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Chemistry: Atoms First 2e
SENIOR CONTRIBUTING AUTHORS PAUL FLOWERS, UNIVERSITY OF NORTH CAROLINA AT PEMBROKE KLAUS THEOPOLD, UNIVERSITY OF DELAWARE RICHARD LANGLEY, STEPHEN F. AUSTIN STATE UNIVERSITY EDWARD J. NETH, UNIVERSITY OF CONNECTICUT WILLIAM R. ROBINSON, PHD
OpenStax Rice University 6100 Main Street MS-375 Houston, Texas 77005
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HARDCOVER BOOK ISBN-13 B&W PAPERBACK BOOK ISBN-13 DIGITAL VERSION ISBN-13 2 3 4 5 6 7 8 9 10 RS 22 19
978-1-947172-64-7 978-1-59399-579-9 978-1-947172-63-0
OPENSTAX
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Contents
Preface
1
CHAPTER 1
Essential Ideas 9
Introduction
9
1.1 Chemistry in Context
9
1.2 Phases and Classification of Matter
14
1.3 Physical and Chemical Properties
23
1.4 Measurements
27
1.5 Measurement Uncertainty, Accuracy, and Precision
33
1.6 Mathematical Treatment of Measurement Results
41
Key Terms
48
Key Equations
49
Summary
49
Exercises
50
CHAPTER 2
Atoms, Molecules, and Ions 61
Introduction
61
2.1 Early Ideas in Atomic Theory
62
2.2 Evolution of Atomic Theory
66
2.3 Atomic Structure and Symbolism
71
2.4 Chemical Formulas
79
Key Terms
94
Key Equations
94
Summary
94
Exercises
95
CHAPTER 3
Electronic Structure and Periodic Properties of Elements 103
Introduction
103
3.1 Electromagnetic Energy
104
3.2 The Bohr Model
116
3.3 Development of Quantum Theory
120
3.4 Electronic Structure of Atoms (Electron Configurations)
133
3.5 Periodic Variations in Element Properties
141
3.6 The Periodic Table
149
3.7 Ionic and Molecular Compounds
154
Key Terms
162
Key Equations
164
Summary
164
Exercises
166
CHAPTER 4
Chemical Bonding and Molecular Geometry 175
Introduction
175
4.1 Ionic Bonding
175
4.2 Covalent Bonding
179
4.3 Chemical Nomenclature
184
4.4 Lewis Symbols and Structures
192
4.5 Formal Charges and Resonance
202
4.6 Molecular Structure and Polarity
206
Key Terms
221
Key Equations
222
Summary
222
Exercises
223
CHAPTER 5
Advanced Theories of Bonding 237
Introduction
237
5.1 Valence Bond Theory
238
5.2 Hybrid Atomic Orbitals
243
5.3 Multiple Bonds
253
5.4 Molecular Orbital Theory
256
Key Terms
271
Key Equations
271
Summary
272
Exercises
272
CHAPTER 6
Composition of Substances and Solutions 277
Introduction
277
6.1 Formula Mass
278
6.2 Determining Empirical and Molecular Formulas
280
6.3 Molarity
287
6.4 Other Units for Solution Concentrations
295
Key Terms
301
Key Equations
301
Summary
301
Exercises
302
CHAPTER 7
Stoichiometry of Chemical Reactions 307
Introduction
307
7.1 Writing and Balancing Chemical Equations
308
7.2 Classifying Chemical Reactions
314
7.3 Reaction Stoichiometry
328
7.4 Reaction Yields
333
7.5 Quantitative Chemical Analysis
338
Key Terms
346
Key Equations
347
Summary
347
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Exercises
348
CHAPTER 8
Gases 359
Introduction
359
8.1 Gas Pressure
360
8.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law
369
8.3 Stoichiometry of Gaseous Substances, Mixtures, and Reactions
381
8.4 Effusion and Diffusion of Gases
393
8.5 The Kinetic-Molecular Theory
398
8.6 Non-Ideal Gas Behavior
402
Key Terms
406
Key Equations
406
Summary
407
Exercises
408
CHAPTER 9
Thermochemistry 419
Introduction
419
9.1 Energy Basics
420
9.2 Calorimetry
429
9.3 Enthalpy
441
9.4 Strengths of Ionic and Covalent Bonds
455
Key Terms
463
Key Equations
464
Summary
464
Exercises
465
CHAPTER 10
Liquids and Solids 475
Introduction
475
10.1 Intermolecular Forces
476
10.2 Properties of Liquids
487
10.3 Phase Transitions
493
10.4 Phase Diagrams
503
10.5 The Solid State of Matter
510
10.6 Lattice Structures in Crystalline Solids
516
Key Terms
534
Key Equations
535
Summary
535
Exercises
536
CHAPTER 11
Solutions and Colloids 547
Introduction
547
11.1 The Dissolution Process
548
11.2 Electrolytes
552
11.3 Solubility
555
11.4 Colligative Properties
564
11.5 Colloids Key Terms Key Equations Summary Exercises
583 592
593 593 594
CHAPTER 12
Thermodynamics 599
Introduction
599
12.1 Spontaneity
599
12.2 Entropy
603
12.3 The Second and Third Laws of Thermodynamics
609
12.4 Free Energy
613
Key Terms
619
Key Equations
619
Summary
619
Exercises
620
CHAPTER 13
Fundamental Equilibrium Concepts 627
Introduction
627
13.1 Chemical Equilibria
628
13.2 Equilibrium Constants
631
13.3 Shifting Equilibria: Le Châtelier’s Principle
639
13.4 Equilibrium Calculations
643
Key Terms
657
Key Equations
657
Summary
657
Exercises
658
CHAPTER 14
Acid-Base Equilibria 669
Introduction
669
14.1 Brønsted-Lowry Acids and Bases
669
14.2 pH and pOH
673
14.3 Relative Strengths of Acids and Bases
678
14.4 Hydrolysis of Salts
692
14.5 Polyprotic Acids
697
14.6 Buffers
700
14.7 Acid-Base Titrations
706
Key Terms
714
Key Equations
714
Summary
715
Exercises
716
CHAPTER 15
Equilibria of Other Reaction Classes 725
Introduction
725
15.1 Precipitation and Dissolution
725
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15.2 Lewis Acids and Bases
15.3 Coupled Equilibria
Key Terms
748
Key Equations
748
Summary
748
Exercises
749
739 743
CHAPTER 16
Electrochemistry 759
Introduction
759
16.1 Review of Redox Chemistry
760
16.2 Galvanic Cells
763
16.3 Electrode and Cell Potentials
766
16.4 Potential, Free Energy, and Equilibrium
772
16.5 Batteries and Fuel Cells
776
16.6 Corrosion
782
16.7 Electrolysis
785
Key Terms
791
Key Equations
792
Summary
792
Exercises
793
CHAPTER 17
Kinetics 799
Introduction
799
17.1 Chemical Reaction Rates
800
17.2 Factors Affecting Reaction Rates
805
17.3 Rate Laws
807
17.4 Integrated Rate Laws
814
17.5 Collision Theory
825
17.6 Reaction Mechanisms
830
17.7 Catalysis
835
Key Terms
846
Key Equations
846
Summary
847
Exercises
848
CHAPTER 18
Representative Metals, Metalloids, and Nonmetals 861
Introduction
861
18.1 Periodicity
862
18.2 Occurrence and Preparation of the Representative Metals
871
18.3 Structure and General Properties of the Metalloids
874
18.4 Structure and General Properties of the Nonmetals
881
18.5 Occurrence, Preparation, and Compounds of Hydrogen
889
18.6 Occurrence, Preparation, and Properties of Carbonates
895
18.7 Occurrence, Preparation, and Properties of Nitrogen
897
18.8 Occurrence, Preparation, and Properties of Phosphorus
901
18.9 Occurrence, Preparation, and Compounds of Oxygen
903
18.10 Occurrence, Preparation, and Properties of Sulfur
917
18.11 Occurrence, Preparation, and Properties of Halogens
919
18.12 Occurrence, Preparation, and Properties of the Noble Gases
924
Key Terms
926
Summary
927
Exercises
928
CHAPTER 19
Transition Metals and Coordination Chemistry 939
Introduction
939
19.1 Occurrence, Preparation, and Properties of Transition Metals and Their Compounds
939
19.2 Coordination Chemistry of Transition Metals
952
19.3 Spectroscopic and Magnetic Properties of Coordination Compounds
966
Key Terms
975
Summary
976
Exercises
977
CHAPTER 20
Nuclear Chemistry 981
Introduction
981
20.1 Nuclear Structure and Stability
982
20.2 Nuclear Equations
988
20.3 Radioactive Decay
991
20.4 Transmutation and Nuclear Energy
1002
20.5 Uses of Radioisotopes
1015
20.6 Biological Effects of Radiation
1019
Key Terms
1027
Key Equations
1028
Summary
1029
Exercises
1030
CHAPTER 21
Organic Chemistry 1037
Introduction
1037
21.1 Hydrocarbons
1038
21.2 Alcohols and Ethers
1055
21.3 Aldehydes, Ketones, Carboxylic Acids, and Esters
21.4 Amines and Amides
1065
Key Terms
1074
Summary
1074
Exercises
1075
1059
Appendix A The Periodic Table
1081
Appendix B Essential Mathematics
1083
Appendix C Units and Conversion Factors
1091
Appendix D Fundamental Physical Constants
1095
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Appendix E Water Properties
1097
Appendix F Composition of Commercial Acids and Bases
1103
Appendix G Standard Thermodynamic Properties for Selected Substances
Appendix H Ionization Constants of Weak Acids
1123
Appendix I Ionization Constants of Weak Bases
1127
Appendix J Solubility Products
1129
Appendix K Formation Constants for Complex Ions
1135
Appendix L Standard Electrode (Half-Cell) Potentials
1137
Appendix M Half-Lives for Several Radioactive Isotopes
1143
Answer Key
1145
Index
1205
1105
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PREFACE
Preface
1
Welcome to Chemistry: Atoms First 2e, 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 library has since scaled to over 30 books for college and AP® courses used by hundreds of thousands of students. OpenStax Tutor, our low-cost personalized learning tool, is being used in college courses throughout the country. Through our partnerships with philanthropic foundations and our alliance with other educational resource organizations, OpenStax is breaking down the most common barriers to learning and empowering students and instructors to succeed.
About OpenStax resources
Customization Chemistry: Atoms First 2e is licensed under a Creative Commons Attribution 4.0 International (CC BY) license, which means that you can distribute, remix, and build upon the content, as long as you provide attribution to OpenStax and its content contributors.
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 certain 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.
Instructors also have the option of creating a customized version of their OpenStax book. The custom version can be made available to students in low-cost print or digital form through their campus bookstore. Visit the Instructor Resources section of your book page on openstax.org for more information.
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. Subject matter experts review all errata suggestions. 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 for a low cost in print.
About Chemistry: Atoms First 2e
This text is an atoms-first adaptation of OpenStax Chemistry 2e. 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.
The second edition has been revised to incorporate clearer, more current, and more dynamic explanations, while maintaining the same organization as the first edition. Substantial improvements have been made in the
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figures, illustrations, and example exercises that support the text narrative.
Coverage and scope In Chemistry: Atoms First 2e, 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 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.
Changes to the second edition OpenStax only undertakes second editions when significant modifications to the text are necessary. In the case of Chemistry: Atoms First 2e, user feedback indicated that we needed to focus on a few key areas, which we have done in the following ways:
• Content revisions for clarity and accuracy. The revision plan varied by chapter based on need. About five chapters were extensively rewritten and another twelve chapters were substantially revised to improve the readability and clarity of the narrative.
• Example and end-of-chapter exercises. The example and end-of-chapter exercises in several chapters were subjected to a rigorous accuracy check and revised to correct any errors, and additional exercises were added to several chapters to more fully support chapter content.
• Art and illustrations. Under the guidance of the authors and expert scientific illustrators, especially those well-versed in creating accessible art, the OpenStax team made changes to much of the art in the first edition of Chemistry: Atoms First. The revisions included correcting errors, redesigning illustrations to improve understanding, and recoloring for overall consistency.
• Accessibility improvements. As with all OpenStax books, the first edition of Chemistry: Atoms First was created with a focus on accessibility. We have emphasized and improved that approach in the second edition. To accommodate users of specific assistive technologies, all alternative text was reviewed and revised for comprehensiveness and clarity. Many illustrations were revised to improve the color contrast, which is important for some visually impaired students. Overall, the OpenStax platform has been continually upgraded to improve accessibility.
Partnership with University of Connecticut and UConn Undergraduate Student Government Chemistry: Atoms First 2e 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 2e, 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 “faces” of contributors in this field as well as
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Preface
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science in 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 2e incorporates links to relevant interactive exercises and animations that help bring topics to life through our Link to Learning feature. Examples include:
• PhET simulations
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Preface
5
• 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
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Technology partners As allies in making high-quality learning materials accessible, our technology partners offer optional low-cost tools that are integrated with OpenStax books. To access the technology options 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
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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 threesemester, introductory chemistry sequence at UConn and is involved with training and coordinating teaching assistants.
William R. Robinson, PhD
Contributing authors Mark Blaser, Shasta College 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
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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 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
Preface
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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.
1.1 Chemistry in Context
LEARNING OBJECTIVES By the end of this section, 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
10
1 • Essential Ideas
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 was 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).
