by TI, as a result of electron-electron repulsion. 2y. Pauli, Z. Plysik, 1925, 31, 765. DF Hund, Z. Physik, 1925, 45. . ad 36 Chapter 2 Atomic Structure Jo the (irst two cases there is only one possible way to arrange the electrons to give the same diagram, because there is only a single electron in each having + or — spin. However, in the third case there are two possible ways in which the elecirons can be arranged: ti 12. to Ato (one exchange of electron) The exchange energy is IL, per possible exchange of parallel electtons and is negative. The higher the number of possible exchanges, the lower the energy. Consequently, the third configuration is lower in energy than the second by IL. The results may be summarized in an energy diagram: Lo. — M + ; Eras | Lit | | | | Io These two pairing terms add to produce the total pairing energy, II: =D + The Coulombic energy, TL.., is positive and is nearly constant for each pair of electrons. The exchange energy, [t., is negative and is also nearly constant for each pos- sible exchange of clectrons with the same spin. When the orbitals are degenerate (have the same energy), both Coulombic and pairing energies favor the unpaired configura- tion over the paired configuration. If there is a difference in energy between the levels involved, this difference, in combination with the total pairing energy. determines the final configuration. For atoms, this usually means that one set of orbitals is filled before another has any electrons. However, this breaks down in some of the transition ele- ments, because the 4s and 3d (or the higher corresponding levels) are so close in ener- gy that the pairing energy is nearly the same as the difference between levels. Section 2-2-4 explains what happens in these cases.  2-2 The Schrôdinger Equation 37 Overall, 2H, + 211. Because IT, is positive and IT, is negative, the energy of the first arrangement is Tower lhan É EXAMPLE : o a 4 as tmomniratelerons (DL to f i xygen With four p electrons, oxygen could have two unpairedelecmons (LD Lo Ts É or il could have no unpaized electrons (1% Tb, Find the number of electrons that É could be exchanged in each case and the Coulombic and exchange energies for the atom. É , bt o? nao pair, energy contribution IL. f ty 2 t . . ua É — — has one electron with | spin and no possibility of exchange p E AO LOL has our possible arangements, three exchange possibilittes (1-2, Ê 1-3,2-3), energy contribution 3 T,: E E ti ?2 t3 tz ti t3 ta f2 t1 ti fa *2 E Overall, 3H, + 0,. ! Ab tas one exchange possibility for each spin pair and two pairs tiro t Ê thesecond; — 2 1 hasthe lower energy. E | EXERCISE 2-4 ] A nitrogen aiom wilh fhree p elecirons could have three unpaired electrons (o ) or it could have one unpaired electron (——.. —— ——), Find the number of electrons that could be exchanged in each case and the Coutombic and ex- change energies for the atom. Which arrangement would be lower in energy? Many schemes have been used 10 predict the order of fling of atomic orbitals. One, known as Klechkowsky's rule, states that the order of [illing the orbitals proceeds from the lowest available value for the sum x + !. When two combinations have the same value, the one wilh the smaller value of x is filicd first. Combined with the other rules, this gives the order of filling of most of the orbitals. One of the simplest methods that fits most atoms uses the periodic table blocked outasin Figure 2-9. The electron configurations of hydrogen and helium are clearly 15! e Ca RA Groups (IUPAC) 1 2 3 (US traditional) JA MA BB IVB VB VIB VIB VILB IB IB JBA IVA VA VIA VIIA VIDA af MESES ES ENCARAR FIGURE 2-9 Atomic Orbital Filling in the Periodie Table, "block | block 40 chapter 2 Atomic Structure FIGURE 2-10 Energy Levcl Splitting and Overtap. The difTer- ences between the upper levels are exaggoratod for casier visualization: 2s p= À EXAMPLES Oxygen “The electron configuration is (182) (252 29º). For the outermost electron, Zt=Z=s 8-[2x(085)]- [5x (035); = 455 (15) (25, 2p) The two Is cleetrons cach contribute 0.85, and the five 2x and 2 electrons (the last electron is not counted, as we are finding Z* tor it) cach contribute 0.35, for a total shiclding constant = 3.45. The net eticetive nuclear charge is then Z* = 4.55. Therefore, the last clecuon is held with about 57% of the force expected for a +8 nucleus and a —1 electron. Nicke! The electron configuration is (15?) (292 29º) (352 3º) (348) (482). For a 3d electron, Z=2-s 28 - [18x (100)]- 7x (035)! = 7,55 (15,28. 2p,35,3p) (3d) h The 18 electrons in the 1s, 2s, 27, 3s. and 3p Jevels contribute 1.00 each, the other 7 in 3d contribute 0.35, and the 4s contribute nothing. The total shiclding constant is $S = 20.45 and Z* = 7.55 for the last 3d electron. 2-2 The Schródinger Equation 41 For the 4s electron, Z*=2-8 = 28 — [10 X (1.00); — [16 x (0.85)] = [1 x (0.35)] = 4.05 (15,25,2p) (Bs. 3p, b (48) The-ten 1s, 25, and 2p electrons each contribute 1.00, the sixteen 3s, 3p, and 3d electrons cach contribute 0.85, and the other 4s eleciron contributes 0.35, for a total S = 23.95 and £Z* = 4.05, considerably smaller than the value for the 3c electron above, The 4s electron is held less tightly than the 34 and should therefore be the first removed in jonization. This is consistent with experimental obscrvations on nickel compounds. N?*, the most common oxi- dation state of nickel, has an electron configuration of [Ar]348 (rather than [Ar]3d%48?), cor tesponding to loss of the 4s clectrons from nickel atoms. AIL the transition metals follow this same pattern of losing 715 electrons more readily than (2 — 1)d electrons. ER MA oidt set EXERCISE 2-5 Caleulate the ctfective nuclear charge on a 5s, à 5p, and à 4d electron in a tin atom. EXERCISE 2-6 Calculate the ctfective nuclear charge on a 75, a 5f, and a 6d electron in a uranium atom. Justification for Skater's rules (aside from the fact that they work) comes from the electron probability curves for the orbitals. The s and p orbitais have higher probabili- ties near the nucleus than do d orbitals of the same n, as shown carlicr in Figure 2-7. Therefore, the shielding of 3d electrons by (3s, 3p) cleetrons is caleulated as 100% cf- fective (a contribution of 1.00). At-the same time, shielding of 3s or 3p electrons by (2s. 2p) electrons is only 85% effective (a contribution of 0.85), because the 35 and 3p orbitals have regions of significant probability close to the nucleus. Therefore, electrons in these orbitals are not completely shielded by (25, 2p) electrons. A complication arises at Cr (Z = 24) and Cu (Z = 29) in the first transition se- ries and in an increasing number of atoms under them in the second and third transition series. This effect places an extra electron in the 3d level and removes one electron from the 45 level. Ct, for example, has a configuration of [Arjas! 34º (rather than [Ar]4s 3a). Traditionalty, this phenomenon has often been explained as a conseguence of the “spe- cial stability of half-filed subshells” Half-filled and filed d and f subshells are. in fact, Iairly common, as shown in Figure 2-11, A more accurate cxplanation considers both interactions (repulsions) between the electrons sharing the same orbital? This ap- proach requires totating the energics of all the electrons with their interactions; results af the complete calculations match the experimental results. Another explanation that is more pietorial and considers the electron-electron in- teracrions was proposed by Rich. He explained the structure of these atoms by specif- ically considering the difference in energy between the energy of one electron in an orbital-and two clectrons in the same orbital. Although the orbital itself is usually as- sumed to have only one energy, the electrastatic repulsion of the two electrons in onc orbital adds the electron pairing energy deseribed previously-as part of Huad's rule. MW can visualize two parallel energy levels, each with electrons of only one spin, separated by the electron pairing encrgy, as shown in Figure 2-12, As the nuclcar charge increas- es, the electrons are more strongly attracted and the energy levels decrease in energy, becoming more stable, with the d orbitals changing more rapidly than the + orbitals because the d orbitals are not shielded as well from the nucleus. Electrons fill the BL, (4. Vanquickenbora, K. Pierloat, and D. Devoghel, J. Chem. Educ., E994, 74, 469. *R, L. Rich, Periodic Correlations, W. A. Benjamin, Mento Park. CA, 1965, pp. 9-1. 