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Atoms First

Chemistry: Atoms First

SENIOR CONTRIBUTING AUTHORS EDWARD J. NETH, UNIVERSITY OF CONNECTICUT PAUL FLOWERS, UNIVERSITY OF NORTH CAROLINA AT PEMBROKE KLAUS THEOPOLD, UNIVERSITY OF DELAWARE RICHARD LANGLEY, STEPHEN F. AUSTIN STATE UNIVERSITY WILLIAM R. ROBINSON, PHD

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Table of Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Chapter 1: Essential Ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.1 Chemistry in Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2 Phases and Classification of Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3 Physical and Chemical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.4 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 1.5 Measurement Uncertainty, Accuracy, and Precision . . . . . . . . . . . . . . . . . . . 36 1.6 Mathematical Treatment of Measurement Results . . . . . . . . . . . . . . . . . . . . 43

Chapter 2: Atoms, Molecules, and Ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2.1 Early Ideas in Atomic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 2.2 Evolution of Atomic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 2.3 Atomic Structure and Symbolism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 2.4 Chemical Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

Chapter 3: Electronic Structure and Periodic Properties of Elements . . . . . . . . . . . . . . . 115 3.1 Electromagnetic Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 3.2 The Bohr Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 3.3 Development of Quantum Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 3.4 Electronic Structure of Atoms (Electron Configurations) . . . . . . . . . . . . . . . . . 148 3.5 Periodic Variations in Element Properties . . . . . . . . . . . . . . . . . . . . . . . . 157 3.6 The Periodic Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 3.7 Molecular and Ionic Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

Chapter 4: Chemical Bonding and Molecular Geometry . . . . . . . . . . . . . . . . . . . . . . 193 4.1 Ionic Bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 4.2 Covalent Bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 4.3 Chemical Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 4.4 Lewis Symbols and Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 4.5 Formal Charges and Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 4.6 Molecular Structure and Polarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

Chapter 5: Advanced Theories of Bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 5.1 Valence Bond Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 5.2 Hybrid Atomic Orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 5.3 Multiple Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 5.4 Molecular Orbital Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282

Chapter 6: Composition of Substances and Solutions . . . . . . . . . . . . . . . . . . . . . . . 307 6.1 Formula Mass and the Mole Concept . . . . . . . . . . . . . . . . . . . . . . . . . . 308 6.2 Determining Empirical and Molecular Formulas . . . . . . . . . . . . . . . . . . . . . 311 6.3 Molarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 6.4 Other Units for Solution Concentrations . . . . . . . . . . . . . . . . . . . . . . . . . 326

Chapter 7: Stoichiometry of Chemical Reactions . . . . . . . . . . . . . . . . . . . . . . . . . 341 7.1 Writing and Balancing Chemical Equations . . . . . . . . . . . . . . . . . . . . . . . 342 7.2 Classifying Chemical Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348 7.3 Reaction Stoichiometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 7.4 Reaction Yields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366 7.5 Quantitative Chemical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371

Chapter 8: Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 8.1 Gas Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396 8.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law . . . . . . . 405 8.3 Stoichiometry of Gaseous Substances, Mixtures, and Reactions . . . . . . . . . . . . 418 8.4 Effusion and Diffusion of Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430 8.5 The Kinetic-Molecular Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435

8.6 Non-Ideal Gas Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441 Chapter 9: Thermochemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459

9.1 Energy Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460 9.2 Calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470 9.3 Enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483 9.4 Strengths of Ionic and Covalent Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . 497

Chapter 10: Liquids and Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519 10.1 Intermolecular Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520 10.2 Properties of Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532 10.3 Phase Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538 10.4 Phase Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549 10.5 The Solid State of Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556 10.6 Lattice Structures in Crystalline Solids . . . . . . . . . . . . . . . . . . . . . . . . . 563

Chapter 11: Solutions and Colloids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 597 11.1 The Dissolution Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 598 11.2 Electrolytes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603 11.3 Solubility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606 11.4 Colligative Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616 11.5 Colloids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635

Chapter 12: Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653 12.1 Spontaneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653 12.2 Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657 12.3 The Second and Third Laws of Thermodynamics . . . . . . . . . . . . . . . . . . . . 663 12.4 Free Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667

Chapter 13: Fundamental Equilibrium Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 679 13.1 Chemical Equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 680 13.2 Equilibrium Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684 13.3 Shifting Equilibria: Le Châtelier’s Principle . . . . . . . . . . . . . . . . . . . . . . . 692 13.4 Equilibrium Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695

Chapter 14: Acid-Base Equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 731 14.1 Brønsted-Lowry Acids and Bases . . . . . . . . . . . . . . . . . . . . . . . . . . . . 732 14.2 pH and pOH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 736 14.3 Relative Strengths of Acids and Bases . . . . . . . . . . . . . . . . . . . . . . . . . 742 14.4 Hydrolysis of Salt Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 760 14.5 Polyprotic Acids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 768 14.6 Buffers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 771 14.7 Acid-Base Titrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 779

Chapter 15: Equilibria of Other Reaction Classes . . . . . . . . . . . . . . . . . . . . . . . . . 805 15.1 Precipitation and Dissolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 806 15.2 Lewis Acids and Bases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 821 15.3 Multiple Equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 826

Chapter 16: Electrochemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 847 16.1 Balancing Oxidation-Reduction Reactions . . . . . . . . . . . . . . . . . . . . . . . 848 16.2 Galvanic Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855 16.3 Standard Reduction Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 859 16.4 The Nernst Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 865 16.5 Batteries and Fuel Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 869 16.6 Corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 876 16.7 Electrolysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 879

Chapter 17: Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895 17.1 Chemical Reaction Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 896 17.2 Factors Affecting Reaction Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 901

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17.3 Rate Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 904 17.4 Integrated Rate Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 911 17.5 Collision Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 921 17.6 Reaction Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 928 17.7 Catalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 933

Chapter 18: Representative Metals, Metalloids, and Nonmetals . . . . . . . . . . . . . . . . . . 965 18.1 Periodicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 966 18.2 Occurrence and Preparation of the Representative Metals . . . . . . . . . . . . . . . 976 18.3 Structure and General Properties of the Metalloids . . . . . . . . . . . . . . . . . . . 980 18.4 Structure and General Properties of the Nonmetals . . . . . . . . . . . . . . . . . . 988 18.5 Occurrence, Preparation, and Compounds of Hydrogen . . . . . . . . . . . . . . . . 996 18.6 Occurrence, Preparation, and Properties of Carbonates . . . . . . . . . . . . . . . 1003 18.7 Occurrence, Preparation, and Properties of Nitrogen . . . . . . . . . . . . . . . . . 1005 18.8 Occurrence, Preparation, and Properties of Phosphorus . . . . . . . . . . . . . . . 1010 18.9 Occurrence, Preparation, and Compounds of Oxygen . . . . . . . . . . . . . . . . 1012 18.10 Occurrence, Preparation, and Properties of Sulfur . . . . . . . . . . . . . . . . . 1027 18.11 Occurrence, Preparation, and Properties of Halogens . . . . . . . . . . . . . . . 1029 18.12 Occurrence, Preparation, and Properties of the Noble Gases . . . . . . . . . . . . 1035

Chapter 19: Transition Metals and Coordination Chemistry . . . . . . . . . . . . . . . . . . . 1053 19.1 Occurrence, Preparation, and Properties of Transition Metals and Their Compounds 1054 19.2 Coordination Chemistry of Transition Metals . . . . . . . . . . . . . . . . . . . . . 1067 19.3 Spectroscopic and Magnetic Properties of Coordination Compounds . . . . . . . . 1082

Chapter 20: Nuclear Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1099 20.1 Nuclear Structure and Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1100 20.2 Nuclear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1107 20.3 Radioactive Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1110 20.4 Transmutation and Nuclear Energy . . . . . . . . . . . . . . . . . . . . . . . . . . 1121 20.5 Uses of Radioisotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1136 20.6 Biological Effects of Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1141

Chapter 21: Organic Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1161 21.1 Hydrocarbons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1162 21.2 Alcohols and Ethers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1180 21.3 Aldehydes, Ketones, Carboxylic Acids, and Esters . . . . . . . . . . . . . . . . . . 1185 21.4 Amines and Amides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1190

Appendix A: The Periodic Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1211 Appendix B: Essential Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1213 Appendix C: Units and Conversion Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1221 Appendix D: Fundamental Physical Constants . . . . . . . . . . . . . . . . . . . . . . . . . . 1223 Appendix E: Water Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1225 Appendix F: Composition of Commercial Acids and Bases . . . . . . . . . . . . . . . . . . . 1231 Appendix G: Standard Thermodynamic Properties for Selected Substances . . . . . . . . . . 1233 Appendix H: Ionization Constants of Weak Acids . . . . . . . . . . . . . . . . . . . . . . . . . 1247 Appendix I: Ionization Constants of Weak Bases . . . . . . . . . . . . . . . . . . . . . . . . . 1251 Appendix J: Solubility Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1253 Appendix K: Formation Constants for Complex Ions . . . . . . . . . . . . . . . . . . . . . . . 1257 Appendix L: Standard Electrode (Half-Cell) Potentials . . . . . . . . . . . . . . . . . . . . . . 1259 Appendix M: Half-Lives for Several Radioactive Isotopes . . . . . . . . . . . . . . . . . . . . 1265 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1339

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Preface

Welcome to Chemistry: Atoms First, an OpenStax resource. This textbook was written to increase student access to high-quality learning materials, maintaining the highest standards of academic rigor at little or no cost.

About OpenStax

OpenStax is a nonprofit based at Rice University, and it’s our mission to improve student access to education. Our first openly licensed college textbook was published in 2012 and our initiative has since scaled to over 20 books used by hundreds of thousands of students across the globe. Our adaptive learning technology, designed to improve learning outcomes through personalized educational paths, is currently being piloted for K–12 and college. The OpenStax mission is made possible through the generous support of philanthropic foundations. Through these partnerships and with the help of additional low-cost resources from our OpenStax Partners, OpenStax is breaking down the most common barriers to learning and empowering students and instructors to succeed.

About OpenStax’s Resources Customization

Chemistry: Atoms First is licensed under the Creative Commons Attribution 4.0 International (CC BY) license, which means you can distribute, remix, and build upon the content, as long as you credit OpenStax for the original creation. Because our books are openly licensed, you are free to use the entire book or pick and choose the sections that are most relevant to the needs of your course. Feel free to remix the content by assigning your students select chapters and sections in your syllabus in the order that you prefer. You can even provide a direct link in your syllabus to the sections in the web view of your book.