FIGURE 1.2 (a) 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. (b) While the equipment used by Alma Levant Hayden in this 1952 picture might not seem as sleek as you might find in a lab today, her approach was highly methodical and carefully recorded. A department head at the FDA, Hayden is most famous for exposing an aggressively marketed anti-cancer drug as nothing more than an unhelpful solution of common substances. (credit a: Chemical Heritage Foundation; b: NIH History Office)
From alchemy came the historical progressions that led to modern chemistry: the isolation of drugs from natural sources, such as plants and animals. But while many of the substances extracted or processed from those natural sources were critical in the treatment of diseases, many were scarce. For example, progesterone, which is critical to women's health, became available as a medicine in 1935, but its animal sources produced extremely small quantities, limiting its availability and increasing its expense. Likewise, in the 1940s, cortisone came into use to treat arthritis and other disorders and injuries, but it took a 36-step process to synthesize. Chemist Percy Lavon Julian turned to a more plentiful source: soybeans. Previously, Julian had developed a lab to isolate soy protein, which was used in firefighting among other applications. He focused on using the soy sterols—substances mostly used in plant membranes—and was able to quickly produce progesterone and later testosterone and other hormones. He later developed a process to do the same for cortisone, and laid the groundwork for modern drug design. Since soybeans and similar plant sources were extremely plentiful, the drugs soon became widely available, saving many lives.
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1.1 • Chemistry in Context
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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.
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
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observations that acts as a guide for gathering and checking information. A hypothesis is tested by experimentation, calculation, and/or comparison with the experiments of others and then refined 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).
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 such as density, solubility, and flammability.
Micro comes from Greek and means “small.” The microscopic domain of chemistry is often visited in the imagination. Some aspects of the microscopic domain are visible through standard optical microscopes, for example, many biological cells. More sophisticated instruments are capable of imaging even smaller entities such as molecules and atoms (see Figure 1.5 (b)).
However, most of the subjects in the microscopic domain of chemistry are too small to be seen even with the most advanced microscopes and may only be pictured in the mind. Other components of the microscopic
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1.1 • Chemistry in Context
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domain include ions and electrons, protons and neutrons, and chemical bonds, each of which is far too small to see.
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, drawings, and calculations. 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 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 cannot be observed with the naked eye. The description of water as comprising 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
LEARNING OBJECTIVES 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 • Distinguish between mass and weight • Apply the law of conservation of matter • Classify matter as an element, compound, homogeneous mixture, or heterogeneous mixture with regard to its
physical state and composition • Define and give examples of atoms and molecules
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 not inflate (increase its volume) 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 its 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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1.2 • Phases and Classification of Matter
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FIGURE 1.7 A plasma torch can be used to cut metal. (credit: “Hypertherm”/Wikimedia Commons)
LINK TO LEARNING
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://openstax.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 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.
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FIGURE 1.8 (a) The mass of beer precursor materials is the same as the mass of beer produced: Sugar has become alcohol and carbon dioxide. (b) The mass of the lead, lead oxide, and sulfuric acid consumed by 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.
Classifying Matter
Matter can be classified 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. Pure substances may be divided 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 are comprised of two or more elements are called compounds. Compounds may be broken down by chemical changes to yield 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 1.9). 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 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).
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1.2 • Phases and Classification of Matter
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FIGURE 1.9 (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)
LINK TO LEARNING
Many compounds break down when heated. This site (http://openstax.org/l/16mercury) shows the breakdown of mercury oxide, HgO. You can also view an example of the photochemical decomposition of silver chloride (http://openstax.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 1.10). Its composition can vary because it may be prepared 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 1.10). 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.
FIGURE 1.10 (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)
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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 that 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 1.11).
FIGURE 1.11 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
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
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1.2 • Phases and Classification of Matter
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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 1.12). This atom would no longer be gold if it were divided any further.
FIGURE 1.12 (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 1.13) shows increasingly close microscopic and atomic-level views of ordinary cotton.
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FIGURE 1.13 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)
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 1.14). 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 1.14 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.
Chemistry in Everyday Life 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
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1.2 • Phases and Classification of Matter
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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).
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,
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 in Everyday Life 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 composed 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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1.3 • Physical and Chemical Properties
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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
LEARNING OBJECTIVES 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 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. Some physical properties, such as density and color, may be observed without changing the physical state of the matter. 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 the chemical identities of the substances contained in the matter. Physical changes are observed 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, and many other types of reactivity. 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) 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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1.3 • Physical and Chemical Properties
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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 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).
Chemistry in Everyday Life
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 substance.
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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. 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 intermediate conductivities). 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
LEARNING OBJECTIVES 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 much of the information that informs the hypotheses, theories, and laws describing 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. (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,
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which can be written as 2.5 10−6 kg.
Units, such as liters, pounds, and centimeters, are standards of comparison for measurements. A 2-liter bottle of a soft drink contains a volume of beverage that is twice that of the accepted volume of 1 liter. The meat used to prepare a 0.25-pound hamburger weighs one-fourth as much as the accepted weight of 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.
The measurement units for seven fundamental properties (“base units”) are listed in Table 1.2. 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. Units for other properties may be derived from these seven base units.
Base Units of the SI System
Property Measured Name of Unit Symbol of Unit
length
meter
m
mass
kilogram
kg
time temperature
second
s
kelvin
K
electric current
ampere
A
amount of substance mole
mol
luminous intensity candela
cd
TABLE 1.2
Everyday measurement units are often defined as fractions or multiples of other units. Milk is commonly packaged in containers of 1 gallon (4 quarts), 1 quart (0.25 gallon), and one pint (0.5 quart). This same approach is used with SI units, 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)
TABLE 1.3
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Prefix Symbol Factor Example
nano n
10−9 4 nanograms (ng) = 4 10−9 g (0.000000004 g)
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 yr)
tera T
1012 5 terawatts (TW) = 5 1012 W (5,000,000,000,000 W)
TABLE 1.3
LINK TO LEARNING
Need a refresher or more practice with scientific notation? Visit this site (http://openstax.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). The kilogram was previously defined by the International Union of Pure and Applied Chemistry (IUPAC) as the mass of a specific reference object. This object was originally one liter of pure water, and more recently it was a metal cylinder made from a platinumiridium alloy with a height and diameter of 39 mm (Figure 1.24). In May 2019, this definition was changed to one that is based instead on precisely measured values of several fundamental physical constants.1 . 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 as previously defined 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
1 For details see https://www.nist.gov/pml/weights-and-measures/si-units-mass
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between these two units and 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 equivalent to 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.
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 is 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
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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.
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.
(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?
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Answer: (a) 0.599 cm3; (b) 8.91 g/cm3
LINK TO LEARNING
To learn more about the relationship between mass, volume, and density, use this interactive simulator (http://openstax.org/l/16phetmasvolden) to explore the density of different materials.
EXAMPLE 1.2
Using Displacement of Water to Determine Density
This exercise uses a simulation (http://openstax.org/l/16phetmasvolden) to illustrate an alternative approach to the determination of density that involves measuring the object’s volume via displacement of water. Use the simulator to determine the densities iron and wood.
Solution Click the “turn fluid into water” button in the simulator to adjust the density of liquid in the beaker to 1.00 g/ mL. Remove the red block from the beaker and note the volume of water is 25.5 mL. Select the iron sample by clicking “iron” in the table of materials at the bottom of the screen, place the iron block on the balance pan, and observe its mass is 31.48 g. Transfer the iron block to the beaker and notice that it sinks, displacing a volume of water equal to its own volume and causing the water level to rise to 29.5 mL. The volume of the iron block is therefore:
The density of the iron is then calculated to be:
Remove the iron block from the beaker, change the block material to wood, and then repeat the mass and volume measurements. Unlike iron, the wood block does not sink in the water but instead floats on the water’s surface. To measure its volume, drag it beneath the water’s surface so that it is fully submerged.
Note: The sink versus float behavior illustrated in this example demonstrates the property of “buoyancy” (see end of chapter Exercise 1.42 and Exercise 1.43).
Check Your Learning Following the water displacement approach, use the simulator to measure the density of the foam sample.
Answer: 0.230 g/mL
1.5 Measurement Uncertainty, Accuracy, and Precision
LEARNING OBJECTIVES 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
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counted does not change while the counting process is underway. The result of such a counting measurement is an example of an exact number. By counting the eggs in a carton, one can determine 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 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 the coin is weighed on a more sensitive balance, the mass might be 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
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(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.
A measurement result is properly reported when its significant digits accurately represent the certainty of the measurement process. 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 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
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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. Take the uncertainty in 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 adding or subtracting numbers, round the result to the same number of decimal places as the number with the least number of decimal places (the least certain value in terms of addition and subtraction).
2. When multiplying or dividing numbers, round the result to the same number of digits as the number with the least number of significant figures (the least certain 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, “round down” and leave the retained digit unchanged; if it is more than 5, “round up” and increase the retained digit by 1. If the dropped digit is 5, and it’s either the last digit in the number or it’s followed only by zeros, round up or down, whichever yields an even value for the retained digit. If any nonzero digits follow the dropped 5, round up. (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 a nonzero digit follows it) • 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:
(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)
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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 adding or subtracting numbers, round the result to the same number of decimal places as the number with the fewest decimal places (i.e., the least certain 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)
Answer is 5.385 g (round to the thousandths place; three decimal places) (b)
Answer is 65 g (round to the ones place; no decimal places)
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
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EXAMPLE 1.5 Multiplication and Division with Significant Figures
Rule: When multiplying or dividing numbers, round the result to the same number of digits as the number with the fewest significant figures (the least certain 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)
(b)
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 for these rules about significant figures and rounding—to correctly represent the certainty of the values reported 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
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
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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:
(rounded to the nearest 0.1 mL, per the rule for addition and subtraction) The density is the mass-to-volume ratio:
(rounded to two significant figures, per the rule for multiplication and division) 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.
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(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 evaluate 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).
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.
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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
LEARNING OBJECTIVES 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
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:
An Olympic-quality sprinter can run 100 m in approximately 10 s, corresponding to an average speed of
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 among 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:
The time can then be computed as:
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1 • Essential Ideas
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,
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 km = 0.62137 mi
1 ft3 = 28.317 L
1 lb = 453.59 g 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
When a quantity (such as distance in inches) is multiplied by an appropriate unit conversion factor, the quantity is converted 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:
Since this simple arithmetic involves quantities, the premise of dimensional analysis requires that we multiply both numbers and units. The numbers of these two quantities are multiplied to yield the number of the
product quantity, 86, whereas the units are multiplied to yield
. Just as for numbers, a ratio of identical
units is also numerically equal to one,
and the unit product thus simplifies to cm. (When identical
units divide to yield a factor of 1, they are said to “cancel.”) Dimensional analysis may be used to confirm the proper application of unit conversion factors as demonstrated in the following example.
EXAMPLE 1.8
Using a Unit Conversion Factor
The mass of a competition frisbee is 125 g. Convert its mass to ounces using the unit conversion factor derived
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1.6 • Mathematical Treatment of Measurement Results
43
from the relationship 1 oz = 28.349 g (Table 1.6).
Solution Given the conversion factor, the mass in ounces may be derived using an equation similar to the one used for converting length from inches to centimeters.
The unit conversion factor may be represented as:
The correct unit conversion factor is the ratio that cancels the units of grams and leaves ounces.
Check Your Learning Convert a volume of 9.345 qt to liters.
Answer: 8.844 L
Beyond simple unit conversions, the factor-label method can be used to solve more complex problems involving computations. Regardless of the details, the basic approach is the same—all the factors involved in the calculation must be appropriately oriented to ensure that their labels (units) will appropriately cancel and/ or combine to yield the desired unit in the result. As your study of chemistry continues, you will encounter many opportunities to apply this approach.
EXAMPLE 1.9
Computing Quantities from Measurement Results and Known Mathematical Relations
What is the density of common antifreeze in units of g/mL? A 4.00-qt sample of the antifreeze weighs 9.26 lb.
Solution
Since
, we need to divide the mass in grams by the volume in milliliters. In general: the
number of units of B = the number of units of A unit conversion factor. The necessary conversion factors are given in Table 1.6: 1 lb = 453.59 g; 1 L = 1.0567 qt; 1 L = 1,000 mL. Mass may be converted from pounds to grams as follows:
Volume may be converted from quarts to milliliters via two steps: Step 1. Convert quarts to liters.
Step 2. Convert liters to milliliters.
Then,
44
1 • Essential Ideas
Alternatively, the calculation could be set up in a way that uses three unit conversion factors sequentially as follows:
Check Your Learning What is the volume in liters of 1.000 oz, given that 1 L = 1.0567 qt and 1 qt = 32 oz (exactly)? Answer: 2.956 × 10−2 L
EXAMPLE 1.10 Computing Quantities from Measurement Results and Known Mathematical Relations
While being driven from Philadelphia to Atlanta, a distance of about 1250 km, a 2014 Lamborghini Aventador Roadster uses 213 L gasoline. (a) What (average) fuel economy, in miles per gallon, did the Roadster get during this trip? (b) If gasoline costs $3.80 per gallon, what was the fuel cost for this trip? Solution (a) First convert distance from kilometers to miles:
and then convert volume from liters to gallons:
Finally,
Alternatively, the calculation could be set up in a way that uses all the conversion factors sequentially, as follows:
(b) Using the previously calculated volume in gallons, we find:
Check Your Learning A Toyota Prius Hybrid uses 59.7 L gasoline to drive from San Francisco to Seattle, a distance of 1300 km (two significant digits). (a) What (average) fuel economy, in miles per gallon, did the Prius get during this trip? (b) If gasoline costs $3.90 per gallon, what was the fuel cost for this trip?
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1.6 • Mathematical Treatment of Measurement Results
45
Answer: (a) 51 mpg; (b) $62
Conversion of Temperature Units
We use the word temperature to refer to the hotness or coldness of a substance. One way we measure a change in temperature is to use the fact that most substances expand when their temperature increases and contract when their temperature decreases. The liquid in a common glass thermometer changes its volume as the temperature changes, and the position of the trapped liquid's surface along a printed scale may be used as a measure of temperature.
