MCAT General Chemistry Review (Kaplan) Guide PDF

MCAT® General Chemistry Review Edited by Alexander Stone Macnow, MD Table of Contents 1. MCAT® General Chemistry Review 1. Cover 1. Title Page 2. Table of Contents 3. The Kaplan MCAT Review Team 4. About Scientific American 5. About the MCAT 6. How This Book Was Created 7. Using This Book 2. Chapter 1: Atomic Structure 1. Atomic Structure 2. Introduction 3. 1.1 Subatomic Particles 4. 1.2 Atomic Mass vs. Atomic Weight 5. 1.3 Rutherford, Planck, and Bohr 6. 1.4 Quantum Mechanical Model of Atoms 7. Conclusion 8. Concept Summary 9. Answers to Concept Checks 10. Equations to Remember 11. Shared Concepts 12. Practice Questions 13. Answers and Explanations 3. Chapter 2: The Periodic Table 1. The Periodic Table 2. Introduction 3. 2.1 The Periodic Table 4. 2.2 Types of Elements 5. 2.3 Periodic Properties of the Elements 6. 2.4 The Chemistry of Groups 7. Conclusion 8. Concept Summary 9. Answers to Concept Checks 10. Shared Concepts 11. Practice Questions 12. Answers and Explanations 4. Chapter 3: Bonding and Chemical Interactions 1. Bonding and Chemical Interactions 2. Introduction 3. 3.1 Bonding 4. 3.2 Ionic Bonds 5. 3.3 Covalent Bonds 6. 3.4 Intermolecular Forces 7. Conclusion 8. Concept Summary 9. Answers to Concept Checks 10. Equations to Remember 11. Shared Concepts 12. Practice Questions 13. Answers and Explanations 5. Chapter 4: Compounds and Stoichiometry 1. Compounds and Stoichiometry 2. Introduction 3. 4.1 Molecules and Moles 4. 4.2 Representation of Compounds 5. 4.3 Types of Chemical Reactions 6. 4.4 Balancing Chemical Equations 7. 4.5 Applications of Stoichiometry 8. 4.6 Ions 9. Conclusion 10. Concept Summary 11. Answers to Concept Checks 12. Equations to Remember 13. Shared Concepts 14. Practice Questions 15. Answers and Explanations 6. Chapter 5: Chemical Kinetics 1. Chemical Kinetics 2. Introduction 3. 5.1 Chemical Kinetics 4. 5.2 Reaction Rates 5. Conclusion 6. Concept Summary 7. Answers to Concept Checks 8. Equations to Remember 9. Shared Concepts 10. Practice Questions 11. Answers and Explanations 7. Chapter 6: Equilibrium 1. Equilibrium 2. Introduction 3. 6.1 Equilibrium 4. 6.2 Le Châtelier’s Principle 5. 6.3 Kinetic and Thermodynamic Control 6. Conclusion 7. Concept Summary 8. Answers to Concept Checks 9. Equations to Remember 10. Shared Concepts 11. Practice Questions 12. Answers and Explanations 8. Chapter 7: Thermochemistry 1. Thermochemistry 2. Introduction 3. 7.1 Systems and Processes 4. 7.2 States and State Functions 5. 7.3 Heat 6. 7.4 Enthalpy 7. 7.5 Entropy 8. 7.6 Gibbs Free Energy 9. Conclusion 10. Concept Summary 11. Answers to Concept Checks 12. Equations to Remember 13. Shared Concepts 14. Practice Questions 15. Answers and Explanations 9. Chapter 8: The Gas Phase 1. The Gas Phase 2. Introduction 3. 8.1 The Gas Phase 4. 8.2 Ideal Gases 5. 8.3 Kinetic Molecular Theory 6. 8.4 Real Gases 7. Conclusion 8. Concept Summary 9. Answers to Concept Checks 10. Equations to Remember 11. Shared Concepts 12. Practice Questions 13. Answers and Explanations 10. Chapter 9: Solutions 1. Solutions 2. Introduction 3. 9.1 Nature of Solutions 4. 9.2 Concentration 5. 9.3 Solution Equilibria 6. 9.4 Colligative Properties 7. Conclusion 8. Concept Summary 9. Answers to Concept Checks 10. Equations to Remember 11. Shared Concepts 12. Practice Questions 13. Answers and Explanations 11. Chapter 10: Acids and Bases 1. Acids and Bases 2. Introduction 3. 10.1 Definitions 4. 10.2 Properties 5. 10.3 Polyvalence and Normality 6. 10.4 Titration and Buffers 7. Conclusion 8. Concept Summary 9. Answers to Concept Checks 10. Equations to Remember 11. Shared Concepts 12. Practice Questions 13. Answers and Explanations 12. Chapter 11: Oxidation–Reduction Reactions 1. Oxidation–Reduction Reactions 2. Introduction 3. 11.1 Oxidation–Reduction Reactions 4. 11.2 Net Ionic Equations 5. Conclusion 6. Concept Summary 7. Answers to Concept Checks 8. Shared Concepts 9. Practice Questions 10. Answers and Explanations 13. Chapter 12: Electrochemistry 1. Electrochemistry 2. Introduction 3. 12.1 Electrochemical Cells 4. 12.2 Cell Potentials 5. 12.3 Electromotive Force and Thermodynamics 6. Conclusion 7. Concept Summary 8. Answers to Concept Checks 9. Equations to Remember 10. Shared Concepts 11. Practice Questions 12. Answers and Explanations 14. About This Book 1. Copyright Information 2. Glossary 3. Index 4. Art Credits 5. Periodic Table of the Elements 6. Special Offer for Kaplan Students The Kaplan MCAT Review Team Alexander Stone Macnow, MD Editor-in-Chief Uneeb Qureshi Kaplan MCAT Faculty MCAT faculty reviewers Elmar R. Aliyev; James Burns; Jonathan Cornfield; Alisha Maureen Crowley; Nikolai Dorofeev, MD; Benjamin Downer, MS; Colin Doyle; M. Dominic Eggert; Marilyn Engle; Eleni M. Eren; Raef Ali Fadel; Tyra Hall-Pogar, PhD; Scott Huff; Samer T. Ismail; Elizabeth A. Kudlaty; Kelly Kyker-Snowman, MS; Ningfei Li; John P. Mahon; Matthew A. Meier; Nainika Nanda; Caroline Nkemdilim Opene; Kaitlyn E. Prenger; Derek Rusnak, MA; Kristen L. Russell, ME; Bela G. Starkman, PhD; Michael Paul Tomani, MS; Nicholas M. White; Kerranna Williamson, MBA; Allison Ann Wilkes, MS; and Tony Yu Thanks to Kim Bowers; Tim Eich; Samantha Fallon; Owen Farcy; Dan Frey; Robin Garmise; Rita Garthaffner; Joanna Graham; Adam Grey; Allison Harm; Beth Hoffberg; Aaron Lemon-Strauss; Keith Lubeley; Diane McGarvey; Petros Minasi; John Polstein; Deeangelee Pooran-Kublall, MD, MPH; Rochelle Rothstein, MD; Larry Rudman; Sylvia Tidwell Scheuring; Carly Schnur; Karin Tucker; Lee Weiss; and the countless others who made this project possible. About Scientific American Scientific American is at the heart of Nature