42 chapter 2 Atomic Slnucture Na Mg HatÊilled à Fledd ALSO PS Cx = = K Ca Se Mn Ni |Cu lZn |Ga Ge As Se Br Kr 3d! 3d? 348 | adlO | 3alo as gs! tds? CL Rb Sr Y 7º ca lim Sp Sb Te 1 Xe ad! ad adid 1 aqio 1 Use Cs Ba La HE Ta W Au Erg Tr Pb Bi Po Ar Ra sell até aftt gps 5 sato sato sd? 5d? sd! A so Er Ra Ac RE Db Sg [Bh | Bo Mt Uuu É Uub Vu Uuh Uuo 6d! Sp ap la spt] sp) sp ld spléi go Galo 1 ggio a 3 ss q! ' Ino 642 633 6d! | 68 | 608 71 UG Half filled Filicdf , Em iGd | To Dy Ho Er Im [Yb | Tu af la af apto af apt? 43 at aptá ! sat 1-5 sd! ' Am Cm) sk iCr IES Em Md [No | Li sf 7 | ag Usp spt spo aps splé, spté od! t eu! 6d! FIGURE 2-11 Electron Configuratons of Transition Metals, Including Lanthanides and Actnides Solid lines surrounding elements desiguate filled (a!º or PS nalf-Filted (dº or f7) subshelis: Dashedliness ding elements designate itregularities in seguential osbital filling. vebieh is also found within some of the solid lines. Electron spin «., . Din qu Number of electrons in balf-sutsbell N IGURI FIGURE 2-12 els for Transition Elements. ) Schematic interpretatton of electron contigarations forwansitiom elements in teruns of intraorbital repulsion and trends in subshell energies. (b) A sunilas digram for ions, showing the shift in the crossover points on removal of an electron. The diagram shows that s electrons ate removed before d elecirons. The shift is even inore pronounced for metal ions having 2-- or greater charges. As a conse- quence, nansilion metal ions with 2+ er greater charges have no s elec- tons. only é electrans in their outer levels. Similar diagrams, although more complex, can be drawn fo the heavier transition elements and lhe lanthanides-(Reprinted with pes sionftom R. 1.. Rich. Períodic Corretations, W. A. Benjamin, Mento Park. ÉS; pp-  “"BSDE “OT LG6E “VIMOS “F "BIOA IDAS "ETTA PUU “AQUÍOCT "DF “UND TATO "PU SE O “LOG SOR SAN “PIOQUISY “Lastro otunSiouy “Uustapues +] -g :odmoS SD (ro 9 LI sh Gt Per oL ma Eai Era oct PET + 691 861 ET ey 1y od us da IL 8H ny q 4 so mM M “L HH PI e O 9 FEI gr ori or FT 8H ter ser sz SE um 01 PET Ed! TL 161 IZ a 1 aL gs ts u PD By Pd mM ng a SW IN Erd à 18 á u bm LH ar ur ser si mu su sm LE “a SIT TI vTr FI eLr uz É 1g 2g sy as "o uz no IN oo ag ua o A H 25 ro BL $ 66 ut 901 ur 8 vEL HI ay (o) s d 's Iv W IN 69 EL EL st e E 68 T a d o N q eg " Ú £ 3H H si Z1 9r st + sr q H or 6 8 L 9 £ £ 2.100 (Ud) jpeg Juaptnoo JejoduoN : + : sz navi Ecs didi não 45  A6 chapter 2 Atomic Structure TABLE 2-9 Crystal Radii for Selected lons Element Radios (pm) Alkali metal ions 3 Lit 90 “ Nat 16 19 K 152 37 Rb! 166 ss cst 181 Alkaline earth ions 4 Bo 54 12 Mg 86 20 ca 14 38 se” 132 56 Ba”! 149 Other cations E APS 5 3% mã 88 Halide ions 9 F no 17 ct 167 35 Br 182 53 I 206 Other anions 8 o? 126 16 sm 170 Sourer: R. DD. Shannon. Acta Crystattogr. 1976. 432, 751. A longer Hist is given io Appendix B-1. AII the values are for 6-covrdinare ions. no polarity. There are other measures of atomic size, such as the van der Waals radius, in which collisions with other atoms are used to define the size. It is difficult to obtain con- sistent data for any such measure, because the polarity, chemical structure, and physical state of molecules change drastically from one compound to another. The numbers shown here are sufficient for a general comparison of one element with another. There are simitar problems in determining the size of ions. Because the stable ions of the different elements have different charges and different numbers of electrons, as well as different erysta! structures for their compounds, it is difficult to find a suitable set of numbers for comparison. Earlier data were based on Pauling”s approach, in which the ratio of the radii of isoelectronic ions was assumed to be equal to the ratio of their effective nuclear charges. More recent calculations are based on a number of consider- ations, including electron density maps from X-ray data that show larger cations and smaller anions than those previously found. Those in Table 2-9 and Appendix B were called “crystal radii” by Shannon * and are generally different from the older values of “jonie radii” by +14 pm for cations and — 14 pm for anions, as well as being revised be- cause of more recent measurements. The radii in Table 2-9 and Appendix B-1 can be used for roneh estimation of the packing of íons in crystals and other calculations, as long as the “fuzzy” nature of atoms and ions is keptin mind. Factors that influence ionic size include the coordination number of the ion, the covalent character of the bonding, distortions of regular crystal geometries, and delo- calization of electrons (metallic or semiconducting character, described in Chapter 7). The radius of the anion is also influenced by the size and charge of the cation (the anion exerts a smaller influence on the radius of the cation). The table in Appendix B-] shows the effect of coordination number. Z'R, D. Shamoa, Acia Crystaliogr, 1976, A32, 751, 280, Johnson, Inorg. Chem, 1973, 12.780. Problems 47 ” : similar numbers of elecirons (F” and Na” differ only in nuclear charge, but the radius of fluoride is 37% larger). The radius decreases as nuclear charge increases for ions with the same electronic structure, such as O”, FT, Na”, and Mg?*, with a much larger change with nuclear charge for Lhe cations. Within a family, the ionic radius increases as £ increases because of the larger number of electrons in the ions and, for the same ele- ment, the radius decreases with increasing charge on the cation, Examples of these trends are shown in Tables 2-10, 2-1t, and 2-12. TOO REA DE TN EM ar TUAS TABLE 2-10 : Crystal Radius.and Nuclear charge e Jon Protons Electrons Radius (pm) oi 8 10 126 Fr 9 10 no Na! n 10 H6 fer 4 19 TABLE 2-11 Crystal Radius and Total Number of Electrons ton Protons Electrons Radius (pm) o z 10 126 s” 16 18 174 Se” 34 36 184 Te” 52 54 207 TABLE 2-12 Crystal Radius and tonic Charge E lon Protons Electrons Radius (pm) : : TE 2 20 100 ] Tê 2 19 8! : To 2 18 75 GENERAL Additional information on the history of atomic theory can be found in J. R. Partington, REFERENCES A Short History of Chemistry, 3td ed., Macmillan, London, 1957, reprinted by Harper & Row, New York. 1960, and in the Journal of Chemical Education. A more Lhorough treatment of the electronic structure of atoms is in M. Gertoch, Orbitals, Terms, und States, John Wiley & Sons, New York, 1086, PROBLEMS | 21 Determine the de Broglie wavelength of a. An electron moving at one-tenth the speed of light, b. A 400 g Frisbee moving at 10 km/h. 1 1 22 Using tbe equation E = lã a) determine the energies and wavelengths of : = . th n=45, and 6. (The red line 5 in this spectrum vas calculated in Exercise 213  50 Chapter 2 Atomic Structure 226 Predict thc largest and smalkest in each series: > a Se Br Rbt sr 2-27 2-28 by Er nb?! « Co!t Co Co? Co Prepare a diagram such as the one in Figure 2-12(a) for the fitih period in the periodic table, elements Zr through Pd. The configurations in Table 2-7 can be uscd to determine the crossover points of ihe lines. Can a diagram be dtawn that is completely consistent with the configurations in Lhe table? There are a number of websites that display atomic orbitals, Use a search engine to lind a. A compleis set of the f orbitals. b. A complete set of the g orbitals. Include the URL for the site with each ol these, along with sketches or printouts of lhe orbitais. [One website that allows display of any orbital, complete with rotation and caling is httpo//vesew-orbitalcom/]  We now Lum from lhe use of quantum mechanics and its description of the atom to an elenentary descripúon of molecules. Although most of the discussion of bonding in this book uses the molecular orbital approach to chemical bonding. simpler methods that provide approximate pictures of the overall shapes and polarities of molecules are also very useful. This chapter provides an overview of Lewis dot structures, valence shell electron pair repulsion (VSEPR), and related topics. The molecular orbital descriptions of some of! the same molecules are presented in Chapter 5 and later chapters, but the ideas of this chapter provide a starting point for that more modern treatment. General chemistry texts include discussions of most of these topics: this chapter provides a re- view for those who have not used lhem recently. Ultimately, any