Temperature scales are defined relative to selected reference temperatures: Two of the most commonly used are the freezing and boiling temperatures of water at a specified atmospheric pressure. On the Celsius scale, 0 °C is defined as the freezing temperature of water and 100 °C as the boiling temperature of water. The space between the two temperatures is divided into 100 equal intervals, which we call degrees. On the Fahrenheit scale, the freezing point of water is defined as 32 °F and the boiling temperature as 212 °F. The space between these two points on a Fahrenheit thermometer is divided into 180 equal parts (degrees).
Defining the Celsius and Fahrenheit temperature scales as described in the previous paragraph results in a slightly more complex relationship between temperature values on these two scales than for different units of measure for other properties. Most measurement units for a given property are directly proportional to one another (y = mx). Using familiar length units as one example:
where y = length in feet, x = length in inches, and the proportionality constant, m, is the conversion factor. The Celsius and Fahrenheit temperature scales, however, do not share a common zero point, and so the relationship between these two scales is a linear one rather than a proportional one (y = mx + b). Consequently, converting a temperature from one of these scales into the other requires more than simple multiplication by a conversion factor, m, it also must take into account differences in the scales’ zero points (b). The linear equation relating Celsius and Fahrenheit temperatures is easily derived from the two temperatures used to define each scale. Representing the Celsius temperature as x and the Fahrenheit temperature as y, the slope, m, is computed to be:
The y-intercept of the equation, b, is then calculated using either of the equivalent temperature pairs, (100 °C, 212 °F) or (0 °C, 32 °F), as:
The equation relating the temperature (T) scales is then:
An abbreviated form of this equation that omits the measurement units is:
Rearrangement of this equation yields the form useful for converting from Fahrenheit to Celsius:
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1 • Essential Ideas
As mentioned earlier in this chapter, the SI unit of temperature is the kelvin (K). Unlike the Celsius and Fahrenheit scales, the kelvin scale is an absolute temperature scale in which 0 (zero) K corresponds to the lowest temperature that can theoretically be achieved. Since the kelvin temperature scale is absolute, a degree symbol is not included in the unit abbreviation, K. The early 19th-century discovery of the relationship between a gas’s volume and temperature suggested that the volume of a gas would be zero at −273.15 °C. In 1848, British physicist William Thompson, who later adopted the title of Lord Kelvin, proposed an absolute temperature scale based on this concept (further treatment of this topic is provided in this text’s chapter on gases).
The freezing temperature of water on this scale is 273.15 K and its boiling temperature is 373.15 K. Notice the numerical difference in these two reference temperatures is 100, the same as for the Celsius scale, and so the linear relation between these two temperature scales will exhibit a slope of . Following the same approach,
the equations for converting between the kelvin and Celsius temperature scales are derived to be:
The 273.15 in these equations has been determined experimentally, so it is not exact. Figure 1.28 shows the relationship among the three temperature scales.
FIGURE 1.28 The Fahrenheit, Celsius, and kelvin temperature scales are compared. Although the kelvin (absolute) temperature scale is the official SI temperature scale, Celsius is commonly used in many scientific contexts and is the scale of choice for nonscience contexts in almost all areas of the world. Very few countries (the U.S. and its territories, the Bahamas, Belize, Cayman Islands, and Palau) still use Fahrenheit for weather, medicine, and cooking.
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1.6 • Mathematical Treatment of Measurement Results
47
EXAMPLE 1.11
Conversion from Celsius
Normal body temperature has been commonly accepted as 37.0 °C (although it varies depending on time of day and method of measurement, as well as among individuals). What is this temperature on the kelvin scale and on the Fahrenheit scale?
Solution
Check Your Learning Convert 80.92 °C to K and °F. Answer: 354.07 K, 177.7 °F
EXAMPLE 1.12 Conversion from Fahrenheit
Baking a ready-made pizza calls for an oven temperature of 450 °F. If you are in Europe, and your oven thermometer uses the Celsius scale, what is the setting? What is the kelvin temperature? Solution
Check Your Learning Convert 50 °F to °C and K.
Answer: 10 °C, 280 K
48 1 • Key Terms
Key Terms
accuracy how closely a measurement aligns with a correct value
atom smallest particle of an element that can enter into a chemical combination
Celsius (°C) unit of temperature; water freezes at 0 °C and boils at 100 °C on this scale
chemical change change producing a different kind of matter from the original kind of matter
chemical property behavior that is related to the change of one kind of matter into another kind of matter
chemistry study of the composition, properties, and interactions of matter
compound pure substance that can be decomposed into two or more elements
cubic centimeter (cm3 or cc) volume of a cube with an edge length of exactly 1 cm
cubic meter (m3) SI unit of volume density ratio of mass to volume for a substance or
object dimensional analysis (also, factor-label method)
versatile mathematical approach that can be applied to computations ranging from simple unit conversions to more complex, multi-step calculations involving several different quantities element substance that is composed of a single type of atom; a substance that cannot be decomposed by a chemical change exact number number derived by counting or by definition extensive property property of a substance that depends on the amount of the substance Fahrenheit unit of temperature; water freezes at 32 °F and boils at 212 °F on this scale gas state in which matter has neither definite volume nor shape heterogeneous mixture combination of substances with a composition that varies from point to point homogeneous mixture (also, solution) combination of substances with a composition that is uniform throughout hypothesis tentative explanation of observations that acts as a guide for gathering and checking information intensive property property of a substance that is independent of the amount of the substance kelvin (K) SI unit of temperature; 273.15 K = 0 ºC kilogram (kg) standard SI unit of mass; 1 kg = approximately 2.2 pounds law statement that summarizes a vast number of experimental observations, and describes or
predicts some aspect of the natural world law of conservation of matter when matter
converts from one type to another or changes form, there is no detectable change in the total amount of matter present length measure of one dimension of an object liquid state of matter that has a definite volume but indefinite shape liter (L) (also, cubic decimeter) unit of volume; 1 L = 1,000 cm3 macroscopic domain realm of everyday things that are large enough to sense directly by human sight and touch mass fundamental property indicating amount of matter matter anything that occupies space and has mass meter (m) standard metric and SI unit of length; 1 m = approximately 1.094 yards microscopic domain realm of things that are much too small to be sensed directly milliliter (mL) 1/1,000 of a liter; equal to 1 cm3 mixture matter that can be separated into its components by physical means molecule bonded collection of two or more atoms of the same or different elements physical change change in the state or properties of matter that does not involve a change in its chemical composition physical property characteristic of matter that is not associated with any change in its chemical composition plasma gaseous state of matter containing a large number of electrically charged atoms and/or molecules precision how closely a measurement matches the same measurement when repeated pure substance homogeneous substance that has a constant composition rounding procedure used to ensure that calculated results properly reflect the uncertainty in the measurements used in the calculation scientific method 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 second (s) SI unit of time SI units (International System of Units) standards fixed by international agreement in the International System of Units (Le Système International d’Unités) significant figures (also, significant digits) all of
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1 • Key Equations 49
the measured digits in a determination, including the uncertain last digit solid state of matter that is rigid, has a definite shape, and has a fairly constant volume symbolic domain specialized language used to represent components of the macroscopic and microscopic domains, such as chemical symbols, chemical formulas, chemical equations, graphs, drawings, and calculations temperature intensive property representing the hotness or coldness of matter
Key Equations
theory well-substantiated, comprehensive, testable explanation of a particular aspect of nature
uncertainty estimate of amount by which measurement differs from true value
unit standard of comparison for measurements unit conversion factor ratio of equivalent
quantities expressed with different units; used to convert from one unit to a different unit volume amount of space occupied by an object weight force that gravity exerts on an object
Summary
1.1 Chemistry in Context
Chemistry deals with the composition, structure, and properties of matter, and the ways by which various forms of matter may be interconverted. Thus, it occupies a central place in the study and practice of science and technology. Chemists use the scientific method to perform experiments, pose hypotheses, and formulate laws and develop theories, so that they can better understand the behavior of the natural world. To do so, they operate in the macroscopic, microscopic, and symbolic domains. Chemists measure, analyze, purify, and synthesize a wide variety of substances that are important to our lives.
1.2 Phases and Classification of Matter
Matter is anything that occupies space and has mass. The basic building block of matter is the atom, the smallest unit of an element that can enter into combinations with atoms of the same or other elements. In many substances, atoms are combined into molecules. On earth, matter commonly exists in three states: solids, of fixed shape and volume; liquids, of variable shape but fixed volume; and gases, of variable shape and volume. Under hightemperature conditions, matter also can exist as a plasma. Most matter is a mixture: It is composed of two or more types of matter that can be present in varying amounts and can be separated by physical means. Heterogeneous mixtures vary in
composition from point to point; homogeneous mixtures have the same composition from point to point. Pure substances consist of only one type of matter. A pure substance can be an element, which consists of only one type of atom and cannot be broken down by a chemical change, or a compound, which consists of two or more types of atoms.
1.3 Physical and Chemical Properties
All substances have distinct physical and chemical properties, and may undergo physical or chemical changes. Physical properties, such as hardness and boiling point, and physical changes, such as melting or freezing, do not involve a change in the composition of matter. Chemical properties, such flammability and acidity, and chemical changes, such as rusting, involve production of matter that differs from that present beforehand.
Measurable properties fall into one of two categories. Extensive properties depend on the amount of matter present, for example, the mass of gold. Intensive properties do not depend on the amount of matter present, for example, the density of gold. Heat is an example of an extensive property, and temperature is an example of an intensive property.
1.4 Measurements
Measurements provide quantitative information that is critical in studying and practicing chemistry. Each measurement has an amount, a unit for comparison,
50 1 • Exercises
and an uncertainty. Measurements can be represented in either decimal or scientific notation. Scientists primarily use SI (International System) units such as meters, seconds, and kilograms, as well as derived units, such as liters (for volume) and g/cm3 (for density). In many cases, it is convenient to use prefixes that yield fractional and multiple units, such as microseconds (10−6 seconds) and megahertz (106 hertz), respectively.
1.5 Measurement Uncertainty, Accuracy, and Precision
Quantities can be defined or measured. Measured quantities have an associated uncertainty that is represented by the number of significant figures in the quantity’s number. The uncertainty of a calculated quantity depends on the uncertainties in the quantities used in the calculation and is
reflected in how the value is rounded. Quantities are characterized with regard to accuracy (closeness to a true or accepted value) and precision (variation among replicate measurement results).
1.6 Mathematical Treatment of Measurement Results
Measurements are made using a variety of units. It is often useful or necessary to convert a measured quantity from one unit into another. These conversions are accomplished using unit conversion factors, which are derived by simple applications of a mathematical approach called the factor-label method or dimensional analysis. This strategy is also employed to calculate sought quantities using measured quantities and appropriate mathematical relations.
Exercises
1.1 Chemistry in Context
1. Explain how you could experimentally determine whether the outside temperature is higher or lower than 0 °C (32 °F) without using a thermometer.
2. Identify each of the following statements as being most similar to a hypothesis, a law, or a theory. Explain your reasoning. (a) Falling barometric pressure precedes the onset of bad weather. (b) All life on earth has evolved from a common, primitive organism through the process of natural selection. (c) My truck’s gas mileage has dropped significantly, probably because it’s due for a tune-up.
3. Identify each of the following statements as being most similar to a hypothesis, a law, or a theory. Explain your reasoning. (a) The pressure of a sample of gas is directly proportional to the temperature of the gas. (b) Matter consists of tiny particles that can combine in specific ratios to form substances with specific properties. (c) At a higher temperature, solids (such as salt or sugar) will dissolve better in water.
4. Identify each of the underlined items as a part of either the macroscopic domain, the microscopic domain, or the symbolic domain of chemistry. For any in the symbolic domain, indicate whether they are symbols for a macroscopic or a microscopic feature. (a) The mass of a lead pipe is 14 lb. (b) The mass of a certain chlorine atom is 35 amu. (c) A bottle with a label that reads Al contains aluminum metal. (d) Al is the symbol for an aluminum atom.
5. Identify each of the underlined items as a part of either the macroscopic domain, the microscopic domain, or the symbolic domain of chemistry. For those in the symbolic domain, indicate whether they are symbols for a macroscopic or a microscopic feature. (a) A certain molecule contains one H atom and one Cl atom. (b) Copper wire has a density of about 8 g/cm3. (c) The bottle contains 15 grams of Ni powder. (d) A sulfur molecule is composed of eight sulfur atoms.
6. According to one theory, the pressure of a gas increases as its volume decreases because the molecules in the gas have to move a shorter distance to hit the walls of the container. Does this theory follow a macroscopic or microscopic description of chemical behavior? Explain your answer.
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1 • Exercises 51
7. The amount of heat required to melt 2 lbs of ice is twice the amount of heat required to melt 1 lb of ice. Is this observation a macroscopic or microscopic description of chemical behavior? Explain your answer.