Publishing Group’s consumer media division, meeting the needs of the general public. Founded in 1845, Scientific American is the longest continuously published magazine in the United States and the leading authoritative publication for science in the general media. In its history, 148 Nobel Prize scientists have contributed 240 articles to Scientific American, including Albert Einstein, Francis Crick, Stanley Prusiner, and Richard Axel. Together with scientificamerican.com and in translation in 14 languages around the world, it reaches more than 5 million consumers and scientists. Other titles include Scientific American Mind and Spektrum der Wissenschaft in Germany. Scientific American won a 2011 National Magazine Award for General Excellence. About the MCAT The structure of the four sections of the MCAT is shown below. Chemical and Physical Foundations of Biological Systems Time 95 minutes Format 59 questions 10 passages 44 questions are passage-based, and 15 are discrete (stand-alone) questions. Score between 118 and 132 What It Tests Biochemistry: 25% Biology: 5% General Chemistry: 30% Organic Chemistry: 15% Physics: 25% Critical Analysis and Reasoning Skills (CARS) Time 90 minutes Format 53 questions 9 passages All questions are passage-based. There are no discrete (stand-alone) questions. Score between 118 and 132 What It Tests Disciplines: Humanities: 50% Social Sciences: 50% Skills: Foundations of Comprehension: 30% Reasoning Within the Text: 30% Reasoning Beyond the Text: 40% Biological and Biochemical Foundations of Living Systems Time 95 minutes Format 59 questions 10 passages 44 questions are passage-based, and 15 are discrete (stand-alone) questions. Score between 118 and 132 What It Tests Biochemistry: 25% Biology: 65% General Chemistry: 5% Organic Chemistry: 5% Psychological, Social, and Biological Foundations of Behavior Time 95 minutes Format 59 questions 10 passages 44 questions are passage-based, and 15 are discrete (stand-alone) questions. Score between 118 and 132 What It Tests Biology: 5% Psychology: 65% Sociology: 30% Total Testing Time 375 minutes (6 hours, 15 minutes) Questions 230 Score 472 to 528 The MCAT also tests four Scientific Inquiry and Reasoning Skills (SIRS): 1. Knowledge of Scientific Concepts and Principles (35% of questions) 2. Scientific Reasoning and Problem-Solving (45% of questions) 3. Reasoning About the Design and Execution of Research (10% of questions) 4. Data-Based and Statistical Reasoning (10% of questions) The MCAT is a computer-based test (CBT) and is offered at Prometric centers during almost every month of the year. There are optional breaks between each section, and there is a lunch break between the second and third section of the exam. Register online for the MCAT at www.aamc.org/mcat. For further questions, contact the MCAT team at the Association of American Medical Colleges: MCAT Resource Center Association of American Medical Colleges (202) 828-0690 www.aamc.org/mcat [email protected] How This Book Was Created The Kaplan MCAT Review project began in November 2012 shortly after the release of the Preview Guide for the MCAT 2015 Exam, 2nd edition. Through thorough analysis by our staff psychometricians, we were able to analyze the relative yield of the different topics on the MCAT, and we began constructing tables of contents for the books of the Kaplan MCAT Review series. Writing of the books began in April 2013. A dedicated staff of 19 writers, 7 editors, and 32 proofreaders worked over 5000 combined hours to produce these books. The format of the books was heavily influenced by weekly meetings with Kaplan’s learning-science team. These books were submitted for publication in July 2014. For any updates after this date, please visit www.kaplanmcat.com. The information presented in these books covers everything listed on the official MCAT content lists—nothing more, nothing less. Every topic in these lists is covered in the same level of detail as is common to the undergraduate and postbaccalaureate classes that are considered prerequisites for the MCAT. Note that your premedical classes may cover topics not discussed in these books, or they may go into more depth than these books do. Additional exposure to science content is never a bad thing, but recognize that all of the content knowledge you are expected to have walking in on Test Day is covered in these books. If you have any questions about the content presented here, email [email protected]. For other questions not related to content, email [email protected]. Each book has been vetted through at least six rounds of review. To that end, the information presented is these books is true and accurate to the best of our knowledge. Still, your feedback helps us improve our prep materials. Please notify us of any inaccuracies or errors in the books by sending an email to [email protected]. Using This Book Kaplan MCAT General Chemistry Review, along with the other six books in the Kaplan MCAT Review series, brings the Kaplan classroom experience to you— right in your home, at your convenience. This book offers the same Kaplan content review, strategies, and practice that make Kaplan the #1 choice for MCAT prep. After all, twice as many doctors prepared with Kaplan for the MCAT than with any other course. This book is designed to help you review the general chemistry topics covered on the MCAT. Please understand that content review—no matter how thorough —is not sufficient preparation for the MCAT! The MCAT tests not only your science knowledge but also your critical reading, reasoning, and problem- solving skills. Do not assume that simply memorizing the contents of this book will earn