Preview general chemistry atoms first by young, susan MVining, williamday, robertabotch, beatrice (2017)

Preview General Chemistry Atoms First by Young, Susan MVining, WilliamDay, RobertaBotch, Beatrice (2017) Preview General Chemistry Atoms First by Young, Susan MVining, WilliamDay, RobertaBotch, Beatrice (2017) Preview General Chemistry Atoms First by Young, Susan MVining, WilliamDay, RobertaBotch, Beatrice (2017) Preview General Chemistry Atoms First by Young, Susan MVining, WilliamDay, RobertaBotch, Beatrice (2017) Preview General Chemistry Atoms First by Young, Susan MVining, WilliamDay, RobertaBotch, Beatrice (2017)

Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 General Chemistry Atoms First Susan M Young Hartwick College William J Vining State University of New York, Oneonta Roberta Day University of Massachusetts, Amherst Beatrice Botch University of Massachusetts, Amherst Australia • Brazil • Mexico • Singapore • United Kingdom • United States Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 General Chemistry: Atoms First © 2018 Cengage Learning Susan M Young, William J Vining, Roberta Day, Beatrice Botch ALL RIGHTS RESERVED No part of this work covered by the copyright herein may be reproduced or distributed in any form or by any means, except as permitted by U.S copyright law, without the prior written permission of the Product Director: Dawn Giovanniello copyright owner Product Manager: Lisa Lockwood Content Developer: Brendan Killion For product information and technology assistance, contact us at Cengage Learning Customer & Sales Support, 1-800-354-9706 Product Assistant: Nellie Mitchell For permission to use material from this text or product, Marketing Manager: Janet Del Mundo submit all requests online at www.cengage.com/permissions Content Project Manager: Teresa L Trego Further permissions questions can be e-mailed to permissionrequest@cengage.com Digital Content Specialist: Alexandra Purcell Art Director: Sarah B Cole Manufacturing Planner: Rebecca Cross Library of Congress Control Number: 2017944192 Intellectual Property Analyst: Christine Myaskovsky ISBN: 978-1-337-61229-6 Intellectual Property Project Manager: Erika Mugavin Cengage Learning Production Service/Compositor: Lumina Datamatics Ltd Text Designer: Pettengill Designs Cover Designer: Sarah B Cole Cover Image Credit: isak55©Shutterstock 20 Channel Center Street Boston, MA 02210 USA Cengage Learning is a leading provider of customized learning solutions with employees residing in nearly 40 different countries and sales in more than 125 countries around the world. Find your local representative at www.cengage.com Cengage Learning products are represented in Canada by Nelson Education, Ltd To learn more about Cengage Learning Solutions, visit www.cengage.com Purchase any of our products at your local college store or at our preferred online store www.cengagebrain.com Printed in the United States of America Print Number: 01   Print Year: 2017 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 Contents Chemistry: Matter on the Atomic Scale 1.1 What Is Chemistry? 1.1a 1.1b The Scale of Chemistry Measuring Matter 1.2 Classification of Matter 1.2a 1.2b 1.2c Atoms and Elements 2.1 Development of Atomic Theory 30 2.1b Early Models and the Advent of Scientific Experimentation Dalton’s Atomic Theory 30 32 Classifying Matter on the Atomic Scale Classifying Pure Substances on the Macroscopic Scale Classifying Mixtures on the Macroscopic Scale 2.2 Subatomic Particles and Atomic Structure 33 2.2a 2.2b Electrons and Protons The Nuclear Model of the Atom 33 37 1.3 Units and Measurement 10 2.3 Atoms and Isotopes 40 1.3a 1.3b 1.3c 1.3d Scientific Units and Scientific Notation SI Base Units Derived Units Significant Figures, Precision, and Accuracy 10 12 14 16 2.3a 2.3b 2.3c Atomic Number, Mass Number, and Atomic Symbols Isotopes and Atomic Weight Nuclear Stability 40 42 44 1.4 Unit Conversions 20 2.4 Elements and the Periodic Table 47 1.4a 1.4b Dimensional Analysis Multistep Problem Solving 20 22 Introduction to the Periodic Table 47 The Mole and Molar Mass of Elements 53 Avogadro’s Number and the Mole Molar Mass of Elements 53 54 Unit Recap 25 2.1a 2.4a 2.5 2.5a 2.5b Unit Recap Contents 29 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 56 iii Electromagnetic ­Radiation and the Electronic ­Structure of the Atom 59 Electron Configurations and the Properties of Atoms 79 3.1 Electromagnetic Radiation 60 4.1 Electron Spin and Magnetism 80 3.1a 3.1b Wavelength and Frequency The Electromagnetic Spectrum 60 61 4.1a 4.1b Electron Spin and the Spin Quantum Number, ms Types of Magnetic Materials 80 80 3.2 Photons and Photon Energy 62 4.2 Orbital Energy 81 3.2a The Photoelectric Effect 62 4.2a Orbital Energies in Single- and Multielectron Species 81 3.3 Atomic Line Spectra and the Bohr Model of Atomic Structure 4.3 Electron Configuration of Elements 82 64 3.3a 3.3b Atomic Line Spectra The Bohr Model 64 65 4.3a 4.3b 4.3c 4.3d The Pauli Exclusion Principle Electron Configurations for Elements in Periods 1–3 Electron Configurations for Elements in Periods 4–7 Electron Configurations and the Periodic Table 82 83 87 91 3.4 Quantum Theory of Atomic Structure 68 3.4a 3.4b Wave Properties of Matter The Schrödinger Equation and Wave Functions 68 70 4.4 Properties of Atoms 93 3.5 Quantum Numbers, Orbitals, and Nodes 71 