1.2 Phases and Classification of Matter
8. Why is an object’s mass, rather than its weight, used to indicate the amount of matter it contains? 9. What properties distinguish solids from liquids? Liquids from gases? Solids from gases? 10. How does a heterogeneous mixture differ from a homogeneous mixture? How are they similar? 11. How does a homogeneous mixture differ from a pure substance? How are they similar? 12. How does an element differ from a compound? How are they similar? 13. How do molecules of elements and molecules of compounds differ? In what ways are they similar? 14. How does an atom differ from a molecule? In what ways are they similar? 15. Many of the items you purchase are mixtures of pure compounds. Select three of these commercial
products and prepare a list of the ingredients that are pure compounds. 16. Classify each of the following as an element, a compound, or a mixture:
(a) copper (b) water (c) nitrogen (d) sulfur (e) air (f) sucrose (g) a substance composed of molecules each of which contains two iodine atoms (h) gasoline 17. Classify each of the following as an element, a compound, or a mixture: (a) iron (b) oxygen (c) mercury oxide (d) pancake syrup (e) carbon dioxide (f) a substance composed of molecules each of which contains one hydrogen atom and one chlorine atom (g) baking soda (h) baking powder 18. A sulfur atom and a sulfur molecule are not identical. What is the difference? 19. How are the molecules in oxygen gas, the molecules in hydrogen gas, and water molecules similar? How do they differ? 20. Why are astronauts in space said to be “weightless,” but not “massless”? 21. Prepare a list of the principal chemicals consumed and produced during the operation of an automobile. 22. Matter is everywhere around us. Make a list by name of fifteen different kinds of matter that you encounter every day. Your list should include (and label at least one example of each) the following: a solid, a liquid, a gas, an element, a compound, a homogenous mixture, a heterogeneous mixture, and a pure substance. 23. When elemental iron corrodes it combines with oxygen in the air to ultimately form red brown iron(III) oxide called rust. (a) If a shiny iron nail with an initial mass of 23.2 g is weighed after being coated in a layer of rust, would you expect the mass to have increased, decreased, or remained the same? Explain. (b) If the mass of the iron nail increases to 24.1 g, what mass of oxygen combined with the iron?
52 1 • Exercises
24. As stated in the text, convincing examples that demonstrate the law of conservation of matter outside of the laboratory are few and far between. Indicate whether the mass would increase, decrease, or stay the same for the following scenarios where chemical reactions take place: (a) Exactly one pound of bread dough is placed in a baking tin. The dough is cooked in an oven at 350 °F releasing a wonderful aroma of freshly baked bread during the cooking process. Is the mass of the baked loaf less than, greater than, or the same as the one pound of original dough? Explain. (b) When magnesium burns in air a white flaky ash of magnesium oxide is produced. Is the mass of magnesium oxide less than, greater than, or the same as the original piece of magnesium? Explain. (c) Antoine Lavoisier, the French scientist credited with first stating the law of conservation of matter, heated a mixture of tin and air in a sealed flask to produce tin oxide. Did the mass of the sealed flask and contents decrease, increase, or remain the same after the heating?
25. Yeast converts glucose to ethanol and carbon dioxide during anaerobic fermentation as depicted in the simple chemical equation here:
(a) If 200.0 g of glucose is fully converted, what will be the total mass of ethanol and carbon dioxide produced? (b) If the fermentation is carried out in an open container, would you expect the mass of the container and contents after fermentation to be less than, greater than, or the same as the mass of the container and contents before fermentation? Explain. (c) If 97.7 g of carbon dioxide is produced, what mass of ethanol is produced?
1.3 Physical and Chemical Properties
26. Classify the six underlined properties in the following paragraph as chemical or physical: Fluorine is a pale yellow gas that reacts with most substances. The free element melts at −220 °C and boils at −188 °C. Finely divided metals burn in fluorine with a bright flame. Nineteen grams of fluorine will react with 1.0 gram of hydrogen.
27. Classify each of the following changes as physical or chemical: (a) condensation of steam (b) burning of gasoline (c) souring of milk (d) dissolving of sugar in water (e) melting of gold
28. Classify each of the following changes as physical or chemical: (a) coal burning (b) ice melting (c) mixing chocolate syrup with milk (d) explosion of a firecracker (e) magnetizing of a screwdriver
29. The volume of a sample of oxygen gas changed from 10 mL to 11 mL as the temperature changed. Is this a chemical or physical change?
30. A 2.0-liter volume of hydrogen gas combined with 1.0 liter of oxygen gas to produce 2.0 liters of water vapor. Does oxygen undergo a chemical or physical change?
31. Explain the difference between extensive properties and intensive properties. 32. Identify the following properties as either extensive or intensive.
(a) volume (b) temperature (c) humidity (d) heat (e) boiling point
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1 • Exercises 53
33. The density (d) of a substance is an intensive property that is defined as the ratio of its mass (m) to its volume (V).
Considering that mass and volume are both extensive properties, explain why their ratio, density, is intensive.
1.4 Measurements
34. Is one liter about an ounce, a pint, a quart, or a gallon? 35. Is a meter about an inch, a foot, a yard, or a mile? 36. Indicate the SI base units or derived units that are appropriate for the following measurements:
(a) the length of a marathon race (26 miles 385 yards) (b) the mass of an automobile (c) the volume of a swimming pool (d) the speed of an airplane (e) the density of gold (f) the area of a football field (g) the maximum temperature at the South Pole on April 1, 1913 37. Indicate the SI base units or derived units that are appropriate for the following measurements: (a) the mass of the moon (b) the distance from Dallas to Oklahoma City (c) the speed of sound (d) the density of air (e) the temperature at which alcohol boils (f) the area of the state of Delaware (g) the volume of a flu shot or a measles vaccination 38. Give the name and symbol of the prefixes used with SI units to indicate multiplication by the following exact quantities. (a) 103 (b) 10−2 (c) 0.1 (d) 10−3 (e) 1,000,000 (f) 0.000001 39. Give the name of the prefix and the quantity indicated by the following symbols that are used with SI base units. (a) c (b) d (c) G (d) k (e) m (f) n (g) p (h) T 40. A large piece of jewelry has a mass of 132.6 g. A graduated cylinder initially contains 48.6 mL water. When the jewelry is submerged in the graduated cylinder, the total volume increases to 61.2 mL. (a) Determine the density of this piece of jewelry. (b) Assuming that the jewelry is made from only one substance, what substance is it likely to be? Explain.
54 1 • Exercises
41. Visit this density simulation (http://openstax.org/l/16phetmasvolden) and click the "turn fluid into water" button to adjust the density of liquid in the beaker to 1.00 g/mL. (a) Use the water displacement approach to measure the mass and volume of the unknown material (select the green block with question marks). (b) Use the measured mass and volume data from step (a) to calculate the density of the unknown material. (c) Link out to the link provided. (d) Assuming this material is a copper-containing gemstone, identify its three most likely identities by comparing the measured density to the values tabulated at this gemstone density guide (https://www.ajsgem.com/articles/gemstone-density-definitive-guide.html). (e) How are mass and density related for blocks of the same volume?
42. Visit this density simulation (http://openstax.org/l/16phetmasvolden) and click the "reset" button to ensure all simulator parameters are at their default values. (a) Use the water displacement approach to measure the mass and volume of the red block. (b) Use the measured mass and volume data from step (a) to calculate the density of the red block. (c) Use the vertical green slide control to adjust the fluid density to values well above, then well below, and finally nearly equal to the density of the red block, reporting your observations.
43. Visit this density simulation (http://openstax.org/l/16phetmasvolden) and click the “turn fluid into water” button to adjust the density of liquid in the beaker to 1.00 g/mL. Change the block material to foam, and then wait patiently until the foam block stops bobbing up and down in the water. (a) The foam block should be floating on the surface of the water (that is, only partially submerged). What is the volume of water displaced? (b) Use the water volume from part (a) and the density of water (1.00 g/mL) to calculate the mass of water displaced. (c) Remove and weigh the foam block. How does the block’s mass compare to the mass of displaced water from part (b)?
1.5 Measurement Uncertainty, Accuracy, and Precision
44. Express each of the following numbers in scientific notation with correct significant figures: (a) 711.0 (b) 0.239 (c) 90743 (d) 134.2 (e) 0.05499 (f) 10000.0 (g) 0.000000738592
45. Express each of the following numbers in exponential notation with correct significant figures: (a) 704 (b) 0.03344 (c) 547.9 (d) 22086 (e) 1000.00 (f) 0.0000000651 (g) 0.007157
46. Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty: (a) the number of eggs in a basket (b) the mass of a dozen eggs (c) the number of gallons of gasoline necessary to fill an automobile gas tank (d) the number of cm in 2 m (e) the mass of a textbook (f) the time required to drive from San Francisco to Kansas City at an average speed of 53 mi/h
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1 • Exercises 55
47. Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty: (a) the number of seconds in an hour (b) the number of pages in this book (c) the number of grams in your weight (d) the number of grams in 3 kilograms (e) the volume of water you drink in one day (f) the distance from San Francisco to Kansas City
48. How many significant figures are contained in each of the following measurements? (a) 38.7 g (b) 2 1018 m (c) 3,486,002 kg (d) 9.74150 10−4 J (e) 0.0613 cm3 (f) 17.0 kg (g) 0.01400 g/mL
49. How many significant figures are contained in each of the following measurements? (a) 53 cm (b) 2.05 108 m (c) 86,002 J (d) 9.740 104 m/s (e) 10.0613 m3 (f) 0.17 g/mL (g) 0.88400 s
50. The following quantities were reported on the labels of commercial products. Determine the number of significant figures in each. (a) 0.0055 g active ingredients (b) 12 tablets (c) 3% hydrogen peroxide (d) 5.5 ounces (e) 473 mL (f) 1.75% bismuth (g) 0.001% phosphoric acid (h) 99.80% inert ingredients
51. Round off each of the following numbers to two significant figures: (a) 0.436 (b) 9.000 (c) 27.2 (d) 135 (e) 1.497 10−3 (f) 0.445
52. Round off each of the following numbers to two significant figures: (a) 517 (b) 86.3 (c) 6.382 103 (d) 5.0008 (e) 22.497 (f) 0.885
56 1 • Exercises
53. Perform the following calculations and report each answer with the correct number of significant figures. (a) 628 342 (b) (5.63 102) (7.4 103) (c) (d) 8119 0.000023 (e) 14.98 + 27,340 + 84.7593 (f) 42.7 + 0.259
54. Perform the following calculations and report each answer with the correct number of significant figures. (a) 62.8 34 (b) 0.147 + 0.0066 + 0.012 (c) 38 95 1.792 (d) 15 – 0.15 – 0.6155 (e) (f) 140 + 7.68 + 0.014 (g) 28.7 – 0.0483 (h)
55. Consider the results of the archery contest shown in this figure. (a) Which archer is most precise? (b) Which archer is most accurate? (c) Who is both least precise and least accurate?
56. Classify the following sets of measurements as accurate, precise, both, or neither. (a) Checking for consistency in the weight of chocolate chip cookies: 17.27 g, 13.05 g, 19.46 g, 16.92 g (b) Testing the volume of a batch of 25-mL pipettes: 27.02 mL, 26.99 mL, 26.97 mL, 27.01 mL (c) Determining the purity of gold: 99.9999%, 99.9998%, 99.9998%, 99.9999%
1.6 Mathematical Treatment of Measurement Results
57. Write conversion factors (as ratios) for the number of: (a) yards in 1 meter (b) liters in 1 liquid quart (c) pounds in 1 kilogram
58. Write conversion factors (as ratios) for the number of: (a) kilometers in 1 mile (b) liters in 1 cubic foot (c) grams in 1 ounce
59. The label on a soft drink bottle gives the volume in two units: 2.0 L and 67.6 fl oz. Use this information to derive a conversion factor between the English and metric units. How many significant figures can you justify in your conversion factor?
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1 • Exercises 57
60. The label on a box of cereal gives the mass of cereal in two units: 978 grams and 34.5 oz. Use this information to find a conversion factor between the English and metric units. How many significant figures can you justify in your conversion factor?
61. Soccer is played with a round ball having a circumference between 27 and 28 in. and a weight between 14 and 16 oz. What are these specifications in units of centimeters and grams?
62. A woman’s basketball has a circumference between 28.5 and 29.0 inches and a maximum weight of 20 ounces (two significant figures). What are these specifications in units of centimeters and grams?
63. How many milliliters of a soft drink are contained in a 12.0-oz can? 64. A barrel of oil is exactly 42 gal. How many liters of oil are in a barrel? 65. The diameter of a red blood cell is about 3 10−4 in. What is its diameter in centimeters? 66. The distance between the centers of the two oxygen atoms in an oxygen molecule is 1.21 10−8 cm. What
is this distance in inches? 67. Is a 197-lb weight lifter light enough to compete in a class limited to those weighing 90 kg or less? 68. A very good 197-lb weight lifter lifted 192 kg in a move called the clean and jerk. What was the mass of the
weight lifted in pounds? 69. Many medical laboratory tests are run using 5.0 μL blood serum. What is this volume in milliliters? 70. If an aspirin tablet contains 325 mg aspirin, how many grams of aspirin does it contain? 71. Use scientific (exponential) notation to express the following quantities in terms of the SI base units in
Table 1.2: (a) 0.13 g (b) 232 Gg (c) 5.23 pm (d) 86.3 mg (e) 37.6 cm (f) 54 μm (g) 1 Ts (h) 27 ps (i) 0.15 mK 72. Complete the following conversions between SI units. (a) 612 g = ________ mg (b) 8.160 m = ________ cm (c) 3779 μg = ________ g (d) 781 mL = ________ L (e) 4.18 kg = ________ g (f) 27.8 m = ________ km (g) 0.13 mL = ________ L (h) 1738 km = ________ m (i) 1.9 Gg = ________ g 73. Gasoline is sold by the liter in many countries. How many liters are required to fill a 12.0-gal gas tank? 74. Milk is sold by the liter in many countries. What is the volume of exactly 1/2 gal of milk in liters? 75. A long ton is defined as exactly 2240 lb. What is this mass in kilograms? 76. Make the conversion indicated in each of the following: (a) the men’s world record long jump, 29 ft 4¼ in., to meters (b) the greatest depth of the ocean, about 6.5 mi, to kilometers (c) the area of the state of Oregon, 96,981 mi2, to square kilometers (d) the volume of 1 gill (exactly 4 oz) to milliliters (e) the estimated volume of the oceans, 330,000,000 mi3, to cubic kilometers. (f) the mass of a 3525-lb car to kilograms (g) the mass of a 2.3-oz egg to grams
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77. Make the conversion indicated in each of the following: (a) the length of a soccer field, 120 m (three significant figures), to feet (b) the height of Mt. Kilimanjaro, at 19,565 ft, the highest mountain in Africa, to kilometers (c) the area of an 8.5- × 11-inch sheet of paper in cm2 (d) the displacement volume of an automobile engine, 161 in.3, to liters (e) the estimated mass of the atmosphere, 5.6 × 1015 tons, to kilograms (f) the mass of a bushel of rye, 32.0 lb, to kilograms (g) the mass of a 5.00-grain aspirin tablet to milligrams (1 grain = 0.00229 oz)
78. Many chemistry conferences have held a 50-Trillion Angstrom Run (two significant figures). How long is this run in kilometers and in miles? (1 Å = 1 10−10 m)
79. A chemist’s 50-Trillion Angstrom Run (see Exercise 1.78) would be an archeologist’s 10,900 cubit run. How long is one cubit in meters and in feet? (1 Å = 1 10−8 cm)
80. The gas tank of a certain luxury automobile holds 22.3 gallons according to the owner’s manual. If the density of gasoline is 0.8206 g/mL, determine the mass in kilograms and pounds of the fuel in a full tank.