you high scores on Test Day; to maximize your scores, you must also improve your reading and test-taking skills through MCAT-style questions and practice tests. MCAT CONCEPT CHECKS At the end of each section, you’ll find a few open-ended questions that you can use to assess your mastery of the material. These MCAT Concept Checks were introduced after multiple conversations with Kaplan’s learning-science team. Research has demonstrated repeatedly that introspection and self-analysis improve mastery, retention, and recall of material. Complete these MCAT Concept Checks to ensure that you’ve got the key points from each section before moving on! PRACTICE QUESTIONS At the end of each chapter, you’ll find 15 MCAT-style practice questions. These are designed to help you assess your understanding of the chapter you just read. Most of these questions focus on the first of the Scientific Inquiry and Reasoning Skills (Knowledge of Scientific Concepts and Principles), although there are occasional questions that fall into the second or fourth SIRS (Scientific Reasoning and Problem-Solving, and Data-Based and Statistical Reasoning, respectively). SIDEBARS The following is a guide to the five types of sidebars you’ll find in Kaplan MCAT General Chemistry Review: Bridge: These sidebars create connections between science topics that appear in multiple chapters throughout the Kaplan MCAT Review series. Key Concept: These sidebars draw attention to the most important takeaways in a given topic, and they sometimes offer synopses or overviews of complex information. If you understand nothing else, make sure you grasp the Key Concepts for any given subject. MCAT Expertise: These sidebars point out how information may be tested on the MCAT or offer key strategy points and test-taking tips that you should apply on Test Day. Mnemonic: These sidebars present memory devices to help recall certain facts. Real World: These sidebars illustrate how a concept in the text relates to the practice of medicine or the world at large. While this is not information you need to know for Test Day, many of the topics in Real World sidebars are excellent examples of how a concept may appear in a passage or discrete (stand-alone) question on the MCAT. This book also contains a thorough glossary and index for easy navigation of the text. In this end, this is your book, so write in the margins, draw diagrams, highlight the key points—do whatever is necessary to help you get that higher score. We look forward to working with you as you achieve your dreams and become the doctor you deserve to be! In This Chapter 1.1 Subatomic Particles Protons Neutrons Electrons 1.2 Atomic Mass vs. Atomic Weight Atomic Mass Atomic Weight 1.3 Rutherford, Planck, and Bohr Bohr Model Applications of the Bohr Model 1.4 Quantum Mechanical Model of Atoms Quantum Numbers Electron Configurations Hund’s Rule Valence Electrons Concept Summary Introduction Chemistry is the investigation of the atoms and molecules that make up our bodies, our possessions, the world around us, and the food that we eat. There are different branches of chemistry, three of which are tested directly on the MCAT: general (inorganic) chemistry, organic chemistry, and biochemistry. Ultimately, all investigations in chemistry are seeking to answer the questions that confront us in the form—the shape, structure, mode, and essence—of the physical world that surrounds us. Many students feel similarly about general chemistry and physics: But I’m premed!, they say. Why do I need to know any of this? What good will this be when I’m a doctor? Do I only need to know this for the MCAT? Recognize that to be an effective doctor, one must understand the physical building blocks that make up the human body. Pharmacologic treatment is based on chemistry; many diagnostic tests used every day detect changes in the chemistry of the body. So, let’s get down to the business of learning and remembering the principles of the physical world that help us understand what all this “stuff ” is, how it works, and why it behaves the way it does—at both the molecular and macroscopic levels. In the process of reading through these chapters and applying your knowledge to practice questions, you’ll prepare yourself for success not only on the Chemical and Physical Foundations of Biological Systems section of the MCAT but also in your future career as a physician. This first chapter starts our review of General Chemistry with a consideration of the fundamental unit of matter—the atom. First, we focus on the subatomic particles that make it up: protons, neutrons, and electrons. We will also review the Bohr and quantum mechanical models of the atom, with a particular focus on the similarities and differences between them. MCAT EXPERTISE The building blocks of the atom are also the building blocks of knowledge for the general chemistry concepts tested on the MCAT. By understanding these particles, we will be able to use that knowledge as the “nucleus” of understanding for all of general chemistry. 