4.4a 4.4b 4.4c 4.4d Trends in Orbital Energies Atomic Size Ionization Energy Electron Affinity 93 95 97 98 3.5a 3.5b 3.5c 3.5d Quantum Numbers Orbital Shapes Nodes Orbital Energy Diagrams and Changes in Electronic State Unit Recap 71 72 74 Unit Recap 100 75 76 iv Contents Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 Ionic and Covalent Compounds 5.1 5.1a 5.1b 5.1c 5.1d 5.1e 103 Formation and Electron Configuration of Ions 104 Coulomb’s Law Cations Anions Lewis Symbols Ion Size 104 105 109 112 113 5.2 Polyatomic Ions and Ionic Compounds 115 5.2a 5.2b 5.2c Polyatomic Ions Representing Ionic Compounds with Formulas Naming Ionic Compounds 115 116 117 5.3 Covalent Compounds 118 5.3a 5.3b Introduction to Covalent Compounds Representing Covalent Compounds with Molecular and Empirical Formulas Representing Covalent Compounds with Molecular Models Naming Covalent Compounds (Binary Nonmetals and Hydrocarbons) Naming Covalent Compounds (Inorganic Acids) Identifying Covalent and Ionic Compounds 118 5.3c 5.3d 5.3e 5.3f Unit Recap 119 122 Covalent Bonding 131 6.1 Covalent Bonding and Lewis Structures 132 6.1a 6.1b 6.1c 6.1d Fundamentals of Covalent Bonding Lewis Structures Drawing Lewis Structures Exceptions to the Octet Rule 132 133 134 137 6.2 Properties of Covalent Bonds 139 6.2a 6.2b 6.2c Bond Order, Bond Length, and Bond Energy Bond Polarity Formal Charge 139 143 146 6.3 Resonance and Bond Properties 148 6.3a 6.3b Resonance Structures Resonance Structures, Bond Order, Bond Length, and Bond Energy Resonance Structures, Formal Charge, and Electronegativity 148 6.3c Unit Recap 150 151 154 122 124 127 128 Contents Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 v Molecular Shape and Bonding Theories 157 7.1 Valence-Shell Electron-Pair Repulsion Theory and Molecular Shape 158 7.1a 7.1b 7.1c VSEPR and Electron-Pair Geometry Shape (Molecular Geometry) Molecular Polarity 158 161 164 7.2 Valence Bond Theory and Hybrid Orbitals 167 7.2a 7.2b 7.2c 7.2d 7.2e Two Theories of Bonding sp3 Hybrid Orbitals sp2 Hybrid Orbitals sp Hybrid Orbitals Hybrid Orbitals and Expanded Valence 167 168 171 172 175 7.3 Pi Bonding 177 7.3a 7.3b 177 7.3c 7.3d Formation of Pi Bonds Pi Bonding in Ethene, C2H4; Acetylene, C2H2; and Allene, CH2CCH2 Pi Bonding in Benzene, C6H6 Conformations and Isomers 7.4 Molecular Orbital Theory 185 7.4a 7.4b 7.4c 7.4d 7.4e 7.4f Sigma Bonding and Antibonding Molecular Orbitals 185 Pi Bonding and Antibonding Molecular Orbitals 186 Molecular Orbital Diagrams (H2 and He2) 186 Molecular Orbital Diagrams 187 Molecular Orbital Diagrams (Heteronuclear Diatomics) 190 Molecular Orbital Diagrams (More Complex Molecules) 191 Unit Recap 179 181 182 Stoichiometry 195 8.1 Stoichiometry and Compound Formulas 196 8.1a 8.1b 8.1c 8.1d 8.1e Molar Mass of Compounds and Element Composition 196 Percent Composition 199 Empirical Formulas from Percent Composition 200 Determining Molecular Formulas 202 Hydrated Compounds 204 8.2 Stoichiometry and Chemical Reactions 206 8.2a 8.2b 8.2c Chemical Reactions and Chemical Equations Balancing Chemical Equations Reaction Stoichiometry 206 208 211 8.3 Stoichiometry and Limiting Reactants 216 8.3a 8.3b Limiting Reactants Percent Yield 216 219 8.4 Chemical Analysis 221 8.4a 8.4b Determining a Chemical Formula Analysis of a Mixture 221 226 Unit Recap 227 192 vi Contents Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 Chemical Reactions and Solution Stoichiometry 229 9.1 Types of Chemical Reactions 230 9.1a 9.1b Combination and Decomposition Reactions Displacement Reactions 230 231 9.2 Aqueous Solutions 233 9.2a 9.2b Compounds in Aqueous Solution Solubility of Ionic Compounds 233 235 9.3 Reactions in Aqueous Solution 237 9.3a 9.3b 9.3c Precipitation Reactions and Net Ionic Equations Acid–Base Reactions Gas-Forming Reactions 237 240 244 9.4 Oxidation–Reduction Reactions 246 9.4a 9.4b 9.4c Oxidation and Reduction Oxidation Numbers and Oxidation States Recognizing Oxidation–Reduction Reactions 246 247 249 9.5 Stoichiometry of Reactions in Aqueous Solution 251 Solution Concentration and Molarity Preparing Solutions of Known Concentration Solution Stoichiometry Titrations (Part 1) Titrations (Part 2) 251 254 258 260 264 9.5a 9.5b 9.5c 9.5d 9.5e Unit Recap 266 10 Thermochemistry 271 10.1 Energy 272 10.1a 10.1b 272 273 Energy and Energy Units Principles of Thermodynamics 10.2 Enthalpy 10.2a 10.2b Enthalpy Representing Energy Change 10.3 Energy, Temperature Changes, and Changes of State 10.3a 10.3b 10.3c Heat Transfer and Temperature Changes: Specific Heat Capacity Heat Transfer between Substances: Thermal Equilibrium and Temperature Changes Energy, Changes of State, and Heating Curves 275 277 278 278 281 283 10.4 Enthalpy Changes and Chemical Reactions 287 10.4a 10.4b 10.4c 10.4d 10.4e Enthalpy Change for a Reaction Enthalpy Change and Chemical Equations Bond Energy and Enthalpy of Reaction Constant-Pressure Calorimetry Constant-Volume Calorimetry 287 288 290 291 293 10.5 Hess’s Law 295 10.5a 295 Hess’s Law 10.6 Standard Heats of Reaction 297 10.6a 10.6b 297 301 Standard Heat of Formation Using Standard Heats of Formation Unit Recap Contents 275 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 304 vii 11 Gases 307 11.1 Properties of Gases 308 11.1a 11.1b 308 309 Overview of Properties of Gases Pressure 11.2 Historical Gas Laws 311 11.2a 11.2b 11.2c 311 312 314 