Main groups 1Aa 1 H 1.008 2A Li Be 6.94 9.012 11 Na 12 Mg 22.99 24.31 19 K Main groups Metals Metalloids Transition metals 26 Fe 8B 27 Co 54.94 55.85 58.93 43 Tc 44 Ru 45 Rh [98] 101.07 102.91 20 Ca 3B 21 Sc 4B 22 Ti 5B 23 V 6B 24 Cr 7B 25 Mn 39.10 40.08 44.96 47.87 50.94 52.00 37 Rb 38 Sr 39 Y 40 Zr 41 Nb 42 Mo 85.47 87.62 88.91 92.91 95.95 56 Ba 57 La 91.22 55 Cs 132.91 137.33 138.91 178.49 180.95 183.84 186.21 190.23 87 Fr 88 Ra 89 Ac 104 Rf 105 Db 106 Sg 107 Bh [223.02] [226.03] [227.03] [261.11] [262.11] [266.12] 58 Ce 72 Hf Lanthanide series Actinide series 5A 15 N 6A 16 7A 17 4.003 B 4A 14 C O F 10 Ne 10.81 12.01 14.01 16.00 19.00 20.18 13 Al 14 Si 15 P 16 S 17 Cl 18 Ar 26.98 28.09 30.97 32.06 35.45 39.95 3A 13 Nonmetals 8A 18 He 10 28 Ni 1B 11 29 Cu 2B 12 30 Zn 58.69 63.55 65.38 69.72 72.63 74.92 78.97 79.90 83.80 106.42 107.87 112.41 114.82 118.71 121.76 127.60 126.90 131.29 78 Pt 79 Au 80 Hg 81 Tl 82 Pb 83 Bi 84 Po 85 At 86 Rn 192.22 195.08 196.97 200.59 204.38 207.2 208.98 [208.98] [209.99] [222.02] 108 Hs 109 Mt 110 Ds 111 Rg 112 Cn 113 114 Fl 115 116 Lv 117* 118 [264.12] [269.13] [268.14] [271] [272] [285] 59 Pr 60 Nd 61 Pm 62 Sm 63 Eu 64 Gd 65 Tb 66 Dy 67 Ho 68 Er 69 Tm 70 Yb 71 Lu 140.12 140.91 144.24 [145] 150.36 151.96 157.25 158.93 162.50 164.93 167.26 168.93 173.05 174.97 90 Th 91 Pa 92 U 93 Np 94 Pu 95 Am 96 Cm 97 Bk 98 Cf 99 Es 100 Fm 101 Md 102 No 103 Lr 232.04 231.04 238.03 [237.05] [244.06] [243.06] [247.07] [247.07] [251.08] [252.08] [257.10] [258.10] [259.10] [262.11] 73 Ta 74 W 75 Re 76 Os 77 Ir 46 Pd 47 Ag 48 Cd 31 Ga 32 Ge 49 In 50 Sn 33 As 51 Sb by the International Union of Pure and Applied Chemistry Atomic masses in brackets are the masses of the longest-lived or most important isotope of radioactive elements *Element 117 is currently under review by IUPAC 52 Te 35 Br 53 I 36 Kr 54 Xe [292] [289] a The labels on top (1A, 2A, etc.) are common American usage The labels below these (1, 2, etc.) are those recommended 34 Se List of Elements with Their Symbols and Atomic Masses Element Actinium Aluminum Americium Antimony Argon Arsenic Astatine Barium Berkelium Beryllium Bismuth Bohrium Boron Bromine Cadmium Calcium Californium Carbon Cerium Cesium Chlorine Chromium Cobalt Copernicium Copper Curium Darmstadtium Dubnium Dysprosium Einsteinium Erbium Europium Fermium Flerovium Fluorine Francium Gadolinium Gallium Germanium Gold Hafnium Hassium Helium Holmium Hydrogen Indium Iodine Iridium Iron Krypton Lanthanum Lawrencium Lead Lithium Livermorium Lutetium Magnesium Manganese Symbol Ac Al Am Sb Ar As At Ba Bk Be Bi Bh B Br Cd Ca Cf C Ce Cs Cl Cr Co Cn Cu Cm Ds Db Dy Es Er Eu Fm Fl F Fr Gd Ga Ge Au Hf Hs He Ho H In I Ir Fe Kr La Lr Pb Li Lv Lu Mg Mn Atomic Number 89 13 95 51 18 33 85 56 97 83 107 35 48 20 98 58 55 17 24 27 112 29 96 110 105 66 99 68 63 100 114 87 64 31 32 79 72 108 67 49 53 77 26 36 57 103 82 116 71 12 25 a Mass of longest-lived or most important isotope b The names of these elements have not yet been decided Atomic Mass a 227.03 26.98 243.06a 121.76 39.95 74.92 209.99a 137.33 247.07a 9.012 208.98 264.12a 10.81 79.90 112.41 40.08 251.08a 12.01 140.12 132.91 35.45 52.00 58.93 285a 63.55 247.07a 271a 262.11a 162.50 252.08a 167.26 151.96 257.10a 289a 19.00 223.02a 157.25 69.72 72.63 196.97 178.49 269.13a 4.003 164.93 1.008 114.82 126.90 192.22 55.85 83.80 138.91 262.11a 207.2 6.94 292a 174.97 24.31 54.94 Element Meitnerium Mendelevium Mercury Molybdenum Neodymium Neon Neptunium Nickel Niobium Nitrogen Nobelium Osmium Oxygen Palladium Phosphorus Platinum Plutonium Polonium Potassium Praseodymium Promethium Protactinium Radium Radon Rhenium Rhodium Roentgenium Rubidium Ruthenium Rutherfordium Samarium Scandium Seaborgium Selenium Silicon Silver Sodium Strontium Sulfur Tantalum Technetium Tellurium Terbium Thallium Thorium Thulium Tin Titanium Tungsten Uranium Vanadium Xenon Ytterbium Yttrium Zinc Zirconium *b *b Symbol Atomic Number Atomic Mass Mt Md Hg Mo Nd Ne Np Ni Nb N No Os O Pd P Pt Pu Po K Pr Pm Pa Ra Rn Re Rh Rg Rb Ru Rf Sm Sc Sg Se Si Ag Na Sr S Ta Tc Te Tb Tl Th Tm Sn Ti W U V Xe Yb Y Zn Zr 109 101 80 42 60 10 93 28 41 102 76 46 15 78 94 84 19 59 61 91 88 86 75 45 111 37 44 104 62 21 106 34 14 47 11 38 16 73 43 52 65 81 90 69 50 22 74 92 23 54 70 39 30 40 268.14a 258.10a 200.59 95.95 144.24 20.18 237.05a 58.69 92.91 14.01 259.10a 190.23 16.00 106.42 30.97 195.08 244.06a 208.98a 39.10 140.91 145a 231.04 226.03a 222.02a 186.21 102.91 272a 85.47 101.07 261.11a 150.36 44.96 266.12a 78.97 28.09 107.87 22.99 87.62 32.06 180.95 98a 127.60 158.93 204.38 232.04 168.93 118.71 47.87 183.84 238.03 50.94 131.293 173.05 88.91 65.38 91.22 113 115 284a 288a Principles of Chemistry A Molecular Approach Third ediTion NivAldo J Tro Westmont College Editor-in-Chief: Jeanne Zalesky Senior Acquisitions Editor: Terry Haugen Director of Development: Jennifer Hart Marketing Manager: Will Moore Development Editor: Erin Mulligan Program Managers: Jessica Moro / Sarah Shefveland 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theoretical Textbooks Chemistry, Physical and theoretical Study and teaching (Higher) I Title QD453.3.T76 2016 540 dc23 2014040200 10—V011—16 15 14 13 12 ISBN 10: 0-321-97194-9; ISBN 13: 978-0-32197194-4 www.pearsonhighered.com To Michael, Ali, Kyle, and Kaden About the Author Nivaldo Tro is a professor of chemistry at Westmont College in Santa Barbara, California, where he has been a faculty member since 1990 He received his Ph.D in chemistry from Stanford University for work on developing and using optical techniques to study the adsorption and desorption of molecules to and from surfaces in ultrahigh vacuum He then went on to the University of California at Berkeley, where he did postdoctoral research on ultrafast reaction dynamics in solution Since coming to Westmont, Professor Tro has been awarded grants from the American Chemical Society Petroleum Research Fund, from the Research Corporation, and from the National Science Foundation to study the dynamics of various processes occurring in thin adlayer films adsorbed on dielectric surfaces He has been honored as Westmont’s outstanding teacher of the year three times and has also received the college’s outstanding researcher of the year award Professor Tro lives in Santa Barbara with his wife, Ann, and their four children, Michael, Ali, Kyle, and Kaden In his leisure time, Professor Tro enjoys mountain biking, surfing, reading to his children, and being outdoors with his family iii Brief Contents Preface Matter, Measurement, and Problem Solving xv 2 Atoms and Elements 42 Molecules, Compounds, and Chemical Equations 76 Chemical Quantities and Aqueous Reactions 124 Gases 176 Thermochemistry 220 The Quantum-Mechanical Model of the Atom 262 Periodic Properties of the Elements 300 Chemical Bonding I: The Lewis Model 340 10 Chemical Bonding II: Molecular Shapes, Valence Bond Theory, and Molecular Orbital Theory 11 Liquids, Solids, and Intermolecular Forces 428 Solutions Chemical Kinetics Chemical Equilibrium Acids and Bases Aqueous Ionic Equilibrium Free Energy and Thermodynamics Electrochemistry Radioactivity and Nuclear Chemistry 478 776 Appendix I: Common Mathematical Operations in Chemistry A-1 Appendix II: Useful Data A-7 12 13 14 15 16 17 18 19 iv 378 518 562 602 646 692 734 Appendix III: Answers to Selected Exercises A-17 Appendix IV: Answers to In-Chapter Practice Problems A-42 Glossary G-1 Credits C-1 Index i-1 Contents Preface xv Matter, Measurement, and Problem Solving 1.1 Atoms and Molecules 1.2 The Scientific Approach to Knowledge 1.3 The Classification of Matter The States of Matter: Solid, Liquid, and Gas Classifying Matter According to Its Composition: Elements, Compounds, and Mixtures 1.4 Physical and Chemical Changes and Physical and Chemical Properties 1.5 Energy: A Fundamental Part of Physical and Chemical Change 1.6 The Units of Measurement 12 13 The Standard Units 13 The Meter: A Measure of Length 14 The Kilogram: A Measure of Mass 14 