description of bonding must be consistent with experimental data on bond lengths, bond angles, and bond strengths. Angles and distances are most fre- quently determined by diffraction (X-ray crystallography, electron difiraction, neutron dilfraction) or spectroscopic (microwave, infrared) methods. For many molecules, there is general agreement on the bonding, although there are alternative ways to describe it. For some others, there is considerable difference of apinion on the best way to describe the bonding. Ta this chapter and Chapter 5, we describe some useful qualitative ap- proaches, including some of the opposing views. a da aC 31 LEWIS ELECTRON- DOT DIAGRAMS Lewis electron-dot diagrams, although very much oversimplified provide a good starting point [or analyzing the bonding in molecules, Credit for their initial use goes 19 6. N. Lewis, au American chemist who contributed much to thermodynamics and chemical honding in the early years of the 20h century. In Lewis diagrams, bonds between two atoms exist when they share one or more pairs of electrons. In addition, some molecules have nonbonding pairs (also called lone pairs) of electrons on atoms. IGN. Lew Am, Chem. Soc., 1916, 38, 762; Valence and the Siruciuro cf Atoms and Molecules, Chemical Catalogue Co., New York, 1923 51 x 52 chapter3 Simple Bonding Theory These electrons contribute to lhe shape and teactivity of the molecule, but do not directly bond the atoms together. Most Lewis structures are based on the concept that eight valence electrons (corresponding to s and p electrons outside the noble gas core) form a particularly stable arrangement, as in the noble gases with s? pÊ configurations, An exception is hydrogen, which is stable with two valence electrons. Also, some molecules require more than eight electrons around a given central atom. A more detailed approach to eleciron-dot diagrams is presented in Appendix D. Simple motecules such as water follow the octet rule, in which eight electrom surround the oxygen atom. The hydrogen atoms share two electrons each with the oxy- gen, forming the familiar picture with two bonds and two lone pairs: Shared electrons are considered to contribute to the electron requirements of both atoms involved; thus, the electron pairs shared by H and O in the water molecule are counted toward both the &-electron requirement of oxygen and the 2-electron require- ment of hydrogen. Some bonds are double bonds, containing four electrons, or triple bonds, contain- ing six electrons: H-—-c=c—H 3-1-1 RESONANCE In many molecules, the choice oÍ which atoms are cormected by multiple bonds is arbi- trary. When several choices exist, all of them should be drawn. For example, as shown in Figure 3-1, three drawings (resonance structures) of COs2” are needed to show the double bond in each of the three possible C—O positions. In fact, experimental evi- dence shows that all the C—O bonds are identical, with bond lengths (129 pm) be- tween double-bond and single-bond distances (116 pm and 143 pm respectively): none of the drawings alone is adequate to describe the molecular structure, which is a combi- nation of ali three, not an equilibrium between them. This is called resonancee to signi- fy that there is more than one possible way in which the valence electrons can be placed in a Lewis structure. Note that in resonance structures, such as those shown for CO; fixed positions. The species CO 2, NO; , and SO, ate isoelectronic (have the same electronic structure). Their Lewis diagrams ate identical, except for the identity of the central atom. When a molecule has several resonance structuzes, its overall electronic energy is lowered, making it more stable. fust as the energy levels of a particle in a box are low- ered by making the box larger, the electronic energy levels of the bonding electrons are Jowered when the electrons can occupy a larger space. The molecular orbital descrip- tion of this effect is presented in Chapter 5. FIGURE 3-1 Lewis Diagrams for co. 54 — chapter3 Simple Bonding Theory 1- :8—C=N: B 1+ 2 1s=c—N: Structures E aTEES, e negati E clectronegative (in the upper right-hand part of the periodic table) elements, and with smaller separation of charges tend to be lavored. Examples of formal charge calcula- tions are given in Appendix D for those who necd more review. Three examples, SCN”, OCN”, and CNO”, will illustrate the use of formal charges in describing electronic structures. SCN” In the thiocyanate ion, SCN”, three resonance structures are consistent with the electron-dot method, as shown in Figure 3-3. Structure A has onty one negative formal charge on the nitrogen atom, the most electronegative atom in the ion, and fits the rules well. Strue- ture B has a single negative charge ou the S. which is less electronegative than N. Structure C has charges of 2— en N and + on 8, consistent wilh the relative electronegativities of the atoms but with a larger charge and greater charge separation than the first. Therefore, these structures lead to the prediction that structure À is most important, structure B is next in im- c FIGURE 3-3 Resonance Struc- tures of Thivcyanato, SCN”. portance, and any contribution from € is minor. The bond lengths in Table 3-1 are consistent with this conchasion, with bond lengths between those of structures A and B. Protonation of the ion forms FINCS, consistent with a negative charge on N in SCN | The bond lengths in FINCS are those of double bonds, consis- tent with he structure H— N = TABLE 3-1 Table of $--€ anetC=-N Bond Lengths (pm) S—€ CN SCN 165 n7 HNCS 156 122 Single bond 181 147 Double bond 155 128 (approximate) Triple bond no SoLkce: A. F Wells, Siructural inorganic Chemistry. 5th ed., Oxford University Press, New York, 1984, pp. 807, 926, 934-936. FIGURE 3-4 Resonance Siruc- mres of Cyanate, OCN”. OCN” The isoelectronic cyanate ion, OCN” (Figure 3-4). has the same possibilities, but the larger clectronegativity of O makes structure B more important than in thiocyanate. The protonated form contains 97% HNCO and 3% HOCN, consistent with structure A and a small contribution from B. The bond lengths in OCN” and FINCO in Table 3-2 are consistent with this picture, but do not agree perfectly. TABLE 3-2 : Table.of OC and'C—N Bond Lengths (pm) O—€C C=N OCN "3 1m HINCO us 120 Single bond 143 147 Double bond no 128 (approximate) Triple bond 13 116 Soure: A. E Wells, Structural Inorganic Chemistry, Sh ea., Oxford University Press, New York, 1984, pp. Bt7, 926. 9 RI Gillo pie and P.L. À. Popelier, Chemical Bonding and Molecular Geome Oxford University Press, New York, 2001, p. 117  FIGURE 3-5 Resonance Struc- tures of Fulminate, CNO”. 3-1 Lewis Electron-Dot Diagrams 55 CNO” The isomeric fulminate jon, CNO” (Figure 3-5), cam be drawn with three similar structures, but the resulting formal charges arc unlikely, Because the order of elecironegarivities isC<N<o0, none of these ate plausíble structures and lhe ion is predicted to be unstable. The only common fulminate salts are of mercury and silver; both are explosive, Fulminie acid is lincar HCNO in the vapor phase, consistent with stmcture C, and coordination complexes of CNO” with many transition metal ions are known with MCNO strucinres. EXERCISE 3-1 Use clectron-dot diagrams and formal charges to find the bond order for each bond in POF;, SOFy. and SO;F Some molecules have satisfactory electron-dot structures with octets, but have better structures with expanded shelis when formal charges are considered. m each of the cases in Figure 3-6, the observed structures are consistent with expanded shelis on the central atom and with the resonance structure that uses multiple honds to minimize formal charges. The multiple bonds may also influence the shapes of the molecules, Octer Expanded Molecule Atom Formal Atom Formal Expanded Charge Charge to: SNF,; s » N s 0 12 N 2 N o SO,Cl, s 2 s 0 12 I- o 0 Xe0; . Xe 3+ Xe 0 14 P o 1- o 0 )—xe—ô: so, s 2 s 0 12 o 1- o 0,1 So;> s 1+ e s 0 19 o I= o o 01- FIGURE 3-6 Formal Chargo and Expanded Shells. A. G. Sharpe, “Cyanides and Fulminates im Comprehensive Coordination Chemistry. G. Wilkinson, R.D. Gillard, and 1. S, McCleveriy, eds. Pergamon Press, New York. 1987, Vol. 2, pp. 12-14, 56 chapter3 Simple Bonding Theory — 344 MUKIPLEBONDSINBEANDB COMPOUNDS A few molecules, such as BeF3, BeCls, and BFx, seem to require multiple bonds to sat- isfy lhe octet rule for Be and B, even though we do not usually expect