Boyle’s Law: P V kB Charles’s Law: V kC T Avogadro’s Law: V kA n 12 Intermolecular Forces and the Liquid State 339 12.1 Kinetic Molecular Theory, States of Matter, and Phase Changes 340 12.1a 12.1b 12.1c 340 342 343 Condensed Phases and Intermolecular Forces Phase Changes Enthalpy of Vaporization 12.2 Vapor Pressure 344 12.2a 12.2b 344 Dynamic Equilibrium and Vapor Pressure Effect of Temperature and Intermolecular Forces on Vapor Pressure Boiling Point Mathematical Relationship between Vapor Pressure and Temperature 11.3 The Combined and Ideal Gas Laws 316 11.3a 11.3b 11.3c 316 317 318 12.2c 12.2d 11.4 Partial Pressure and Gas Law Stoichiometry 321 12.3 Other Properties of Liquids 354 11.4a 11.4b 11.4c 321 323 324 12.3a 12.3b 12.3c 354 356 356 11.5 Kinetic Molecular Theory 326 12.4 The Nature of Intermolecular Forces 357 11.5a 11.5b 11.5c 11.5d 326 328 331 333 12.4a 12.4b 12.4c Dipole–Dipole Intermolecular Forces Dipole–Induced Dipole Forces Induced Dipole–Induced Dipole Forces 357 359 360 12.5 Intermolecular Forces and the Properties of Liquids 361 12.5a 12.5b 12.5c 361 362 364 The Combined Gas Law The Ideal Gas Law The Ideal Gas Law, Molar Mass, and Density Introduction to Dalton’s Law of Partial Pressures Partial Pressure and Mole Fractions of Gases Gas Laws and Stoichiometry Kinetic Molecular Theory and the Gas Laws Molecular Speed, Mass, and Temperature Gas Diffusion and Effusion Nonideal Gases Unit Recap 336 Surface Tension Viscosity Capillary Action Effect of Polarizability on Physical Properties Effect of Hydrogen Bonding on Physical Properties Quantitative Comparison of Intermolecular Forces Unit Recap 346 349 352 367 viii Contents Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 13 The Solid State 371 14 Chemical Mixtures: Solutions and Other Mixtures 372 13.1a 13.1b 372 373 14.1 Quantitative Expressions of Concentration 412 13.2 Metallic Solids 376 14.1a 14.1b 412 413 13.2a 13.2b 13.2c 13.2d 376 377 378 382 Types of Solids The Unit Cell Simple Cubic Unit Cell Body-Centered Cubic Structure Closest-Packed Structure X-ray Diffraction 13.3 Ionic Solids 384 13.3a 13.3b 13.3c 13.3d 384 388 391 392 Holes in Cubic Unit Cells Cesium Chloride and Sodium Chloride Structures Zinc Blende (ZnS) Structure Complex Solids 13.4 Bonding in Metallic and Ionic Solids 394 13.4a 13.4b 394 396 Band Theory Lattice Energy and Born–Haber Cycles 13.5 Phase Diagrams 399 13.5a 13.5b 399 400 Phase Changes Involving Solids Phase Diagrams Unit Recap 406 Review of Solubility Concentration Units 14.2 Inherent Control of Solubility 14.2a 14.2b 14.2c 14.2d Entropy and Thermodynamic Control of Chemical Processes Gas–Gas Mixtures Liquid–Liquid Mixtures Solid–Liquid Mixtures 417 417 419 421 423 14.3 External Control of Solubility 426 14.3a 14.3b 426 428 Pressure Effects: Solubility of Gases in Liquids Effect of Temperature on Solubility 14.4 Colligative Properties 430 14.4a 14.4b 14.4c 14.4d 430 435 437 439 Osmotic Pressure Vapor Pressure Lowering Boiling Point Elevation Freezing Point Depression 14.5 Other Types of Mixtures 441 14.5a 14.5b 441 442 Alloys Colloids Unit Recap Contents 411 13.1 Introduction to Solids Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 445 ix C—H s bond H C C H H C C H One C—C s bond and two C—C p bonds Figure 7.3.6  Sigma bonding in acetylene The sp-hybridized carbon atoms in acetylene each have two unhybridized p orbitals that are not involved in sigma bonding, and each contains a single electron (Figure 7.3.7) Energy, E 2p Two unhybridized p orbitals Orbital hybridization 2s Two sp hybrid orbitals on each C in C2H2 Isolated C atom Figure 7.3.7  Formation of hybrid orbitals for the carbon atoms in acetylene Each pair of unhybridized 2p orbitals (one 2p orbital from each carbon atom) forms a pi bond between the carbon atoms There are two pairs of unhybridized 2p orbitals, so two pi bonds are formed The two pi bonds are oriented 90° from each other because the unhybridized 2p orbitals on each carbon are at 90° from each other A complete picture of the sigma and pi bonding in acetylene is shown in Figure 7.3.8 H C C H Figure 7.3.8  Sigma and pi bonding in acetylene Allene The outer C atoms in allene are sp2 hybridized, and the central C atom is sp hybridized Each hybrid orbital is used to form a sigma bond to another atom (Figure 7.3.9) The three C atoms in allene are also connected by pi bonds Because each 180 Unit Molecular Shape and Bonding Theories Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 C—H s bond H H C H H C H H C H C C Interactive Figure 7.3.10 Explore sigma and pi bonding in allene C H H One C—C s bond and one C—C p bond H H C C C H Figure 7.3.9  Sigma bonding in allene Sigma and pi bonding in allene p orbital on the outer C atoms overlaps with a different p orbital on the central C atom, the two outer 3CH2 groups are aligned at 90° to each other (Interactive Figure 7.3.10) 7.3c Pi Bonding in Benzene, C6H6 The cyclic compound benzene, C6H6, is one of the most important organic molecules The molecule is composed of six carbon atoms in a ring with alternating single and double bonds, and each carbon also bonds to a single hydrogen atom Benzene has two equivalent resonance structures H H H C C H C H H C C C C H C C C C H H H H H C C C C C C H H C H H 2 Each C atom in benzene is sp hybridized, and the sp hybrid orbitals are used to form sigma bonds to two carbon