The Second: A Measure of Time 14 The Kelvin: A Measure of Temperature 14 Prefix Multipliers 16 Derived Units: Volume and Density 17 Volume 17 Density 18 Calculating Density 18 1.7 The reliability of a Measurement 19 Counting Significant Figures 21 Exact Numbers 22 Significant Figures in Calculations 23 Precision and Accuracy 24 1.8 Solving Chemical Problems 25 Converting from One Unit to Another 25 General ProblemSolving Strategy 27 Units Raised to a Power 29 Problems Involving an Equation 30 Chapter in review 33 Key Terms 33 Key Concepts 33 Key Equations and Relationships 34 Key Learning Objectives 34 Exercises Problems by Topic 34 Cumulative Problems 38 Challenge Problems 39 Conceptual Problems 40 Questions for Group Work 41 Answers to Conceptual Connections 41 34 Atoms and Elements 2.1 imaging and Moving individual Atoms 2.2 Modern Atomic Theory and the laws That led to it 42 43 45 The Law of Conservation of Mass 45 The Law of Definite Proportions 46 The Law of Multiple Proportions 47 John Dalton and the Atomic Theory 48 2.3 The discovery of the Electron 48 Cathode Rays 49 Millikan’s Oil Drop Experiment: The Charge of the Electron 50 2.4 The Structure of the Atom 2.5 Subatomic Particles: Protons, Neutrons, and Electrons in Atoms 50 52 Elements: Defined by Their Numbers of Protons 53 Isotopes: When the Number of Neutrons Varies 54 Ions: Losing and Gaining Electrons 56 2.6 Finding Patterns: The Periodic law and the Periodic Table 57 Ions and the Periodic Table 59 2.7 Atomic Mass: The Average Mass of an Element’s Atoms 2.8 Molar Mass: Counting Atoms by Weighing Them 61 62 The Mole: A Chemist’s “Dozen” 62 Converting between Number of Moles and Number of Atoms 63 Converting between Mass and Amount (Number of Moles) 64 Chapter in review 68 Key Terms 68 Key Concepts 69 Key Equations and Relationships 69 Key Learning Objectives 69 Exercises 70 Problems by Topic 70 Cumulative Problems 72 Challenge Problems 73 Conceptual Problems 74 Questions for Group Work 74 Answers to Conceptual Connections 75 v vi Contents Molecules, Compounds, and Chemical Equations 76 3.1 Hydrogen, oxygen, and Water 3.2 Chemical Bonds 77 79 Ionic Bonds 79 Covalent Bonds 80 3.3 representing Compounds: Chemical Formulas and Molecular Models 80 Types of Chemical Formulas 80 Molecular Models 82 3.4 An Atomic-level view of Elements and Compounds 3.5 ionic Compounds: Formulas and Names 82 86 Writing Formulas for Ionic Compounds 87 Naming Ionic Compounds 87 Naming Binary Ionic Compounds Containing a Metal That Forms Only One Type of Cation 89 Naming Binary Ionic Compounds Containing a Metal That Forms More Than One Kind of Cation 90 Naming Ionic Compounds Containing Polyatomic Ions 91 Hydrated Ionic Compounds 92 3.6 Molecular Compounds: Formulas and Names 93 Naming Molecular Compounds 93 Naming Acids 94 Naming Binary Acids 95 Naming Oxyacids 95 96 Molar Mass of a Compound 97 Using Molar Mass to Count Molecules by Weighing 97 3.8 Composition of Compounds 99 Conversion Factors from Chemical Formulas 101 102 Chapter in review 107 111 114 Key Terms 114 Key Concepts 114 Key Equations and Relationships 115 Key Learning Objectives 116 Exercises 4.1 Climate Change and the Combustion of Fossil Fuels 125 4.2 reaction Stoichiometry: How Much Carbon dioxide? 127 4.3 limiting reactant, Theoretical Yield, and Percent Yield 131 Limiting Reactant, Theoretical Yield, and Percent Yield from Initial Reactant Masses 133 Solution Concentration 138 Using Molarity in Calculations 139 Solution Stoichiometry 143 4.5 Types of Aqueous Solutions and Solubility Writing Balanced Chemical Equations 109 3.11 organic Compounds 124 4.4 Solution Concentration and Solution Stoichiometry 137 Calculating Molecular Formulas for Compounds 104 Combustion Analysis 105 3.10 Writing and Balancing Chemical Equations Aqueous reactions Making Pizza: The Relationships Among Ingredients 127 Making Molecules: Mole-to-Mole Conversions 128 Making Molecules: Mass-to-Mass Conversions 128 3.7 Formula Mass and the Mole Concept for Compounds 3.9 determining a Chemical Formula from Experimental data Chemical Quantities and 144 Electrolyte and Nonelectrolyte Solutions 145 The Solubility of Ionic Compounds 146 4.6 Precipitation reactions 148 4.7 representing Aqueous reactions: Molecular, ionic, and Complete ionic Equations 152 4.8 Acid–Base and Gas-Evolution reactions 154 Acid–Base Reactions 154 Gas-Evolution Reactions 157 117 Problems by Topic 117 Cumulative Problems 120 Challenge Problems 121 Conceptual Problems 122 Questions for Group Work 122 Answers to Conceptual Connections 122 4.9 oxidation–reduction reactions 159 Oxidation States 161 Identifying Redox Reactions 163 Combustion Reactions 165 Chapter in review 167 Key Terms 167 Key Concepts 167 Key Equations and Relationships 168 Key Learning Objectives 168 Exercises 168 Problems by Topic 168 Cumulative Problems 172 Challenge Problems 173 Conceptual Problems 174 Questions for Group Work 175 Answers to Conceptual Connections 175 Gases 5.1 Breathing: Putting Pressure to Work 5.2 Pressure: The result of Molecular Collisions Pressure Units 179 176 177 178 vii Contents 6.4 Quantifying Heat and Work 230 Heat 230 Thermal Energy Transfer 232 Work: Pressure–Volume Work 234 6.5 Measuring 𝚫E for Chemical reactions: Constantvolume Calorimetry 235 6.6 Enthalpy: The Heat Evolved in a Chemical reaction at Constant Pressure 238 Exothermic and Endothermic Processes: A Molecular View 240 Stoichiometry Involving ∆H: Thermochemical Equations 241 5.3 The Simple Gas laws: Boyle’s law, Charles’s law, and Avogadro’s law 180 Boyle’s Law: Volume and Pressure 181 Charles’s Law: Volume and Temperature 183 Avogadro’s Law: Volume and Amount (in Moles) 185 5.4 The ideal Gas law 5.5 Applications of the ideal Gas law: Molar volume, density, and Molar Mass of a Gas 186 188 Molar Volume at Standard Temperature and Pressure 189 Density of a Gas 189 Molar Mass of a Gas 191 5.6 Mixtures of Gases and Partial Pressures 192 Collecting Gases over Water 196 5.7 Gases in Chemical reactions: Stoichiometry revisited 6.7 Constant-Pressure Calorimetry: Measuring 𝚫Hrxn 6.8 Hess’s law and other relationships involving 𝚫Hrxn 6.9 Enthalpies of reaction from Standard Heats of Formation 242 244 247 Standard States and Standard Enthalpy Changes 247 Calculating the Standard Enthalpy Change for a Reaction 249 Chapter in review 253 Key Terms 253 Key Concepts 253 Key Equations and Relationships 254 Key Learning Objectives 254 Exercises 255 Problems by Topic 255 Cumulative Problems 258 Challenge Problems 259 Conceptual Problems 260 Questions for Group Work 260 Answers to Conceptual Connections 261 198 Molar Volume and Stoichiometry 200 5.8 Kinetic Molecular Theory: A Model for Gases 201 The Nature of Pressure 202 Boyle’s Law 202 Charles’s Law 202 Avogadro’s Law 202 Dalton’s Law 202 Temperature and Molecular Velocities 203 5.9 Mean Free Path, diffusion, and Effusion of Gases 205 5.10 real Gases: The Effects of Size and intermolecular Forces 207 The Effect of the Finite Volume of Gas Particles 207 The Effect of Intermolecular Forces 208 Van der Waals Equation 209 Chapter in review 210 Key Terms 210 Key Concepts 210 Key Equations and Relationships 211 Key Learning Objectives 211 Exercises 212 Problems by Topic 212 Cumulative Problems 215 Challenge Problems 217 Conceptual Problems 218 Questions for Group Work 218 Answers to Conceptual Connections 219 Thermochemistry 6.1 Chemical Hand Warmers 6.2 The Nature of Energy: Key definitions 220 221 222 Units of Energy 224 6.3 The First law of Thermodynamics: There is No Free lunch Internal Energy 225 225 The Quantum-Mechanical Model of the Atom 7.1 Schrödinger’s Cat 7.2 The Nature of light 262 264 264 The Wave Nature of Light 265 The Electromagnetic Spectrum 267 Interference and Diffraction 268 The Particle Nature of Light 270 7.3 Atomic Spectroscopy and the Bohr Model 273 7.4 The Wave Nature of Matter: The de Broglie Wavelength, the Uncertainty Principle, and indeterminacy 275 The de Broglie Wavelength 276 The