multiple bonds for fluorine and chlorine. Structures minimizing formal charges Tor these molecules have only four elecirons in the valence shell of Be and six electrons in the valence shell of B, in both cases less than the osual octer. The alternative, requiring cight electrons on the central atom, predicts multiple bonds, with BeF; analogous to CO, and BE; analo- sous to SO; (Figure 3-7). These structures, however, resultin formal charges (2— on Be and 1+ on Fin BeF>, and 1- on B and 1+ on he double-bonded Fin BF3). which are unlikely by the usual rules. Hi has not been experimentally determined whether the bond lengths in BeF, and BeCly are those of double bonds, because molecules with elear-cut double bonds are not available for comparison. In the solid, a complex network is formed with coordina- tion number 4 for the Be atom (see Figure 3-7). BeCls tends to dimerize to a 3-coordi- nate structure in the vapor phase, but the linear monomer is also known at high temperatures. The monomeric structure is unstable: in the dimer and polymer, the halo- gen atoms share lone pairs with the Be atom and bring it closer to the octet structure. The monomer is still frequently drawn as a singly bonded structure with only four elee- ecules (Lesis acid behavior, discussed in Chapter 6). Bond lengths in all the boron trihalides are shorter than expected for single honds, so the partial double bond character predicted seems reasonable in spite of the formal charges. Molecular orbital calculations for these molecules support significant double bond character. On the other hand, they combine readily with other molecules that can SE N Bel F F E pBe F, >p PT rá E / Predictod Actual solid cl ci Ê a NG Na PARAN C1=Be=cI Bee PA, Be BE Cl-Bel ,Be—C) a cl Predicted Solid Vapor FIGURE 3-7 Strucmures of BeF,, BeCts, and BF;. (Reference A. E Wells. Structural Inorgante Chemistry, Slh ed, Oxford Universi- ty Press, Oxford, England, 1984, The B—H band length is 13i-pmy pp. 412, 1047) the culçulated single-bond length is 152 pm. Predicted 3-2 Valence Shell Electron Pair Repulsion Theory 59 FIGURE 3-9 Conversion ofa Cube into a Square Antiprism. the center of the plane. The regular square antiprism structure (SN = 8) is like a cube with the top and bottom faces twisted 45º into the antiprism arrangement, as shown in Figure 3-9. K has three different bond angles for adjacent fluorines. [TaFs]"” has square antiprism symmetry, but is distorted from this ideal in the solid.” (A simple cube ter of the cube, because all edges are equal and any square face can be taken as the bot- tom ortop.) 3-2-1 LONE PAIR REPULSION We must keep in mind that we are always attempting to match our explanations to ex- perimental data, The explanation that fits the data best should be the current favorite, but-new-theories are continually being suggested and tested. Because we are working with such a wide variety of atoms and molecular structures, itis unlikely that a single, and molecolar structures are relative ely simple, their apriication to compleam molecules is not. Ft is also helpful to keep in mind that for many purposes, prediction of exact bond F sy 09.5º angles is not usually required. To a first approximation, lone pairs, single bonds, double H-C—H E bonds, and triple bonds can all be treated simitarly when predicting molecular shapes. 1 H H However, better predictions of overall shapes can be made by considering some impor- tant differences between lone pairs and bonding pairs. These methods are sulficient to show the trends and explain the bonding, as in explaining why the E—N—H angle in H-N—H ammonia is smaller than the tetrabedral angle in methane and larger than the H H—0O—H angle in water. 106,6º Steric number = 4 AO: H «ou The isoelectronic molecules CH4, NHs, and HO (Figure 3-10) illustrate the effect of lone pairs on molecular shape, Methane has four identical bonds between carbon and 104,5º each of the hydrogens. When the four pairs of electrons are arranged as far [rom each FIGURE 3-10 Shapes ví Meihane, Other as possible, the result is the familiar tetrahedral shape. The Letrahedron, with all Ammonia. and Water. H—C—H angles measuring 109.5º, has four identical bonds. 1. L. Board, W.J. Martin, M. E. Smith, and J. E. Whitney, 4 Am. Chem, Soc.. 1954, 76, 3820.  60 —chapter3 Simple Bonding Theory Ammonia also has four pairs of clectrons around the central atom, but thrce are bonding pairs betwcen N and H and the fourth is a lonc pair on the nitrogen. The nuclei am y ethres o ú n ly tetrahedral shape. Because each of the three bonding pairs is attracied by two positive- ly charged nuclei (H and N), thesc pairs are kwgely confined to the regions between the H and N atoms. The lone pair, on thc other hand, is concentrated near the nitrogen; ithas no second nucleus to confine it to a small region of space. ConscquentIy, the lone pair tends to spread out and to oceupy more space around the nitrogen than the bonding pairs. As a result, thc E—N — H angles are 106.6”, ncarly 3º smaller tan the angles in methane, The same principles apply to the water molecule, in which two lone pairs and two tonding pairs repcl each other. Again, the electron pairs have a nearly tetrahedral arrangement, with the atoms arranged in a V shape. The angle of largest repulsion, be- iween the tro lone pairs, is not directly measurable. However, the lone pair-bonding -, catei e pair! o pair (bp- e and as a result the H-—- O —H bond angle às only 104.5”, another 2.1º decrease from the ammonia angles. The net result is that we can predict approximate molecular shapes by assigning more space to lone electron pairs; being attracted to one nucleus rather than two, the lone puirs are able to spread out and occupy more space. Axial Tone pair FIGURE 3-11 Stuciure ot SF4. Steric number = 5 For trigonal bipyramidal geometry, there arc two possible locations of lonc pairs, axial and equatorial. Tf there is a single lone pair, for example in SF4, the fone pair occupies an equatorial position. This position provides the lone pair with the most space and min- imizes thc interactions between the Tone pair and bonding pairs. Tt the lone pair were axial, it would have three 90º interactions with bonding pairs; in an equatorial position it has only two such interactions, as shown in Figure 3-11, The actual structure is dis- torted by the one pair as it spreads out im space and cffectively squeezes the rest of the molecule together. CIF; provides a second example of the influence of Ione pairs in molecules hav- ing a steric number of 5. Therc are three possible structures for CiF4, as shown m Figure 3-12. Lone pairs in the figure are designated Zp and bonding pairs arc bp. In determining the structure of molecules, the lone pair-lone pair interactions , o ex ane: In addition, interactions at angles of 90º or less are most important; larger angles gen- crally have less influence, In CIFs, structure B can be eliminated quickly becanse of FIGURE 3-12 Possible Structures ol Cir, í i A de PGS r-a I í A R c Experimental Caleulared Experimental A B c tp-tp 180º 90º 129” cannot be determined tp-bp Gal 90º 3a 90º Au 90 cannot be determined Sat DOS 2a 120º dedo 3a 20190? 2 ut 90º 24875 Lar t20s Axja CEF 169.8 pm. Equatorial CL—F 159.8 pm 3-2 Valence Shell Electron Pair Repulsion Theory 61 the 90º fp-íp angle. The ip-tp angles are large for A and €, so the choice must come from the /p-bp and bp-bp angles. Because the /p-bp angles are more important, €, which has only four 90º fp-bp interactions, is favored over A, which has six such in- teractions. Experiments have confirmed that the structure is based on C, with sligl distortions due to the lone pairs. The Jone pair-bonding pair repulsion causes the tp-bp angles to be larger than 90º and the bp-bp angles less than 90º (actually, 87.5º). The CI—F bond distances show the repulsive effects as well, with the axial fluorines (approximately 90º !p-bp angles) at 169.8 pm and the equatorial fluorine (in the plane with two lone pairs) at 159.8 pm.