atoms and one hydrogen atom The trigonal planar electron-pair geometry around each carbon atom results in a planar ring structure (Figure 7.3.11) Like ethene, each sp2-hybridized carbon atom in benzene has an unhybridized p orbital that is used to form pi bonds, and the pi bonds lie above and below the plane containing the carbon–carbon and carbon–hydrogen sigma bonds The pi bonding in benzene is more complex than in ethene, however, because of the benzene resonance structures The two equivalent resonance structures for benzene indicate that the molecule does not have three pi bonds that are each localized between two carbon atoms Instead, the six unhybridized p orbitals on carbon form one delocalized pi bonding system that lies above and below the plane of the molecule (Figure 7.3.12) Unit Molecular Shape and Bonding Theories H H Figure 7.3.11  Sigma bonding in benzene H H H C C C C C C H H H Figure 7.3.12  Pi bonding in benzene Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 181 Although it can be difficult to represent the resonance hybrid for a molecule, chemists often use a ring when drawing the structure of benzene to represent the delocalized pi bonding system H H H C C C C C C H Interactive Figure 7.3.13 Explore sigma and pi bonding in benzene H H or C C C C C H H H H Viewing the sigma and pi systems in benzene together shows the planar shape of the molecule and the delocalized pi electron density that lies above and below the plane of the molecule (Interactive Figure 7.3.13) Pi bonds form due to overlap of two or more p orbitals, but they can also form from the overlap of p and d orbitals or two d orbitals In ethene, acetylene, allene, and benzene, the number of pi bonds formed by a carbon atom is related to the number of unhybridized p orbitals available on that atom The general relationship between atom hybridization, the number of unhybridized p orbitals, and the number of possible p2p pi bonds is shown in Interactive Table 7.3.1 C H H Sigma and pi bonding in benzene Interactive Table 7.3.1 Relationship between Hybridization and Number of Possible p–p Pi Bonds Number of Structural Pairs on the Central Atom Hybridization Unhybridized p Orbitals Number of Possible p–p Pi Bonds sp Two p 2 One p None sp sp 7.3d Conformations and Isomers The presence or absence of pi bonds in a molecule affects its physical properties For example, acetylene, C2H2, has two pi bonds and reacts with H2, whereas ethane, C2H6, has no pi bonds and does not react with H2 In addition, pi bonds affect the physical shape of a molecule, which relates to the number of possible conformations and isomers a molecule can adopt 182 Unit Molecular Shape and Bonding Theories Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 Conformations are the different three-dimensional arrangements of atoms in a molecule that can be interconverted by rotation around single bonds Consider the butane conformations shown in Interactive Figure 7.3.14 Each differs only in the orientation of the right side of the molecule The structures were generated by rotating one half of the molecule with respect to the other half, around the carbon–carbon sigma bond Carbon–carbon sigma bond rotation in butane occurs easily because a sigma bond has bonding electron density directly between two bonded atoms Rotation around a sigma bond does not affect the bonding electrons that lie between the bonded nuclei There is no limit to the number of possible conformations of a butane molecule, and the ends of the molecule rotate freely at room temperature Isomers are two or more substances that have the same chemical formula but have different properties because of the different arrangement of atoms Molecules with pi bonds are one example of compounds that can exist as more than one isomer Consider the bond rotation in a molecule containing a pi bond Because a pi bond has electron density both above and below the internuclear axis, a pi bond cannot rotate freely Rotation around a double bond (a sigma bond and a pi bond) results in breaking the pi bond, a process that requires a significant amount of energy Such free rotation therefore does not happen at room temperature (Interactive Figure 7.3.15) The energy barrier that prevents rotation of pi bonds means that two isomers that differ by rotation about the pi bond will not easily interconvert at room temperature Consider the two possible isomers of 1,2-dichloroethene (Figure 7.3.16) Cl Cl C H C H H cis-1,2-dichloroethene Explore conformations in alkanes Some conformations of butane Interactive Figure 7.3.15 Compare single- and double-bond rotation H Cl C Interactive Figure 7.3.14 C H H H C Cl trans-1,2-dichloroethene Figure 7.3.16  Two unique isomers of 1,2-dichloroethene H (a) C H H H H C C H H (b) Carbon–carbon bond rotation in (a) ethane and (b) ethene These two structures differ only in the placement of the Cl and H atoms about the C5C double bond In the structure labeled cis, both Cl atoms are on the same side of the double bond, whereas in the structure labeled trans, the Cl atoms are on opposite sides of the double bond These two structures cannot interconvert easily because doing so would require breaking the C3C pi bond; therefore, the two structures represent two unique isomers Unit Molecular Shape and Bonding Theories Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 183 