Errata

All OpenStax textbooks undergo a rigorous review process. However, like any professional-grade textbook, errors sometimes occur. Since our books are web-based, we can make updates periodically when deemed pedagogically necessary. If you have a correction to suggest, submit it through the link on your book page on openstax.org. All errata suggestions are reviewed by subject matter experts. OpenStax is committed to remaining transparent about all updates, so you will also find a list of past errata changes on your book page on openstax.org.

Format

You can access this textbook for free in web view or PDF through openstax.org, and in low-cost print.

About Chemistry: Atoms First

This text is an atoms-first adaptation of OpenStax Chemistry. The intention of “atoms-first” involves a few basic principles: first, it introduces atomic and molecular structure much earlier than the traditional approach, and it threads these themes through subsequent chapters. This approach may be chosen as a way to delay the introduction of material such as stoichiometry that students traditionally find abstract and difficult, thereby allowing students time to acclimate their study skills to chemistry. Additionally, it gives students a basis for understanding the application of quantitative principles to the chemistry that underlies the entire course. It also aims to center the study of chemistry on the atomic foundation that many will expand upon in a later course covering organic chemistry, easing that transition when the time arrives.

Coverage and Scope

In Chemistry: Atoms First , we strive to make chemistry, as a discipline, interesting and accessible to students. With this objective in mind, the content of this textbook has been developed and arranged to provide a logical progression from fundamental to more advanced concepts of chemical science. All of the material included in a traditional general chemistry course is here. It has been reorganized in an atoms-first approach and, where necessary, new material has been added to allow for continuity and to improve the flow of topics. The text can be used for a traditional two-semester introduction to chemistry or for a three-semester introduction, an approach becoming more common

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at many institutions. The goal is to provide a progressive, graduated introduction to chemistry that focuses on the fundamentally atom-focused nature of the subject. Topics are introduced within the context of familiar experiences whenever possible, treated with an appropriate rigor to satisfy the intellect of the learner, and reinforced in subsequent discussions of related content. The organization and pedagogical features were developed and vetted with feedback from chemistry educators dedicated to the project.

Chapter 1: Essential Ideas

Chapter 2: Atoms, Molecules, and Ions

Chapter 3: Electronic Structure and Periodic Properties of Elements

Chapter 4: Chemical Bonding and Molecular Geometry

Chapter 5: Advanced Theories of Bonding

Chapter 6: Composition of Substances and Solutions

Chapter 7: Stoichiometry of Chemical Reactions

Chapter 8: Gases

Chapter 9: Thermochemistry

Chapter 10: Liquids and Solids

Chapter 11: Solutions and Colloids

Chapter 12: Thermodynamics

Chapter 13: Fundamental Equilibrium Concepts

Chapter 14: Acid-Base Equilibria

Chapter 15: Equilibria of Other Reaction Classes

Chapter 16: Electrochemistry

Chapter 17: Kinetics

Chapter 18: Representative Metals, Metalloids, and Nonmetals

Chapter 19: Transition Metals and Coordination Chemistry

Chapter 20: Nuclear Chemistry

Chapter 21: Organic Chemistry

Partnership with University of Connecticut and UConn Undergraduate Student Government

Chemistry: Atoms First is a peer-reviewed, openly licensed introductory textbook produced through a collaborative publishing partnership between OpenStax and the University of Connecticut and UConn Undergraduate Student Government Association.

Pedagogical Foundation

Throughout Chemistry: Atoms First, you will find features that draw the students into scientific inquiry by taking selected topics a step further. Students and educators alike will appreciate discussions in these feature boxes.

Chemistry in Everyday Life ties chemistry concepts to everyday issues and real-world applications of science that students encounter in their lives. Topics include cell phones, solar thermal energy power plants, plastics recycling, and measuring blood pressure.

How Sciences Interconnect feature boxes discuss chemistry in context of its interconnectedness with other scientific disciplines. Topics include neurotransmitters, greenhouse gases and climate change, and proteins and enzymes.

Portrait of a Chemist features present a short bio and an introduction to the work of prominent figures from history and present day so that students can see the “face” of contributors in this field as well as science in

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action.

Comprehensive Art Program

Our art program is designed to enhance students’ understanding of concepts through clear, effective illustrations, diagrams, and photographs.

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..

Interactives That Engage

Chemistry: Atoms First incorporates links to relevant interactive exercises and animations that help bring topics to life through our Link to Learning feature. Examples include:

PhET simulations

IUPAC data and interactives

TED talks

Assessments That Reinforce Key Concepts

In-chapter Examples walk students through problems by posing a question, stepping out a solution, and then asking students to practice the skill with a “Check Your Learning” component. The book also includes assessments at the end of each chapter so students can apply what they’ve learned through practice problems.

Additional Resources Student and Instructor Resources

We’ve compiled additional resources for both students and instructors, including Getting Started Guides, PowerPoint slides, and an instructor answer guide. Instructor resources require a verified instructor account, which can be requested on your openstax.org log-in. Take advantage of these resources to supplement your OpenStax book.

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Partner Resources

OpenStax partners are our allies in the mission to make high-quality learning materials affordable and accessible to students and instructors everywhere. Their tools integrate seamlessly with our OpenStax titles at a low cost. To access the partner resources for your text, visit your book page on openstax.org.

About the University of Connecticut

The University of Connecticut is one of the top public research universities in the nation, with more than 30,000 students pursuing answers to critical questions in labs, lecture halls, and the community. Knowledge exploration throughout the University’s network of campuses is united by a culture of innovation. An unprecedented commitment from the state of Connecticut ensures UConn attracts internationally renowned faculty and the world’s brightest students. A tradition of coaching winning athletes makes UConn a standout in Division l sports and fuels our academic spirit. As a vibrant, progressive leader, UConn fosters a diverse and dynamic culture that meets the challenges of a changing global society.

About Our Team Senior Contributing Authors

Paul Flowers, University of North Carolina–Pembroke Dr. Paul Flowers earned a BS in Chemistry from St. Andrews Presbyterian College in 1983 and a PhD in Analytical Chemistry from the University of Tennessee in 1988. After a one-year postdoctoral appointment at Los Alamos National Laboratory, he joined the University of North Carolina–Pembroke in the fall of 1989. Dr. Flowers teaches courses in general and analytical chemistry, and conducts experimental research involving the development of new devices and methods for microscale chemical analysis.

Klaus Theopold, University of Delaware Dr. Klaus Theopold (born in Berlin, Germany) received his Vordiplom from the Universität Hamburg in 1977. He then decided to pursue his graduate studies in the United States, where he received his PhD in inorganic chemistry from UC Berkeley in 1982. After a year of postdoctoral research at MIT, he joined the faculty at Cornell University. In 1990, he moved to the University of Delaware, where he is a Professor in the Department of Chemistry and Biochemistry and serves as an Associate Director of the University’s Center for Catalytic Science and Technology. Dr. Theopold regularly teaches graduate courses in inorganic and organometallic chemistry as well as General Chemistry.

Richard Langley, Stephen F. Austin State University Dr. Richard Langley earned BS degrees in Chemistry and Mineralogy from Miami University of Ohio in the early 1970s and went on to receive his PhD in Chemistry from the University of Nebraska in 1977. After a postdoctoral fellowship at the Arizona State University Center for Solid State Studies, Dr. Langley taught in the University of Wisconsin system and participated in research at Argonne National Laboratory. Moving to Stephen F. Austin State University in 1982, Dr. Langley today serves as Professor of Chemistry. His areas of specialization are solid state chemistry, synthetic inorganic chemistry, fluorine chemistry, and chemical education.

Edward J. Neth, University of Connecticut (Chemistry: Atoms First) Dr. Edward J. Neth earned his BS in Chemistry (minor in Politics) at Fairfield University in 1985 and his MS (1988) and PhD (1995; Inorganic/Materials Chemistry) at the University of Connecticut. He joined the University of Connecticut in 2004 as a lecturer and currently teaches general and inorganic chemistry; his background includes having worked as a network engineer in both corporate and university settings, and he has served as Director of Academic Computing at New Haven University. He currently teaches a three-semester, introductory chemistry sequence at UConn and is involved with training and coordinating teaching assistants.

William R. Robinson, PhD

Contributing Authors

Mark Blaser, Shasta College

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Simon Bott, University of Houston Donald Carpenetti, Craven Community College Andrew Eklund, Alfred University Emad El-Giar, University of Louisiana at Monroe Don Frantz, Wilfrid Laurier University Paul Hooker, Westminster College Jennifer Look, Mercer University George Kaminski, Worcester Polytechnic Institute Carol Martinez, Central New Mexico Community College Troy Milliken, Jackson State University Vicki Moravec, Trine University Jason Powell, Ferrum College Thomas Sorensen, University of Wisconsin–Milwaukee Allison Soult, University of Kentucky

Reviewers

Casey Akin, College Station Independent School District Lara AL-Hariri, University of Massachusetts–Amherst Sahar Atwa, University of Louisiana at Monroe Todd Austell, University of North Carolina–Chapel Hill Bobby Bailey, University of Maryland–University College Robert Baker, Trinity College Jeffrey Bartz, Kalamazoo College Greg Baxley, Cuesta College Ashley Beasley Green, National Institute of Standards and Technology Patricia Bianconi, University of Massachusetts Lisa Blank, Lyme Central School District Daniel Branan, Colorado Community College System Dorian Canelas, Duke University Emmanuel Chang, York College Carolyn Collins, College of Southern Nevada Colleen Craig, University of Washington Yasmine Daniels, Montgomery College–Germantown Patricia Dockham, Grand Rapids Community College Erick Fuoco, Richard J. Daley College Andrea Geyer, University of Saint Francis Daniel Goebbert, University of Alabama John Goodwin, Coastal Carolina University Stephanie Gould, Austin College Patrick Holt, Bellarmine University Kevin Kolack, Queensborough Community College Amy Kovach, Roberts Wesleyan College Judit Kovacs Beagle, University of Dayton Krzysztof Kuczera, University of Kansas Marcus Lay, University of Georgia Pamela Lord, University of Saint Francis Oleg Maksimov, Excelsior College John Matson, Virginia Tech Katrina Miranda, University of Arizona Douglas Mulford, Emory University Mark Ott, Jackson College