1.1 Subatomic Particles Although you may have encountered in your university-level chemistry classes such subatomic particles as quarks, leptons, and gluons, the MCAT’s approach to atomic structure is much simpler. There are three subatomic particles that you must understand: protons, neutrons, and electrons. Figure 1.1. Matter: From Macroscopic to Microscopic PROTONS Protons are found in the nucleus of an atom, as shown in Figure 1.1. Each proton has an amount of charge equal to the fundamental unit of charge (e = 1.6 × 10−19 C), and we denote this fundamental unit of charge as “+1 e” or simply “+1” for the proton. Protons have a mass of approximately one atomic mass unit (amu). The atomic number (Z) of an element, as shown in Figure 1.2, is equal to the number of protons found in an atom of that element. As such, it acts as a unique identifier for each element because elements are defined by the number of protons they contain. For example, all atoms of oxygen contain eight protons; all atoms of gadolinium contain 64 protons. While all atoms of a given element have the same atomic number, they do not necessarily have the same mass—as we will see in our discussion of isotopes. Figure 1.2. Potassium, from the Periodic Table Potassium has the symbol K (Latin: kalium), atomic number 19, and atomic weight of approximately 39.1. NEUTRONS Neutrons, as the name implies, are neutral—they have no charge. A neutron’s mass is only slightly larger than that of the proton, and together, the protons and the neutrons of the nucleus make up almost the entire mass of an atom. Every atom has a characteristic mass number (A), which is the sum of the protons and neutrons in the atom’s nucleus. A given element can have a variable number of neutrons; thus, while atoms of the same element always have the same atomic number, they do not necessarily have the same mass number. Atoms that share an atomic number but have different mass numbers are known as isotopes of the element, as shown in Figure 1.3. For example, carbon (Z = 6) has three naturally occurring isotopes: 12 13 6 C, with six protons and six neutrons; 6 C, with six protons and seven neutrons; and 14 6 C, with six protons and eight neutrons. The convention ZAX is used to show both the atomic number (Z) and the mass number (A) of atom X. Figure 1.3. Various Isotopes of Hydrogen Atoms of the same element have the same atomic number (Z = 1), but may have varying mass numbers (Az = 1, 2, or 3). ELECTRONS Electrons move through the space surrounding the nucleus and are associated with varying levels of energy. Each electron has a charge equal in magnitude to that of a proton, but with the opposite (negative) sign, denoted by “−1 e” or simply “–e.” The mass of an electron is approximately that of a proton. Because subatomic particles’ masses are so small, the electrostatic force of attraction between the unlike charges of the proton and electron is far greater than the gravitational force of attraction based on their respective masses. Electrons move around the nucleus at varying distances, which correspond to varying levels of electrical potential energy. The electrons closer to the nucleus are at lower energy levels, while those that are further out (in higher shells) have higher energy. The electrons that are farthest from the nucleus have the strongest interactions with the surrounding environment and the weakest interactions with the nucleus. These electrons are called valence electrons; they are much more likely to become involved in bonds with other atoms because they experience the least electrostatic pull from their own nucleus. Generally speaking, the valence electrons determine the reactivity of an atom. As we will discuss in Chapter 3 of MCAT General Chemistry Review, the sharing of these valence electrons in covalent bonds allows elements to fill their highest energy level to increase stability. In the neutral state, there are equal numbers of protons and electrons; losing electrons results in the atom gaining a positive charge, while gaining electrons results in the atom gaining a negative charge. A positively charged atom is called a cation, and a negatively charged atom is called an anion. BRIDGE Valence electrons will be very important to us in both general and organic chemistry. Knowing how tightly held those electrons are will allow us to understand many of an atom’s properties and how it interacts with other atoms, especially in bonding. Bonding is so important that it is discussed in Chapter 3 of both MCAT General Chemistry Review and MCAT Organic Chemistry Review. Some basic features of the three subatomic particles are shown in Table 1.1. Subatomic Particle Symbol Relative Mass Charge Location Proton p, p+, or 11H 1 +1 Nucleus Neutron n0 or 01n 1 0 Nucleus Electron e− or −10e 0 −1 Orbitals Table 1.1. Subatomic Particles Example: Determine the number of protons, neutrons, and electrons in a nickel-58 atom and in a nickel-60 +2 cation. Solution: 58Ni has an atomic number of 28 and a mass number of 58. Therefore, 58Ni will have 28 protons, 28 electrons, and 58 – 28, or 30, neutrons. 60Ni2+ has the same number of protons as the neutral 58Ni atom. However, 60Ni2+ has a positive charge because it has lost two electrons; 2+ thus, Ni2+ will have 26 electrons. Also, the mass number is two units higher than for the 58Ni atom, and this difference in mass must be due to two extra neutrons; thus, it has a total of 32 neutrons. MCAT Concept Check 1.1: Before you move on, assess your understanding of the material with these questions. 