Example Problem 7.3.2  Identify isomers and conformations Consider the following set of molecules Gray spheres represent carbon atoms, white spheres represent hydrogen atoms, and green spheres represent chlorine atoms Which pairs represent conformations of the same molecule, and which pairs represent isomers? A B C D Solution: You are asked to identify conformations and isomers of a compound You are given a set of molecular structures B and C are conformations of the same compound They have the same chemical formula 1C3H3Cl3 and are related by rotation around a carbon–carbon single bond C and D are isomers They have the same chemical formula 1C3H3Cl3 and are related by rotation around a carbon–carbon double bond C is the cis isomer, and D is the trans isomer B and D are also isomers B is the cis isomer, and D is the trans isomer They are related by rotation around a carbon–carbon double bond and rotation around a carbon–carbon single bond A is a unique compound 1C3H2Cl4 Video Solution 7.3.2 184 Unit Molecular Shape and Bonding Theories Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 7.4 Molecular Orbital Theory 7.4a Sigma Bonding and Antibonding Molecular Orbitals Molecular orbital theory is similar in many ways to valence bond theory Bond formation is viewed in a similar manner, where overlapping orbitals on different atoms increase attractive forces between electrons and nuclei The two theories differ, however, in how the resulting orbital combinations are viewed In valence bond theory, orbitals in a molecule are thought to be localized on atoms, with some overlap of the orbitals between bonded nuclei In molecular orbital theory, orbitals in a molecule are thought to be spread out (delocalized) over many atoms Valence bond theory is often referred to as a localized bonding theory, whereas molecular orbital theory is referred to as a delocalized bonding theory One of the most important and unique aspects of molecular orbital theory is its ability to predict the shapes and energies of orbitals that contain no electrons That is, molecular orbital theory explains not only how electrons are arranged in the ground state but also how they might be arranged in an excited electronic state According to molecular orbital theory, when any number of atomic orbitals overlap to form molecular orbitals, an equal number of molecular orbitals are formed When two s orbitals overlap, for example, they form two new orbitals: one at a lower energy than the original s orbitals and one at a higher energy than the original s orbitals Consider the formation of H2 Each H atom has a single electron in a 1s orbital Adding the two 1s orbitals (the 1s wave functions) together results in the formation of a bonding molecular orbital (Figure 7.4.1) that increases the electron density between the bonded nuclei This bonding molecular orbital is a sigma 1s2 molecular orbital because electron density lies along the internuclear axis It is labeled s1s, where the subscript identifies the atomic orbitals that contributed to form the molecular orbital This molecular orbital is lower in energy than the separated hydrogen 1s orbitals because electrons occupying this orbital experience increased attractive forces to the hydrogen nuclei Subtracting the two 1s orbitals (the 1s wave functions) results in the formation of an antibonding molecular orbital (Interactive Figure 7.4.2) that decreases the ­electron density between the bonded nuclei This bonding molecular orbital is a sigma 1s2 ­molecular orbital because electron density lies along the internuclear axis It is labeled s*1s, where the asterisk (*) indicates its antibonding nature and the subscript identifies the atomic orbitals that contributed to form the molecular orbital This molecular orbital is higher in energy than the separated hydrogen 1s orbitals because electrons occupying this orbital experience decreased attractive forces to the hydrogen nuclei In addition, the antibonding molecular orbital has a node, a plane on which there is zero probability for finding an electron Unit Molecular Shape and Bonding Theories 1s 1s s-molecular orbital (bonding) Figure 7.4.1  A bonding s1s molecular orbital Interactive Figure 7.4.2 Explore bonding and antibonding molecular orbitals Nodal plane 1s Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 21s s*-molecular orbital (antibonding) An antibonding s*1s molecular orbital 185 Sigma bonding and antibonding molecular orbitals can also form from the interactions of p orbitals When two 2p orbitals are added and subtracted in a head-on alignment along the internuclear axis, one sigma bonding 1s2p molecular orbital and one sigma antibonding 1s*2p molecular orbital result (Figure 7.4.3) Notice the formation of a new planar node in the antibonding 1s*2p molecular orbital Nodal plane 2pz 7.4b Pi Bonding and Antibonding Molecular Orbitals Just as in valence bond theory, pi 1p2 molecular orbitals result from the sideways overlap of p orbitals When two 2p orbitals are added and subtracted, a pi bonding orbital and a pi antibonding orbital form (Interactive Figure 7.4.4) The p2p molecular orbital is lower in energy than the original 2p orbitals; the p* 2p molecular orbital is higher in energy (less stable) than the original 2p orbitals Because there are two 2p orbitals on each atom that can overlap to form pi bonds, a total of four pi