Uncertainty Principle 277 Indeterminacy and Probability Distribution Maps 279 57 2.6 Finding Patterns: The Periodic Law and the Periodic Table Neutral sodium atoms, for example, are chemically unstable, reacting violently with most things they contact Sodium cations (Na+ ), in contrast, are relatively inert—we eat them all the time in sodium chloride (NaCl or table salt) As we stated earlier, in ordinary matter, cations and anions always occur together so that matter is charge-neutral overall CONCEPTuAL CONNECTION ThE NuCLEAr ATOM AND ISOTOPES 2.5 In light of the nuclear model for the atom, which statement is true? (a) For a given element, the isotope of an atom with a greater number of neutrons is larger than one with a smaller number of neutrons (b) For a given element, the size of an atom is the same for all of the element’s isotopes 2.6 Finding Patterns: The Periodic Law and the Periodic Table The modern periodic table grew out of the work of Dmitri Mendeleev (1834–1907), a nineteenth-century Russian chemistry professor In his time, about 65 different elements had been discovered Through the work of a number of chemists, many of the properties of these elements—such as their relative masses, their chemical activity, and some of their physical properties—were known However, there was no systematic way of organizing them In 1869, Mendeleev noticed that certain groups of elements had similar properties Mendeleev found that when he listed elements in order of increasing mass, their properties recurred in a periodic pattern (FigurE 2.10▼) The Periodic Law H He Li Be B C N O F 10 Ne 11 Na 12 Mg 13 Al 14 Si 15 P 16 S 17 Cl 18 Ar 19 K 20 Ca Elements with similar properties occur with a regular pattern ▲ Dmitri Mendeleev, a Russian chemistry professor who proposed the periodic law and arranged early versions of the periodic table, was honored on a Soviet postage stamp Periodic means exhibiting a repeating pattern ◀ FigurE 2.10 recurring Properties These elements are listed in order of increasing atomic number Elements with similar properties are shown in the same color Notice that the colors form a repeating pattern, much like musical notes form a repeating pattern on a piano keyboard Mendeleev summarized these observations in the periodic law, which states: When the elements are arranged in order of increasing mass, certain sets of properties recur periodically Mendeleev then organized all the known elements in a table consisting of a series of rows in which mass increases from left to right The rows were arranged so that elements with similar properties aligned in the same vertical columns (FigurE 2.11▶) Since many elements had not yet been discovered, Mendeleev’s table contained some gaps, which allowed him to predict the existence and even some properties of yet undiscovered elements For example, Mendeleev predicted the existence of an element he called ekasilicon, which fell below silicon on the table In 1886, eka-silicon was discovered by German chemist Clemens Winkler (1838–1904), who named it germanium, after his home country Mendeleev’s original listing has evolved into the modern periodic table shown in FigurE 2.12▶ (on the next page) In the modern table, elements are listed in order of increasing atomic number rather than increasing relative mass The modern periodic table also contains more elements than Mendeleev’s original table because more have been discovered since his time Mendeleev’s periodic law was based on observation Like all scientific laws, the periodic law summarized many observations but did not give the underlying reason for the observations—only theories that For now, we can simply accept the periodic law as it is, but in Chapters and we will examine a powerful theory—called quantum mechanics—that explains the law and gives the underlying reasons for it A Simple Periodic Table H He Li Be 11 12 Na Mg 19 K B C N O 13 14 15 16 Al Si P S F 17 Cl 10 Ne 18 Ar 20 Ca Elements with similar properties fall into columns ▲ FigurE 2.11 Making a Periodic Table The elements in Figure 2.10 can be arranged in a table in which atomic number increases from left to right and elements with similar properties (as represented by the different colors) are aligned in columns 58 Chapter Atoms and Elements Major Divisions of the Periodic Table Silicon Carbon Arsenic Metals 1A 1 H Li 2A Be 11 Na 12 Mg 19 K Metalloids Strontium Nonmetals Chromium Copper Gold Lead 3A 13 B 4A 14 C 5A 15 N 6A 16 O 7A 17 F 8A 18 He 10 Ne 2B 12 30 Zn 13 Al 14 Si 15 P 16 S 17 Cl 18 Ar 28 Ni 1B 11 29 Cu 31 Ga 32 Ge 33 As 34 Se 35 Br 36 Kr 45 Rh 46 Pd 47 Ag 48 Cd 49 In 50 Sn 51 Sb 52 Te 53 I 54 Xe 76 Os 77 Ir 78 Pt 79 Au 80 Hg 81 Tl 82 Pb 83 Bi 84 Po 85 At 86 Rn 108 Hs 109 Mt 110 Ds 111 Rg 112 Cn 113 114 Fl 115 116 Lv 117 118 4B 22 Ti 5B 23 V 6B 24 Cr 7B 25 Mn 8B 10 20 Ca 3B 21 Sc 26 Fe 27 Co 37 Rb 38 Sr 39 Y 40 Zr 41 Nb 42 Mo 43 Tc 44 Ru 55 Cs 56 Ba 57 La 72 Hf 73 Ta 74 W 75 Re 87 Fr 88 Ra 89 Ac 104 Rf 105 Db 106 Sg 107 Bh Lanthanides 58 Ce 59 Pr 60 Nd 61 Pm 62 Sm 63 Eu 64 Gd 65 Tb 66 Dy 67 Ho 68 Er 69 Tm 70 Yb 71 Lu Actinides 90 Th 91 Pa 92 U 93 Np 94 Pu 95 Am 96 Cm 97 Bk 98 Cf 99 Es 100 Fm 101 Md 102 No 103 Lr Metals, Nonmetals, and Metalloids The elements in the periodic table fall into these three broad classes ▲ FigurE 2.12 Metalloids are sometimes called semimetals Sulfur As Figure 2.12 shows, we can broadly classify the elements in the periodic table as metals, nonmetals, or metalloids Metals, found on the left side and middle of the periodic table, have the following properties: They are good conductors of heat and electricity; they can be pounded into flat sheets (malleability); they can be drawn into wires (ductility); they are often shiny; and they tend to lose electrons when they undergo chemical changes Good examples of metals include chromium, copper, strontium, and lead Nonmetals are found on the upper right side of the periodic table The dividing line between metals and nonmetals is the zigzag diagonal line running from boron to astatine Nonmetals have varied properties—some are solids at room temperature, others are liquids or gases—but as a whole they tend to be poor conductors of heat and electricity, and they all tend to gain electrons when they undergo chemical changes Good examples of nonmetals include oxygen, carbon, sulfur, bromine, and iodine Many of the elements that lie along the zigzag diagonal line that divides metals and nonmetals are metalloids that show mixed properties Several metalloids are also classified as semiconductors because of their intermediate (and highly temperature-dependent) electrical conductivity Our ability to change and control the conductivity of semiconductors makes them useful in the manufacture of the electronic chips and circuits central to computers, cellular telephones, and many other devices Good examples of metalloids include silicon, arsenic, and antimony The periodic table, as shown in FigurE 2.13▶, can also be broadly divided into main-group elements, whose properties tend to be largely predictable based on their position in the periodic table, and transition elements or transition metals, whose properties tend to be less Bromine Iodine 2.6 Finding Patterns: The Periodic Law and the Periodic Table Transition elements Main-group elements Group number Li 2A Be 11 Na 12 Mg 19 K Periods 1A 1 H Main-group elements 8A 18 3A 13 B 4A 14 C 5A 15 N 6A 16 O 7A 17 F He 10 Ne 2B 12 30 Zn 13 Al 14 Si 15 P 16 S 17 Cl 18 Ar 28 Ni 1B 11 29 Cu 31 Ga 32 Ge 33 As 34 Se 35 Br 36 Kr 45 Rh 46 Pd 47 Ag 48 Cd 49 In 50 Sn 51 Sb 52 Te 53 I 54 Xe 76 Os 77 Ir 78 Pt 79 Au 80 Hg 81 Tl 82 Pb 83 Bi 84 Po 85 At 86 Rn 108 Hs 109 Mt 110 Ds 111 Rg 112 Cn 113 114 Fl 115 116 Lv 117 118 4B 22 Ti 5B 23 V 6B 24 Cr 7B 25 Mn 8B 10 20 Ca 3B 21 Sc 26 Fe 27 Co 37 Rb 38 Sr 39 Y 40 Zr 41 Nb 42 Mo 43 Tc 44 Ru 55 Cs 56 Ba 57 La 72 Hf 73 Ta 74 W 75 Re 87 Fr 88 Ra 89 Ac 104 Rf 105 Db 106 Sg 107 Bh The Periodic Table: Main-Group and Transition Elements The elements