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Adrienne Oxley, Columbia College Richard Pennington, Georgia Gwinnett College Rodney Powell, Coastal Carolina Community College Jeanita Pritchett, Montgomery College–Rockville Aheda Saber, University of Illinois at Chicago Raymond Sadeghi, University of Texas at San Antonio Nirmala Shankar, Rutgers University Jonathan Smith, Temple University Bryan Spiegelberg, Rider University Ron Sternfels, Roane State Community College Cynthia Strong, Cornell College Kris Varazo, Francis Marion University Victor Vilchiz, Virginia State University Alex Waterson, Vanderbilt University Juchao Yan, Eastern New Mexico University Mustafa Yatin, Salem State University Kazushige Yokoyama, State University of New York at Geneseo Curtis Zaleski, Shippensburg University Wei Zhang, University of Colorado–Boulder

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Chapter 1

Essential Ideas

Figure 1.1 Chemical substances and processes are essential for our existence, providing sustenance, keeping us clean and healthy, fabricating electronic devices, enabling transportation, and much more. (credit “left”: modification of work by “vxla”/Flickr; credit “left middle”: modification of work by “the Italian voice”/Flickr; credit “right middle”: modification of work by Jason Trim; credit “right”: modification of work by “gosheshe”/Flickr)

Chapter Outline

1.1 Chemistry in Context

1.2 Phases and Classification of Matter

1.3 Physical and Chemical Properties

1.4 Measurements

1.5 Measurement Uncertainty, Accuracy, and Precision

1.6 Mathematical Treatment of Measurement Results

Introduction Your alarm goes off and, after hitting “snooze” once or twice, you pry yourself out of bed. You make a cup of coffee to help you get going, and then you shower, get dressed, eat breakfast, and check your phone for messages. On your way to school, you stop to fill your car’s gas tank, almost making you late for the first day of chemistry class. As you find a seat in the classroom, you read the question projected on the screen: “Welcome to class! Why should we study chemistry?”

Do you have an answer? You may be studying chemistry because it fulfills an academic requirement, but if you consider your daily activities, you might find chemistry interesting for other reasons. Most everything you do and encounter during your day involves chemistry. Making coffee, cooking eggs, and toasting bread involve chemistry. The products you use—like soap and shampoo, the fabrics you wear, the electronics that keep you connected to your world, the gasoline that propels your car—all of these and more involve chemical substances and processes. Whether you are aware or not, chemistry is part of your everyday world. In this course, you will learn many of the essential principles underlying the chemistry of modern-day life.

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1.1 Chemistry in Context

By the end of this module, you will be able to:

• Outline the historical development of chemistry

• Provide examples of the importance of chemistry in everyday life

• Describe the scientific method

• Differentiate among hypotheses, theories, and laws

• Provide examples illustrating macroscopic, microscopic, and symbolic domains

Throughout human history, people have tried to convert matter into more useful forms. Our Stone Age ancestors chipped pieces of flint into useful tools and carved wood into statues and toys. These endeavors involved changing the shape of a substance without changing the substance itself. But as our knowledge increased, humans began to change the composition of the substances as well—clay was converted into pottery, hides were cured to make garments, copper ores were transformed into copper tools and weapons, and grain was made into bread.

Humans began to practice chemistry when they learned to control fire and use it to cook, make pottery, and smelt metals. Subsequently, they began to separate and use specific components of matter. A variety of drugs such as aloe, myrrh, and opium were isolated from plants. Dyes, such as indigo and Tyrian purple, were extracted from plant and animal matter. Metals were combined to form alloys—for example, copper and tin were mixed together to make bronze—and more elaborate smelting techniques produced iron. Alkalis were extracted from ashes, and soaps were prepared by combining these alkalis with fats. Alcohol was produced by fermentation and purified by distillation.

Attempts to understand the behavior of matter extend back for more than 2500 years. As early as the sixth century BC, Greek philosophers discussed a system in which water was the basis of all things. You may have heard of the Greek postulate that matter consists of four elements: earth, air, fire, and water. Subsequently, an amalgamation of chemical technologies and philosophical speculations were spread from Egypt, China, and the eastern Mediterranean by alchemists, who endeavored to transform “base metals” such as lead into “noble metals” like gold, and to create elixirs to cure disease and extend life (Figure 1.2).

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Figure 1.2 This portrayal shows an alchemist’s workshop circa 1580. Although alchemy made some useful contributions to how to manipulate matter, it was not scientific by modern standards. (credit: Chemical Heritage Foundation)

From alchemy came the historical progressions that led to modern chemistry: the isolation of drugs from natural sources, metallurgy, and the dye industry. Today, chemistry continues to deepen our understanding and improve our ability to harness and control the behavior of matter. This effort has been so successful that many people do not realize either the central position of chemistry among the sciences or the importance and universality of chemistry in daily life.

Chemistry: The Central Science

Chemistry is sometimes referred to as “the central science” due to its interconnectedness with a vast array of other STEM disciplines (STEM stands for areas of study in the science, technology, engineering, and math fields). Chemistry and the language of chemists play vital roles in biology, medicine, materials science, forensics, environmental science, and many other fields (Figure 1.3). The basic principles of physics are essential for understanding many aspects of chemistry, and there is extensive overlap between many subdisciplines within the two fields, such as chemical physics and nuclear chemistry. Mathematics, computer science, and information theory provide important tools that help us calculate, interpret, describe, and generally make sense of the chemical world. Biology and chemistry converge in biochemistry, which is crucial to understanding the many complex factors and processes that keep living organisms (such as us) alive. Chemical engineering, materials science, and nanotechnology combine chemical principles and empirical findings to produce useful substances, ranging from gasoline to fabrics to electronics. Agriculture, food science, veterinary science, and brewing and wine making help provide sustenance in the form of food and drink to the world’s population. Medicine, pharmacology, biotechnology, and botany identify and produce substances that help keep us healthy. Environmental science, geology, oceanography, and atmospheric science incorporate many chemical ideas to help us better understand and protect our physical world. Chemical ideas are used to help understand the universe in astronomy and cosmology.

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Figure 1.3 Knowledge of chemistry is central to understanding a wide range of scientific disciplines. This diagram shows just some of the interrelationships between chemistry and other fields.

What are some changes in matter that are essential to daily life? Digesting and assimilating food, synthesizing polymers that are used to make clothing, containers, cookware, and credit cards, and refining crude oil into gasoline and other products are just a few examples. As you proceed through this course, you will discover many different examples of changes in the composition and structure of matter, how to classify these changes and how they occurred, their causes, the changes in energy that accompany them, and the principles and laws involved. As you learn about these things, you will be learning chemistry, the study of the composition, properties, and interactions of matter. The practice of chemistry is not limited to chemistry books or laboratories: It happens whenever someone is involved in changes in matter or in conditions that may lead to such changes.

The Scientific Method

Chemistry is a science based on observation and experimentation. Doing chemistry involves attempting to answer questions and explain observations in terms of the laws and theories of chemistry, using procedures that are accepted by the scientific community. There is no single route to answering a question or explaining an observation, but there is an aspect common to every approach: Each uses knowledge based on experiments that can be reproduced to verify the results. Some routes involve a hypothesis, a tentative explanation of observations that acts as a guide for gathering and checking information. We test a hypothesis by experimentation, calculation, and/or comparison with the experiments of others and then refine it as needed.

Some hypotheses are attempts to explain the behavior that is summarized in laws. The laws of science summarize a vast number of experimental observations, and describe or predict some facet of the natural world. If such a hypothesis turns out to be capable of explaining a large body of experimental data, it can reach the status of a theory. Scientific theories are well-substantiated, comprehensive, testable explanations of particular aspects of nature. Theories are accepted because they provide satisfactory explanations, but they can be modified if new data become available. The path of discovery that leads from question and observation to law or hypothesis to theory, combined with experimental verification of the hypothesis and any necessary modification of the theory, is called the scientific method (Figure 1.4).

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Figure 1.4 The scientific method follows a process similar to the one shown in this diagram. All the key components are shown, in roughly the right order. Scientific progress is seldom neat and clean: It requires open inquiry and the reworking of questions and ideas in response to findings.

The Domains of Chemistry

Chemists study and describe the behavior of matter and energy in three different domains: macroscopic, microscopic, and symbolic. These domains provide different ways of considering and describing chemical behavior.

Macro is a Greek word that means “large.” The macroscopic domain is familiar to us: It is the realm of everyday things that are large enough to be sensed directly by human sight or touch. In daily life, this includes the food you eat and the breeze you feel on your face. The macroscopic domain includes everyday and laboratory chemistry, where we observe and measure physical and chemical properties, or changes such as density, solubility, and flammability.

The microscopic domain of chemistry is almost always visited in the imagination. Micro also comes from Greek and means “small.” Some aspects of the microscopic domains are visible through a microscope, such as a magnified image of graphite or bacteria. Viruses, for instance, are too small to be seen with the naked eye, but when we’re suffering from a cold, we’re reminded of how real they are.

However, most of the subjects in the microscopic domain of chemistry—such as atoms and molecules—are too small to be seen even with standard microscopes and often must be pictured in the mind. Other components of the microscopic domain include ions and electrons, protons and neutrons, and chemical bonds, each of which is far too small to see. This domain includes the individual metal atoms in a wire, the ions that compose a salt crystal, the changes in individual molecules that result in a color change, the conversion of nutrient molecules into tissue and energy, and the evolution of heat as bonds that hold atoms together are created.

The symbolic domain contains the specialized language used to represent components of the macroscopic and microscopic domains. Chemical symbols (such as those used in the periodic table), chemical formulas, and chemical equations are part of the symbolic domain, as are graphs and drawings. We can also consider calculations as part of the symbolic domain. These symbols play an important role in chemistry because they help interpret the behavior of the macroscopic domain in terms of the components of the microscopic domain. One of the challenges for

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students learning chemistry is recognizing that the same symbols can represent different things in the macroscopic and microscopic domains, and one of the features that makes chemistry fascinating is the use of a domain that must be imagined to explain behavior in a domain that can be observed.

A helpful way to understand the three domains is via the essential and ubiquitous substance of water. That water is a liquid at moderate temperatures, will freeze to form a solid at lower temperatures, and boil to form a gas at higher temperatures (Figure 1.5) are macroscopic observations. But some properties of water fall into the microscopic domain—what we cannot observe with the naked eye. The description of water as comprised of two hydrogen atoms and one oxygen atom, and the explanation of freezing and boiling in terms of attractions between these molecules, is within the microscopic arena. The formula H2O, which can describe water at either the macroscopic or microscopic levels, is an example of the symbolic domain. The abbreviations (g) for gas, (s) for solid, and (l) for liquid are also symbolic.