81. As an instructor is preparing for an experiment, he requires 225 g phosphoric acid. The only container readily available is a 150-mL Erlenmeyer flask. Is it large enough to contain the acid, whose density is 1.83 g/mL?
82. To prepare for a laboratory period, a student lab assistant needs 125 g of a compound. A bottle containing 1/4 lb is available. Did the student have enough of the compound?
83. A chemistry student is 159 cm tall and weighs 45.8 kg. What is her height in inches and weight in pounds? 84. In a recent Grand Prix, the winner completed the race with an average speed of 229.8 km/h. What was his
speed in miles per hour, meters per second, and feet per second? 85. Solve these problems about lumber dimensions.
(a) To describe to a European how houses are constructed in the US, the dimensions of “two-by-four” lumber must be converted into metric units. The thickness width length dimensions are 1.50 in. 3.50 in. 8.00 ft in the US. What are the dimensions in cm cm m? (b) This lumber can be used as vertical studs, which are typically placed 16.0 in. apart. What is that distance in centimeters? 86. The mercury content of a stream was believed to be above the minimum considered safe—1 part per billion (ppb) by weight. An analysis indicated that the concentration was 0.68 parts per billion. What quantity of mercury in grams was present in 15.0 L of the water, the density of which is 0.998 g/ml?
87. Calculate the density of aluminum if 27.6 cm3 has a mass of 74.6 g. 88. Osmium is one of the densest elements known. What is its density if 2.72 g has a volume of 0.121 cm3? 89. Calculate these masses.
(a) What is the mass of 6.00 cm3 of mercury, density = 13.5939 g/cm3? (b) What is the mass of 25.0 mL octane, density = 0.702 g/cm3? 90. Calculate these masses. (a) What is the mass of 4.00 cm3 of sodium, density = 0.97 g/cm3 ? (b) What is the mass of 125 mL gaseous chlorine, density = 3.16 g/L? 91. Calculate these volumes. (a) What is the volume of 25 g iodine, density = 4.93 g/cm3? (b) What is the volume of 3.28 g gaseous hydrogen, density = 0.089 g/L? 92. Calculate these volumes. (a) What is the volume of 11.3 g graphite, density = 2.25 g/cm3? (b) What is the volume of 39.657 g bromine, density = 2.928 g/cm3? 93. Convert the boiling temperature of gold, 2966 °C, into degrees Fahrenheit and kelvin. 94. Convert the temperature of scalding water, 54 °C, into degrees Fahrenheit and kelvin. 95. Convert the temperature of the coldest area in a freezer, −10 °F, to degrees Celsius and kelvin. 96. Convert the temperature of dry ice, −77 °C, into degrees Fahrenheit and kelvin. 97. Convert the boiling temperature of liquid ammonia, −28.1 °F, into degrees Celsius and kelvin. 98. The label on a pressurized can of spray disinfectant warns against heating the can above 130 °F. What are the corresponding temperatures on the Celsius and kelvin temperature scales?
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1 • Exercises 59
99. The weather in Europe was unusually warm during the summer of 1995. The TV news reported temperatures as high as 45 °C. What was the temperature on the Fahrenheit scale?
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CHAPTER 2
Atoms, Molecules, and Ions
Figure 2.1 Analysis of molecules in an exhaled breath can provide valuable information, leading to early diagnosis of diseases or detection of environmental exposure to harmful substances. (credit: modification of work by Paul Flowers)
CHAPTER OUTLINE 2.1 Early Ideas in Atomic Theory 2.2 Evolution of Atomic Theory 2.3 Atomic Structure and Symbolism 2.4 Chemical Formulas
INTRODUCTION Lung diseases and lung cancers are among the world's most devastating illnesses partly due to delayed detection and diagnosis. Most noninvasive screening procedures aren't reliable, and patients often resist more accurate methods due to discomfort with the procedures or with the potential danger that the procedures cause. But what if you could be accurately diagnosed through a simple breath test? Early detection of biomarkers, substances that indicate an organism’s disease or physiological state, could allow diagnosis and treatment before a condition becomes serious or irreversible. Recent studies have shown that your exhaled breath can contain molecules that may be biomarkers for recent exposure to environmental contaminants or for pathological conditions ranging from asthma to lung cancer. Scientists are working to develop biomarker “fingerprints” that could be used to diagnose a specific disease based on the amounts and identities of certain molecules in a patient’s exhaled breath. In Sangeeta Bhatia's lab at MIT, a team used substances that react specifically inside diseased lung tissue; the products of the reactions will be present as biomarkers that can be identified through mass spectrometry (an analytical method discussed later in the chapter). A potential application would allow patients with early symptoms to inhale or ingest a "sensor" substance, and, minutes later, to breathe into a detector for diagnosis. Similar research by scientists such as Laura López-Sánchez has provided similar processes for lung cancer. An essential concept underlying this goal is that of a molecule’s identity, which is determined by the numbers and types of atoms it contains, and how
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they are bonded together. This chapter will describe some of the fundamental chemical principles related to the composition of matter, including those central to the concept of molecular identity.
2.1 Early Ideas in Atomic Theory
LEARNING OBJECTIVES By the end of this section, you will be able to:
• State the postulates of Dalton’s atomic theory • Use postulates of Dalton’s atomic theory to explain the laws of definite and multiple proportions
The earliest recorded discussion of the basic structure of matter comes from ancient Greek philosophers, the scientists of their day. In the fifth century BC, Leucippus and Democritus argued that all matter was composed of small, finite particles that they called atomos, a term derived from the Greek word for “indivisible.” They thought of atoms as moving particles that differed in shape and size, and which could join together. Later, Aristotle and others came to the conclusion that matter consisted of various combinations of the four “elements”—fire, earth, air, and water—and could be infinitely divided. Interestingly, these philosophers thought about atoms and “elements” as philosophical concepts, but apparently never considered performing experiments to test their ideas.
The Aristotelian view of the composition of matter held sway for over two thousand years, until English schoolteacher John Dalton helped to revolutionize chemistry with his hypothesis that the behavior of matter could be explained using an atomic theory. First published in 1807, many of Dalton’s hypotheses about the microscopic features of matter are still valid in modern atomic theory. Here are the postulates of Dalton’s atomic theory.
1. Matter is composed of exceedingly small particles called atoms. An atom is the smallest unit of an element that can participate in a chemical change.
2. An element consists of only one type of atom, which has a mass that is characteristic of the element and is the same for all atoms of that element (Figure 2.2). A macroscopic sample of an element contains an incredibly large number of atoms, all of which have identical chemical properties.
FIGURE 2.2 A pre-1982 copper penny (left) contains approximately 3 1022 copper atoms (several dozen are represented as brown spheres at the right), each of which has the same chemical properties. (credit: modification of work by “slgckgc”/Flickr)
3. Atoms of one element differ in properties from atoms of all other elements. 4. A compound consists of atoms of two or more elements combined in a small, whole-number ratio. In a
given compound, the numbers of atoms of each of its elements are always present in the same ratio (Figure 2.3).
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FIGURE 2.3 Copper(II) oxide, a powdery, black compound, results from the combination of two types of atoms—copper (brown spheres) and oxygen (red spheres)—in a 1:1 ratio. (credit: modification of work by “Chemicalinterest”/Wikimedia Commons)
5. Atoms are neither created nor destroyed during a chemical change, but are instead rearranged to yield substances that are different from those present before the change (Figure 2.4).
FIGURE 2.4 When the elements copper (a shiny, red-brown solid, shown here as brown spheres) and oxygen (a clear and colorless gas, shown here as red spheres) react, their atoms rearrange to form a compound containing copper and oxygen (a powdery, black solid). (credit copper: modification of work by http://images-ofelements.com/copper.php)
Dalton’s atomic theory provides a microscopic explanation of the many macroscopic properties of matter that you’ve learned about. For example, if an element such as copper consists of only one kind of atom, then it cannot be broken down into simpler substances, that is, into substances composed of fewer types of atoms. And if atoms are neither created nor destroyed during a chemical change, then the total mass of matter present when matter changes from one type to another will remain constant (the law of conservation of matter).
EXAMPLE 2.1
Testing Dalton’s Atomic Theory
In the following drawing, the green spheres represent atoms of a certain element. The purple spheres represent atoms of another element. If the spheres touch, they are part of a single unit of a compound. Does the following chemical change represented by these symbols violate any of the ideas of Dalton’s atomic theory? If so, which one?
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Solution The starting materials consist of two green spheres and two purple spheres. The products consist of only one green sphere and one purple sphere. This violates Dalton’s postulate that atoms are neither created nor destroyed during a chemical change, but are merely redistributed. (In this case, atoms appear to have been destroyed.)
Check Your Learning In the following drawing, the green spheres represent atoms of a certain element. The purple spheres represent atoms of another element. If the spheres touch, they are part of a single unit of a compound. Does the following chemical change represented by these symbols violate any of the ideas of Dalton’s atomic theory? If so, which one?
Answer: The starting materials consist of four green spheres and two purple spheres. The products consist of four green spheres and two purple spheres. This does not violate any of Dalton’s postulates: Atoms are neither created nor destroyed, but are redistributed in small, whole-number ratios.
Dalton knew of the experiments of French chemist Joseph Proust, who demonstrated that all samples of a pure compound contain the same elements in the same proportion by mass. This statement is known as the law of definite proportions or the law of constant composition. The suggestion that the numbers of atoms of the elements in a given compound always exist in the same ratio is consistent with these observations. For example, when different samples of isooctane (a component of gasoline and one of the standards used in the octane rating system) are analyzed, they are found to have a carbon-to-hydrogen mass ratio of 5.33:1, as shown in Table 2.1.
Constant Composition of Isooctane
Sample Carbon Hydrogen Mass Ratio
A
14.82 g 2.78 g
B
22.33 g 4.19 g
C
19.40 g 3.64 g
TABLE 2.1
It is worth noting that although all samples of a particular compound have the same mass ratio, the converse is not true in general. That is, samples that have the same mass ratio are not necessarily the same substance. For example, there are many compounds other than isooctane that also have a carbon-to-hydrogen mass ratio of 5.33:1.00.
Dalton also used data from Proust, as well as results from his own experiments, to formulate another interesting law. The law of multiple proportions states that when two elements react to form more than one compound, a fixed mass of one element will react with masses of the other element in a ratio of small, whole
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numbers. For example, copper and chlorine can form a green, crystalline solid with a mass ratio of 0.558 g chlorine to 1 g copper, as well as a brown crystalline solid with a mass ratio of 1.116 g chlorine to 1 g copper. These ratios by themselves may not seem particularly interesting or informative; however, if we take a ratio of these ratios, we obtain a useful and possibly surprising result: a small, whole-number ratio.
This 2-to-1 ratio means that the brown compound has twice the amount of chlorine per amount of copper as the green compound.
This can be explained by atomic theory if the copper-to-chlorine ratio in the brown compound is 1 copper atom to 2 chlorine atoms, and the ratio in the green compound is 1 copper atom to 1 chlorine atom. The ratio of chlorine atoms (and thus the ratio of their masses) is therefore 2 to 1 (Figure 2.5).
FIGURE 2.5 Compared to the copper chlorine compound in (a), where copper is represented by brown spheres and chlorine by green spheres, the copper chlorine compound in (b) has twice as many chlorine atoms per copper atom. (credit a: modification of work by “Benjah-bmm27”/Wikimedia Commons; credit b: modification of work by “Walkerma”/Wikimedia Commons)
EXAMPLE 2.2 Laws of Definite and Multiple Proportions
A sample of compound A (a clear, colorless gas) is analyzed and found to contain 4.27 g carbon and 5.69 g oxygen. A sample of compound B (also a clear, colorless gas) is analyzed and found to contain 5.19 g carbon and 13.84 g oxygen. Are these data an example of the law of definite proportions, the law of multiple proportions, or neither? What do these data tell you about substances A and B? Solution In compound A, the mass ratio of oxygen to carbon is:
In compound B, the mass ratio of oxygen to carbon is:
The ratio of these ratios is:
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This supports the law of multiple proportions. This means that A and B are different compounds, with A having one-half as much oxygen per amount of carbon (or twice as much carbon per amount of oxygen) as B. A possible pair of compounds that would fit this relationship would be A = CO and B = CO2.