in the periodic table are arranged in columns The two columns at the left and the six columns at the right (in yellow) comprise the main-group elements Each of these eight columns is a group or family The properties of main-group elements can generally be predicted from their position in the periodic table The properties of the elements in the middle of the table (in blue), known as transition elements, are less predictable ▲ FigurE 2.13 predictable based solely on their position in the periodic table Main-group elements are in columns labeled with a number and the letter A Transition elements are in columns labeled with a number and the letter B An alternative labeling system does not use letters, but only the numbers 1–18 Both systems are shown in most of the periodic tables in this book Each column within the main-group regions of the periodic table is a family or group of elements The elements within a group usually have similar properties For example, the group 8A elements, referred to as the noble gases, are mostly unreactive The most familiar noble gas is probably helium, used to fill buoyant balloons Helium is chemically stable—it does not combine with other elements to form compounds—and is therefore safe to put into balloons Other noble gases include neon (often used in electronic signs), argon (a small component of Earth’s atmosphere), krypton, and xenon The group 1A elements, the alkali metals, are all reactive metals A marble-sized piece of sodium, for example, explodes violently when dropped into water Other alkali metals include lithium, potassium, and rubidium The group 2A elements, the alkaline earth metals, are also fairly reactive, although not quite as reactive as the alkali metals Calcium reacts fairly vigorously when dropped into water but will not explode as dramatically as sodium Other alkaline earth metals include magnesium (a common low-density metal), strontium, and barium The group 7A elements, the halogens, are very reactive nonmetals The most familiar halogen is probably chlorine, a greenish-yellow gas with a pungent odor Chlorine is used as a sterilizing and disinfecting agent (because it reacts with important molecules in living organisms) Other halogens include bromine, a red-brown liquid that easily evaporates into a gas; iodine, a purple solid; and fluorine, a pale-yellow gas Ions and the Periodic Table Recall that, in chemical reactions, metals tend to lose electrons (thus forming cations) and nonmetals tend to gain them (thus forming anions) The number of electrons lost or gained, and therefore the charge of the resulting ion, is often predictable for a given element, especially main-group elements Main-group elements tend to form ions that have 59 60 Chapter Atoms and Elements Elements That Form Ions with Predictable Charges 7A 1A H+ 2A 3A 4A Li+ Transition metals Al3+ H– 5A 6A N3– O2– F– S2– Cl– Na+ Mg2+ K+ Ca2+ Se2– Br– Rb+ Sr2+ Te2– I– Cs+ Ba2+ ▲ FigurE 2.14 Elements That Form Ions with Predictable Charges 8A N o b l e G a s e s the same number of electrons as the nearest noble gas (the noble gas that has the number of electrons closest to that of the element) A main-group metal tends to lose electrons, forming a cation with the same number of electrons as the nearest noble gas A main-group nonmetal tends to gain electrons, forming an anion with the same number of electrons as the nearest noble gas For example, lithium, a metal with three electrons, tends to lose one electron to form a 1+ cation having two electrons, the same number of electrons as helium Chlorine, a nonmetal with 17 electrons, tends to gain one electron to form a 1- anion having 18 electrons, the same number of electrons as argon In general, the alkali metals (group 1A) tend to lose one electron and therefore form 1+ ions The alkaline earth metals (group 2A) tend to lose two electrons and therefore form 2+ ions The halogens (group 7A) tend to gain one electron and therefore form 1ions The oxygen family nonmetals (group 6A) tend to gain two electrons and therefore form 2- ions Typically, for main-group elements that form predictable cations, the charge of the cation is equal to the group number For main-group elements that form predictable anions, the charge of the anion is equal to the group number minus eight Transition elements form cations with various charges The most common ions formed by main-group elements are shown in FigurE 2.14▲ In Chapters and 8, when we learn about quantummechanical theory, we will discuss why these groups form ions as they ExamplE 2.4 Predicting the Charge of Ions Predict the charges of the monoatomic (single atom) ions formed by these main-group elements (a) Al (b) S SOLuTION (a) Aluminum is a main-group metal and therefore loses electrons to form a cation with the same number of electrons as the nearest noble gas Aluminum atoms have 13 electrons and the nearest noble gas is neon, which has 10 electrons Aluminum tends to lose electrons to form a cation with a 3+ charge (Al3 + ) (b) Sulfur is a nonmetal and therefore gains electrons to form an anion with the same number of electrons as the nearest noble gas Sulfur atoms have 16 electrons and the nearest noble gas is argon, which has 18 electrons Sulfur tends to gain electrons to form an anion with a 2- charge (S2 - ) FOr PrACTICE 2.4 Predict the charges of the monoatomic ions formed by these main-group elements (a) N (b) Rb 2.7 Atomic Mass: The Average Mass of an Element’s Atoms 61 2.7 Atomic Mass: The Average Mass of an Element’s Atoms An important part of Dalton’s atomic theory was his assertion that all atoms of a given element have the same mass However, in Section 2.5, we learned that, because of isotopes, the atoms of a given element often have different masses, so Dalton was not completely correct We can, however, calculate an average mass—called the atomic mass—for each element The atomic mass of each element is listed directly beneath the element’s symbol in the periodic table and represents the average mass of the isotopes that compose that element weighted according to the natural abundance of each isotope For example, the periodic table lists the atomic mass of chlorine as 35.45 amu Naturally occurring chlorine consists of 75.77% chlorine-35 atoms (mass 34.97 amu) and 24.23% chlorine-37 atoms (mass 36.97 amu) We calculate its atomic mass as follows: Atomic mass = 0.7577134.97 amu2 + 0.2423136.97 amu2 = 35.45 amu Notice that the atomic mass of chlorine is closer to 35 than 37 Naturally occurring chlorine contains more chlorine-35 atoms than chlorine-37 atoms, so the weighted average mass of chlorine is closer to 35 amu than to 37 amu In general, we calculate the atomic mass according to the equation: Atomic mass is sometimes called atomic weight, average atomic mass, or average atomic weight 17 Cl 35.45 chlorine To use percentages in calculations, convert them to their decimal value by dividing by 100 Atomic mass ∙ a (fraction of isotope n) : (mass of isotope n) n ∙ (fraction of isotope : mass of isotope 1) ∙ (fraction of isotope : mass of isotope 2) ∙ (fraction of isotope : mass of isotope 3) ∙ N where the fractions of each isotope are the percent natural abundances converted to their decimal values The concept of atomic mass is useful because it allows us to assign a characteristic mass to each element, and as we will see shortly, it allows us to quantify the number of atoms in a sample of that element ExamplE 2.5 In this book, we use the atomic masses recommended by IUPAC for users needing an atomic mass value for an unspecified sample Detailed studies of the atomic masses of many samples, however, have shown that atomic masses are not constants of nature because the exact isotopic abundances in any given sample depend on the history of the sample Atomic Mass Copper has two naturally occurring isotopes: Cu-63 with mass 62.9296 amu and a natural abundance of 69.17%, and Cu-65 with mass 64.9278 amu and a natural abundance of 30.83% Calculate the