º Angles involving tone pairs cannot be determined experimentally. The angles in Figure 3-12 are calculated assuming maximum symme- try consistent with the experimental shape. Additional examples of structures with lone pairs are illustrated im Figure 3-13. Notice that the structures based on a trigonal bipyramidal arrangement of electron pai around a central atom always place any lone pairs in the equatorial plane, as in SF4, BrFs, and XcF,. These are the shapes that minimize both lone pair-lone pair and lone pair-bonding pair repulsions. The shapes are called teeter-tolter or seesaw (SEj P á PI - Pp 4) distorted T (BrF'3), and linear (XeF;). Number of Lone Pairs on Central Atom Steric Number None f 5 2 ICl=Be=cT: F í 3 b As ' A cer Fo 95º EA a é 4 é A Hey = AN 106.6º 104,5º 4d q ZP—CI 5 Gi - e cI F es [E [LF 6 F=S— E—Xe—E ” Fr Al a! E b Era Ps FIGURE 3-13 Structures Containing Lone Pairs. A. E Wells, Struciaral inorganie Chemistry, Sh cd., Oxford University Press, New York, 984, p. 390. 64 chapter3 Simple Bonding Theory TABLE 3-3 Electrónegativity (Pauling Units) . 1 2 12 13 14 15 16 17 18 H He 2300 4.160 Ti Bo B c N o E Ne 0.912 1.576 2051 2.544 3.066 3.610 4.193 4787 Na Mg Al Si Pp s ci Ar 0.869 1.293 1.613 1916 2.253 2.589 2.869 3.242 x Ca Zn Ga Ge As Se Br Kr 0.734 1.034 1.588 1.756 1.994 220 2.424 2.685 2.966 Rb Sr cd in Sn Sb Re 1 Xe 0.706 0.963 1521 1.656 1.824 1.984 2158 2339 2.582 cs Ba 1lg TI Pb Bi Po At Rn 0.659 0881 1.765 1.789 1.854 201 (2.19) (2.39) Cuaoy Source: 3. B. Maan, T. L. Meck, and L. C. Allen, 4 Am. Chem. Soe., 2000, 122, 2780, Table 2. Electronegativity scales The concept of electronegativity was first introduced by Linus Pauling in the 1930s as a means of describing bond energies. Bond energies of polar bonds (formed by atoms with different electronegativities) are larger than the average of the bond energies of the two homonuclear species. For example, HCl has a bond energy of 428 KJ/mol, com- pared to a calculated value of 336 kJ/mol, the average of the bond energies of Hs (432 kJ/mol) and Cl (240 kJ/mol). From data like these, Pauling calculated elec- tronegativity values that could be used to predict other bond energies. More recent val- ves have come from other molecular properties and from atomic properties, such as ionization energy and electron affinity. Regardless of the method of calculation, the scale used is usually adjusted to give values near those of Panling to allow better com- parison. Table 3-4 summarizes approaches used for determining different scales. TABLE 3-4, o Electronegativity. Scales . Principal Authors Method of Calculation or Description Pauling!O Bond energies Mulliken!! Average of electron affinity and ionization energy Alived & Rochow!Z Electrostatic attraction proportional to Z*/1? Sanderson Electron densities of Pearson!* Average of cleetron affinity and ionization energy aten? Average energy of valonco shell electrons, configuration encrgies Jattgló Orbital electronegativities 19,, Panling. The Nature of the Chemical Bond, 3rd ed., 1960, Comet University Press, Ilhaca, NY; A. L. Alired, 1. Inorg. Nucl, Chem., 1961, 17,215. UR. S. Mulliken, 4 Chem. Phys. 1934, 2, 782; 1935, 3, 573; W. Moffitt, Proc. R. Soc, (London), 1950, 4202, 548; R. G. Pare R. A. Dometly, M. Levy, and W. . Palke, 4. Chem Phtys., 1978, 68, 3801-3807; R.G. Pearson, Jnorg. Chem.. 1988, 27, 7341: . G. Bratsch, 4. Chem, Fduc., 1988, 65. 34-41], 223-226. 2a L AlredandE. G. Rochow, 2 lnorg Nucl Chet, 1958. 5, 264. BR, T. Sanderson, 4. Chem. Educ, 1952, 29, 539: 1984, 37, 2, 238; Inorganic Chemistry, Van Nostrand-Reinhold, New York, 1967. Up. G. Pearson, Ace. Chem. Res., 1990, 23, 1. SSL, €. Allen, 1. Am, Chem. Soc., 1989, 177, 9003; J. B. Maun, E. L. Meek, and L. C. Allen, 7. Am, Chem. Soc., 2000, 122, 2780; É B. Mans, T. L. Meek, E. '£. Knight, J. F. Capitani, and L. C. Allen, 4. Am Chem. Soc., 2000, 122, 5132. 167. Tiinze and HH. Julie, 4 Am. Chem. Soc, 1962, 84, 340: 4. Phys. Chem, 1963, 67, [50]; ]. E. Huhcoy, fnorganic Chemistry. 3rd ed., Harper & Raw, Now York, 1983, pp. 152-156. 3-2 Valence Shell Electron Pair Repulsion Theory 65 Appendix B-4 shows electronegativity values for a larger set of elements. Any set cah be used for the prediction of hond angles and molecular shape; specific sets are more useful for the calculation of properties for which they are designed. A graphic represen- tation of electronegativity is in Figure 8-1 Caleulation of electronegativities from bond energies requires averaging over a number of compounds to cancel out experimental uncertainties and other minor effects Methods that use ionization energies and other atomic properties can be caleulated more directly. The electronegativities reported here and in Appendix B-4 are suitable Tor most uses, but the tal values for atoms in molecules may difler from this average, depending on their electronic environment. Many of those interested in electronegativity agree that it depends on the structure of the molecule as well as the atom. Jalfé used this idea to develop a theory of the elec- tions of properties that change with subtle changes in structure, but we will not discuss this aspect further. The differences between values from the different scales are rela- tively small, except for those of the transition metals." AH will give the same. results in qualitative arguments, the way most chemists use them. Remember that all electronegativities are measures of an atom's ability to attract electrons from a neighboring atom so which it is bonded. A critique of all electronega- tivity scales, and particularly Pauling's. describes conditions that all sales should meet and many of their deficiencies.!* With the exception of helium and neon, which have large calculated electronega- tivities and no known stable compounds, fluorine has the largest value, and electroneg- ativity decreases toward the lower left corner of the periodic table. Hydrogen, although usually classified with Group 1 (IA), is quite dissimilar from the alkali metals in its electronegativity. as well as in many other properties, both chemical and physical. Hy- drogen's chemistry is dislinctive from all the groups. Electronegativities of the noble gases can be calculated more easily from ioniza- ton energies than from bond energies. Because the noble gases have higher ionization energies than the halogens, other calculations have suggested that the electronegativi- ties of the noble gases may match or even exceed those of the halogens!? (Table 3-3). The noble gas atoms are somewhat smaljer than the neighboring halogen atoms (for ex- ample maller than se ofa greater elfectivi ar cl charge, which is able to attract noble gas electrons strongly toward the nucleus, is also likely to exert a strong attraction on electrons of neighboring atoms; hence. the high electronegativities predicted for the noble gases are reasonable. Electronegativity and bond angles Many bond angles can be explained by either electronegativity or size arguments. Mol- ecules that have a larger difference in electronegativity values between their central and outer atoms have smaller bond angles. The atom with larger electronegativity draws the electrons toward itself and away from the central atom, reducing the repulsive effect of those bonding electrons. The compounds of the halogeas in Table 3-5 show this effect; the compounds containing fluorine have smaller angles than those containing chlorine, which in turn have smaller angles than those containing bromine or iodine, As a result, the lone pair effect is relatívely larger and forces smaller bond angles. The same result is obtained if size is considered; as the size of the outer atom increases in the F< Cl<Br< Iseres, the angle increases. VB. Mann, T. L. Meek, E. T. Knight. 3. F. Capitani, and 1.. C. Allen, 4. Am. Chem. Soc., 2000, 122, 5132, SL. R. Murphy. T.L. Meek, A. L. Afired, and E. C. Allen, 4 Amt. Chery. Soc., 2000, 122. 5867 PLC. Alten and). E. Huhcey, J. Inorg. Nucl. Chem.. 1980, 42. 1523.  66 Chapter 3 Simple Bonding Theory TABLE 3-5 Bond Angles and Lengths Bond Bond Bond Bond Bona Bona Bona. Bona Angle Lengih Angle Lengih Angle Length Angle Length Molecule (9) cpm) Molecule (3) (pm) Molecule (º) (pm) Molecule (º) (pm) HO 104.5 97 OF, 103.3 och 110.9 Ho8 92 135 SE, 98 159 SCl; 103 203 HoSe 9 146 Hate 90 169 NHs 16.6 101.5 NE; wW22 3 NCh 106.8 175 PII, 938 142 Pra 978 157 PCI; 1003 204 PBr; 101 220 AsHa 9183 I519 AsFa 962 176 AsCIs g7 7 AsBrs 9.7 2% SbH; 913 1707 SbF; 873 192 SbCh 92 283 SbBr 95 249 Sourer: N. N. Greenwood and A. Earnshaw, Chemistry of the Elements, 2nd ed.. Butterwonth-Hcinemann, Oxford, 1997, pp. 557, 767: Wells, Structural Inorganic Chemistry, 5th ed.. Oxtord University Press, Oxford. 1987, pp. 705, 793. 