Figure 1.5 (a) Moisture in the air, icebergs, and the ocean represent water in the macroscopic domain. (b) At the molecular level (microscopic domain), gas molecules are far apart and disorganized, solid water molecules are close together and organized, and liquid molecules are close together and disorganized. (c) The formula H2O symbolizes water, and (g), (s), and (l) symbolize its phases. Note that clouds are actually comprised of either very small liquid water droplets or solid water crystals; gaseous water in our atmosphere is not visible to the naked eye, although it may be sensed as humidity. (credit a: modification of work by “Gorkaazk”/Wikimedia Commons)

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1.2 Phases and Classification of Matter

By the end of this section, you will be able to:

• Describe the basic properties of each physical state of matter: solid, liquid, and gas

• Define and give examples of atoms and molecules

• Classify matter as an element, compound, homogeneous mixture, or heterogeneous mixture with regard to its physical state and composition

• Distinguish between mass and weight

• Apply the law of conservation of matter

Matter is defined as anything that occupies space and has mass, and it is all around us. Solids and liquids are more obviously matter: We can see that they take up space, and their weight tells us that they have mass. Gases are also matter; if gases did not take up space, a balloon would stay collapsed rather than inflate when filled with gas.

Solids, liquids, and gases are the three states of matter commonly found on earth (Figure 1.6). A solid is rigid and possesses a definite shape. A liquid flows and takes the shape of a container, except that it forms a flat or slightly curved upper surface when acted upon by gravity. (In zero gravity, liquids assume a spherical shape.) Both liquid and solid samples have volumes that are very nearly independent of pressure. A gas takes both the shape and volume of its container.

Figure 1.6 The three most common states or phases of matter are solid, liquid, and gas.

A fourth state of matter, plasma, occurs naturally in the interiors of stars. A plasma is a gaseous state of matter that contains appreciable numbers of electrically charged particles (Figure 1.7). The presence of these charged particles imparts unique properties to plasmas that justify their classification as a state of matter distinct from gases. In addition to stars, plasmas are found in some other high-temperature environments (both natural and man-made), such as lightning strikes, certain television screens, and specialized analytical instruments used to detect trace amounts of metals.

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Figure 1.7 A plasma torch can be used to cut metal. (credit: “Hypertherm”/Wikimedia Commons)

In a tiny cell in a plasma television, the plasma emits ultraviolet light, which in turn causes the display at that location to appear a specific color. The composite of these tiny dots of color makes up the image that you see. Watch this video (http://openstaxcollege.org/l/16plasma) to learn more about plasma and the

places you encounter it.

Some samples of matter appear to have properties of solids, liquids, and/or gases at the same time. This can occur when the sample is composed of many small pieces. For example, we can pour sand as if it were a liquid because it is composed of many small grains of solid sand. Matter can also have properties of more than one state when it is a mixture, such as with clouds. Clouds appear to behave somewhat like gases, but they are actually mixtures of air (gas) and tiny particles of water (liquid or solid).

The mass of an object is a measure of the amount of matter in it. One way to measure an object’s mass is to measure the force it takes to accelerate the object. It takes much more force to accelerate a car than a bicycle because the car has much more mass. A more common way to determine the mass of an object is to use a balance to compare its mass with a standard mass.

Although weight is related to mass, it is not the same thing. Weight refers to the force that gravity exerts on an object. This force is directly proportional to the mass of the object. The weight of an object changes as the force of gravity changes, but its mass does not. An astronaut’s mass does not change just because she goes to the moon. But her weight on the moon is only one-sixth her earth-bound weight because the moon’s gravity is only one-sixth that of the earth’s. She may feel “weightless” during her trip when she experiences negligible external forces (gravitational or any other), although she is, of course, never “massless.”

The law of conservation of matter summarizes many scientific observations about matter: It states that there is no detectable change in the total quantity of matter present when matter converts from one type to another (a chemical change) or changes among solid, liquid, or gaseous states (a physical change). Brewing beer and the operation of batteries provide examples of the conservation of matter (Figure 1.8). During the brewing of beer, the ingredients (water, yeast, grains, malt, hops, and sugar) are converted into beer (water, alcohol, carbonation, and flavoring substances) with no actual loss of substance. This is most clearly seen during the bottling process, when glucose turns

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into ethanol and carbon dioxide, and the total mass of the substances does not change. This can also be seen in a lead-acid car battery: The original substances (lead, lead oxide, and sulfuric acid), which are capable of producing electricity, are changed into other substances (lead sulfate and water) that do not produce electricity, with no change in the actual amount of matter.

Figure 1.8 (a) The mass of beer precursor materials is the same as the mass of beer produced: Sugar has become alcohol and carbonation. (b) The mass of the lead, lead oxide plates, and sulfuric acid that goes into the production of electricity is exactly equal to the mass of lead sulfate and water that is formed.

Although this conservation law holds true for all conversions of matter, convincing examples are few and far between because, outside of the controlled conditions in a laboratory, we seldom collect all of the material that is produced during a particular conversion. For example, when you eat, digest, and assimilate food, all of the matter in the original food is preserved. But because some of the matter is incorporated into your body, and much is excreted as various types of waste, it is challenging to verify by measurement.

Atoms and Molecules

An atom is the smallest particle of an element that has the properties of that element and can enter into a chemical combination. Consider the element gold, for example. Imagine cutting a gold nugget in half, then cutting one of the halves in half, and repeating this process until a piece of gold remained that was so small that it could not be cut in half (regardless of how tiny your knife may be). This minimally sized piece of gold is an atom (from the Greek atomos, meaning “indivisible”) (Figure 1.9). This atom would no longer be gold if it were divided any further.

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Figure 1.9 (a) This photograph shows a gold nugget. (b) A scanning-tunneling microscope (STM) can generate views of the surfaces of solids, such as this image of a gold crystal. Each sphere represents one gold atom. (credit a: modification of work by United States Geological Survey; credit b: modification of work by “Erwinrossen”/Wikimedia Commons)

The first suggestion that matter is composed of atoms is attributed to the Greek philosophers Leucippus and Democritus, who developed their ideas in the 5th century BCE. However, it was not until the early nineteenth century that John Dalton (1766–1844), a British schoolteacher with a keen interest in science, supported this hypothesis with quantitative measurements. Since that time, repeated experiments have confirmed many aspects of this hypothesis, and it has become one of the central theories of chemistry. Other aspects of Dalton’s atomic theory are still used but with minor revisions (details of Dalton’s theory are provided in the chapter on atoms and molecules).

An atom is so small that its size is difficult to imagine. One of the smallest things we can see with our unaided eye is a single thread of a spider web: These strands are about 1/10,000 of a centimeter (0.0001 cm) in diameter. Although the cross-section of one strand is almost impossible to see without a microscope, it is huge on an atomic scale. A single carbon atom in the web has a diameter of about 0.000000015 centimeter, and it would take about 7000 carbon atoms to span the diameter of the strand. To put this in perspective, if a carbon atom were the size of a dime, the cross-section of one strand would be larger than a football field, which would require about 150 million carbon atom “dimes” to cover it. (Figure 1.10) shows increasingly close microscopic and atomic-level views of ordinary cotton.

Figure 1.10 These images provide an increasingly closer view: (a) a cotton boll, (b) a single cotton fiber viewed under an optical microscope (magnified 40 times), (c) an image of a cotton fiber obtained with an electron microscope (much higher magnification than with the optical microscope); and (d and e) atomic-level models of the fiber (spheres of different colors represent atoms of different elements). (credit c: modification of work by “Featheredtar”/Wikimedia Commons)

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An atom is so light that its mass is also difficult to imagine. A billion lead atoms (1,000,000,000 atoms) weigh about 3 × 10−13 grams, a mass that is far too light to be weighed on even the world’s most sensitive balances. It would require over 300,000,000,000,000 lead atoms (300 trillion, or 3 × 1014) to be weighed, and they would weigh only 0.0000001 gram.

It is rare to find collections of individual atoms. Only a few elements, such as the gases helium, neon, and argon, consist of a collection of individual atoms that move about independently of one another. Other elements, such as the gases hydrogen, nitrogen, oxygen, and chlorine, are composed of units that consist of pairs of atoms (Figure 1.11). One form of the element phosphorus consists of units composed of four phosphorus atoms. The element sulfur exists in various forms, one of which consists of units composed of eight sulfur atoms. These units are called molecules. A molecule consists of two or more atoms joined by strong forces called chemical bonds. The atoms in a molecule move around as a unit, much like the cans of soda in a six-pack or a bunch of keys joined together on a single key ring. A molecule may consist of two or more identical atoms, as in the molecules found in the elements hydrogen, oxygen, and sulfur, or it may consist of two or more different atoms, as in the molecules found in water. Each water molecule is a unit that contains two hydrogen atoms and one oxygen atom. Each glucose molecule is a unit that contains 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms. Like atoms, molecules are incredibly small and light. If an ordinary glass of water were enlarged to the size of the earth, the water molecules inside it would be about the size of golf balls.

Figure 1.11 The elements hydrogen, oxygen, phosphorus, and sulfur form molecules consisting of two or more atoms of the same element. The compounds water, carbon dioxide, and glucose consist of combinations of atoms of different elements.

Classifying Matter

We can classify matter into several categories. Two broad categories are mixtures and pure substances. A pure substance has a constant composition. All specimens of a pure substance have exactly the same makeup and properties. Any sample of sucrose (table sugar) consists of 42.1% carbon, 6.5% hydrogen, and 51.4% oxygen by mass. Any sample of sucrose also has the same physical properties, such as melting point, color, and sweetness, regardless of the source from which it is isolated.

We can divide pure substances into two classes: elements and compounds. Pure substances that cannot be broken down into simpler substances by chemical changes are called elements. Iron, silver, gold, aluminum, sulfur, oxygen, and copper are familiar examples of the more than 100 known elements, of which about 90 occur naturally on the earth, and two dozen or so have been created in laboratories.

Pure substances that can be broken down by chemical changes are called compounds. This breakdown may produce either elements or other compounds, or both. Mercury(II) oxide, an orange, crystalline solid, can be broken down by heat into the elements mercury and oxygen (Figure 1.12). When heated in the absence of air, the compound sucrose is broken down into the element carbon and the compound water. (The initial stage of this process, when the sugar is turning brown, is known as caramelization—this is what imparts the characteristic sweet and nutty flavor to caramel

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apples, caramelized onions, and caramel). Silver(I) chloride is a white solid that can be broken down into its elements, silver and chlorine, by absorption of light. This property is the basis for the use of this compound in photographic films and photochromic eyeglasses (those with lenses that darken when exposed to light).