atomic mass of copper SOLuTION Convert the percent natural abundances into decimal form by dividing by 100 69.17 = 0.6917 100 30.83 = 0.3083 Fraction Cu@65 = 100 Calculate the atomic mass using the equation given in the text Atomic mass = 0.6917 (62.9296 amu) + 0.3083 (64.9278 amu) = 43.5284 amu + 20.0172 amu = 63.5456 = 63.55 amu Fraction Cu@63 = FOr PrACTICE 2.5 Magnesium has three naturally occurring isotopes with masses of 23.99 amu, 24.99 amu, and 25.98 amu and natural abundances of 78.99%, 10.00%, and 11.01%, respectively Calculate the atomic mass of magnesium FOr MOrE PrACTICE 2.5 Gallium has two naturally occurring isotopes: Ga-69 with a mass of 68.9256 amu and a natural abundance of 60.11%, and Ga-71 Use the atomic mass of gallium listed in the periodic table to determine the mass of Ga-71 62 Chapter Atoms and Elements CONCEPTuAL CONNECTION 2.6 ATOMIC MASS Recall from Conceptual Connection 2.4 that carbon has two naturally occurring stable isotopes: C-12 (natural abundance is 98.93%; mass is 12.0000 amu) and C-13 (natural abundance is 1.07%; mass is 13.0034 amu) Without doing any calculations, determine which mass is closest to the atomic mass of carbon (a) 12.00 amu KEY CONCEpT VIDEO The Mole Concept (b) 12.50 amu (c) 13.00 amu 2.8 Molar Mass: Counting Atoms by Weighing Them Have you ever bought shrimp by count? Count indicates the number of shrimp per pound For example, 41–50 count shrimp have between 41 and 50 shrimp per pound The smaller the count, the larger the shrimp The big tiger prawns have counts as low as 10–15, which means that each shrimp can weigh up to 1/10 of a pound The nice thing about categorizing shrimp this way is that you can count the shrimp by weighing them For example, two pounds of 41–50 count shrimp contain between 82 and 100 shrimp A similar (but more precise) concept exists for atoms Counting atoms is much more difficult than counting shrimp, yet we often need to know the number of atoms in a given mass of atoms Why? Because chemical processes happen between particles For elements, those particles are atoms For example, when hydrogen and oxygen combine to form water, two hydrogen atoms combine with one oxygen atom to form one water molecule If we want to know how much hydrogen to react with a given mass of oxygen to form water, we need to know the number of atoms in the given mass of oxygen We also need to know the mass of hydrogen that contains exactly twice that number of atoms As another example, consider intravenous fluids—fluids that are delivered to patients by directly dripping the fluid into their veins Intravenous fluids are saline (salt) solutions that must have a specific number of sodium and chloride ions per liter of fluid in order to be effective The result of using an intravenous fluid with the wrong number of sodium and chloride ions could be fatal Atoms are far too small to count by any ordinary means As we saw earlier, even if you could somehow count atoms, and counted them 24 hours a day for as long as you lived, you would barely begin to count the number of atoms in something as small as a grain of sand Therefore, if we want to know the number of atoms in anything of ordinary size, we count them by weighing The Mole: A Chemist’s “Dozen” When we count large numbers of objects, we often use units such as a dozen (12 objects) or a gross (144 objects) to organize our counting and to keep our numbers more manageable With atoms, quadrillions of which may be in a speck of dust, we need a much larger number for this purpose The chemist’s “dozen” is the mole (abbreviated mol), which is defined as the amount of material containing 6.0221421 * 1023 particles mol = 6.0221421 * 1023 particles This number is Avogadro’s number, named after Italian physicist Amedeo Avogadro (1776–1856), and is a convenient number to use when working with atoms, molecules, and ions In this book, we usually round Avogadro’s number to four significant figures or 6.022 * 1023 Notice that the definition of the mole is an amount of a substance We will often refer to the number of moles of substance as the amount of the substance 2.8 Molar Mass: Counting Atoms by Weighing Them The first thing to understand about the mole is that it can specify Avogadro’s number of anything For example, mol of marbles corresponds to 6.022 * 1023 marbles, and mol of sand grains corresponds to 6.022 * 1023 sand grains One mole of anything is 6.022 * 1023 units of that thing One mole of atoms, ions, or molecules, however, makes up objects of everyday sizes For example, 22 copper pennies contain approximately mol of copper atoms, and a tablespoon of water contains approximately mol of water molecules The second, and more fundamental, thing to understand about the mole is how it gets its specific value 63 Twenty-two copper pennies contain approximately mol of copper atoms The value of the mole is equal to the number of atoms in exactly 12 grams of pure carbon-12 (12 g C ∙ mol C atoms ∙ 6.022 : 1023 C atoms) This definition of the mole gives us a relationship between mass (grams of carbon) and number of atoms (Avogadro’s number) This relationship, as we will discuss shortly, allows us to count atoms by weighing them Converting between Number of Moles and Number of Atoms Converting between number of moles and number of atoms is similar to converting between dozens of shrimp and number of shrimp To convert between moles of atoms and number of atoms, we use the conversion factors: 23 mol atoms 6.022 * 10 atoms or 23 mol atoms 6.022 * 10 atoms Beginning in 1982, pennies became almost all zinc, with only a copper coating Before 1982, however, pennies were mostly copper One tablespoon of water contains approximately one mole of water molecules Example 2.6 demonstrates the use of these conversion factors ExamplE 2.6 Converting between Number of Moles and Number of Atoms Calculate the number of copper atoms in 2.45 mol of copper (Cu) SOrT You are given the amount of copper in moles and asked to find the number of copper atoms GIvEN 2.45 mol Cu FIND Cu atoms STrATEGIZE Convert between number of moles and number of atoms by using Avogadro’s number as a conversion factor CONCEPTuAL PLAN mol Cu One tablespoon is approximately 15 mL; one mole of water occupies 18 mL Cu atoms 23 6.022 × 10 Cu atoms mol Cu SOLvE Follow the conceptual plan to solve the problem Begin with 2.45 mol Cu and multiply by Avogadro’s number to get to Cu atoms rELATIONShIPS uSED 6.022 * 1023 = mol 1Avogadro’s number SOLuTION 2.45 mol Cu * 6.022 * 1023 Cu atoms mol Cu = 1.48 * 1024 Cu atoms ChECK Atoms are small, so it makes sense that the answer is large The number of moles of copper is almost 2.5, so the number of atoms is almost 2.5 times Avogadro’s number FOr PrACTICE 2.6 A pure silver ring contains 2.80 * 1022 silver atoms How many moles of silver atoms does it contain? 