846, and 879 es pounds based on the clectroncgativity argument and the smallest angle based on the size argument: instead, it has nearly the same angle as NCls. Similar problems arc found for H,0, H5S, PHs, AsH;. and SbHs. The two cffects scem to counterbalance each other, resulting in the intermediate angles. Similar arguments can be made in situations in which the outer atoms remain the same but the central atom is changed. For example, consider the hydrogen series and the chlorine series in Table 3-5. For these molecules, the clectronegalivity and size of the central atom need to be considered. As the central atom becomes more electronegative, it pulls clectrons in bonding pairs more strongly toward itself, This effect increascs the concentration of bonding pair electrons near the central atom, causing the bonding pairs to repel cach other more strongly, increasing the bond angles. In these situations, the compound with the most electronegative central atom has the largest bond angle. The size of the central atom can also be used to determine the angles in the series When the central atom is larger, all the electron pairs are naturally at greater distances from each other. However. the effect is greater for the bonded pairs, which are pulled away from the central atom by outer atoms. This leads to a relatively larger repulsive cffect by the tone pairs and decreasing angles in the order O = S > Se > TeandN>P>As> Sb. EXERCISE 3-4 Wiich-compoundtras the smalest bond anglc in cach series? a OSF OSCI, OSBr; (halogen —S — halogen anglc) b. SbCl; SbBr; Sbl; c Pl; Asla Sbta 3-2-4 LIGAND CLOSE-PACKING Another approach to bond angles has becn developed by Gillespie? The ligand close- packing (LCP) model uses the distances between lhe outer atoms in molecules as a guide. For a series of molecules with the same central atom, the nonbonded distances between the outer atoms are consistent, but the bond angles and bond lengths change. For example, a series of BF;X and BF;X compounds, where X = F, OH, NH», CL, H, CHs, CFs, and PHS, have B—F bond distances of 130.7 to 142.4 pm and F—B —F %R. 1 Gillespie, Coord. Chem. Rev., 2000, 197, 51  FIGURE 3-18 Canceltation of Bond Dipotes due tó Molecular Symmetry. 3-4 Hydrogen Bonding 69 a o 1 f c s Qu ca 05% Zero net dipole for all three molecules create small temporary dipoles, with extremely short lifetimes. These dipoles in turn altraet or repel electrons in adjacent molecules, setting up dipoles in them as well. The result is an overall attraction among molecules. These attraclive forces ate called London or dispersion forces, and make liquefaction of the noble gases and non- polar molecules such as hydrogen, nitrogen, and carbon dioxide possible. As a general rule, London forces are more important when there are more electrons in a molecule, because the attraction of the nuclei is shielded by inner electrons and Lhe electron cloud is more polarizable. 3-4. Ammonia, water, and hydrogen fluoride all have much higher boiling points tan other HYDROGEN similar molecules, as shown in Figure 3-19, In water and hydrogen fluoride, these high BONDING boing points are caused by hydrogen bonds, in which hydrogen atoms bonded to O or Falso form weaker bonds to a lone pair of electrons on another O or F. Bonds between hydrogen. and these strongly elecuronegative atoms are very polar, with a partial positive charge on the hydrogen. This pariially positive H is strongly attracted to the partially negative O or F of neighboring molecules. Tn the past, the attraction among these molecules was considered primarily electrostatic in nature, but an alternative molecular orbital approach, which will be described in Chapters 5 and 6, gives a more complete description of this phenomenon. Regardless of the detailed explanation of 100 4 HO TOC) —S04 -100 + FIGURE 3-19 Boiling Poinis ví Hydrogen Compounds SH =150 4 CH, —BX T T 1 Period  70 | chapter3 Simple Bonding Theory the forces involved in hydrogen bonding, the strongly positive E and the strongly negative tone pairs tend to line up and hold the molecules together. Other atoms with high clectronegativity, such as CI, can also form hydrogen bonds in strongly polar molecules such as chloroform, CHCI;. In general, boiling points rise with increasing molecular weight, both because the additional mass requires higher temperature for rapid movement of the molecules and because the larger number of clectrons in the heavier molecules provides larger London forces. The difference in temperature between the actual boiling point of water and the extrapolation of the line connecting the boiling points of the heavier analogous com- pounds is almost 200º C. Ammonia and hydrogen fluoride have similar but smaller dif- ferences trom the extrapolated values for their families. Water has a much larger effect, because each molecule can have as many as four hydrogen bonds (two through the lone pairs and two through the hydrogen atoms). Hydrogen fluoride can average no more than two, becanse HF has only one H available. Hydrogen bonding in ammonia is less certain. Several experimental studies? in the gas phase fit a model of the dimer with a “cyclic” structure, although probably asym- metric, as shown in Figure 3-2(b). Theoretical studies depend on the method of calcula- tion, the size of the basis set used (hos many functions are used in the fitting). and the assumptions uscd by the investigators, and conclude that the strueture is either linear or cyelic, but that in any case it is very far from nigid É The umbrella vibrational mode (in- verting the NH tripod like an umbrella in a high wind) and the interchange mode (in «which the angles betscen the molecules switch) appear to have transitions that allow casy conversions between the two extremes of a dimer «with a near-linear N— H—N hy- drogen bond and a centrosymmetric dimer with Cop symmetry. Linear N—H—N bonds seem more likely in larger clusters, as confirmed by both experiment and calcula- tion. There is no doubt that the ammonia molecule can accept a hydrogen and form a hy- drogen bond through the lone pair on the nitrogen atom «ith HoO, HF, and other polar molecules, but it does not readity donate a hydrogen atom to another molecule. On the other hand, hydrogen donation from nitrogen to carbonyl oxygen is common in proteins and hydrogen bonding in both directions to nitrogen is found in the DNA double helix. FIGURE 3-20 Dimer Structures in the Gas Phase. (a) Known hydrogen- bonded simctures. Rg *= hydrogen bond distance. (b) Proposed struc- lures of the NH dimer and trimer. (ay “DB, D, Nelson, Jr, G. T, Fraser, and W, Klemperer, Science, 1987. 238, 167 R. Trichtenieht, and M. Hartmann, 4. Chem. Phys., 1997, 107, 7179; F. Huisken and 1988. Yu 27 S. Lee and S.Y. Park, 4 Chem Phys, 2001, 112, 230; A. van der Avoirl, E. H. T. Olthof. and PES. Wormer, furados Discuss. 1994, 97. 45. and references therein. 1. Behrens, U. Buck, ertsch, Chem. Phys., 3-4 Hydrogen Bonding 71 Water has other unusual properties because of hydrogen bonding. For example, striking feature is the decrease in density as water fr . The tetruhedral structure around each oxygen atom with two regular bonds to hydrogen and two hydrogen bonds to other molecules requires a very open structure with large spaces between ice mole- cules (Figure 3-21). This makes the solid less dense than the more random liquid water surrounding 1t, so ice floats, Life on earth would be very different if this were not so. Lakes, rivers, und oceans would freeze from the bottom up, ice cubes would sink, and ice fishing would be impossible. The results are difficult to imagine, but would certain- ly reguire a much different biology and geology. The same forces cause coiling of pro- tein and polynucleic acid molecules (Figure 3-22); 4 combination of hydrogen bonding with other dipolar forces imposes considerable secondary structure on these large mol- ecules. In Figure 3-22(a), hydrogen bonds between carbony] oxygen atoms and hydro- gens attached to nitrogen atoms hold the molecule in a helical strucmre. In Figure 3-22(b), similar hydrogen bonds hold the parallel peptide chains together; the bond angles of the chains result in the pleated appearance of the sheet formed by the peptides. These are two of the many different strucmwres that can be formed from pep- tídes, depending on the side-chain groups R and the surrounding environment, Another example is a theory of anesthesia by non-hydrogen bonding molecules such as cyclopropane, chloroform, and nitrous oxide, proposed by Puuling.