molecular orbitals are possible, two pi bonding molecular orbitals 1p2p and two pi antibonding molecular orbitals 1p* 2p 7.4c Molecular Orbital Diagrams (H2 and He2) One of the strengths of molecular orbital theory is its ability to describe the energy of both occupied and unoccupied molecular orbitals for a molecule A molecular orbital diagram shows both the energy of the atomic orbitals (from the atoms that are combining) and the energy of the molecular orbitals Consider the molecular orbital diagram for H2 (Figure 7.4.5) 2pz s*2pz molecular orbital (antibonding) 2pz –2pz s2pz molecular orbital (bonding) Figure 7.4.3  Bonding 1s2p and antibonding 1s*2p molecular orbitals Interactive Figure 7.4.4 Compare sigma and pi bonding and antibonding molecular orbitals Nodal plane 2px –2px p*2px molecular orbital (antibonding) 2px p2px molecular orbital (bonding) Energy s*1s 2px Molecular orbitals Bonding (p2p) and antibonding (p*2p) molecular orbitals 1s 1s Atomic orbital Atomic orbital s1s Figure 7.4.5  Molecular orbital diagram for H2 186 Unit Molecular Shape and Bonding Theories Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 Notice the following features of the H2 molecular orbital diagram: ●● ●● ●● ●● The atomic orbitals are placed on the outside of the diagram, and the molecular orbitals are placed between the atomic orbitals, in the center of the diagram Valence electrons are shown in atomic orbitals, and electrons are assigned to molecular orbitals according to the Pauli exclusion principle and Hund’s rule Dashed lines are used to connect molecular orbitals to the atomic orbitals that contribute to their formation Bonding molecular orbitals are lower in energy than the atomic orbitals that contribute to their formation ␴*1s Antibonding molecular orbitals are higher in energy than the atomic orbitals that ­contribute to their formation The electron configuration for H2 is written 1s1s 2 , showing the presence of two ­electrons in the s1s molecular orbital The molecular orbital diagram for dihelium 1He2 is the same as that of hydrogen, with the addition of two more electrons (Figure 7.4.6) The electron configuration for dihelium is 1s1s 2 1s*1s 2 Molecular orbital diagrams provide a method for determining the bond order between two atoms in a molecule (7.1) bond order ½ [number of electrons in bonding orbitals number of electrons in antibonding orbitals] Molecular orbitals Energy ●● 1s 1s Atomic orbital Atomic orbital ␴1s Figure 7.4.6  Molecular orbital diagram for He Interactive Figure 7.4.7 Predict electron configuration and bond properties for first-row diatomic species (7.1) ␴* H3H bond order in H2 ½ [2 0] He3He bond order in He2 ½ [2 2] The bond order in H2 is the same as that predicted from its Lewis dot structure The bond order in He2 is zero, suggesting that this molecule probably does not exist Calculated bond orders for other hydrogen and helium species (Interactive Figure 7.4.7) suggest that H21, H22, and He21 have weak bonds 1bond order 0.52 and are predicted to exist 7.4d Molecular Orbital Diagrams The homonuclear diatomic molecules of the second period, Li2 F2, have both 2s and 2p valence atomic orbitals The molecular orbital diagram for the second-row homonuclear diatomics (Figure 7.4.8) therefore shows the formation of molecular orbitals from overlap of these valence atomic orbitals Unit Molecular Shape and Bonding Theories ␴ H2+ H2 H22 He2+ He2 2 2 Number of antibonding electrons 1 1.0 0.5 0.5 Species Number of bonding electrons Bond order 0.5 Molecular orbital diagrams for first-row diatomic species Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 187 s*2p s*2p p*2p p*2p p*2p p*2p 2p 2p 2p 2p 2p 2p 2p 2p 2p p2p p2p Energy, E Energy, E s2p 2p 2p 2p p2p p2p s2p s*2s s*2s 2s 2s Atomic orbitals (a) 2s Atomic orbitals s2s Molecular orbitals 2s Atomic orbitals (b) Atomic orbitals s2s Molecular orbitals Figure 7.4.8  Molecular orbital diagram for the second-row homonuclear diatomic molecules (a) Li2, Be2, B2, C2, N2 and (b) O2, F2, Ne2 Notice the following features of the molecular orbital diagram for the second-row homonuclear diatomics: ●● ●● ●● For Li2, Be2, B2, C2, and N2, the p2p molecular orbitals are lower in energy than the s2 p molecular orbital For O2, F2, and Ne2, the energies of these molecular orbitals is reversed Only the valence atomic orbitals and resulting valence molecular orbitals are shown in the molecular orbital diagram Each atom contributes four atomic orbitals (2s and three 2p orbitals), resulting in the formation of eight molecular orbitals There are two p2p molecular orbitals (of equal energy) and two p*2p molecular orbitals (of equal energy) We will follow the common practice of using the relative molecular orbital energies in Figure 7.4.8(a) for all of the homonuclear diatomic molecules because it correctly predicts the number of bonding and antibonding electrons and the bond order in these ­species The homonuclear molecular orbital diagram for oxygen, O2 , is shown in Figure 7.4.9 The molecular orbital diagram shows that the O3O bond order is two and that oxygen is­ paramagnetic with two unpaired electrons s*2p p*2p p*2p 2p 2p 2p s2p p2p p2p s*2s 2s 2s Atomic orbitals O2: [He](s2s)2(s*2s)2(p2p)4(s2p)2(p*2p)2 Paramagnetic (two unpaired electrons) O3O bond order in O2 ½ [8 4] 2p 2p 2p Energy, E ●● s2s Atomic orbitals Molecular orbitals