64 Chapter Atoms and Elements Converting between Mass and Amount (Number of Moles) To count atoms by weighing them, we need one other conversion factor—the mass of mol of atoms For the isotope carbon-12, we know that this mass is exactly 12 grams, which is numerically equivalent to carbon-12’s atomic mass in atomic mass units Since the masses of all other elements are defined relative to carbon-12, the same relationship holds for all elements The mass of mol of atoms of an element is the molar mass An element’s molar mass in grams per mole is numerically equal to the element’s atomic mass in atomic mass units For example, copper has an atomic mass of 63.55 amu and a molar mass of 63.55 g>mol One mole of copper atoms therefore has a mass of 63.55 g Just as the count for shrimp depends on the size of the shrimp, the mass of mol of atoms depends on the element: mol of aluminum atoms (which are lighter than copper atoms) has a mass of 26.98 g; mol of carbon atoms (which are even lighter than aluminum atoms) has a mass of 12.01 g; and mol of helium atoms (lighter still) has a mass of 4.003 g 26.98 g aluminum = mol aluminum = 6.022 × 1023 Al atoms 12.01 g carbon = mol carbon = 6.022 × 1023 C atoms Al C 4.003 g helium = mol helium = 6.022 × 1023 He atoms He The lighter the atom, the less mass it takes to make mol dozen peas dozen marbles ▲ The two dishes contain the same number of objects (12), but the masses are different because peas are less massive than marbles Similarly, a mole of light atoms will have less mass than a mole of heavier atoms 2.8 Molar Mass: Counting Atoms by Weighing Them Therefore, the molar mass of any element becomes a conversion factor between the mass (in grams) of that element and the amount (in moles) of that element For carbon: 12.01 g C = mol C or 12.01 g C mol C or mol C 12.01 g C Example 2.7 demonstrates the use of these conversion factors ExamplE 2.7 Converting between Mass and Amount (Number of Moles) Calculate the amount of carbon (in moles) contained in a 0.0265-g pencil “lead.” (Assume that the pencil lead is made of pure graphite, a form of carbon.) SOrT You are given the mass of carbon and asked to find the amount of carbon in moles GIvEN 0.0265 g C FIND mol C STrATEGIZE Convert between mass and amount (in moles) of an element by using the molar mass of the element CONCEPTuAL PLAN gC mol C mol 12.01 g SOLvE Follow the conceptual plan to solve the problem rELATIONShIPS uSED 12.01 g C = mol C 1carbon molar mass2 SOLuTION 0.0265 g C * mol C = 2.21 * 10-3 mol C 12.01 g C ChECK The given mass of carbon is much less than the molar mass of carbon Therefore the answer (the amount in moles) is much less than mol of carbon FOr PrACTICE 2.7 Calculate the amount of copper (in moles) in a 35.8 g pure copper sheet FOr MOrE PrACTICE 2.7 Calculate the mass (in grams) of 0.473 mol of titanium We now have all the tools to count the number of atoms in a sample of an element by weighing it To this, first we obtain the mass of the sample Then we convert the mass to amount in moles using the element’s molar mass Finally, we convert to number of atoms using Avogadro’s number The conceptual plan for these kinds of calculations takes the following form: g element mol element molar mass of element number of atoms Avogadro’s number Examples 2.8 and 2.9 demonstrate these conversions 65 66 Chapter Atoms and Elements ExamplE 2.8 The Mole Concept—Converting between Mass and Number of Atoms How many copper atoms are in a copper penny with a mass of 3.10 g? (Assume that the penny is composed of pure copper.) SOrT You are given the mass of copper and asked to find the number of copper atoms GIvEN 3.10 g Cu FIND Cu atoms STrATEGIZE Convert between the mass of an element in grams and the number of atoms of the element by first converting to moles (using the molar mass of the element) and then to number of atoms (using Avogadro’s number) CONCEPTuAL PLAN g Cu mol Cu number of Cu atoms mol Cu 6.022 × 1023 Cu atoms 63.55 g Cu mol Cu rELATIONShIPS uSED 63.55 g Cu = mol Cu 1molar mass of copper 6.022 * 1023 = mol (Avogadro’s number) SOLvE Follow the conceptual plan to solve the problem Begin with 3.10 g Cu and multiply by the appropriate conversion factors to arrive at the number of Cu atoms SOLuTION 3.10 g Cu * mol Cu 6.022 * 1023 Cu atoms * 63.55 g Cu mol Cu = 2.94 * 1022 Cu atoms ChECK The answer (the number of copper atoms) is less than 6.022 * 1023 (one mole) This is consistent with the given mass of copper atoms, which is less than the molar mass of copper FOr PrACTICE 2.8 How many carbon atoms are there in a 1.3-carat diamond? Diamonds are a form of pure carbon 11 carat = 0.20 grams2 FOr MOrE PrACTICE 2.8 Calculate the mass of 2.25 * 1022 tungsten atoms Notice that numbers with large exponents, such as 6.022 * 1023, are deceptively large Twenty-two copper pennies contain 6.022 * 1023 or mol of copper atoms, but 6.022 * 1023 pennies would cover Earth’s entire surface to a depth of 300 m Even objects small by everyday standards occupy a huge space when we have a mole of them For example, a grain of sand has a mass of less than mg and a diameter of less than 0.1 mm, yet mol of sand grains would cover the state of Texas to a depth of several feet For every increase of in the exponent of a number, the number increases by a factor of 10, so 1023 is incredibly large One mole has to be a large number, however, if it is to have practical value, because atoms are so small ExamplE 2.9 The Mole Concept An aluminum sphere contains 8.55 * 1022 aluminum atoms What is the radius of the sphere in centimeters? The density of aluminum is 2.70 g>cm3 SOrT You are given the number of aluminum atoms in a sphere and the density of aluminum You are asked to find the radius of the sphere GIvEN 8.55 * 1022 Al atoms d = 2.70 g>cm3 FIND radius (r) of sphere 2.8 Molar Mass: Counting Atoms by Weighing Them STrATEGIZE The heart of this problem is density, which relates mass to volume, and though you aren’t given the mass directly, you are given the number of atoms, which you can use to find mass CONCEPTuAL PLAN Number of Al atoms Convert from number of atoms to number of moles using Avogadro’s number as a conversion factor Convert from number of moles to mass using molar mass as a conversion factor Once you calculate the volume, find the radius from the volume using the formula for the volume of a sphere SOLvE Follow the conceptual plan to solve the problem Begin with 8.55 * 1022 Al atoms and multiply by the appropriate conversion factors to arrive at volume in cm3 mol Al 26.98 g Al cm3 mol Al 2.70 g Al r V= π r3 rELATIONShIPS AND EQuATIONS uSED 6.022 * 1023 = mol 1Avogadro’s number 26.98 g Al = mol Al 1molar mass of aluminum2 2.70 g Al = cm3 Al 1density of aluminum2 V = pr3 1volume of a sphere SOLuTION 8.55 * 1022 Al atoms * * Then solve the equation for the volume of a sphere for r and substitute the volume to calculate r V (in cm3) g Al 6.022 × 1023 Al atoms V (in cm3) 3 Convert from mass to volume (in cm ) using density as a conversion factor mol Al V = r = mol Al 6.022 * 1023 Al atoms 26.98 g Al cm3 * = 1.4187 cm3 mol Al 2.70 g Al pr 3(1.4187 cm3) 3V = = 0.697 cm A 4p 4p B ChECK The units of the answer (cm) are correct The magnitude cannot be estimated accurately, but a radius of about onehalf of a centimeter is reasonable for just over one-tenth of a mole of aluminum atoms FOr PrACTICE 2.9 A titanium cube contains 2.86 * 1023 atoms What is the edge length of the cube? The density of titanium is 4.50 g>cm3 FOr MOrE PrACTICE 2.9 Find the number of atoms in a copper rod with a length of 9.85 cm and a radius of 1.05 cm The density of copper is 8.96 g>cm3 AvOGADrO’S NuMbEr CONCEPTuAL CONNECTION 2.7 CONCEPTuAL CONNECTION 2.8 Why is Avogadro’s number defined as 6.022 * 1023 and not a simpler round number such as 1.00 * 1023? ThE MOLE Without doing any calculations, determine which sample contains the most atoms (a) a g sample of copper (b) a g sample of carbon (c) a 10 g sample of uranium 67 68 Chapter Atoms and Elements Self-Assessment Quiz Q1 Two samples of a compound containing elements A and B are decomposed The first sample produces 15 g A and 35 g B The second sample produces 25 g of A and what mass of B? a 11 g B b 58 g B c 21 g B d 45 g B Q2 A compound containing only carbon and hydrogen has a carbon-to-hydrogen mass ratio of 11.89 Which carbon-tohydrogen mass ratio is possible for a different compound composed only of carbon and hydrogen? a 2.50 b 3.97 c 4.66 d 7.89 Q3 Which idea came out of Rutherford’s gold foil experiment? a That atoms contained protons and neutrons b That matter was composed of atoms c That elements have isotopes d That atoms are mostly empty space Q4 A student re-creates the Millikan oil drop experiment and tabulates the relative charges of the oil drops in terms of a constant, a Drop #1 a Drop #2 a Drop #3 a Drop #4 3a Q6 An isotope of an element contains 82 protons and 122 neutrons What is the symbol for the isotope? a 204 b 122 c 122 d 204 82 Pb 82 Pb 40 Zr 40 Zr Q7 Determine the number of electrons in the Cr3+ ion a 24 electrons b 27 electrons c electrons d 21 