É These molecules ure of a size and shape that can fil neatly into a hydrogen-bonded water structure with even Luger open spaces than ordinary ice. Such structures. with mole- cules trapped in holes in a solid, are called elathrates. Pauling proposed that similar hydrogen-bonded microerystals form even more readily in nerve tissue because of the presence of other solutes in the tissue. These microcrystals could then interfere with the transmission of nerve impulses. Similar structures of methane and waler are believed to o NENE FIGURE 3-21 Iwo Dravings of Ice. (a) From LL. Brovm and H. E. LeMay, dr, Chemistry The Central Science, Prentice Hall, Englewood CUÍIs, NJ, 1988, p. 628. Reproduced with permission. The rectangular lines are included to aid visualization; all bonding às between hydrogen and oxygen atoms. (b) Copyright O 1976 by W. G. Davies and J, W. Moore, used by permission: reprinted from Chemistry, 3. W, Moore, W. G. Davies, and R. W. Collins, MeGraw-Bill, New York, 1978. All rights reserved. 3, Pauting, Science, 1961, 134,15. 74 Chapter 3 Simple Bonding Theory 3.7 Sketch the most likely structure o! PCt4Br, and explain your reasoning. 3-8 — Give Lewis dot structures and sketch the shapes ol the tolos ing” a. SeCly bs e. PSCIa (P is central) d TE4 e. PH” £ TeFÊ” 8 Ns à. SeOCL (Se is central) i PHy! à NO 39 Give Lewis dot sunciures and sketch the shapes of the following: a Cl” b. PO; (one H is bonded to P) e BH” d. POCI; e. 107 £ TO(OH) g SOC h. CIOF4T à Xe; j. cIorm* 30 Gise Lewis dor-sirucrares and-skoteh-the shapes cÉ the following: a. SOFg (one Fisattachedto O) h. POF; + CIO d. NO; e S/04% (symmenie, withan S-—S bond) fo Nou (symmetric, with anN—N bond) 311 a Compare the simctures of the azide ion, N3”, and the oz0ne molecule, Os. b. How would you expect he structure of the ozonide ion, Os”, to difier Itom that of ozone? 3.12 Give Lesis dot struciures and shapes for the following: a. VOC b. PCI; e. SOr4 d. CIO, e. CIO; £ P4Os (P4Og is a closed structure with overall tetrahedral acrangement of phosphorus atoms, an oxygen atom bridges each pair of phosphorus atoms.) 313 — Consider the series NH;, N(CH5)s, N(SiHay, and N(GeHs)s. These have bond an- eles at the nitrogen atom of 106.6, 110.9º, 120º, and 120º, respectively. Account tor this trend. 3:34 Explain the trends in bond angfes and bond lengths of the following ions: x—0 0—x—o (pr) Angle CIT 149 107º Bro; 165 104s To, 181 190º 3.15 — Compare the bond orders expected in CIO” and CIOy " ions. 3.16 Give Lewis dot simctures and sketch the shapes for the following: a. PH; b. HoSe e. SeRy d. PFs e TCly £. XeO; e NO; bh. SnCly i PO 1 Stg k. IFs L ICI; ma. 047 n. BI5C] 317 Which of the moleentes or ions in Problem 3-16 are polar? 3:18 Carbon monoxide has à larger bond dissociation energy (1072 KJ/mol) than molecular nitrogen (945 kJ/mol). Suggest an explanation. 349 a Which has the longer axial P— distance, PEXCHa)s or PEACE)? Explain briefly. b. 4150 has oxygen in the center, Predict the approximate bond angle in this molecule and explain your answer. . Problems 75 €. Predict the structure of CAL. (Reference: X, Li, L-S, Wang, A. L Boldyrev, and 1. Simons, 3. Am. Chem. Soc. 1999, 727. 6033.) 320 For each of the following bonds. indicate which atom is more negative. Then rank the series in order of polarity. a C—N b N—O «o d O—Cl e P—Br ft 8—CI 321 Lxplain the following: a. PCIs is a stable molccule, but NC'1s is not. b. SF, and SFç are known, but OF, and OF; are not. 3-22 Provide explanations for the [ollowing: a. Methano?, CHGOH, has a mueh higher boiling point than methyl mercaptan, CHsSH. b. Carbon monoxide has slightly higher melting and boiling points than N>. e. The ortho isomer of hydroxybenzoic acid |C;Ha(OHXCO-H)] has a much lower melting point than the meia and para isomers. e. Acetic acid in the gas phase has a significantly lower pressure (approaching a limit of one half) than predicted by the ideal gas law. f. Mixtures of acetone and chloroform. exhibit significant negative deviations from Raoult's law (which states that the vapor pressure of a volatile liquid is proportional 10 its mole fraction). For example, an equimolar mixture of acetone and chloroform has a lower vapor pressure than either of the pure liguids, 323 LC. Allen has suggested that a more meaningful formal charge can be obtained by tak- ing into account the clectronegativities of the atoms involved. Allen's formula for this type of charge. referred to as the Lewis-Langmuir (1.-L.) charge. of an atom, A, bonded to another atom, B, is (US) group ber of-unshared ber of bonds 1 charge = — TIA 4 Lica = umberotA electronsona 2 22x + xp betncen A and B where xa and xp designate the electronegalivities, Using this equation. calculate the L-L charges for CO. NO”, and HF and compare the results veith the corresponding for- D fhink-theL-Leh res-better ionofelee distrá t L charges area better representation of electron distri bution? (Reference: T. €. Allen, J. Am. Chem. Soc., 1989, 1H1,9115.) 3-24 Predict the structure of KCF;CI,. Do you expect the CH; group to be in an axial or equatorial position? Why? (Reference: R. Minkwitz and M. Merkci, Jnorg. Chem, 1999, 38. 5041.) 3-25 — Two ions isocleetronic with carbon suboxide, C304. are Ns” and OCNCO”. Whereas C30, is linear, borh Ns” and OCNCO” are bent at the central nitrogen. Suggest an explanation. Also predict which has the smaller outer atom — N — outer atom. angle and explain your reasoning. (References; T. Bernhardi, 'T. Drews, and KR. Seppelt, Angew, Chem., Int. Ed., 1999,38,2232. K. O, Clriste, W. W. Wilson, J. A. Sheehy, and TA. Boutr, Angew. Chem, Int. Ed., 1999, 38, 2004.) 3-26 The rhiazyl dichloride ion, NSCI5”, has recently been reported. This ion is isoelectrome with thionyl dichloride, OSC, & Which of these species has the smaller CI—S — C1 angle? Explain briefly. b, Which do you predict to have the longer S—CI bond? Why? (Reference: E. Kessenich, F Kopp, P Mayer, and À. Schulz, Angew. Chem, Int. Ed., 2001, 40, 1904.) 3-27 Alhough the CF distance: and the F—C—F bond angles ditfer considerably in EC=CF;, FCO, CF4. and FCO (CE distances: 131.9 to 139.2 pm; F—C—F bond angles: 101.3º to 109.5º), the F--- F distance in all four structures is very nearty the same (215 to 218 pm). Explain, using he LCP model of Gillespie. (Reference: R. J. Gillespie, Coord. Chem. Rev., 2000, 197,51.)  Symmetry is à phenomenon cf the natural world, as well as the world of human inven- tion (Figure 4-1), Tn nature, many types of flowers and plants, snowflakes, insects, cer- tain fruits and vegetables, and a wide variety of microscopic plants and animals exhibit characteristic symmetey. Many engincering achievements have a degree of symmetry that contribmes to their esthetic appeal. Examples include cloverleaf intersections, the pyramids of ancient Egypt, and the Biffel Tower. Symmetry concepts can be extremely useful in chemistry. By analyzing the sym- metry of molecules, wwe can predict infrared spectra, deseribe the types of orbitals uscd in bonding, predict optical activity, interpret electronic spectra, and study a number of additional molecular properties. Im this chapter, we first definc symmetey very specifi- cally in terms of five fundamental symmetry operations. We then describe how molc- cules can be classified on the basis of the types of sy mmetry they possess. We conclude with examples of how symmetry can be used to predict optical activity of molecules and to determine the number and types of infrared-active stretching vibrations. In Iater chapters, symmetry will be a valuabls tool in the construction of molecu- lar orbitals (Chapters 5 and 10) and in the interpretation of electronic spectra of coordi- nation compounds (Chapter 11) and vibrational spectra ot organometaltic compounds (Chapter 13). A molecular model kit is a very useful study aid for this chapter, even for those who can visualize three-dimensional objects easily. We strongly encourage the use of such a kit. 41 SYMMETRY ELEMENTS AND OPERATIONS All molecules can be described in terms of their symmetry, even if it is only to say they have none. Molecules or any other objects may contain symmetry elements such as mitror planes, axcs of rotation, and inversion centers. The actual reflection. rotation, or inversion is called the symmetry operation. To contain a given symmetry clement, a molecule must have exactly lhe same appearance after the operation as belore, In other words, photographs of the molceule (if such photographs were possible!) iaken from the same location before and after the symmetry operation would be indistinguishable. Ha symmetry operation yicids a molecule that can be distinguished from the original in 4-1 Symmetry Elements and Operations 79 FIGURE 4-3 Reficetions, (a) (b) such as acetylene or carbon dioxide have an infinite number of mirror planes that include the center line of the object. When the plane is perpendicular to the principal axis of rotation, it is called o, (horizontal). Other planes, which contain the principal axis of rotation, are labeled Tp OT Tg. Inversion (7) is a more complex operation. Each point moves through the center of the molecule to a position opposite the original position and as far from the central point as when it started.! An example of a molecule having a center of inversion is ethane in the staggered conformation, for which he inversion operation is shown in Figure 4-4. Many molecules that seem at first glance to have an inversion center do not: for example, methane and other tetrahedral molecules lack inversion symmetry. To see this, hold a methane model with two hydrogen atoms in the vertical plane on the right and two hydrogen atoms in the horizontal plane on the left, as in Figure 4-4. Inversion re- sults in two hydrogen atoms in the horizontal plane on the right and two hydrogen atoms ih the vertical plane on the left. Inversion is therefore not a symmetry operation of meihane, because the orientation of the molecule following the i operation differs from the original orientation. have inversion centers: tetrahedra, triangles, and pentagons do not (Figure 4-5). A rotation-reflection operation (S,) (sometimes called improper rotation) re- quires rotation of 360º/n, followed by reflection through a plane perpendicular to the axis of rotation. In methane, for example, a line through the carbon and bisecting the à ams, anguta » OCA Hg Eh Ko, H “St-er q os E o E Conter of inversion H, H 3 4 HZ i K ——+» BOTS 4 H H, FIGURE 4-4 Inversion. No center of inversion *Phis operation must be distinguished from lhe inversion of a lelrahedral carbon in a bimolecular re- action, which is more like that of an umbrella in a high wind. 80 chapter 4 Symmetry and Group Theory FIGURE 4-5 Figures (a) With and (b) Without Inversion Centers. O ASBO tb) angle between two hydrogen atoms on each side is an S4 axis. Phere are three such lines, for a total of three S4 axes. The operation requires a 90º rotation of the molecule followed by reflection through the plane perpendicular to the axis of rotation. Two 5, operations in suecession generate a C,;> operation. In methane, two S$4 operations gen- erate a C. These operations ate shown in Figure 4-6, along with a table of € and $ eguivalences for methane. Molecules sometimes have an S, axis tharis coincident with a C, axis. For example, in addition to the rotation axes described previously, snowilakes have S; (= 1), Sa, and S6 axes coincident with the Cg axis. Molecules may also have S2, axes coincident with C,: methane is an example, with Sq axcs coincident with Cy axes, as shown in Figure 4-6. Note that an S» operation is the same as inversion; an $, operation is the same as arcflection plane. The i and o notations are preferred in fhese cases. Symmetry elements and operations are summarized in Table 4-1. Rotation Angle Syminetry Operation 90? Sá 180º & Es!) a e 360º E ES FisS,; FIGURE 4-6 Improper Rotation or Rotatiun-Reflection 4-1 Symmetry Elements and Operations 81 TABLE 4.1 - RC - Summary Table of Symmetry Elements and. Operations Symmetry Operation Symmetry Element Operation Examples H Identity, E None Ali atoms unshitted CHECIBr A Br G Rotation, €> Rotation axis Rotation by 360º» prdichlorobenzene CI > q €s Ca e Cyclopentadienyi eroup G Benzenc <DD> , HO Reflection, o Mirror plane Reflection through a mirror z H plane no . Ferrocene (stagis Inversion. i Inversion center (point) Inversion through the center errocene (stugigered) Fe timproper axis) teflection in the plane perpendicular to the rotation axis 8, 6 , Elhane (staggered) fx Se Ferrocene (stageered) Fe Rotatin-reftection, 54 Rotaúion-reilection axis Rotation by 360%/m, followed by CH f ulg Sã  84 —chapter4 Symmety and Group Theory H E Harem (ON [+ / NaN PHS O NT nfs H H—C 0=c=0 F ar UN H Hei co, PF, ECCH, [Coten)a Pt" NH, H H F | é Ho A Ce NH E b / p Fil A , c=c c—ct 8— 0-0 HZDH o Eq Br / N / va | / n a H Br H Br Fe H cH, CHrCIBr HC=CCIBr HCIBrC — CHCIBr SF, HO, Br Br 1.5-dibromonaphthalene 1,3,5,7-tetrafluoro- eyclooctutetraene a BH unit) FIGURE 4-8 Molcenles to be Assigned to Point Groups. “on = eihylenediamine = NHsCHoCH&NH;, represented by NON. dodecahydro-cioso-dadecahorate (2-iom, B,aH55?” (cach comer has 4-2-1 GROUPS OF LOW AND HIGH SYMMETRY high symmetry. TABLE 4-2 Groups of Low Symmetry t. Determine whether the molecule belongs to one of the special cases of low or cases. These groups have tew or no symmetry operations and are described in Table 4-2. Group Symmetry Examples H | €, No symmetry other than CHFCIBr Am the identity operation Ff T es cl Bo cl G Only one mirror plane H,C=CCIBr X=€ H Br Br A Clay Fo Only an inversion center; HCBBrC- CHCIBr Se -Cva fow molecular examples (staggered conformation) 42 PointGroups 85 Low symmetry CRFCIBr has no symmetry other than the identity operation and has Cy symmetry, HoC==CCIBr has only one mirror plane and C, symmetry, and HCIBrC — CHCIBr in High symmetry Molecules with many symmetry operations may fit one of the high-symmetry cases of lincar, tctrabedral, octahedral, or icosahedraf symmetry with the characteristics de- scribed in Table 4-3. Molecules with very high symmetry are of two types, linear and polyhedral. Linear molecules having a center of inversion have Do. Symmetry; those lacking an inversion center have Cy Symmetry. The highly symmetric point groups Tu. On, and 4, are described in Table 4-3, Ltis helpful to note the C, axes of these mol- ccules. Molecules with T; symmetry have only €; and C; axes: those with Oy, sym- metry have Cy axes in addition to Ca and C5: and 4, molecules have €s, C3, and € axes. TABLE43 CC Groups of High Symmetr . Group — Description Examples Cor 1 cu s linea Vi finit a aa These molecules are linear, eith am infini je number of Ay ea freBlection plan q HE containing the rotation axis, They do not have a center of inversion, Doca These molevules are linear, with an infinite number of rotations and an infinite number of reflection planes containing lhe rotation axis. They also have perpendicular Co axes, a perpenilicutar reflection plane, and an inversion center. Ta Most (but not alt) molecules in this point group have H the tamiliar tetraheúra) geometry. They have foue C; | Ca axes, Three S4 axos, and six o planes. They have no Cy LH axes He H O, These molecuies include those of octahedral structure, F although some other geometrical forms, such as the cube, F share lhe same set of syimmetry operations. Among Lheir 48 F—sÉ-E Symmetry operations are four C, rotations, three C4 Á | rotations, and an inversion. F q h Ecosahedral structures are best recognized by their six Gs axes (as well as mamy olher Symmetry operations —120 total). BH,” with BH at euch vertex of an icosahedrou In addition, there are four other groups, 7, Ty, O, and 1, which are rarely seen in náture, These groups are discussed at lhe end of this sectáon. 86 chapter 4 Symmetry and Group Theory HCirhas Cosa * mmetry COy has Dyy symimetry; CHy-has tetrahedral (T,) symmetry, SF; has octahedral (04) symmetry, and BH bas icosabedral (4) symmetry “Fhere are now seven molecules left to be assigned to point groups ont of the original 15 4-2-2 OTHER GROUPS 2. Find the rotation axis with the highest n, the highest order C, axis for the molecule. This is the principal axis of the molecule, The rotation axes for the examples are shown in Figure 4-9. If they are all equiv- alent, any one can be chosen as the principal axis. FIGURE 4-9 Rotation Axes. & A E F FR JE N 7 N Fo | € fo > a E y NC NA F ! Us Pe, €, perpendicular to he plane of the page [Cote Br ! O ng Ha & 0-0, Br H €, porpendienlar to lhe HO, plane of the molecule | S-dibromonaphthalene | 3. Does the molecule have any C; axes perpendicular 10 the C, axis? FIGURE 4-10 Perpendicutar C; Axes. “The C, axes are shown im Figure 4-10. NHL, 1 5-dibromonaphihalone No No Gà | HO, No No 13.5,7-tetrafluoroeylooctaterracne f NT Ns f2 Ç No + Se? LN Hg B UN ELCCH, ICotem* Yes Yes