1. Which subatomic particle is the most important for determining each of the following properties of an atom? Charge: Atomic number: Isotope: 2. In nuclear medicine, isotopes are created and used for various purposes; for instance, 18O is created from 18F. Determine the number of protons, neutrons, and electrons in each of these species. Particle Protons Neutrons Electrons 18O 18F 1.2 Atomic Mass vs. Atomic Weight There are a few different terms used by chemists to describe the heaviness of an element: atomic mass and mass number, which are essentially synonymous, and atomic weight. While the atomic weight is a constant for a given element and is reported in the Periodic Table, the atomic mass or mass number varies from one isotope to another. In this section, carefully compare and contrast the different definitions of these terms—because they are similar, they can be easy to mix up on the MCAT. KEY CONCEPT Atomic number (Z) = number of protons Mass number (A) = number of protons + number of neutrons Number of protons = number of electrons (in a neutral atom) Electrons are not included in mass calculations because they are much smaller. ATOMIC MASS As we’ve seen, the mass of one proton is approximately one amu. The size of the atomic mass unit is defined as exactly the mass of the carbon-12 atom, approximately 1.66 × 10−24 g. Because the carbon-12 nucleus has six protons and six neutrons, an amu is approximately equal to the mass of a proton or a neutron. The difference in mass between protons and neutrons is extremely small; in fact, it is roughly equal to the mass of an electron. The atomic mass of an atom (in amu) is nearly equal to its mass number, the sum of protons and neutrons (in reality, some mass is lost as binding energy, as discussed in Chapter 9 of MCAT Physics and Math Review). Atoms of the same element with varying mass numbers are called isotopes (from the Greek for “same place”). Isotopes differ in their number of neutrons and are referred to by the name of the element followed by the mass number; for example, carbon-12 or iodine-131. Only the three isotopes of hydrogen, shown in Figure 1.3, are given unique names: protium (Greek: “first”) has one proton and an atomic mass of 1 amu; deuterium (“second”) has one proton and one neutron and an atomic mass of 2 amu; tritium (“third”) has one proton and two neutrons and an atomic mass of 3 amu. Because isotopes have the same number of protons and electrons, they generally exhibit similar chemical properties. ATOMIC WEIGHT In nature, almost all elements exist as two or more isotopes, and these isotopes are usually present in the same proportions in any sample of a naturally occurring element. The weighted average of these different isotopes is referred to as the atomic weight and is the number reported on the Periodic Table. For example, chlorine has two main naturally occurring isotopes: chlorine-35 and chlorine-37. Chlorine-35 is about three times more abundant than chlorine-37; therefore, the atomic weight of chlorine is closer to 35 than 37. On the Periodic Table, it is listed as 35.5. Figure 1.4 illustrates the half-lives of the different isotopes of the elements; because half-life corresponds with stability, it also helps determine the relative proportions of these different isotopes. Figure 1.4. Half-Lives of the Different Isotopes of Elements Half-life is a marker of stability; generally, longer-lasting isotopes are more abundant. KEY CONCEPT When an element has two or more isotopes, no one isotope will have a mass exactly equal to the element’s atomic weight. Bromine, for example, is listed in the Periodic Table as having a mass of 79.9 amu. This is an average of the two naturally occurring isotopes, bromine-79 and bromine-81, which occur in almost equal proportions. There are no bromine atoms with an actual mass of 79.9 amu. The utility of the atomic weight is that it represents both the mass of the “average” atom of that element, in amu, and the mass of one mole of the element, in grams. A mole is a number of “things” (atoms, ions, molecules) equal to Avogadro’s number, N A = 6.02 × 1023. For example, the atomic weight of carbon is which means that the average carbon atom has a mass of 12.0 amu (carbon-12 is far more abundant than carbon-13 or carbon-14), and 6.02 × 1023 carbon atoms have a combined mass of 12.0 grams. MNEMONIC Atomic mass is nearly synonymous with mass number. Atomic weight is a weighted average of naturally occurring isotopes of that element. Example: Element Q consists of three different isotopes: A, B, andC. Isotope A has an atomic mass of 40 amu and accounts for 60 percent of naturally occurring Q. Isotope B has an atomic mass of 44 amu and accounts for 25 percent of Q. Finally, isotope C has an atomic mass of 41 amu and accounts for 15 percent of Q. What is the atomic weight of element Q? Solution: The atomic weight is the weighted average of the naturally occurring isotopes of that element. 0.60 (40 amu) + 0.25 (44 amu) + 0.15 (41 amu) = 24.00 amu + 11.00 amu + 6.15 amu = 41.15 amu. The atomic weight of element Q is MCAT Concept Check 1.2: Before you move on, assess your understanding of the material with these questions. 1. What are the definitions of atomic mass and atomic weight? Atomic mass: Atomic weight: 2. While mass is typically written in grams per mole is the ratio moles per gram also acceptable? 3. Calculate and compare the subatomic particles that make up the following atoms. Isotope Protons Neutrons Electrons 19O 16O 17O 19F 16F 238U 240U 1.3 Rutherford, Planck, and Bohr In 1910, Ernest Rutherford provided experimental evidence that an atom has a dense, positively charged nucleus that accounts for only a small portion of the atom’s volume. Eleven years earlier, Max Planck developed the first quantum theory, proposing that energy emitted as electromagnetic radiation from matter comes in discrete bundles called quanta. The energy of a quantum, he determined, is given by the Planck relation: E = hf Equation 1.1 where h is a proportionality constant known as Planck’s constant, equal to 6.626 × 10−34 J·s, and f (sometimes designated by the Greek letter nu, ν) is the frequency of the radiation. BRIDGE Recall from Chapter 8 of MCAT Physics Review that the speed of light (or any wave) can be calculated using v = fλ. The speed of light, c, is This equation can be incorporated into the equation for quantum energy to provide different