electrons Q8 Which pair of elements you expect to be most similar in their chemical properties? a K and Fe b O and Si c Ne and N d Br and I Q9 Which element is not a main-group element? a Se b Mo c Sr d Ba Q10 What is the charge of the ion most commonly formed by S? a 2+ b 1+ c 1d 2Q11 A naturally occurring sample of an element contains only two isotopes The first isotope has a mass of 68.9255 amu and a natural abundance of 60.11% The second isotope has a mass of 70.9247 amu Find the atomic mass of the element a 70.13 amu b 69.72 amu c 84.06 amu d 69.93 amu Q12 Which sample contains the greatest number of atoms? a 14 g C b 49 g Cr c 102 g Ag d 202 g Pb What charge for the electron (in terms of a) is consistent with these data? a a b a c a d a 2 Q5 Determine the number of protons and neutrons in the isotope Fe-58 a 26 protons and 58 neutrons b 32 protons and 26 neutrons c 26 protons and 32 neutrons d 58 protons and 58 neutrons Q13 Determine the number of atoms in 1.85 mL of mercury (The density of mercury is 13.5 g >mL.) a 3.02 * 1027 atoms b 4.11 * 1020 atoms 22 c 7.50 * 10 atoms d 1.50 * 1025 atoms Q14 A 20.0 g sample of an element contains 4.95 * 1023 atoms Identify the element a Cr b O c Mg d Fe Answers: 1:b; 2:b; 3:d; 4:a; 5:c; 6:a; 7:d; 8:d; 9:b; 10:d; 11:b; 12:a; 13:c; 14:c Chapter in review Key Terms Section 2.2 law of conservation of mass (45) law of definite proportions (46) law of multiple proportions (47) atomic theory (48) Section 2.3 cathode rays (49) cathode ray tube (49) electrical charge (49) electron (49) Section 2.4 radioactivity (51) nuclear theory (52) nucleus (52) proton (52) neutron (52) Section 2.5 atomic mass unit (amu) (52) atomic number (Z) (53) chemical symbol (53) isotope (55) natural abundance (55) mass number (A) (55) ion (56) cation (56) anion (56) Section 2.6 periodic law (57) metal (58) nonmetal (58) metalloid (58) semiconductor (58) main-group elements (58) transition elements (transition metals) (58) family (group) (59) noble gases (59) alkali metals (59) alkaline earth metals (59) halogens (59) Section 2.7 atomic mass (61) Section 2.8 mole (mol) (62) Avogadro’s number (62) molar mass (64) Chapter in review 69 Key Concepts imaging and Moving individual Atoms (2.1) ▶  The number of protons in the nucleus of the atom is the atomic ▶  Although it was only 200 years ago that John Dalton proposed his atomic theory, technology has progressed to the level where scientists can use techniques such as scanning tunneling microscopy (STM) to image and move individual atoms number (Z) and defines the element ▶  The sum of the number of protons and neutrons is the mass number (A) ▶  Atoms of an element that have different numbers of neutrons (and therefore different mass numbers) are isotopes The Atomic Theory (2.2) ▶  Each element is composed of indestructible particles called atoms ▶  All atoms of a given element have the same mass and other properties ▶  Atoms combine in simple, whole-number ratios to form compounds ▶  Atoms of one element cannot change into atoms of another element In a chemical reaction, atoms change the way that they are bound together with other atoms to form new substances ▶  Atoms that have lost or gained electrons become charged and are ions Cations are positively charged and anions are negatively charged The Periodic Table (2.6) ▶  The periodic table tabulates all known elements in order of in- creasing atomic number ▶  The periodic table is arranged so that similar elements are grouped together in columns ▶  Elements on the left side and in the center of the periodic The Electron (2.3) ▶  J J Thomson discovered the electron in the late 1800s through experiments examining the properties of cathode rays He deduced that electrons are negatively charged, and then measured their charge-to-mass ratio ▶  Robert Millikan measured the charge of the electron, which—in conjunction with Thomson’s results—led to the calculation of the mass of an electron table are metals and tend to lose electrons in their chemical changes ▶  Elements on the upper right side of the periodic table are nonmetals and tend to gain electrons in their chemical changes ▶  Elements located on the boundary between these two classes are metalloids Atomic Mass and the Mole (2.7, 2.8) ▶  The atomic mass of an element, listed directly below its symbol The Nuclear Atom (2.4) ▶  In 1909, Ernest Rutherford probed the inner structure of the atom by working with a form of radioactivity called alpha radiation and developed the nuclear theory of the atom ▶  Nuclear theory states that the atom is mainly empty space, with most of its mass concentrated in a tiny region called the nucleus and most of its volume occupied by the relatively light electrons Subatomic Particles (2.5) in the periodic table, is a weighted average of the masses of the naturally occurring isotopes of the element ▶  One mole of an element is the amount of that element that contains Avogadro’s number (6.022 * 1023) of atoms ▶  Any sample of an element with a mass (in grams) that equals its atomic mass contains one mole of the element For example, the atomic mass of carbon is 12.01 amu; therefore 12.01 grams of carbon contain mol of carbon atoms ▶  Atoms are composed of three fundamental particles: the proton (1 amu, +1 charge), the neutron (1 amu, charge), and the electron (∙ amu, -1 charge) Key Equations and relationships relationship between Mass Number (A), Number of Protons (p), and Number of Neutrons (n) (2.5) Avogadro’s Number (2.8) mol = 6.0221421 * 1023 particles A = number of protons (p) + number of neutrons (n) Atomic Mass (2.7) Atomic mass = a (fraction of isotope n) * (mass of isotope n) n Key Learning Objectives Chapter Objectives assessment Restate and Apply the Law of Definite Proportions (2.2) Example 2.1 For Practice 2.1 Exercises 3, Restate and Apply the Law of Multiple Proportions (2.2) Example 2.2 For Practice 2.2 Exercises 7–10 Work with Atomic Numbers, Mass Numbers, and Isotope Symbols (2.5) Example 2.3 For Practice 2.3 Exercises 21–26 70 Chapter Atoms and Elements Predict the Charge of Ions (2.6) Example 2.4 For Practice 2.4 Exercises 29–32 Calculate Atomic Mass (2.7) Example 2.5 For Practice 2.5 For More Practice 2.5 Exercises 41–44 Convert between Moles and Number of Atoms (2.8) Example 2.6 For Practice 2.6 Exercises 45, 46 Convert between Mass and Amount (in Moles) (2.8) Example 2.7 For Practice 2.7 For More Practice 2.7 Exercises 47, 48 Apply the Mole Concept (2.8) Examples 2.8, 2.9 For Practice 2.8, 2.9 For More Practice 2.8, 2.9 Exercises 49–56, 72, 73 Exercises Problems by Topic Note: Answers to all odd-numbered Problems, numbered in blue, can be found in Appendix III Exercises in the Problems by Topic section are paired, with each odd-numbered problem followed by a similar even-numbered problem Exercises in the Cumulative Problems section are also paired, but somewhat more loosely (Challenge Problems and Conceptual Problems, because of their nature, are unpaired.) The Laws of Conservation of Mass, Definite Proportions, and Multiple Proportions A hydrogen-filled balloon is ignited, and 1.50 g of hydrogen reacts with 12.0 g of oxygen How many grams of water vapor are formed? (Assume that water vapor is the only product.) An automobile gasoline tank holds 21 kg of gasoline When the gasoline burns, 84 kg of oxygen is consumed and carbon dioxide and water are produced What total combined mass of carbon dioxide and water is produced? Two samples of carbon tetrachloride are decomposed into their constituent elements One sample produces 38.9 g of carbon and 448 g of chlorine, and the other sample produces 14.8 g of carbon and 134 g of chlorine Are these results consistent with the law of definite proportions? Explain your answer Two samples of sodium chloride are decomposed into their constituent elements One sample produces 6.98 g of sodium and 10.7 g of chlorine, and the other sample produces 11.2 g of sodium and 17.3 g of chlorine Are these results