Check Your Learning
A sample of compound X (a clear, colorless, combustible liquid with a noticeable odor) is analyzed and found to contain 14.13 g carbon and 2.96 g hydrogen. A sample of compound Y (a clear, colorless, combustible liquid with a noticeable odor that is slightly different from X’s odor) is analyzed and found to contain 19.91 g carbon and 3.34 g hydrogen. Are these data an example of the law of definite proportions, the law of multiple proportions, or neither? What do these data tell you about substances X and Y?
Answer: In compound X, the mass ratio of carbon to hydrogen is
In compound Y, the mass ratio of carbon to
hydrogen is
The ratio of these ratios is
This small, whole-
number ratio supports the law of multiple proportions. This means that X and Y are different compounds.
2.2 Evolution of Atomic Theory
LEARNING OBJECTIVES By the end of this section, you will be able to:
• Outline milestones in the development of modern atomic theory • Summarize and interpret the results of the experiments of Thomson, Millikan, and Rutherford • Describe the three subatomic particles that compose atoms • Define isotopes and give examples for several elements
If matter is composed of atoms, what are atoms composed of? Are they the smallest particles, or is there something smaller? In the late 1800s, a number of scientists interested in questions like these investigated the electrical discharges that could be produced in low-pressure gases, with the most significant discovery made by English physicist J. J. Thomson using a cathode ray tube. This apparatus consisted of a sealed glass tube from which almost all the air had been removed; the tube contained two metal electrodes. When high voltage was applied across the electrodes, a visible beam called a cathode ray appeared between them. This beam was deflected toward the positive charge and away from the negative charge, and was produced in the same way with identical properties when different metals were used for the electrodes. In similar experiments, the ray was simultaneously deflected by an applied magnetic field, and measurements of the extent of deflection and the magnetic field strength allowed Thomson to calculate the charge-to-mass ratio of the cathode ray particles. The results of these measurements indicated that these particles were much lighter than atoms (Figure 2.6).
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FIGURE 2.6 (a) J. J. Thomson produced a visible beam in a cathode ray tube. (b) This is an early cathode ray tube, invented in 1897 by Ferdinand Braun. (c) In the cathode ray, the beam (shown in yellow) comes from the cathode and is accelerated past the anode toward a fluorescent scale at the end of the tube. Simultaneous deflections by applied electric and magnetic fields permitted Thomson to calculate the mass-to-charge ratio of the particles composing the cathode ray. (credit a: modification of work by Nobel Foundation; credit b: modification of work by Eugen Nesper; credit c: modification of work by “Kurzon”/Wikimedia Commons)
Based on his observations, here is what Thomson proposed and why: The particles are attracted by positive (+) charges and repelled by negative (−) charges, so they must be negatively charged (like charges repel and unlike charges attract); they are less massive than atoms and indistinguishable, regardless of the source material, so they must be fundamental, subatomic constituents of all atoms. Although controversial at the time, Thomson’s idea was gradually accepted, and his cathode ray particle is what we now call an electron, a negatively charged, subatomic particle with a mass more than one thousand-times less that of an atom. The term “electron” was coined in 1891 by Irish physicist George Stoney, from “electric ion.”
LINK TO LEARNING
Click here (http://openstax.org/l/16JJThomson) to hear Thomson describe his discovery in his own voice.
In 1909, more information about the electron was uncovered by American physicist Robert A. Millikan via his “oil drop” experiments. Millikan created microscopic oil droplets, which could be electrically charged by friction as they formed or by using X-rays. These droplets initially fell due to gravity, but their downward progress could be slowed or even reversed by an electric field lower in the apparatus. By adjusting the electric field strength and making careful measurements and appropriate calculations, Millikan was able to determine the charge on individual drops (Figure 2.7).
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FIGURE 2.7 Millikan’s experiment measured the charge of individual oil drops. The tabulated data are examples of a few possible values. Looking at the charge data that Millikan gathered, you may have recognized that the charge of an oil droplet is always a multiple of a specific charge, 1.6 10−19 C. Millikan concluded that this value must therefore be a fundamental charge—the charge of a single electron—with his measured charges due to an excess of one electron (1 times 1.6 10−19 C), two electrons (2 times 1.6 10−19 C), three electrons (3 times 1.6 10−19 C), and so on, on a given oil droplet. Since the charge of an electron was now known due to Millikan’s research, and the charge-to-mass ratio was already known due to Thomson’s research (1.759 1011 C/kg), it only required a simple calculation to determine the mass of the electron as well.
Scientists had now established that the atom was not indivisible as Dalton had believed, and due to the work of Thomson, Millikan, and others, the charge and mass of the negative, subatomic particles—the electrons—were known. However, the positively charged part of an atom was not yet well understood. In 1904, Thomson proposed the “plum pudding” model of atoms, which described a positively charged mass with an equal amount of negative charge in the form of electrons embedded in it, since all atoms are electrically neutral. A competing model had been proposed in 1903 by Hantaro Nagaoka, who postulated a Saturn-like atom, consisting of a positively charged sphere surrounded by a halo of electrons (Figure 2.8).
FIGURE 2.8 (a) Thomson suggested that atoms resembled plum pudding, an English dessert consisting of moist cake with embedded raisins (“plums”). (b) Nagaoka proposed that atoms resembled the planet Saturn, with a ring of
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electrons surrounding a positive “planet.” (credit a: modification of work by “Man vyi”/Wikimedia Commons; credit b: modification of work by “NASA”/Wikimedia Commons)
The next major development in understanding the atom came from Ernest Rutherford, a physicist from New Zealand who largely spent his scientific career in Canada and England. He performed a series of experiments using a beam of high-speed, positively charged alpha particles (α particles) that were produced by the radioactive decay of radium; α particles consist of two protons and two neutrons (you will learn more about radioactive decay in the chapter on nuclear chemistry). Rutherford and his colleagues Hans Geiger (later famous for the Geiger counter) and Ernest Marsden aimed a beam of α particles, the source of which was embedded in a lead block to absorb most of the radiation, at a very thin piece of gold foil and examined the resultant scattering of the α particles using a luminescent screen that glowed briefly where hit by an α particle.
What did they discover? Most particles passed right through the foil without being deflected at all. However, some were diverted slightly, and a very small number were deflected almost straight back toward the source (Figure 2.9). Rutherford described finding these results: “It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.”1
FIGURE 2.9 Geiger and Rutherford fired α particles at a piece of gold foil and detected where those particles went, as shown in this schematic diagram of their experiment. Most of the particles passed straight through the foil, but a few were deflected slightly and a very small number were significantly deflected.
Here is what Rutherford deduced: Because most of the fast-moving α particles passed through the gold atoms undeflected, they must have traveled through essentially empty space inside the atom. Alpha particles are positively charged, so deflections arose when they encountered another positive charge (like charges repel each other). Since like charges repel one another, the few positively charged α particles that changed paths abruptly must have hit, or closely approached, another body that also had a highly concentrated, positive charge. Since the deflections occurred a small fraction of the time, this charge only occupied a small amount of the space in the gold foil. Analyzing a series of such experiments in detail, Rutherford drew two conclusions:
1. The volume occupied by an atom must consist of a large amount of empty space. 2. A small, relatively heavy, positively charged body, the nucleus, must be at the center of each atom.
LINK TO LEARNING
View this simulation (http://openstax.org/l/16Rutherford) of the Rutherford gold foil experiment. Adjust the slit width to produce a narrower or broader beam of α particles to see how that affects the scattering pattern.
1 Ernest Rutherford, “The Development of the Theory of Atomic Structure,” ed. J. A. Ratcliffe, in Background to Modern Science, eds. Joseph Needham and Walter Pagel, (Cambridge, UK: Cambridge University Press, 1938), 61–74. Accessed September 22, 2014, https://ia600508.us.archive.org/3/items/backgroundtomode032734mbp/backgroundtomode032734mbp.pdf.
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This analysis led Rutherford to propose a model in which an atom consists of a very small, positively charged nucleus, in which most of the mass of the atom is concentrated, surrounded by the negatively charged electrons, so that the atom is electrically neutral (Figure 2.10). After many more experiments, Rutherford also discovered that the nuclei of other elements contain the hydrogen nucleus as a “building block,” and he named this more fundamental particle the proton, the positively charged, subatomic particle found in the nucleus. With one addition, which you will learn next, this nuclear model of the atom, proposed over a century ago, is still used today.
FIGURE 2.10 The α particles are deflected only when they collide with or pass close to the much heavier, positively charged gold nucleus. Because the nucleus is very small compared to the size of an atom, very few α particles are deflected. Most pass through the relatively large region occupied by electrons, which are too light to deflect the rapidly moving particles.
LINK TO LEARNING
The Rutherford Scattering simulation (http://openstax.org/l/16PhetScatter) allows you to investigate the differences between a “plum pudding” atom and a Rutherford atom by firing α particles at each type of atom.
Another important finding was the discovery of isotopes. During the early 1900s, scientists identified several substances that appeared to be new elements, isolating them from radioactive ores. For example, a “new element” produced by the radioactive decay of thorium was initially given the name mesothorium. However, a more detailed analysis showed that mesothorium was chemically identical to radium (another decay product), despite having a different atomic mass. This result, along with similar findings for other elements, led the English chemist Frederick Soddy to realize that an element could have types of atoms with different masses that were chemically indistinguishable. These different types are called isotopes—atoms of the same element that differ in mass. Soddy was awarded the Nobel Prize in Chemistry in 1921 for this discovery.
One puzzle remained: The nucleus was known to contain almost all of the mass of an atom, with the number of protons only providing half, or less, of that mass. Different proposals were made to explain what constituted the remaining mass, including the existence of neutral particles in the nucleus. As you might expect, detecting uncharged particles is very challenging, and it was not until 1932 that James Chadwick found evidence of neutrons, uncharged, subatomic particles with a mass approximately the same as that of protons. The existence of the neutron also explained isotopes: They differ in mass because they have different numbers of
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neutrons, but they are chemically identical because they have the same number of protons. This will be explained in more detail later.
2.3 Atomic Structure and Symbolism
LEARNING OBJECTIVES By the end of this section, you will be able to:
• Write and interpret symbols that depict the atomic number, mass number, and charge of an atom or ion • Define the atomic mass unit and average atomic mass • Calculate average atomic mass and isotopic abundance
The development of modern atomic theory revealed much about the inner structure of atoms. It was learned that an atom contains a very small nucleus composed of positively charged protons and uncharged neutrons, surrounded by a much larger volume of space containing negatively charged electrons. The nucleus contains the majority of an atom’s mass because protons and neutrons are much heavier than electrons, whereas electrons occupy almost all of an atom’s volume. The diameter of an atom is on the order of 10−10 m, whereas the diameter of the nucleus is roughly 10−15 m—about 100,000 times smaller. For a perspective about their relative sizes, consider this: If the nucleus were the size of a blueberry, the atom would be about the size of a football stadium (Figure 2.11).
FIGURE 2.11 If an atom could be expanded to the size of a football stadium, the nucleus would be the size of a single blueberry. (credit middle: modification of work by “babyknight”/Wikimedia Commons; credit right: modification of work by Paxson Woelber)
Atoms—and the protons, neutrons, and electrons that compose them—are extremely small. For example, a carbon atom weighs less than 2 10−23 g, and an electron has a charge of less than 2 10−19 C (coulomb). When describing the properties of tiny objects such as atoms, we use appropriately small units of measure, such as the atomic mass unit (amu) and the fundamental unit of charge (e). The amu was originally defined based on hydrogen, the lightest element, then later in terms of oxygen. Since 1961, it has been defined with regard to the most abundant isotope of carbon, atoms of which are assigned masses of exactly 12 amu. (This isotope is known as “carbon-12” as will be discussed later in this module.) Thus, one amu is exactly of the mass of one carbon-12 atom: 1 amu = 1.6605 10−24 g. (The Dalton (Da) and the unified atomic mass unit (u) are alternative units that are equivalent to the amu.) The fundamental unit of charge (also called the elementary charge) equals the magnitude of the charge of an electron (e) with e = 1.602 10−19 C.
A proton has a mass of 1.0073 amu and a charge of 1+. A neutron is a slightly heavier particle with a mass 1.0087 amu and a charge of zero; as its name suggests, it is neutral. The electron has a charge of 1− and is a much lighter particle with a mass of about 0.00055 amu (it would take about 1800 electrons to equal the mass of one proton). The properties of these fundamental particles are summarized in Table 2.2. (An observant student might notice that the sum of an atom’s subatomic particles does not equal the atom’s actual mass: The total mass of six protons, six neutrons, and six electrons is 12.0993 amu, slightly larger than 12.00 amu. This “missing” mass is known as the mass defect, and you will learn about it in the chapter on nuclear chemistry.)
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Properties of Subatomic Particles
Name
Location
Charge (C) Unit Charge Mass (amu)
Mass (g)
electron outside nucleus −1.602 10−19
1−
0.00055 0.00091 10−24
proton
nucleus
1.602 10−19
1+
1.00727 1.67262 10−24
neutron
nucleus
0
0
1.00866 1.67493 10−24
TABLE 2.2
The number of protons in the nucleus of an atom is its atomic number (Z). This is the defining trait of an element: Its value determines the identity of the atom. For example, any atom that contains six protons is the element carbon and has the atomic number 6, regardless of how many neutrons or electrons it may have. A neutral atom must contain the same number of positive and negative charges, so the number of protons equals the number of electrons. Therefore, the atomic number also indicates the number of electrons in an atom. The total number of protons and neutrons in an atom is called its mass number (A). The number of neutrons is therefore the difference between the mass number and the atomic number: A – Z = number of neutrons.