Figure 7.4.9  Molecular orbital diagram for O2 188 Unit Molecular Shape and Bonding Theories Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 As shown in Interactive Figure 7.4.10, in its liquid state, O is attracted to a strong magnet Notice that valence bond theory and Lewis dot structures not explain why liquid oxygen is attracted to a magnetic field This is one example of the more accurate nature of molecular orbital theory Abbreviated molecular diagrams for the second-row homonuclear diatomics are shown in Interactive Figure 7.4.11 Interactive Figure 7.4.10 Explore the paramagnetic nature of O2 Interactive Figure 7.4.11 Investigate molecular orbital diagrams for the second-row homonuclear diatomics s*2p p*2p s2p p2p Liquid oxygen adheres to the poles of a strong magnet s*2s s2s Species Be2 B2 C2 N2 O2 F2 2 8 Number of antibonding electrons 2 2 1 Number of bonding electrons Bond order Li2 Molecular orbital diagrams for Li2 F2 Example Problem 7.4.1  Predict electron configuration and bond properties for homonuclear diatomic molecules What is the Ne3Ne bond order in Ne2 and Ne1 2? Solution: You are asked to identify the bond order in a diatomic molecule or ion You are given the formula of the molecule or ion c Unit Molecular Shape and Bonding Theories Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 189 b Example Problem 7.4.1  (continued) To answer this question, the homonuclear diatomic molecular orbital diagram must be filled in with the appropriate number of electrons The diagram below on the left is filled in for Ne2, which has a total of eight bonding electrons and eight antibonding electrons The bond order is therefore In Ne21, however, there are only seven antibonding electrons, and the bond order is s*2p s*2p p*2p p*2p p*2p p*2p 2p 2p 2p 2p 2p 2p p2p p2p 2p 2p 2p s2p Energy, E Energy, E s2p 2p 2p 2p p2p p2p Video Solution 7.4.1 s*2s 2s s*2s 2s 2s s2s 2s s2s Interactive Figure 7.4.12 Explore molecular orbital diagrams for heteronuclear diatomic molecules s*2p 7.4e Molecular Orbital Diagrams (Heteronuclear Diatomics) 2 NO: [He](s2s) (s*2s) (p2p) (s2p) (p*2p) p*2p p*2p 2p 2p 2p 2p 2p 2p Energy, E Using what we have learned about homonuclear diatomic molecular orbital diagrams, we can now construct diagrams for heteronuclear diatomic molecules, compounds composed of two atoms of different elements The molecular orbital diagram for the heteronuclear diatomic compound nitrogen monoxide, NO, is shown in Interactive Figure 7.4.12 s2p p2p Paramagnetic (one unpaired electron) N3O bond order in NO ½ [8 3] 2.5 Notice that the heteronuclear diatomic diagram is very similar to the homonuclear diagram For example, the diagrams have the same types of molecular orbitals (sigma and pi, bonding and antibonding) However, the energy of the valence atomic orbitals is not the same Oxygen is more electronegative than nitrogen, and its atomic orbitals are lower in energy 2s p2p s*2s s 2s N atomic orbitals NO molecular orbitals 2s O atomic orbitals Molecular orbital diagram for nitrogen monoxide 190 Unit Molecular Shape and Bonding Theories Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 7.4f Molecular Orbital Diagrams (More Complex Molecules) Most molecules are much more complex than those we have examined here Molecular orbital theory has proved to be very powerful in interpreting and predicting the bonding in virtually all molecules The molecular orbital diagram for a slightly more complex compound, methanev, s shown in Figure 7.4.13, along with the valence bond theory model of bonding in methane Energy, E s* s* 2p 2p 2p 1s 1s 1s 1s Atomic orbitals s 2s Atomic orbitals sp3 hybrid orbital H Sigma bond s Molecular orbitals H H C H Figure 7.4.13  Both molecular orbital theory and valence bond theory show the presence of four sigma bonds in methane Although the molecular orbital diagram in Figure 7.4.13 does not greatly resemble that of the diatomics, it is possible to recognize that the diagram shows four sigma bonding molecular orbitals, each with two electrons This diagram therefore reinforces the valence bond theory model of methane, with four C3H sigma bonds Today, although molecular orbital diagrams for complex molecules can be developed on paper, “molecular modeling” computer programs are typically used to calculate molecular orbital shapes and energies These programs not always produce accurate results, however, and their results must be compared against experimental information For example, photoelectron spectroscopy is one of the more direct methods used to determine orbital energies. In photoelectron spectroscopy, ultraviolet light or x-rays are used to remove electrons from molecules Assuming the energy levels of an ionized molecule are essentially the same as those in the uncharged molecule, scientists can use photoelectron spectra to understand orbital energies in molecules Lower-energy peaks correspond to higher-energy orbitals because less energy is required to remove electrons in those orbitals The photoelectron spectrum for methane (Interactive Figure 7.4.14) shows two distinct energies, which correspond to the two different energies of the occupied sigma bonding molecular orbitals in the molecular orbital diagram for CH4 shown in Figure 7.4.13 Unit Molecular Shape and Bonding Theories Interactive Figure 7.4.14 Explore the MO diagram for a complex molecule 1.3 1.5 