consistent with the law of definite proportions? Explain your answer The mass ratio of sodium to fluorine in sodium fluoride is 1.21:1 A sample of sodium fluoride produces 28.8 g of sodium upon decomposition How much fluorine (in grams) forms? Upon decomposition, one sample of magnesium fluoride produced 1.65 kg of magnesium and 2.57 kg of fluorine A second sample produced 1.32 kg of magnesium How much fluorine (in grams) did the second sample produce? Two different compounds containing osmium and oxygen have the following masses of oxygen per gram of osmium: 0.168 and 0.3369 g Demonstrate that these amounts are consistent with the law of multiple proportions Palladium forms three different compounds with sulfur The mass of sulfur per gram of palladium in each compound is tabulated here Compound grams S per gram Pd A 0.603 B 0.301 C 0.151 Show that these masses are consistent with the law of multiple proportions Sulfur and oxygen form both sulfur dioxide and sulfur trioxide When samples of these are decomposed, the sulfur dioxide produces 3.49 g oxygen and 3.50 g sulfur, while the sulfur trioxide produces 6.75 g oxygen and 4.50 g sulfur Calculate the mass of oxygen per gram of sulfur for each sample and show that these results are consistent with the law of multiple proportions 10 Sulfur and fluorine form several different compounds, including sulfur hexafluoride and sulfur tetrafluoride Decomposition of a sample of sulfur hexafluoride produces 4.45 g of fluorine and 1.25 g of sulfur, while decomposition of a sample of sulfur tetrafluoride produces 4.43 g of fluorine and 1.87 g of sulfur Calculate the mass of fluorine per gram of sulfur for each sample and show that these results are consistent with the law of multiple proportions Atomic Theory, Nuclear Theory, and Subatomic Particles 11 Which statements are consistent with Dalton’s atomic theory as it was originally stated? Why? a Sulfur and oxygen atoms have the same mass b All cobalt atoms are identical c Potassium and chlorine atoms combine in a 1:1 ratio to form potassium chloride d Lead atoms can be converted into gold 12 Which statements are inconsistent with Dalton’s atomic theory as it was originally stated? Why? a All carbon atoms are identical b An oxygen atom combines with 1.5 hydrogen atoms to form a water molecule c Two oxygen atoms combine with a carbon atom to form a carbon dioxide molecule d The formation of a compound often involves the destruction of one or more atoms 13 Which statements are consistent with Rutherford’s nuclear theory as it was originally stated? Why? a The volume of an atom is mostly empty space b The nucleus of an atom is small compared to the size of the atom c Neutral lithium atoms contain more neutrons than protons d Neutral lithium atoms contain more protons than electrons 14 Which statements are inconsistent with Rutherford’s nuclear theory as it was originally stated? Why? a Since electrons are smaller than protons, and since a hydrogen atom contains only one proton and one electron, it must follow that the volume of a hydrogen atom is mostly due to the proton b A nitrogen atom has seven protons in its nucleus and seven electrons outside of its nucleus c A phosphorus atom has 15 protons in its nucleus and 150 electrons outside of its nucleus d The majority of the mass of a fluorine atom is due to its nine electrons Exercises 15 A chemist in an imaginary universe, where electrons have a different charge than they in our universe, performs the Millikan oil drop experiment to measure the electron’s charge The charges of several drops are tabulated here What is the charge of the electron in this imaginary universe? Drop# Charge A -6.9 * 10 - 19 C B -9.2 * 10 - 19 C C -11.5 * 10 - 19 C D -4.6 * 10 - 19 C 16 Imagine a unit of charge called the zorg A chemist performs the oil drop experiment and measures the charge of each drop in zorgs Based on the results listed here, what is the charge of the electron in zorgs (z)? How many electrons are in each drop? Drop# Charge A -4.8 * 10 - z B -9.6 * 10 - z C -6.4 * 10 - z D -12.8 * 10 - z 17 On a dry day, your body can accumulate static charge from walking across a carpet or from brushing your hair If your body develops a charge of -15 mC (microcoulombs), how many excess electrons has it acquired? What is their collective mass? 18 How many electrons does it take to equal the mass of a proton? 19 Which statements about subatomic particles are true? a If an atom has an equal number of protons and electrons, it is charge-neutral b Electrons are attracted to protons c Electrons are much lighter than neutrons d Protons have twice the mass of neutrons 20 Which statements about subatomic particles are false? a Protons and electrons have charges of the same magnitude but opposite sign b Protons have about the same mass as neutrons c Some atoms don’t have any protons d Protons and neutrons have charges of the same magnitude but opposite sign isotopes and ions 21 Write isotopic symbols of the form AZX for each isotope a the sodium isotope with 12 neutrons b the oxygen isotope with neutrons c the aluminum isotope with 14 neutrons d the iodine isotope with 74 neutrons 22 Write isotopic symbols of the form X-A (e.g., C-13) for each isotope a the argon isotope with 22 neutrons b the plutonium isotope with 145 neutrons c the phosphorus isotope with 16 neutrons d the fluorine isotope with 10 neutrons 23 Determine the number of protons and the number of neutrons in each isotope a 147 N b 23 c 222 d 208 11 Na 86 Rn 82 Pb 24 Determine the number of protons and the number of neutrons in each isotope a 40 b 226 c 99 d 33 19 K 43 Tc 15 P 88 Ra 71 25 The amount of carbon-14 in artifacts and fossils is often used to establish their age Determine the number of protons and the number of neutrons in a carbon-14 isotope and write its symbol in the form AZX 26 Uranium-235 is used in nuclear fission Determine the number of protons and the number of neutrons in uranium-235 and write its symbol in the form AZX 27 Determine the number of protons and the number of electrons in each ion a Ni2 + b S2c Br d Cr3 + 28 Determine the number of protons and the number of electrons in each ion a Al3 + b Se2 c Ga3 + d Sr2 + 29 Predict the charge of the monoatomic (single atom) ion formed by each element a O b K c Al d Rb 30 Predict the charge of the monoatomic (single atom) ion formed by each element a Mg b N c F d Na 31 Fill in the blanks to complete the table Symbol ion Formed Number of Electrons in ion Number of Protons in ion Ca Ca2 + _ _ _ 2+ _ Be Se _ _ 34 In _ _ 49 32 Fill in the blanks to complete the table Symbol ion Formed Number of Electrons in ion Number of Protons in ion Cl _ _ 17 Te 54 _ Br _ Br- _ _ _ Sr2 + _ 38 The Periodic Table and Atomic Mass 33 Write the name of each element and classify it as a metal, nonmetal, or metalloid a Na b Mg c Br d N e As 34 Write the symbol for each element and classify it as a metal, nonmetal, or metalloid a lead b iodine c potassium d silver e xenon 35 Determine whether or not each element is a main-group element a tellurium b potassium c vanadium d manganese 36 Determine whether or not each element is a transition element a Cr b Br c Mo d Cs 37 Classify each element as an alkali metal, alkaline earth metal, halogen, or noble gas a sodium b iodine c calcium d barium e krypton ... [222.02] 10 8 Hs 10 9 Mt 11 0 Ds 11 1 Rg 11 2 Cn 11 3 11 4 Fl 11 5 11 6 Lv 11 7* 11 8 [264 .12 ] [269 .13 ] [268 .14 ] [2 71] [272] [285] 59 Pr 60 Nd 61 Pm 62 Sm 63 Eu 64 Gd 65 Tb 66 Dy 67 Ho 68 Er 69 Tm 70 Yb 71 Lu 14 0 .12 ... 7A 17 4.003 B 4A 14 C O F 10 Ne 10 . 81 12. 01 14. 01 16.00 19 .00 20 .18 13 Al 14 Si 15 P 16 S 17 Cl 18 Ar 26.98 28.09 30.97 32.06 35.45 39.95 3A 13 Nonmetals 8A 18 He 10 28 Ni 1B 11 29 Cu 2B 12 30... 200.59 95.95 14 4.24 20 .18 237.05a 58.69 92. 91 14. 01 259 .10 a 19 0.23 16 .00 10 6.42 30.97 19 5.08 244.06a 208.98a 39 .10 14 0. 91 145a 2 31. 04 226.03a 222.02a 18 6. 21 102. 91 272a 85.47 10 1.07 2 61. 11a 15 0.36