Figure 1.12 (a)The compound mercury(II) oxide, (b)when heated, (c) decomposes into silvery droplets of liquid mercury and invisible oxygen gas. (credit: modification of work by Paul Flowers)

Many compounds break down when heated. This site (http://openstaxcollege.org/l/16mercury) shows the breakdown of mercury oxide, HgO. You can also view an example of the photochemical decomposition of silver chloride (http://openstaxcollege.org/l/16silvchloride) (AgCl), the basis

of early photography.

The properties of combined elements are different from those in the free, or uncombined, state. For example, white crystalline sugar (sucrose) is a compound resulting from the chemical combination of the element carbon, which is a black solid in one of its uncombined forms, and the two elements hydrogen and oxygen, which are colorless gases when uncombined. Free sodium, an element that is a soft, shiny, metallic solid, and free chlorine, an element that is a yellow-green gas, combine to form sodium chloride (table salt), a compound that is a white, crystalline solid.

A mixture is composed of two or more types of matter that can be present in varying amounts and can be separated by physical changes, such as evaporation (you will learn more about this later). A mixture with a composition that varies from point to point is called a heterogeneous mixture. Italian dressing is an example of a heterogeneous mixture (Figure 1.13). Its composition can vary because we can make it from varying amounts of oil, vinegar, and herbs. It is not the same from point to point throughout the mixture—one drop may be mostly vinegar, whereas a different drop may be mostly oil or herbs because the oil and vinegar separate and the herbs settle. Other examples of heterogeneous mixtures are chocolate chip cookies (we can see the separate bits of chocolate, nuts, and cookie dough) and granite (we can see the quartz, mica, feldspar, and more).

A homogeneous mixture, also called a solution, exhibits a uniform composition and appears visually the same throughout. An example of a solution is a sports drink, consisting of water, sugar, coloring, flavoring, and electrolytes mixed together uniformly (Figure 1.13). Each drop of a sports drink tastes the same because each drop contains the same amounts of water, sugar, and other components. Note that the composition of a sports drink can vary—it could be made with somewhat more or less sugar, flavoring, or other components, and still be a sports drink. Other examples of homogeneous mixtures include air, maple syrup, gasoline, and a solution of salt in water.

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Figure 1.13 (a) Oil and vinegar salad dressing is a heterogeneous mixture because its composition is not uniform throughout. (b) A commercial sports drink is a homogeneous mixture because its composition is uniform throughout. (credit a “left”: modification of work by John Mayer; credit a “right”: modification of work by Umberto Salvagnin; credit b “left: modification of work by Jeff Bedford)

Although there are just over 100 elements, tens of millions of chemical compounds result from different combinations of these elements. Each compound has a specific composition and possesses definite chemical and physical properties by which we can distinguish it from all other compounds. And, of course, there are innumerable ways to combine elements and compounds to form different mixtures. A summary of how to distinguish between the various major classifications of matter is shown in (Figure 1.14).

Figure 1.14 Depending on its properties, a given substance can be classified as a homogeneous mixture, a heterogeneous mixture, a compound, or an element.

Eleven elements make up about 99% of the earth’s crust and atmosphere (Table 1.1). Oxygen constitutes nearly one- half and silicon about one-quarter of the total quantity of these elements. A majority of elements on earth are found in chemical combinations with other elements; about one-quarter of the elements are also found in the free state.

Elemental Composition of Earth

Element Symbol Percent Mass Element Symbol Percent Mass

oxygen O 49.20 chlorine Cl 0.19

silicon Si 25.67 phosphorus P 0.11

aluminum Al 7.50 manganese Mn 0.09

Table 1.1

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Elemental Composition of Earth

Element Symbol Percent Mass Element Symbol Percent Mass

iron Fe 4.71 carbon C 0.08

calcium Ca 3.39 sulfur S 0.06

sodium Na 2.63 barium Ba 0.04

potassium K 2.40 nitrogen N 0.03

magnesium Mg 1.93 fluorine F 0.03

hydrogen H 0.87 strontium Sr 0.02

titanium Ti 0.58 all others - 0.47

Table 1.1

Decomposition of Water / Production of Hydrogen

Water consists of the elements hydrogen and oxygen combined in a 2 to 1 ratio. Water can be broken down into hydrogen and oxygen gases by the addition of energy. One way to do this is with a battery or power supply, as shown in (Figure 1.15).

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Figure 1.15 The decomposition of water is shown at the macroscopic, microscopic, and symbolic levels. The battery provides an electric current (microscopic) that decomposes water. At the macroscopic level, the liquid separates into the gases hydrogen (on the left) and oxygen (on the right). Symbolically, this change is presented by showing how liquid H2O separates into H2 and O2 gases.

The breakdown of water involves a rearrangement of the atoms in water molecules into different molecules, each composed of two hydrogen atoms and two oxygen atoms, respectively. Two water molecules form one oxygen molecule and two hydrogen molecules. The representation for what occurs, 2H2 O(l) ⟶ 2H2(g) + O2(g), will be explored in more depth in later chapters.

The two gases produced have distinctly different properties. Oxygen is not flammable but is required for combustion of a fuel, and hydrogen is highly flammable and a potent energy source. How might this knowledge be applied in our world? One application involves research into more fuel-efficient transportation. Fuel-cell vehicles (FCV) run on hydrogen instead of gasoline (Figure 1.16). They are more efficient than vehicles with internal combustion engines, are nonpolluting, and reduce greenhouse gas emissions, making us less dependent on fossil fuels. FCVs are not yet economically viable, however, and current hydrogen production depends on natural gas. If we can develop a process to economically decompose water, or produce hydrogen in another environmentally sound way, FCVs may be the way of the future.

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Figure 1.16 A fuel cell generates electrical energy from hydrogen and oxygen via an electrochemical process and produces only water as the waste product.

Chemistry of Cell Phones

Imagine how different your life would be without cell phones (Figure 1.17) and other smart devices. Cell phones are made from numerous chemical substances, which are extracted, refined, purified, and assembled using an extensive and in-depth understanding of chemical principles. About 30% of the elements that are found in nature are found within a typical smart phone. The case/body/frame consists of a combination of sturdy, durable polymers comprised primarily of carbon, hydrogen, oxygen, and nitrogen [acrylonitrile butadiene styrene (ABS) and polycarbonate thermoplastics], and light, strong, structural metals, such as aluminum, magnesium, and iron. The display screen is made from a specially toughened glass (silica glass strengthened by the addition of aluminum, sodium, and potassium) and coated with a material to make it conductive (such as indium tin oxide). The circuit board uses a semiconductor material (usually silicon); commonly used metals like copper, tin, silver, and gold; and more unfamiliar elements such as yttrium, praseodymium, and gadolinium. The battery relies upon lithium ions and a variety of other materials, including iron, cobalt, copper, polyethylene oxide, and polyacrylonitrile.

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Figure 1.17 Almost one-third of naturally occurring elements are used to make a cell phone. (credit: modification of work by John Taylor)

1.3 Physical and Chemical Properties

By the end of this section, you will be able to:

• Identify properties of and changes in matter as physical or chemical

• Identify properties of matter as extensive or intensive

The characteristics that enable us to distinguish one substance from another are called properties. A physical property is a characteristic of matter that is not associated with a change in its chemical composition. Familiar examples of physical properties include density, color, hardness, melting and boiling points, and electrical conductivity. We can observe some physical properties, such as density and color, without changing the physical state of the matter observed. Other physical properties, such as the melting temperature of iron or the freezing temperature of water, can only be observed as matter undergoes a physical change. A physical change is a change in the state or properties of matter without any accompanying change in its chemical composition (the identities of the substances contained in the matter). We observe a physical change when wax melts, when sugar dissolves in coffee, and when steam condenses into liquid water (Figure 1.18). Other examples of physical changes include magnetizing and demagnetizing metals (as is done with common antitheft security tags) and grinding solids into powders (which can sometimes yield noticeable changes in color). In each of these examples, there is a change in the physical state, form, or properties of the substance, but no change in its chemical composition.

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Figure 1.18 (a) Wax undergoes a physical change when solid wax is heated and forms liquid wax. (b) Steam condensing inside a cooking pot is a physical change, as water vapor is changed into liquid water. (credit a: modification of work by “95jb14”/Wikimedia Commons; credit b: modification of work by “mjneuby”/Flickr)

The change of one type of matter into another type (or the inability to change) is a chemical property. Examples of chemical properties include flammability, toxicity, acidity, reactivity (many types), and heat of combustion. Iron, for example, combines with oxygen in the presence of water to form rust; chromium does not oxidize (Figure 1.19). Nitroglycerin is very dangerous because it explodes easily; neon poses almost no hazard because it is very unreactive.

Figure 1.19 (a) One of the chemical properties of iron is that it rusts; (b) one of the chemical properties of chromium is that it does not. (credit a: modification of work by Tony Hisgett; credit b: modification of work by “Atoma”/Wikimedia Commons)

To identify a chemical property, we look for a chemical change. A chemical change always produces one or more types of matter that differ from the matter present before the change. The formation of rust is a chemical change because rust is a different kind of matter than the iron, oxygen, and water present before the rust formed. The explosion of nitroglycerin is a chemical change because the gases produced are very different kinds of matter from the original substance. Other examples of chemical changes include reactions that are performed in a lab (such as copper reacting with nitric acid), all forms of combustion (burning), and food being cooked, digested, or rotting (Figure 1.20).

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Figure 1.20 (a) Copper and nitric acid undergo a chemical change to form copper nitrate and brown, gaseous nitrogen dioxide. (b) During the combustion of a match, cellulose in the match and oxygen from the air undergo a chemical change to form carbon dioxide and water vapor. (c) Cooking red meat causes a number of chemical changes, including the oxidation of iron in myoglobin that results in the familiar red-to-brown color change. (d) A banana turning brown is a chemical change as new, darker (and less tasty) substances form. (credit b: modification of work by Jeff Turner; credit c: modification of work by Gloria Cabada-Leman; credit d: modification of work by Roberto Verzo)

Properties of matter fall into one of two categories. If the property depends on the amount of matter present, it is an extensive property. The mass and volume of a substance are examples of extensive properties; for instance, a gallon of milk has a larger mass and volume than a cup of milk. The value of an extensive property is directly proportional to the amount of matter in question. If the property of a sample of matter does not depend on the amount of matter present, it is an intensive property. Temperature is an example of an intensive property. If the gallon and cup of milk are each at 20 °C (room temperature), when they are combined, the temperature remains at 20 °C. As another example, consider the distinct but related properties of heat and temperature. A drop of hot cooking oil spattered on your arm causes brief, minor discomfort, whereas a pot of hot oil yields severe burns. Both the drop and the pot of oil are at the same temperature (an intensive property), but the pot clearly contains much more heat (extensive property).