derivations. BOHR MODEL In 1913, Danish physicist Niels Bohr used the work of Rutherford and Planck to develop his model of the electronic structure of the hydrogen atom. Starting from Rutherford’s findings, Bohr assumed that the hydrogen atom consisted of a central proton around which an electron traveled in a circular orbit. He postulated that the centripetal force acting on the electron as it revolved around the nucleus was created by the electrostatic force between the positively charged proton and the negatively charged electron. Bohr used Planck’s quantum theory to correct certain assumptions that classical physics made about the pathways of electrons. Classical mechanics postulates that an object revolving in a circle, such as an electron, may assume an infinite number of values for its radius and velocity. The angular momentum (L = mvr) and kinetic energy of the object could therefore take on any value. However, by incorporating Planck’s quantum theory into his model, Bohr placed restrictions on the possible values of the angular momentum. Bohr predicted that the possible values for the angular momentum of an electron orbiting a hydrogen nucleus could be given by: Equation 1.2 where n is the principal quantum number, which can be any positive integer, and h is Planck’s constant. Because the only variable is the principal quantum number, the angular momentum of an electron changes only in discrete amounts with respect to the principal quantum number. Note the similarities between quantized angular momentum and Planck’s concept of quantized energy. MCAT EXPERTISE When you see a formula in your review or on Test Day, focus on ratios and relationships. This simplifies our calculations to a conceptual understanding, which is usually enough to lead us to the right answer. Further, the MCAT tends to ask how changes in one variable may affect another variable, rather than a plug-and-chug application of complex equations. Bohr then related the permitted angular momentum values to the energy of the electron to obtain: Equation 1.3 where RH is the experimentally determined Rydberg unit of energy, equal to Therefore, like angular momentum, the energy of the electron changes in discrete amounts with respect to the quantum number. A value of zero energy was assigned to the state in which the proton and electron are separated completely, meaning that there is no attractive force between them. Therefore, the electron in any of its quantized states in the atom will have an attractive force toward the proton; this is represented by the negative sign in Equation 1.3. Ultimately, the only thing the energy equation is saying is that the energy of an electron increases—becomes less negative—the farther out from the nucleus that it is located (increasing n). This is an important point: while the magnitude of the fraction is getting smaller, the actual value it represents is getting larger (becoming less negative). KEY CONCEPT At first glance, it may not be clear that the energy (E) is directly proportional to the principal quantum number (n) in Equation 1.3. Take notice of the negative sign, which causes the values to approach zero from a more negative value as n increases (thereby increasing the energy). Negative signs are as important as a variable’s location in a fraction when it comes to determining proportionality. Think of the concept of quantized energy as being similar to the change in gravitational potential energy that you experience when you ascend or descend a flight of stairs. Unlike a ramp, on which you could take an infinite number of steps associated with a continuum of potential energy changes, a staircase only allows you certain changes in height and, as a result, allows only certain discrete (quantized) changes of potential energy. Bohr came to describe the structure of the hydrogen atom as a nucleus with one proton forming a dense core, around which a single electron revolved in a defined pathway (orbit) at a discrete energy value. If one could transfer an amount of energy exactly equal to the difference between one orbit and another, this could result in the electron “jumping” from one orbit to a higher-energy one. These orbits had increasing radii, and the orbit with the smallest, lowest-energy radius was defined as the ground state (n = 1). More generally, the ground state of an atom is the state of lowest energy, in which all electrons are in the lowest possible orbitals. In Bohr’s model, the electron was promoted to an orbit with a larger radius (higher energy), the atom was said to be in the excited state. In general, an atom is in an excited state when at least one electron has moved to a subshell of higher than normal energy. Bohr likened his model of the hydrogen atom to the planets orbiting the sun, in which each planet traveled along a roughly circular pathway at set distances—and energy values—from the sun. Bohr’s Nobel Prize-winning model was reconsidered over the next two decades, but remains an important conceptualization of atomic behavior. In particular, remember that we now know that electrons are not restricted to specific pathways, but tend to be localized in certain regions of space. MCAT EXPERTISE Note that all systems tend toward minimal energy; thus on the MCAT, atoms of any element will generally exist in the ground state unless subjected to extremely high temperatures or irradiation. APPLICATIONS OF THE BOHR MODEL The Bohr model of the hydrogen atom (and other one-electron systems, such as He+ and Li2+) is useful for explaining the atomic emission and absorption spectra of atoms. MNEMONIC As electrons go from a lower energy level to a higher energy level, they get AHED: Absorb light Higher potential Excited Distant (from the nucleus) Atomic Emission Spectra At room temperature, the majority of atoms in a sample are in the ground state. However, electrons can be excited to higher energy levels by heat or other energy forms to yield excited states. Because the lifetime of an excited state is brief, the electrons will return rapidly to the ground state, resulting in the emission of discrete amounts of energy in the form of photons, as shown in Figure 1.5. Figure 1.5. Atomic Emission of a Photon as a Result of a Ground State Transition The electromagnetic energy of these photons can be determined using the following equation: Equation 1.4 where h is Planck’s constant, c is the speed of light in a vacuum and λ is the wavelength of the radiation. Note that Equation 1.4 is just a combination of two other equations: E = hf and c = f λ. The electrons in an atom can be excited to different energy levels. When these electrons return to their ground states, each will emit a photon with a wavelength characteristic of the specific energy transition it undergoes. As described above, these energy transitions do not form a continuum, but rather are quantized to certain values. Thus, the spectrum is composed of light at specified frequencies. It is sometimes called a line spectrum, where each line on the emission spectrum corresponds to a specific electron transition. Because each element can have its electrons excited to a different set of distinct energy levels, each possesses a unique atomic emission spectrum, which can be used as a fingerprint for the element. One particular application of atomic emission spectroscopy is in the analysis of stars and planets: while a physical sample may be impossible to procure, the light from a star can be resolved into its component wavelengths, which are then matched to the known line spectra of the elements as shown in Figure 1.6. Figure 1.6. Line Spectrum with Transition Wavelengths for Various Celestial Bodies REAL WORLD Emissions from electrons dropping from an excited state to a ground state give rise to fluorescence. What we see is the color of the emitted light. The Bohr model of the hydrogen atom explained the atomic emission spectrum of hydrogen, which is the simplest emission spectrum among all the elements. The group of hydrogen emission lines corresponding to transitions from energy levels n ≥ 2 to n = 1 is known as the Lyman series. The group corresponding to transitions from energy levels n ≥ 3 to n = 2 is known as the Balmer series, and includes four wavelengths in the visible region. The Lyman series includes larger energy transitions than the Balmer series; it therefore has shorter photon wavelengths in the UV region of the electromagnetic spectrum. The Paschen series corresponds to transitions from n ≥ 4 to n = 3. These energy transition series can be seen in Figure 1.7. Figure 1.7. Wavelengths of Electron Orbital Transitions Energy is inversely proportional to wavelength: The energy associated with a change in the principal quantum number from a higher initial value ni to a lower final value nf is equal to the energy of the photon predicted by Planck’s quantum theory. Combining Bohr’s and Planck’s calculations, we can derive: Equation 1.5 This complex-appearing equation essentially says: The energy of the emitted photon corresponds to the difference in energy between the higher-energy initial state and the lower-energy final state. KEY CONCEPT This equation is nothing new; it is simply derived from conservation of energy by setting the energy of a photon equal to the energy of the electron transition (from ). Note that unlike other equations, this is initial minus final; the negative sign in the equation accounts for absorption and emission. Thus, a positive E corresponds to emission, and a negative E corresponds to absorption. Atomic Absorption Spectra When an electron is excited to a higher energy level, it must absorb exactly the right amount of energy to make that transition. This means that exciting the electrons of a particular element results in energy absorption at specific wavelengths. Thus, in addition to a unique emission spectrum, every element possesses a characteristic absorption spectrum. Not surprisingly, the wavelengths of absorption correspond exactly to the wavelengths of emission because the difference in energy between levels remains unchanged. Identification of elements in the gas phase requires absorption spectra. BRIDGE ΔE is the same for absorption or emission between any two energy levels according to the conservation of energy, as discussed in Chapter 2 of MCAT Physics and Math Review. This is also the same as the energy of the photon of light absorbed or emitted. Atomic emission and absorption spectra are complex topics, but the takeaway is that each element has a characteristic set of energy levels. For electrons to move from a lower energy level to a higher energy level, they must absorb the right amount of energy to do so. They absorb this energy in the form of light. Similarly, when electrons move from a higher energy level to a lower energy level, they emit the same amount of energy in the form of light. REAL WORLD Absorption is the basis for the color of compounds. We see the color of the light that is not absorbed by the compound. MCAT Concept Check 1.3: Before you move on, assess your understanding of the material with these questions. Note: For these questions, try to estimate the calculations without a calculator to mimic Test Day conditions. Double-check your answers with a calculator and refer to the answers for confirmation of your results. 