Atoms are electrically neutral if they contain the same number of positively charged protons and negatively charged electrons. When the numbers of these subatomic particles are not equal, the atom is electrically charged and is called an ion. The charge of an atom is defined as follows:
Atomic charge = number of protons − number of electrons
As will be discussed in more detail, atoms (and molecules) typically acquire charge by gaining or losing electrons. An atom that gains one or more electrons will exhibit a negative charge and is called an anion. Positively charged atoms called cations are formed when an atom loses one or more electrons. For example, a neutral sodium atom (Z = 11) has 11 electrons. If this atom loses one electron, it will become a cation with a 1+ charge (11 − 10 = 1+). A neutral oxygen atom (Z = 8) has eight electrons, and if it gains two electrons it will become an anion with a 2− charge (8 − 10 = 2−).
EXAMPLE 2.3
Composition of an Atom
Iodine is an essential trace element in our diet; it is needed to produce thyroid hormone. Insufficient iodine in the diet can lead to the development of a goiter, an enlargement of the thyroid gland (Figure 2.12).
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FIGURE 2.12 (a) Insufficient iodine in the diet can cause an enlargement of the thyroid gland called a goiter. (b) The addition of small amounts of iodine to salt, which prevents the formation of goiters, has helped eliminate this concern in the US where salt consumption is high. (credit a: modification of work by “Almazi”/Wikimedia Commons; credit b: modification of work by Mike Mozart)
The addition of small amounts of iodine to table salt (iodized salt) has essentially eliminated this health concern in the United States, but as much as 40% of the world’s population is still at risk of iodine deficiency. The iodine atoms are added as anions, and each has a 1− charge and a mass number of 127. Determine the numbers of protons, neutrons, and electrons in one of these iodine anions.
Solution The atomic number of iodine (53) tells us that a neutral iodine atom contains 53 protons in its nucleus and 53 electrons outside its nucleus. Because the sum of the numbers of protons and neutrons equals the mass number, 127, the number of neutrons is 74 (127 − 53 = 74). Since the iodine is added as a 1− anion, the number of electrons is 54 [53 – (1–) = 54].
Check Your Learning An ion of platinum has a mass number of 195 and contains 74 electrons. How many protons and neutrons does it contain, and what is its charge?
Answer: 78 protons; 117 neutrons; charge is 4+
Chemical Symbols
A chemical symbol is an abbreviation that we use to indicate an element or an atom of an element. For example, the symbol for mercury is Hg (Figure 2.13). We use the same symbol to indicate one atom of mercury (microscopic domain) or to label a container of many atoms of the element mercury (macroscopic domain).
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FIGURE 2.13 The symbol Hg represents the element mercury regardless of the amount; it could represent one atom of mercury or a large amount of mercury.
The symbols for several common elements and their atoms are listed in Table 2.3. Some symbols are derived from the common name of the element; others are abbreviations of the name in another language. Most symbols have one or two letters, but three-letter symbols have been used to describe some elements that have atomic numbers greater than 112. To avoid confusion with other notations, only the first letter of a symbol is capitalized. For example, Co is the symbol for the element cobalt, but CO is the notation for the compound carbon monoxide, which contains atoms of the elements carbon (C) and oxygen (O). All known elements and their symbols are in the periodic table in Figure 3.37 (also found in Figure A1).
Some Common Elements and Their Symbols
Element
Symbol
Element
Symbol
aluminum Al
iron
Fe (from ferrum)
bromine Br
lead
Pb (from plumbum)
calcium
Ca
magnesium Mg
carbon
C
mercury
Hg (from hydrargyrum)
chlorine Cl
nitrogen
N
chromium Cr
oxygen
O
cobalt
Co
potassium K (from kalium)
copper
Cu (from cuprum) silicon
Si
fluorine
F
silver
Ag (from argentum)
gold
Au (from aurum) sodium
Na (from natrium)
helium
He
sulfur
S
TABLE 2.3
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Element
Symbol
Element
Symbol
hydrogen H
tin
Sn (from stannum)
iodine
I
zinc
Zn
TABLE 2.3
Traditionally, the discoverer (or discoverers) of a new element names the element. However, until the name is recognized by the International Union of Pure and Applied Chemistry (IUPAC), the recommended name of the new element is based on the Latin word(s) for its atomic number. For example, element 106 was called unnilhexium (Unh), element 107 was called unnilseptium (Uns), and element 108 was called unniloctium (Uno) for several years. These elements are now named after scientists (or occasionally locations); for example, element 106 is now known as seaborgium (Sg) in honor of Glenn Seaborg, a Nobel Prize winner who was active in the discovery of several heavy elements. Element 109 was named in honor of Lise Meitner, who discovered nuclear fission, a phenomenon that would have world-changing impacts; Meitner also contributed to the discovery of some major isotopes, discussed immediately below.
LINK TO LEARNING
Visit this site (http://openstax.org/l/16IUPAC) to learn more about IUPAC, the International Union of Pure and Applied Chemistry, and explore its periodic table.
Isotopes
The symbol for a specific isotope of any element is written by placing the mass number as a superscript to the left of the element symbol (Figure 2.14). The atomic number is sometimes written as a subscript preceding the symbol, but since this number defines the element’s identity, as does its symbol, it is often omitted. For example, magnesium exists as a mixture of three isotopes, each with an atomic number of 12 and with mass numbers of 24, 25, and 26, respectively. These isotopes can be identified as 24Mg, 25Mg, and 26Mg. These isotope symbols are read as “element, mass number” and can be symbolized consistent with this reading. For instance, 24Mg is read as “magnesium 24,” and can be written as “magnesium-24” or “Mg-24.” 25Mg is read as “magnesium 25,” and can be written as “magnesium-25” or “Mg-25.” All magnesium atoms have 12 protons in their nucleus. They differ only because a 24Mg atom has 12 neutrons in its nucleus, a 25Mg atom has 13 neutrons, and a 26Mg has 14 neutrons.
FIGURE 2.14 The symbol for an atom indicates the element via its usual two-letter symbol, the mass number as a left superscript, the atomic number as a left subscript (sometimes omitted), and the charge as a right superscript.
Information about the naturally occurring isotopes of elements with atomic numbers 1 through 10 is given in Table 2.4. Note that in addition to standard names and symbols, the isotopes of hydrogen are often referred to using common names and accompanying symbols. Hydrogen-2, symbolized 2H, is also called deuterium and sometimes symbolized D. Hydrogen-3, symbolized 3H, is also called tritium and sometimes symbolized T.
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Nuclear Compositions of Atoms of the Very Light Elements
Element Symbol
Atomic Number
Number of Protons
Number of Neutrons
Mass (amu)
% Natural Abundance
1
1
(protium)
0
1.0078
99.989
hydrogen
1
1
(deuterium)
1
2.0141
0.0115
1
1
(tritium)
helium
2
2
2
2
lithium
3
3
3
3
beryllium
4
4
boron
5
5
5
5
6
6
carbon
6
6
6
6
nitrogen
7
7
7
7
8
8
oxygen
8
8
8
8
fluorine
9
9
neon
10
10
TABLE 2.4
2
3.01605
— (trace)
1
3.01603
0.00013
2
4.0026
100
3
6.0151
7.59
4
7.0160
92.41
5
9.0122
100
5
10.0129
19.9
6
11.0093
80.1
6
12.0000
98.89
7
13.0034
1.11
8
14.0032
— (trace)
7
14.0031
99.63
8
15.0001
0.37
8
15.9949
99.757
9
16.9991
0.038
10
17.9992
0.205
10
18.9984
100
10
19.9924
90.48
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Element Symbol
Atomic Number
Number of Protons
Number of Neutrons
Mass (amu)
% Natural Abundance
10
10
11
20.9938
0.27
10
10
12
21.9914
9.25
TABLE 2.4
LINK TO LEARNING
Use this Build an Atom simulator (http://openstax.org/l/16PhetAtomBld) to build atoms of the first 10 elements, see which isotopes exist, check nuclear stability, and gain experience with isotope symbols.
Atomic Mass
Because each proton and each neutron contribute approximately one amu to the mass of an atom, and each electron contributes far less, the atomic mass of a single atom is approximately equal to its mass number (a whole number). However, the average masses of atoms of most elements are not whole numbers because most elements exist naturally as mixtures of two or more isotopes.
The mass of an element shown in a periodic table or listed in a table of atomic masses is a weighted, average mass of all the isotopes present in a naturally occurring sample of that element. This is equal to the sum of each individual isotope’s mass multiplied by its fractional abundance.
For example, the element boron is composed of two isotopes: About 19.9% of all boron atoms are 10B with a mass of 10.0129 amu, and the remaining 80.1% are 11B with a mass of 11.0093 amu. The average atomic mass
for boron is calculated to be:
It is important to understand that no single boron atom weighs exactly 10.8 amu; 10.8 amu is the average mass of all boron atoms, and individual boron atoms weigh either approximately 10 amu or 11 amu.
EXAMPLE 2.4
Calculation of Average Atomic Mass
A meteorite found in central Indiana contains traces of the noble gas neon picked up from the solar wind during the meteorite’s trip through the solar system. Analysis of a sample of the gas showed that it consisted of 91.84% 20Ne (mass 19.9924 amu), 0.47% 21Ne (mass 20.9940 amu), and 7.69% 22Ne (mass 21.9914 amu). What is the average mass of the neon in the solar wind?
Solution
The average mass of a neon atom in the solar wind is 20.15 amu. (The average mass of a terrestrial neon atom is 20.1796 amu. This result demonstrates that we may find slight differences in the natural abundance of
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isotopes, depending on their origin.) Check Your Learning A sample of magnesium is found to contain 78.70% of 24Mg atoms (mass 23.98 amu), 10.13% of 25Mg atoms (mass 24.99 amu), and 11.17% of 26Mg atoms (mass 25.98 amu). Calculate the average mass of a Mg atom.
Answer: 24.31 amu
We can also do variations of this type of calculation, as shown in the next example.
EXAMPLE 2.5
Calculation of Percent Abundance
Naturally occurring chlorine consists of 35Cl (mass 34.96885 amu) and 37Cl (mass 36.96590 amu), with an average mass of 35.453 amu. What is the percent composition of Cl in terms of these two isotopes? Solution The average mass of chlorine is the fraction that is 35Cl times the mass of 35Cl plus the fraction that is 37Cl times the mass of 37Cl.
If we let x represent the fraction that is 35Cl, then the fraction that is 37Cl is represented by 1.00 − x. (The fraction that is 35Cl + the fraction that is 37Cl must add up to 1, so the fraction of 37Cl must equal 1.00 − the fraction of 35Cl.)
Substituting this into the average mass equation, we have:
So solving yields: x = 0.7576, which means that 1.00 − 0.7576 = 0.2424. Therefore, chlorine consists of 75.76% 35Cl and 24.24% 37Cl. Check Your Learning Naturally occurring copper consists of 63Cu (mass 62.9296 amu) and 65Cu (mass 64.9278 amu), with an average mass of 63.546 amu. What is the percent composition of Cu in terms of these two isotopes? Answer: 69.15% Cu-63 and 30.85% Cu-65
LINK TO LEARNING
Visit this site (http://openstax.org/l/16PhetAtomMass) to make mixtures of the main isotopes of the first 18 elements, gain experience with average atomic mass, and check naturally occurring isotope ratios using the Isotopes and Atomic Mass simulation.
As you will learn, isotopes are important in nature and especially in human understanding of science and medicine. Let's consider just one natural, stable isotope: Oxygen-18, which is noted in the table above and is referred to as one of the environmental isotopes. It is important in paleoclimatology, for example, because scientists can use the ratio between Oxygen-18 and Oxygen-16 in an ice core to determine the temperature of
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precipitation over time. Oxygen-18 was also critical to the discovery of metabolic pathways and the mechanisms of enzymes. Mildred Cohn pioneered the usage of these isotopes to act as tracers, so that researchers could follow their path through reactions and gain a better understanding of what is happening. One of her first discoveries provided insight into the phosphorylation of glucose that takes place in mitochondria. And the methods of using isotopes for this research contributed to entire fields of study.
The occurrence and natural abundances of isotopes can be experimentally determined using an instrument called a mass spectrometer. Mass spectrometry (MS) is widely used in chemistry, forensics, medicine, environmental science, and many other fields to analyze and help identify the substances in a sample of material. In a typical mass spectrometer (Figure 2.15), the sample is vaporized and exposed to a high-energy electron beam that causes the sample’s atoms (or molecules) to become electrically charged, typically by losing one or more electrons. These cations then pass through a (variable) electric or magnetic field that deflects each cation’s path to an extent that depends on both its mass and charge (similar to how the path of a large steel ball rolling past a magnet is deflected to a lesser extent that that of a small steel ball). The ions are detected, and a plot of the relative number of ions generated versus their mass-to-charge ratios (a mass spectrum) is made. The height of each vertical feature or peak in a mass spectrum is proportional to the fraction of cations with the specified mass-to-charge ratio. Since its initial use during the development of modern atomic theory, MS has evolved to become a powerful tool for chemical analysis in a wide range of applications.
FIGURE 2.15 Analysis of zirconium in a mass spectrometer produces a mass spectrum with peaks showing the different isotopes of Zr.
LINK TO LEARNING
See an animation (http://openstax.org/l/16MassSpec) that explains mass spectrometry. Watch this video (http://openstax.org/l/16RSChemistry) from the Royal Society for Chemistry for a brief description of the rudiments of mass spectrometry.