Hazard Diamond

You may have seen the symbol shown in Figure 1.21 on containers of chemicals in a laboratory or workplace. Sometimes called a “fire diamond” or “hazard diamond,” this chemical hazard diamond provides valuable information that briefly summarizes the various dangers of which to be aware when working with a particular

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substance.

Figure 1.21 The National Fire Protection Agency (NFPA) hazard diamond summarizes the major hazards of a chemical substance.

The National Fire Protection Agency (NFPA) 704 Hazard Identification System was developed by NFPA to provide safety information about certain substances. The system details flammability, reactivity, health, and other hazards. Within the overall diamond symbol, the top (red) diamond specifies the level of fire hazard (temperature range for flash point). The blue (left) diamond indicates the level of health hazard. The yellow (right) diamond describes reactivity hazards, such as how readily the substance will undergo detonation or a violent chemical change. The white (bottom) diamond points out special hazards, such as if it is an oxidizer (which allows the substance to burn in the absence of air/oxygen), undergoes an unusual or dangerous reaction with water, is corrosive, acidic, alkaline, a biological hazard, radioactive, and so on. Each hazard is rated on a scale from 0 to 4, with 0 being no hazard and 4 being extremely hazardous.

While many elements differ dramatically in their chemical and physical properties, some elements have similar properties. We can identify sets of elements that exhibit common behaviors. For example, many elements conduct heat and electricity well, whereas others are poor conductors. These properties can be used to sort the elements into three classes: metals (elements that conduct well), nonmetals (elements that conduct poorly), and metalloids (elements that have properties of both metals and nonmetals).

The periodic table is a table of elements that places elements with similar properties close together (Figure 1.22). You will learn more about the periodic table as you continue your study of chemistry.

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Figure 1.22 The periodic table shows how elements may be grouped according to certain similar properties. Note the background color denotes whether an element is a metal, metalloid, or nonmetal, whereas the element symbol color indicates whether it is a solid, liquid, or gas.

1.4 Measurements

By the end of this section, you will be able to:

• Explain the process of measurement

• Identify the three basic parts of a quantity

• Describe the properties and units of length, mass, volume, density, temperature, and time

• Perform basic unit calculations and conversions in the metric and other unit systems

Measurements provide the macroscopic information that is the basis of most of the hypotheses, theories, and laws that describe the behavior of matter and energy in both the macroscopic and microscopic domains of chemistry. Every measurement provides three kinds of information: the size or magnitude of the measurement (a number); a standard of comparison for the measurement (a unit); and an indication of the uncertainty of the measurement. While the number and unit are explicitly represented when a quantity is written, the uncertainty is an aspect of the measurement result that is more implicitly represented and will be discussed later.

The number in the measurement can be represented in different ways, including decimal form and scientific notation.

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(Scientific notation is also known as exponential notation; a review of this topic can be found in Appendix B.) For example, the maximum takeoff weight of a Boeing 777-200ER airliner is 298,000 kilograms, which can also be written as 2.98 × 105 kg. The mass of the average mosquito is about 0.0000025 kilograms, which can be written as 2.5 × 10−6 kg.

Units, such as liters, pounds, and centimeters, are standards of comparison for measurements. When we buy a 2-liter bottle of a soft drink, we expect that the volume of the drink was measured, so it is two times larger than the volume that everyone agrees to be 1 liter. The meat used to prepare a 0.25-pound hamburger is measured so it weighs one- fourth as much as 1 pound. Without units, a number can be meaningless, confusing, or possibly life threatening. Suppose a doctor prescribes phenobarbital to control a patient’s seizures and states a dosage of “100” without specifying units. Not only will this be confusing to the medical professional giving the dose, but the consequences can be dire: 100 mg given three times per day can be effective as an anticonvulsant, but a single dose of 100 g is more than 10 times the lethal amount.

We usually report the results of scientific measurements in SI units, an updated version of the metric system, using the units listed in Table 1.2. Other units can be derived from these base units. The standards for these units are fixed by international agreement, and they are called the International System of Units or SI Units (from the French, Le Système International d’Unités). SI units have been used by the United States National Institute of Standards and Technology (NIST) since 1964.

Base Units of the SI System

Property Measured Name of Unit Symbol of Unit

length meter m

mass kilogram kg

time second s

temperature kelvin K

electric current ampere A

amount of substance mole mol

luminous intensity candela cd

Table 1.2

Sometimes we use units that are fractions or multiples of a base unit. Ice cream is sold in quarts (a familiar, non-SI base unit), pints (0.5 quart), or gallons (4 quarts). We also use fractions or multiples of units in the SI system, but these fractions or multiples are always powers of 10. Fractional or multiple SI units are named using a prefix and the name of the base unit. For example, a length of 1000 meters is also called a kilometer because the prefix kilo means “one thousand,” which in scientific notation is 103 (1 kilometer = 1000 m = 103 m). The prefixes used and the powers to which 10 are raised are listed in Table 1.3.

Common Unit Prefixes

Prefix Symbol Factor Example

femto f 10−15 1 femtosecond (fs) = 1 × 10−15 s (0.000000000000001 s)

pico p 10−12 1 picometer (pm) = 1 × 10−12 m (0.000000000001 m)

nano n 10−9 4 nanograms (ng) = 4 × 10−9 g (0.000000004 g)

Table 1.3

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Common Unit Prefixes

Prefix Symbol Factor Example

micro µ 10−6 1 microliter (μL) = 1 × 10−6 L (0.000001 L)

milli m 10−3 2 millimoles (mmol) = 2 × 10−3 mol (0.002 mol)

centi c 10−2 7 centimeters (cm) = 7 × 10−2 m (0.07 m)

deci d 10−1 1 deciliter (dL) = 1 × 10−1 L (0.1 L )

kilo k 103 1 kilometer (km) = 1 × 103 m (1000 m)

mega M 106 3 megahertz (MHz) = 3 × 106 Hz (3,000,000 Hz)

giga G 109 8 gigayears (Gyr) = 8 × 109 yr (8,000,000,000 Gyr)

tera T 1012 5 terawatts (TW) = 5 × 1012 W (5,000,000,000,000 W)

Table 1.3

Need a refresher or more practice with scientific notation? Visit this site (http://openstaxcollege.org/l/16notation) to go over the basics of scientific notation.

SI Base Units

The initial units of the metric system, which eventually evolved into the SI system, were established in France during the French Revolution. The original standards for the meter and the kilogram were adopted there in 1799 and eventually by other countries. This section introduces four of the SI base units commonly used in chemistry. Other SI units will be introduced in subsequent chapters.

Length

The standard unit of length in both the SI and original metric systems is the meter (m). A meter was originally specified as 1/10,000,000 of the distance from the North Pole to the equator. It is now defined as the distance light in a vacuum travels in 1/299,792,458 of a second. A meter is about 3 inches longer than a yard (Figure 1.23); one meter is about 39.37 inches or 1.094 yards. Longer distances are often reported in kilometers (1 km = 1000 m = 103

m), whereas shorter distances can be reported in centimeters (1 cm = 0.01 m = 10−2 m) or millimeters (1 mm = 0.001 m = 10−3 m).

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Figure 1.23 The relative lengths of 1 m, 1 yd, 1 cm, and 1 in. are shown (not actual size), as well as comparisons of 2.54 cm and 1 in., and of 1 m and 1.094 yd.

Mass

The standard unit of mass in the SI system is the kilogram (kg). A kilogram was originally defined as the mass of a liter of water (a cube of water with an edge length of exactly 0.1 meter). It is now defined by a certain cylinder of platinum-iridium alloy, which is kept in France (Figure 1.24). Any object with the same mass as this cylinder is said to have a mass of 1 kilogram. One kilogram is about 2.2 pounds. The gram (g) is exactly equal to 1/1000 of the mass of the kilogram (10−3 kg).

Figure 1.24 This replica prototype kilogram is housed at the National Institute of Standards and Technology (NIST) in Maryland. (credit: National Institutes of Standards and Technology)

Temperature

Temperature is an intensive property. The SI unit of temperature is the kelvin (K). The IUPAC convention is to use kelvin (all lowercase) for the word, K (uppercase) for the unit symbol, and neither the word “degree” nor the degree symbol (°). The degree Celsius (°C) is also allowed in the SI system, with both the word “degree” and the degree symbol used for Celsius measurements. Celsius degrees are the same magnitude as those of kelvin, but the two scales place their zeros in different places. Water freezes at 273.15 K (0 °C) and boils at 373.15 K (100 °C) by definition, and normal human body temperature is approximately 310 K (37 °C). The conversion between these two units and

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the Fahrenheit scale will be discussed later in this chapter.

Time

The SI base unit of time is the second (s). Small and large time intervals can be expressed with the appropriate prefixes; for example, 3 microseconds = 0.000003 s = 3 × 10−6 and 5 megaseconds = 5,000,000 s = 5 × 106 s. Alternatively, hours, days, and years can be used.

Derived SI Units

We can derive many units from the seven SI base units. For example, we can use the base unit of length to define a unit of volume, and the base units of mass and length to define a unit of density.

Volume

Volume is the measure of the amount of space occupied by an object. The standard SI unit of volume is defined by the base unit of length (Figure 1.25). The standard volume is a cubic meter (m3), a cube with an edge length of exactly one meter. To dispense a cubic meter of water, we could build a cubic box with edge lengths of exactly one meter. This box would hold a cubic meter of water or any other substance.

A more commonly used unit of volume is derived from the decimeter (0.1 m, or 10 cm). A cube with edge lengths of exactly one decimeter contains a volume of one cubic decimeter (dm3). A liter (L) is the more common name for the cubic decimeter. One liter is about 1.06 quarts.