1.8 2.1 2.4 Ionization energy / MJ●mol–1 Photoelectron spectrum for methane Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 191 Unit Recap Key Concepts 7.1  Valence-Shell Electron-Pair Repulsion Theory and Molecular Shape ●● ●● ●● Shapes of molecules and ions made up of nonmetals are predicted using VSEPR theory, which states that electron pairs (structural and nonbonding) repel one another and are arranged to avoid one another as best as possible (7.1a) Electron-pair geometry is the arrangement of structural electron pairs around the central atom, and molecular geometry is the arrangement of atoms around the central atom (7.1a) For a molecule to be polar, it must contain polar bonds that are arranged so that there is an uneven charge distribution (7.1c) 7.2  Valence Bond Theory and Hybrid Orbitals ●● ●● ●● ●● ●● ●● ●● ●● ●● According to valence bond theory, valence atomic orbitals on adjacent atoms overlap, each pair of overlapping valence orbitals is occupied by two valence electrons to form a chemical bond, and valence electrons are either involved in bonding between two atoms (shared bonding pairs) or reside on a single atom (nonbonding lone pairs) (7.2a) A sigma 1s2 bond is a covalent bond with a bonding region along the internuclear axis (7.2a) Hybrid orbitals are equal-energy orbitals that are a combination of atomic orbitals (7.2b) Hybrid orbitals are used in valence bond theory to explain bonding in complex molecules (7.2b) Four sp3 hybrid orbitals result from “mixing” an atom’s single s and three p valence atomic orbitals The angle between any two sp3 hybrid orbitals is 109.5° (7.2b) Three sp2 hybrid orbitals result from “mixing” an atom’s single s and two of its three p valence atomic orbitals The angle between any two sp2 hybrid orbitals is 120° (7.2c) Two sp hybrid orbitals result from “mixing” an atom’s single s and one of its three p valence atomic orbitals The angle between two sp hybrid orbitals is 180° (7.2d) Five sp3d hybrid orbitals result from “mixing” an atom’s single s, its three p, and one of its d valence atomic orbitals The angle between sp3d hybrid orbitals is 180°, 120°, or 90° (7.2e) Six sp3d2 hybrid orbitals result from “mixing” an atom’s single s, its three p, and two of its d valence atomic orbitals The angle between sp3d2 hybrid orbitals is 180° or 90° (7.2e) 7.3  Pi Bonding ●● ●● A pi 1p2 bond occurs when two orbitals overlap to form a bond where the bonding region is above and below the internuclear axis (7.3a) The number of pi bonds an atom forms is related to the number of unhybridized p orbitals available (7.3c) 192 Unit Molecular Shape and Bonding Theories Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 ●● ●● Conformations are the different three-dimensional arrangements of atoms in a ­molecule that can be interconverted by rotation around single bonds (7.3d) Isomers are two or more substances that have the same chemical formula but have ­different properties because of the different arrangement of atoms (7.3d) 7.4  Molecular Orbital Theory ●● ●● ●● ●● ●● According to molecular orbital theory, orbitals in a molecule are thought to be spread out (delocalized) over many atoms (7.4a) A bonding molecular orbital has increased electron density between bonded nuclei Bonding molecular orbitals can be either sigma or pi molecular orbitals (7.4a, 7.4b) An antibonding molecular orbital has decreased electron density between bonded nuclei Antibonding molecular orbitals can be either sigma or pi molecular orbitals (7.4a, 7.4b) A molecular orbital diagram shows the relative energy of the molecules atomic (valence) orbitals and molecular orbitals (7.4c) The bond order between two atoms in a molecule can be calculated from the number of electrons in bonding and antibonding molecular orbitals (7.4c) Key Equations bond order ½ [number of electrons in bonding orbitals number of electrons in antibonding orbitals] (7.1) Key Terms 7.1  Valence-Shell Electron-Pair Repulsion Theory and Molecular Shape valence-shell electron-pair repulsion (VSEPR) structural electron pairs electron-pair geometry shape (molecular geometry) bond angle sigma 1s2 bond hybrid orbitals sp3 hybrid orbital sp2 hybrid orbital sp hybrid orbital sp3d hybrid orbital sp3d2 hybrid orbital 7.2  Valence Bond Theory and Hybrid Orbitals valence bond theory molecular orbital theory orbital overlap 7.3  Pi Bonding pi 1p2 bond conformations isomers 7.4  Molecular Orbital Theory bonding molecular orbital antibonding molecular orbital molecular orbital diagram bond order homonuclear diatomic molecule heteronuclear diatomic molecule Unit 7  Review and Challenge Problems Unit Molecular Shape and Bonding Theories Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 193 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-202 ... WCN 02-200-202 General Chemistry: Atoms First © 2018 Cengage Learning Susan M Young, William J Vining, Roberta Day, Beatrice Botch ALL RIGHTS RESERVED No part of this work covered by the copyright.. .General Chemistry Atoms First Susan M Young Hartwick College William J Vining State University of New York, Oneonta Roberta Day University of Massachusetts, Amherst Beatrice Botch... environments for chemistry Beatrice Botch University of Massachusetts Beatrice Botch is the Director of General Chemistry at the University of Massachusetts She received her B.A in Chemistry from