2.4 Chemical Formulas
LEARNING OBJECTIVES By the end of this section, you will be able to:
• Symbolize the composition of molecules using molecular formulas and empirical formulas • Represent the bonding arrangement of atoms within molecules using structural formulas • Define the amount unit mole and the related quantity Avogadro's number • Explain the relation between mass, moles, and numbers of atoms or molecules and perform calculations
deriving these quantities from one another
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Molecular and Empirical Formulas
A molecular formula is a representation of a molecule that uses chemical symbols to indicate the types of atoms followed by subscripts to show the number of atoms of each type in the molecule. (A subscript is used only when more than one atom of a given type is present.) Molecular formulas are also used as abbreviations for the names of compounds.
The structural formula for a compound gives the same information as its molecular formula (the types and numbers of atoms in the molecule) but also shows how the atoms are connected in the molecule. The structural formula for methane contains symbols for one C atom and four H atoms, indicating the number of atoms in the molecule (Figure 2.16). The lines represent bonds that hold the atoms together. (A chemical bond is an attraction between atoms or ions that holds them together in a molecule or a crystal.) We will discuss chemical bonds and see how to predict the arrangement of atoms in a molecule later. For now, simply know that the lines are an indication of how the atoms are connected in a molecule. A ball-and-stick model shows the geometric arrangement of the atoms with atomic sizes not to scale, and a space-filling model shows the relative sizes of the atoms.
FIGURE 2.16 A methane molecule can be represented as (a) a molecular formula, (b) a structural formula, (c) a ball-and-stick model, and (d) a space-filling model. Carbon and hydrogen atoms are represented by black and white spheres, respectively. Although many elements consist of discrete, individual atoms, some exist as molecules made up of two or more atoms of the element chemically bonded together. For example, most samples of the elements hydrogen, oxygen, and nitrogen are composed of molecules that contain two atoms each (called diatomic molecules) and thus have the molecular formulas H2, O2, and N2, respectively. Other elements commonly found as diatomic molecules are fluorine (F2), chlorine (Cl2), bromine (Br2), and iodine (I2). The most common form of the element sulfur is composed of molecules that consist of eight atoms of sulfur; its molecular formula is S8 (Figure 2.17).
FIGURE 2.17 A molecule of sulfur is composed of eight sulfur atoms and is therefore written as S8. It can be represented as (a) a structural formula, (b) a ball-and-stick model, and (c) a space-filling model. Sulfur atoms are represented by yellow spheres. It is important to note that a subscript following a symbol and a number in front of a symbol do not represent the same thing; for example, H2 and 2H represent distinctly different species. H2 is a molecular formula; it represents a diatomic molecule of hydrogen, consisting of two atoms of the element that are chemically bonded together. The expression 2H, on the other hand, indicates two separate hydrogen atoms that are not combined as a unit. The expression 2H2 represents two molecules of diatomic hydrogen (Figure 2.18).
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FIGURE 2.18 The symbols H, 2H, H2, and 2H2 represent very different entities.
Compounds are formed when two or more elements chemically combine, resulting in the formation of bonds. For example, hydrogen and oxygen can react to form water, and sodium and chlorine can react to form table salt. We sometimes describe the composition of these compounds with an empirical formula, which indicates the types of atoms present and the simplest whole-number ratio of the number of atoms (or ions) in the compound. For example, titanium dioxide (used as pigment in white paint and in the thick, white, blocking type of sunscreen) has an empirical formula of TiO2. This identifies the elements titanium (Ti) and oxygen (O) as the constituents of titanium dioxide, and indicates the presence of twice as many atoms of the element oxygen as atoms of the element titanium (Figure 2.19).
FIGURE 2.19 (a) The white compound titanium dioxide provides effective protection from the sun. (b) A crystal of titanium dioxide, TiO2, contains titanium and oxygen in a ratio of 1 to 2. The titanium atoms are gray and the oxygen atoms are red. (credit a: modification of work by “osseous”/Flickr) As discussed previously, we can describe a compound with a molecular formula, in which the subscripts indicate the actual numbers of atoms of each element in a molecule of the compound. In many cases, the molecular formula of a substance is derived from experimental determination of both its empirical formula and its molecular mass (the sum of atomic masses for all atoms composing the molecule). For example, it can be determined experimentally that benzene contains two elements, carbon (C) and hydrogen (H), and that for every carbon atom in benzene, there is one hydrogen atom. Thus, the empirical formula is CH. An experimental determination of the molecular mass reveals that a molecule of benzene contains six carbon atoms and six hydrogen atoms, so the molecular formula for benzene is C6H6 (Figure 2.20).
FIGURE 2.20 Benzene, C6H6, is produced during oil refining and has many industrial uses. A benzene molecule can be represented as (a) a structural formula, (b) a ball-and-stick model, and (c) a space-filling model. (d) Benzene is a clear liquid. (credit d: modification of work by Sahar Atwa)
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If we know a compound’s formula, we can easily determine the empirical formula. (This is somewhat of an academic exercise; the reverse chronology is generally followed in actual practice.) For example, the molecular formula for acetic acid, the component that gives vinegar its sharp taste, is C2H4O2. This formula indicates that a molecule of acetic acid (Figure 2.21) contains two carbon atoms, four hydrogen atoms, and two oxygen atoms. The ratio of atoms is 2:4:2. Dividing by the lowest common denominator (2) gives the simplest, whole-number ratio of atoms, 1:2:1, so the empirical formula is CH2O. Note that a molecular formula is always a wholenumber multiple of an empirical formula.
FIGURE 2.21 (a) Vinegar contains acetic acid, C2H4O2, which has an empirical formula of CH2O. It can be represented as (b) a structural formula and (c) as a ball-and-stick model. (credit a: modification of work by “HomeSpot HQ”/Flickr)
EXAMPLE 2.6
Empirical and Molecular Formulas
Molecules of glucose (blood sugar) contain 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms. What are the molecular and empirical formulas of glucose? Solution The molecular formula is C6H12O6 because one molecule actually contains 6 C, 12 H, and 6 O atoms. The simplest whole-number ratio of C to H to O atoms in glucose is 1:2:1, so the empirical formula is CH2O. Check Your Learning A molecule of metaldehyde (a pesticide used for snails and slugs) contains 8 carbon atoms, 16 hydrogen atoms, and 4 oxygen atoms. What are the molecular and empirical formulas of metaldehyde? Answer: Molecular formula, C8H16O4; empirical formula, C2H4O
LINK TO LEARNING
You can explore molecule building (http://openstax.org/l/16molbuilding) using an online simulation.
Portrait of a Chemist Lee Cronin
What is it that chemists do? According to Lee Cronin (Figure 2.22), chemists make very complicated molecules by “chopping up” small molecules and “reverse engineering” them. He wonders if we could “make a really cool universal chemistry set” by what he calls “app-ing” chemistry. Could we “app” chemistry?
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In a 2012 TED talk, Lee describes one fascinating possibility: combining a collection of chemical “inks” with a 3D printer capable of fabricating a reaction apparatus (tiny test tubes, beakers, and the like) to fashion a “universal toolkit of chemistry.” This toolkit could be used to create custom-tailored drugs to fight a new superbug or to “print” medicine personally configured to your genetic makeup, environment, and health situation. Says Cronin, “What Apple did for music, I’d like to do for the discovery and distribution of prescription drugs.”2 View his full talk (http://openstax.org/l/16LeeCronin) at the TED website.
FIGURE 2.22 Chemist Lee Cronin has been named one of the UK’s 10 most inspirational scientists. The youngest chair at the University of Glasgow, Lee runs a large research group, collaborates with many scientists worldwide, has published over 250 papers in top scientific journals, and has given more than 150 invited talks. His research focuses on complex chemical systems and their potential to transform technology, but also branches into nanoscience, solar fuels, synthetic biology, and even artificial life and evolution. (credit: image courtesy of Lee Cronin)
It is important to be aware that it may be possible for the same atoms to be arranged in different ways: Compounds with the same molecular formula may have different atom-to-atom bonding and therefore different structures. For example, could there be another compound with the same formula as acetic acid, C2H4O2? And if so, what would be the structure of its molecules? If you predict that another compound with the formula C2H4O2 could exist, then you demonstrated good chemical insight and are correct. Two C atoms, four H atoms, and two O atoms can also be arranged to form a methyl formate, which is used in manufacturing, as an insecticide, and for quick-drying finishes. Methyl formate molecules have one of the oxygen atoms between the two carbon atoms, differing from the arrangement in acetic acid molecules. Acetic acid and methyl formate are examples of isomers—compounds with the same chemical formula but different molecular structures (Figure 2.23). Note that this small difference in the arrangement of the atoms has a major effect on their respective chemical properties. You would certainly not want to use a solution of methyl formate as a substitute for a solution of acetic acid (vinegar) when you make salad dressing.
2 Lee Cronin, “Print Your Own Medicine,” Talk presented at TED Global 2012, Edinburgh, Scotland, June 2012.
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FIGURE 2.23 Molecules of (a) acetic acid and methyl formate (b) are structural isomers; they have the same formula (C2H4O2) but different structures (and therefore different chemical properties).
Many types of isomers exist (Figure 2.24). Acetic acid and methyl formate are structural isomers, compounds in which the molecules differ in how the atoms are connected to each other. There are also various types of spatial isomers, in which the relative orientations of the atoms in space can be different. For example, the compound carvone (found in caraway seeds, spearmint, and mandarin orange peels) consists of two isomers that are mirror images of each other. S-(+)-carvone smells like caraway, and R-(−)-carvone smells like spearmint.
FIGURE 2.24 Molecules of carvone are spatial isomers; they only differ in the relative orientations of the atoms in space. (credit bottom left: modification of work by “Miansari66”/Wikimedia Commons; credit bottom right: modification of work by Forest & Kim Starr)
LINK TO LEARNING
Select this link (http://openstax.org/l/16isomers) to view an explanation of isomers, spatial isomers, and why they have different smells (select the video titled “Mirror Molecule: Carvone”).
The Mole The identity of a substance is defined not only by the types of atoms or ions it contains, but by the quantity of each type of atom or ion. For example, water, H2O, and hydrogen peroxide, H2O2, are alike in that their respective molecules are composed of hydrogen and oxygen atoms. However, because a hydrogen peroxide molecule contains two oxygen atoms, as opposed to the water molecule, which has only one, the two
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substances exhibit very different properties. Today, we possess sophisticated instruments that allow the direct measurement of these defining microscopic traits; however, the same traits were originally derived from the measurement of macroscopic properties (the masses and volumes of bulk quantities of matter) using relatively simple tools (balances and volumetric glassware). This experimental approach required the introduction of a new unit for amount of substances, the mole, which remains indispensable in modern chemical science.
The mole is an amount unit similar to familiar units like pair, dozen, gross, etc. It provides a specific measure of the number of atoms or molecules in a sample of matter. One Latin connotation for the word “mole” is “large mass” or “bulk,” which is consistent with its use as the name for this unit. The mole provides a link between an easily measured macroscopic property, bulk mass, and an extremely important fundamental property, number of atoms, molecules, and so forth. A mole of substance is that amount in which there are 6.02214076 × 1023 discrete entities (atoms or molecules). This large number is a fundamental constant known as Avogadro's number (NA) or the Avogadro constant in honor of Italian scientist Amedeo Avogadro. This constant is properly reported with an explicit unit of “per mole,” a conveniently rounded version being 6.022 1023/mol.
Consistent with its definition as an amount unit, 1 mole of any element contains the same number of atoms as 1 mole of any other element. The masses of 1 mole of different elements, however, are different, since the masses of the individual atoms are drastically different. The molar mass of an element (or compound) is the mass in grams of 1 mole of that substance, a property expressed in units of grams per mole (g/mol) (see Figure 2.25).
FIGURE 2.25 Each sample contains 6.022 1023 atoms —1.00 mol of atoms. From left to right (top row): 65.4 g zinc, 12.0 g carbon, 24.3 g magnesium, and 63.5 g copper. From left to right (bottom row): 32.1 g sulfur, 28.1 g silicon, 207 g lead, and 118.7 g tin. (credit: modification of work by Mark Ott)
The molar mass of any substance is numerically equivalent to its atomic or formula weight in amu. Per the amu definition, a single 12C atom weighs 12 amu (its atomic mass is 12 amu). A mole of 12C atoms weighs 12 g (its molar mass is 12 g/mol). This relationship holds for all elements, since their atomic masses are measured relative to that of the amu-reference substance, 12C. Extending this principle, the molar mass of a compound in grams is likewise numerically equivalent to its formula mass in amu (Figure 2.26).
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2 • Atoms, Molecules, and Ions
FIGURE 2.26 Each sample contains 6.02 1023 molecules or formula units—1.00 mol of the compound or element. Clock-wise from the upper left: 130.2 g of C8H17OH (1-octanol, formula mass 130.2 amu), 454.4 g of HgI2 (mercury(II) iodide, formula mass 454.4 amu), 32.0 g of CH3OH (methanol, formula mass 32.0 amu) and 256.5 g of S8 (sulfur, formula mass 256.5 amu). (credit: Sahar Atwa)
Element Average Atomic Mass (amu) Molar Mass (g/mol) Atoms/Mole
C
12.01
12.01
6.022 1023
H
1.008
1.008
6.022 1023
O
16.00
16.00
6.022 1023
Na
22.99
22.99
6.022 1023
Cl
35.45
35.45
6.022 1023
While atomic mass and molar mass are numerically equivalent, keep in mind that they are vastly different in terms of scale, as represented by the vast difference in the magnitudes of their respective units (amu versus g). To appreciate the enormity of the mole, consider a small drop of water weighing about 0.03 g (see Figure 2.27). Although this represents just a tiny fraction of 1 mole of water (~18 g), it contains more water molecules than can be clearly imagined. If the molecules were distributed equally among the roughly seven billion people on earth, each person would receive more than 100 billion molecules.
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