A cubic centimeter (cm3) is the volume of a cube with an edge length of exactly one centimeter. The abbreviation cc (for cubic centimeter) is often used by health professionals. A cubic centimeter is also called a milliliter (mL) and is 1/1000 of a liter.

Figure 1.25 (a) The relative volumes are shown for cubes of 1 m3, 1 dm3 (1 L), and 1 cm3 (1 mL) (not to scale). (b) The diameter of a dime is compared relative to the edge length of a 1-cm3 (1-mL) cube.

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Density

We use the mass and volume of a substance to determine its density. Thus, the units of density are defined by the base units of mass and length.

The density of a substance is the ratio of the mass of a sample of the substance to its volume. The SI unit for density is the kilogram per cubic meter (kg/m3). For many situations, however, this as an inconvenient unit, and we often use grams per cubic centimeter (g/cm3) for the densities of solids and liquids, and grams per liter (g/L) for gases. Although there are exceptions, most liquids and solids have densities that range from about 0.7 g/cm3 (the density of gasoline) to 19 g/cm3 (the density of gold). The density of air is about 1.2 g/L. Table 1.4 shows the densities of some common substances.

Densities of Common Substances

Solids Liquids Gases (at 25 °C and 1 atm)

ice (at 0 °C) 0.92 g/cm3 water 1.0 g/cm3 dry air 1.20 g/L

oak (wood) 0.60–0.90 g/cm3 ethanol 0.79 g/cm3 oxygen 1.31 g/L

iron 7.9 g/cm3 acetone 0.79 g/cm3 nitrogen 1.14 g/L

copper 9.0 g/cm3 glycerin 1.26 g/cm3 carbon dioxide 1.80 g/L

lead 11.3 g/cm3 olive oil 0.92 g/cm3 helium 0.16 g/L

silver 10.5 g/cm3 gasoline 0.70–0.77 g/cm3 neon 0.83 g/L

gold 19.3 g/cm3 mercury 13.6 g/cm3 radon 9.1 g/L

Table 1.4

While there are many ways to determine the density of an object, perhaps the most straightforward method involves separately finding the mass and volume of the object, and then dividing the mass of the sample by its volume. In the following example, the mass is found directly by weighing, but the volume is found indirectly through length measurements.

density = massvolume

Example 1.1

Calculation of Density

Gold—in bricks, bars, and coins—has been a form of currency for centuries. In order to swindle people into paying for a brick of gold without actually investing in a brick of gold, people have considered filling the centers of hollow gold bricks with lead to fool buyers into thinking that the entire brick is gold. It does not work: Lead is a dense substance, but its density is not as great as that of gold, 19.3 g/cm3. What is the density of lead if a cube of lead has an edge length of 2.00 cm and a mass of 90.7 g?

Solution

The density of a substance can be calculated by dividing its mass by its volume. The volume of a cube is calculated by cubing the edge length.

volume of lead cube = 2.00 cm × 2.00 cm × 2.00 cm = 8.00 cm3

density = massvolume = 90.7 g

8.00 cm3 = 11.3 g

1.00 cm3 = 11.3 g/cm3

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(We will discuss the reason for rounding to the first decimal place in the next section.)

Check Your Learning

(a) To three decimal places, what is the volume of a cube (cm3) with an edge length of 0.843 cm?

(b) If the cube in part (a) is copper and has a mass of 5.34 g, what is the density of copper to two decimal places?

Answer: (a) 0.599 cm3; (b) 8.91 g/cm3

To learn more about the relationship between mass, volume, and density, use this interactive simulator (http://openstaxcollege.org/l/16phetmasvolden) to explore the density of different materials, like wood, ice, brick, and aluminum.

Example 1.2

Using Displacement of Water to Determine Density

This PhET simulation (http://openstaxcollege.org/l/16phetmasvolden) illustrates another way to determine density, using displacement of water. Determine the density of the red and yellow blocks.

Solution

When you open the density simulation and select Same Mass, you can choose from several 5.00-kg colored blocks that you can drop into a tank containing 100.00 L water. The yellow block floats (it is less dense than water), and the water level rises to 105.00 L. While floating, the yellow block displaces 5.00 L water, an amount equal to the weight of the block. The red block sinks (it is more dense than water, which has density = 1.00 kg/L), and the water level rises to 101.25 L.

The red block therefore displaces 1.25 L water, an amount equal to the volume of the block. The density of the red block is:

density = massvolume = 5.00 kg 1.25 L = 4.00 kg/L

Note that since the yellow block is not completely submerged, you cannot determine its density from this information. But if you hold the yellow block on the bottom of the tank, the water level rises to 110.00 L, which means that it now displaces 10.00 L water, and its density can be found:

density = massvolume = 5.00 kg 10.00 L = 0.500 kg/L

Check Your Learning

Remove all of the blocks from the water and add the green block to the tank of water, placing it approximately in the middle of the tank. Determine the density of the green block.

Answer: 2.00 kg/L

Link to Learning

Chapter 1 | Essential Ideas 35

1.5 Measurement Uncertainty, Accuracy, and Precision

By the end of this section, you will be able to:

• Define accuracy and precision

• Distinguish exact and uncertain numbers

• Correctly represent uncertainty in quantities using significant figures

• Apply proper rounding rules to computed quantities

Counting is the only type of measurement that is free from uncertainty, provided the number of objects being counted does not change while the counting process is underway. The result of such a counting measurement is an example of an exact number. If we count eggs in a carton, we know exactly how many eggs the carton contains. The numbers of defined quantities are also exact. By definition, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilogram. Quantities derived from measurements other than counting, however, are uncertain to varying extents due to practical limitations of the measurement process used.

Significant Figures in Measurement

The numbers of measured quantities, unlike defined or directly counted quantities, are not exact. To measure the volume of liquid in a graduated cylinder, you should make a reading at the bottom of the meniscus, the lowest point on the curved surface of the liquid.

Figure 1.26 To measure the volume of liquid in this graduated cylinder, you must mentally subdivide the distance between the 21 and 22 mL marks into tenths of a milliliter, and then make a reading (estimate) at the bottom of the meniscus.

Refer to the illustration in Figure 1.26. The bottom of the meniscus in this case clearly lies between the 21 and 22 markings, meaning the liquid volume is certainly greater than 21 mL but less than 22 mL. The meniscus appears to be a bit closer to the 22-mL mark than to the 21-mL mark, and so a reasonable estimate of the liquid’s volume would

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be 21.6 mL. In the number 21.6, then, the digits 2 and 1 are certain, but the 6 is an estimate. Some people might estimate the meniscus position to be equally distant from each of the markings and estimate the tenth-place digit as 5, while others may think it to be even closer to the 22-mL mark and estimate this digit to be 7. Note that it would be pointless to attempt to estimate a digit for the hundredths place, given that the tenths-place digit is uncertain. In general, numerical scales such as the one on this graduated cylinder will permit measurements to one-tenth of the smallest scale division. The scale in this case has 1-mL divisions, and so volumes may be measured to the nearest 0.1 mL.

This concept holds true for all measurements, even if you do not actively make an estimate. If you place a quarter on a standard electronic balance, you may obtain a reading of 6.72 g. The digits 6 and 7 are certain, and the 2 indicates that the mass of the quarter is likely between 6.71 and 6.73 grams. The quarter weighs about 6.72 grams, with a nominal uncertainty in the measurement of ± 0.01 gram. If we weigh the quarter on a more sensitive balance, we may find that its mass is 6.723 g. This means its mass lies between 6.722 and 6.724 grams, an uncertainty of 0.001 gram. Every measurement has some uncertainty, which depends on the device used (and the user’s ability). All of the digits in a measurement, including the uncertain last digit, are called significant figures or significant digits. Note that zero may be a measured value; for example, if you stand on a scale that shows weight to the nearest pound and it shows “120,” then the 1 (hundreds), 2 (tens) and 0 (ones) are all significant (measured) values.

Whenever you make a measurement properly, all the digits in the result are significant. But what if you were analyzing a reported value and trying to determine what is significant and what is not? Well, for starters, all nonzero digits are significant, and it is only zeros that require some thought. We will use the terms “leading,” “trailing,” and “captive” for the zeros and will consider how to deal with them.

Starting with the first nonzero digit on the left, count this digit and all remaining digits to the right. This is the number of significant figures in the measurement unless the last digit is a trailing zero lying to the left of the decimal point.

Captive zeros result from measurement and are therefore always significant. Leading zeros, however, are never significant—they merely tell us where the decimal point is located.

The leading zeros in this example are not significant. We could use exponential notation (as described in Appendix B) and express the number as 8.32407 × 10−3; then the number 8.32407 contains all of the significant figures, and 10−3 locates the decimal point.

The number of significant figures is uncertain in a number that ends with a zero to the left of the decimal point location. The zeros in the measurement 1,300 grams could be significant or they could simply indicate where the

Chapter 1 | Essential Ideas 37

decimal point is located. The ambiguity can be resolved with the use of exponential notation: 1.3 × 103 (two significant figures), 1.30 × 103 (three significant figures, if the tens place was measured), or 1.300 × 103 (four significant figures, if the ones place was also measured). In cases where only the decimal-formatted number is available, it is prudent to assume that all trailing zeros are not significant.

When determining significant figures, be sure to pay attention to reported values and think about the measurement and significant figures in terms of what is reasonable or likely when evaluating whether the value makes sense. For example, the official January 2014 census reported the resident population of the US as 317,297,725. Do you think the US population was correctly determined to the reported nine significant figures, that is, to the exact number of people? People are constantly being born, dying, or moving into or out of the country, and assumptions are made to account for the large number of people who are not actually counted. Because of these uncertainties, it might be more reasonable to expect that we know the population to within perhaps a million or so, in which case the population should be reported as 3.17 × 108 people.

Significant Figures in Calculations

A second important principle of uncertainty is that results calculated from a measurement are at least as uncertain as the measurement itself. We must take the uncertainty in our measurements into account to avoid misrepresenting the uncertainty in calculated results. One way to do this is to report the result of a calculation with the correct number of significant figures, which is determined by the following three rules for rounding numbers:

1. When we add or subtract numbers, we should round the result to the same number of decimal places as the number with the least number of decimal places (the least precise value in terms of addition and subtraction).

2. When we multiply or divide numbers, we should round the result to the same number of digits as the number with the least number of significant figures (the least precise value in terms of multiplication and division).

3. If the digit to be dropped (the one immediately to the right of the digit to be retained) is less than 5, we “round down” and leave the retained digit unchanged; if it is more than 5, we “round up” and increase the retained digit by 1; if the dropped digit is 5, we round up or down, whichever yields an even value for the retained digit. (The last part of this rule may strike you as a bit odd, but it’s based on reliable statistics and is aimed at avoiding any bias when dropping the digit “5,” since it is equally close to both possible values of the retained digit.)

The following examples illustrate the application of this rule in rounding a few different numbers to three significant figures:

• 0.028675 rounds “up” to 0.0287 (the dropped digit, 7, is greater than 5)

• 18.3384 rounds “down” to 18.3 (the dropped digit, 3, is less than 5)

• 6.8752 rounds “up” to 6.88 (the dropped digit is 5, and the retained digit is even)

• 92.85 rounds “down” to 92.8 (the dropped digit is 5, and the retained digit is even)

Let’s work through these rules with a few examples.

Example 1.3

Rounding Numbers

Round the following to the indicated number of significant figures:

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(a) 31.57 (to two significant figures)

(b) 8.1649 (to three significant figures)

(c) 0.051065 (to four significant figures)

(d) 0.90275 (to four significant figures)

Solution

(a) 31.57 rounds “up” to 32 (the dropped digit is 5, and the retained digit is even)

(b) 8.1649 rounds “down” to 8.16 (the dropped digit, 4, is less than 5)

(c) 0.051065 rounds “down” to 0.05106 (the dropped digit is 5, and the retained digit is even)

(d) 0.90275 rounds “up” to 0.9028 (the dropped digit is 5, and the retained digit is even)

Check Your Learning

Round the following to the indicated number of significant figures:

(a) 0.424 (to two significant figures)

(b) 0.0038661 (to three significant figures)

(c) 421.25 (to four significant figures)

(d) 28,683.5 (to five significant figures)

Answer: (a) 0.42; (b) 0.00387; (c) 421.2; (d) 28,684

Example 1.4

Addition and Subtraction with Significant Figures

Rule: When we add or subtract numbers, we should round the result to the same number of decimal places as the number with the least number of decimal places (i.e., the least precise value in terms of addition and subtraction).

(a) Add 1.0023 g and 4.383 g.

(b) Subtract 421.23 g from 486 g.

Solution

(a) 1.0023 g

+ 4.383 g 5.3853 g

Answer is 5.385 g (round to the thousandths place; three decimal places)

(b) 486 g

−421.23 g 64.77 g

Answer is 65 g (round to the ones place; no decimal places)

Chapter 1 | Essential Ideas 39

Check Your Learning

(a) Add 2.334 mL and 0.31 mL.

(b) Subtract 55.8752 m from 56.533 m.

Answer: (a) 2.64 mL; (b) 0.658 m

Example 1.5

Multiplication and Division with Significant Figures

Rule: When we multiply or divide numbers, we should round the result to the same number of digits as the number with the least number of significant figures (the least precise value in terms of multiplication and division).

(a) Multiply 0.6238 cm by 6.6 cm.

(b) Divide 421.23 g by 486 mL.

Solution

(a) 0.6238 cm × 6.6 cm = 4.11708 cm2 ⟶ result is 4.1 cm2 (round to two significant fig es ) four significant fig es × two significant fig es ⟶ two significant fig es answer

(b)

421.23 g 486 mL = 0.86728... g/mL ⟶ result is 0.867 g/mL

⎛ ⎝round to three significant fig es ⎞⎠

fi e significant fig es three significant fig es ⟶ three significant fig es answer

Check Your Learning

(a) Multiply 2.334 cm and 0.320 cm.

(b) Divide 55.8752 m by 56.53 s.

Answer: (a) 0.747 cm2 (b) 0.9884 m/s

In the midst of all these technicalities, it is important to keep in mind the reason why we use significant figures and rounding rules—to correctly represent the certainty of the values we report and to ensure that a calculated result is not represented as being more certain than the least certain value used in the calculation.

Example 1.6

Calculation with Significant Figures

One common bathtub is 13.44 dm long, 5.920 dm wide, and 2.54 dm deep. Assume that the tub is rectangular and calculate its approximate volume in liters.

Solution

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V = l × w × d = 13.44 dm × 5.920 dm × 2.54 dm = 202.09459... dm3 (value from calculator) = 202 dm3 , or 202 L ⎛⎝answer rounded to three significant fig es ⎞⎠

Check Your Learning

What is the density of a liquid with a mass of 31.1415 g and a volume of 30.13 cm3?

Answer: 1.034 g/mL

Example 1.7

Experimental Determination of Density Using Water Displacement

A piece of rebar is weighed and then submerged in a graduated cylinder partially filled with water, with results as shown.

(a) Use these values to determine the density of this piece of rebar.

(b) Rebar is mostly iron. Does your result in (a) support this statement? How?

Solution

The volume of the piece of rebar is equal to the volume of the water displaced:

volume = 22.4 mL − 13.5 mL = 8.9 mL = 8.9 cm3

(rounded to the nearest 0.1 mL, per the rule for addition and subtraction)

The density is the mass-to-volume ratio:

density = massvolume = 69.658 g 8.9 cm3

= 7.8 g/cm3

(rounded to two significant figures, per the rule for multiplication and division)

Chapter 1 | Essential Ideas 41

From Table 1.4, the density of iron is 7.9 g/cm3, very close to that of rebar, which lends some support to the fact that rebar is mostly iron.

Check Your Learning

An irregularly shaped piece of a shiny yellowish material is weighed and then submerged in a graduated cylinder, with results as shown.

(a) Use these values to determine the density of this material.

(b) Do you have any reasonable guesses as to the identity of this material? Explain your reasoning.

Answer: (a) 19 g/cm3; (b) It is likely gold; the right appearance for gold and very close to the density given for gold in Table 1.4.

Accuracy and Precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to know both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or accepted value. Precise values agree with each other; accurate values agree with a true value. These characterizations can be extended to other contexts, such as the results of an archery competition (Figure 1.27).

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Figure 1.27 (a) These arrows are close to both the bull’s eye and one another, so they are both accurate and precise. (b) These arrows are close to one another but not on target, so they are precise but not accurate. (c) These arrows are neither on target nor close to one another, so they are neither accurate nor precise.

Suppose a quality control chemist at a pharmaceutical company is tasked with checking the accuracy and precision of three different machines that are meant to dispense 10 ounces (296 mL) of cough syrup into storage bottles. She proceeds to use each machine to fill five bottles and then carefully determines the actual volume dispensed, obtaining the results tabulated in Table 1.5.

Volume (mL) of Cough Medicine Delivered by 10-oz (296 mL) Dispensers

Dispenser #1 Dispenser #2 Dispenser #3

283.3 298.3 296.1

284.1 294.2 295.9

283.9 296.0 296.1

284.0 297.8 296.0

284.1 293.9 296.1

Table 1.5

Considering these results, she will report that dispenser #1 is precise (values all close to one another, within a few tenths of a milliliter) but not accurate (none of the values are close to the target value of 296 mL, each being more than 10 mL too low). Results for dispenser #2 represent improved accuracy (each volume is less than 3 mL away from 296 mL) but worse precision (volumes vary by more than 4 mL). Finally, she can report that dispenser #3 is working well, dispensing cough syrup both accurately (all volumes within 0.1 mL of the target volume) and precisely (volumes differing from each other by no more than 0.2 mL).

1.6 Mathematical Treatment of Measurement Results

By the end of this section, you will be able to:

• Explain the dimensional analysis (factor label) approach to mathematical calculations involving quantities

• Use dimensional analysis to carry out unit conversions for a given property and computations involving two or more properties

Chapter 1 | Essential Ideas 43

It is often the case that a quantity of interest may not be easy (or even possible) to measure directly but instead must be calculated from other directly measured properties and appropriate mathematical relationships. For example, consider measuring the average speed of an athlete running sprints. This is typically accomplished by measuring the time required for the athlete to run from the starting line to the finish line, and the distance between these two lines, and then computing speed from the equation that relates these three properties:

speed = distancetime

An Olympic-quality sprinter can run 100 m in approximately 10 s, corresponding to an average speed of

100 m 10 s = 10 m/s

Note that this simple arithmetic involves dividing the numbers of each measured quantity to yield the number of the computed quantity (100/10 = 10) and likewise dividing the units of each measured quantity to yield the unit of the computed quantity (m/s = m/s). Now, consider using this same relation to predict the time required for a person running at this speed to travel a distance of 25 m. The same relation between the three properties is used, but in this case, the two quantities provided are a speed (10 m/s) and a distance (25 m). To yield the sought property, time, the equation must be rearranged appropriately:

time = distancespeed

The time can then be computed as:

25 m 10 m/s = 2.5 s

Again, arithmetic on the numbers (25/10 = 2.5) was accompanied by the same arithmetic on the units (m/m/s = s) to yield the number and unit of the result, 2.5 s. Note that, just as for numbers, when a unit is divided by an identical unit (in this case, m/m), the result is “1”—or, as commonly phrased, the units “cancel.”

These calculations are examples of a versatile mathematical approach known as dimensional analysis (or the factor- label method). Dimensional analysis is based on this premise: the units of quantities must be subjected to the same mathematical operations as their associated numbers. This method can be applied to computations ranging from simple unit conversions to more complex, multi-step calculations involving several different quantities.

Conversion Factors and Dimensional Analysis

A ratio of two equivalent quantities expressed with different measurement units can be used as a unit conversion factor. For example, the lengths of 2.54 cm and 1 in. are equivalent (by definition), and so a unit conversion factor may be derived from the ratio,

2.54 cm 1 in. (2.54 cm = 1 in.) or 2.54

cm in.

Several other commonly used conversion factors are given in Table 1.6.

Common Conversion Factors

Length Volume Mass

1 m = 1.0936 yd 1 L = 1.0567 qt 1 kg = 2.2046 lb

1 in. = 2.54 cm (exact) 1 qt = 0.94635 L 1 lb = 453.59 g

1 km = 0.62137 mi 1 ft3 = 28.317 L 1 (avoirdupois) oz = 28.349 g

1 mi = 1609.3 m 1 tbsp = 14.787 mL 1 (troy) oz = 31.103 g

Table 1.6

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When we multiply a quantity (such as distance given in inches) by an appropriate unit conversion factor, we convert the quantity to an equivalent value with different units (such as distance in centimeters). For example, a basketball player’s vertical jump of 34 inches can be converted to centimeters by:

34 in. × 2.54 cm 1 in.

= 86 cm