1. The valence electron in a lithium atom jumps from energy level n = 2 to n = 4. What is the energy of this transition in joules? In eV? (Note: 2. If an electron emits 3 eV of energy, what is the corresponding wavelength of the emitted photon? (Note: 1 eV = 1.60 × 10−19 J, h = 6.626 × 10−34 J · s) 3. Calculate the energy of a photon of wavelength 662 nm. (Note: h = 6.626 × 10−34 J · s) 1.4 Quantum Mechanical Model of Atoms While Bohr’s model marked a significant advancement in the understanding of the structure of atoms, his model ultimately proved inadequate to explain the structure and behavior of atoms containing more than one electron. The model’s failure was a result of not taking into account the repulsion between multiple electrons surrounding the nucleus. Modern quantum mechanics has led to a more rigorous and generalizable study of the electronic structure of atoms. The most important difference between Bohr’s model and the modern quantum mechanical model is that Bohr postulated that electrons follow a clearly defined circular pathway or orbit at a fixed distance from the nucleus, whereas modern quantum mechanics has shown that this is not the case. Rather, we now understand that electrons move rapidly and are localized within regions of space around the nucleus called orbitals. The confidence by which those in Bohr’s time believed they could identify the location (or pathway) of the electron was now replaced by a more modest suggestion that the best we can do is describe the probability of finding an electron within a given region of space surrounding the nucleus. In the current quantum mechanical model, it is impossible to pinpoint exactly where an electron is at any given moment in time. This is expressed best by the Heisenberg uncertainty principle: It is impossible to simultaneously determine, with perfect accuracy, the momentum and the position of an electron. If we want to assess the position of an electron, the electron has to stop (thereby removing its momentum); if we want to assess its momentum, the electron has to be moving (thereby changing its position). This can be seen visually in Figure 1.8. Figure 1.8. Heisenberg Uncertainty Principle Known momentum and uncertain position (left); known position but uncertain momentum (right). λ = confidence interval of position; px = confidence interval of momentum. QUANTUM NUMBERS Modern atomic theory postulates that any electron in an atom can be completely described by four quantum numbers: n, l, ml, and ms. Furthermore, according to the Pauli exclusion principle, no two electrons in a given atom can possess the same set of four quantum numbers. The position and energy of an electron described by its quantum numbers is known as its energy state. The value of n limits the values of l, which in turn limit the values of ml. In other words, for a given value of n, only particular values of l are permissible; given a value of l, only particular values of ml are permissible. The values of the quantum numbers qualitatively give information about the orientation of the orbitals. As we examine the four quantum numbers more closely, pay attention especially to l and ml because these two tend to give students the greatest difficulty. MCAT EXPERTISE Think of the quantum numbers as becoming more specific as one goes from n to l to ml to ms. This is like an address: one lives in a particular state (n), in a particular city (l), on a particular street (ml), at a particular house number (ms). Principal Quantum Number The first quantum number is commonly known as the principal quantum number and is denoted by the letter n. This is the quantum number used in Bohr’s model that can theoretically take on any positive integer value. The larger the integer value of n, the higher the energy level and radius of the electron’s shell. Within each shell, there is a capacity to hold a certain number of electrons, given by: Maximum number of electrons within a shell = 2n 2 Equation 1.6 where n is the principal quantum number. The difference in energy between two shells decreases as the distance from the nucleus increases because the energy difference is a function of For example, the energy difference between the n = 3 and the n = 4 shells is less than the energy difference between the n = 1 and the shells. This can be seen in Figure 1.7. Remember that electrons do not travel in precisely defined orbits; it just simplifies the visual representation of the electrons’ motion. BRIDGE Remember, a larger integer value for the principal quantum number indicates a larger radius and higher energy. This is similar to gravitational potential energy, as discussed in Chapter 2 of MCAT Physics Review, where the higher or farther the object is above the Earth, the higher its potential energy will be. Azimuthal Quantum Number The second quantum number is called the azimuthal (angular momentum) quantum number and is designated by the letter l. The second quantum number refers to the shape and number of subshells within a given principal energy level (shell). The azimuthal quantum number is very important because it has important implications for chemical bonding and bond angles. The value of n limits the value of l in the following way: for any given value of n, the range of possible values for l is 0 to (n – 1). For example, within the first principal energy level, n = 1, the only possible value for l is 0; within the second principal energy level, n = 2, the possible values for l are 0 and 1. A simpler way to remember this relationship is that the n-value also tells you the number of possible subshells. Therefore, there’s only one subshell (l = 0) in the first principal energy level; there are two subshells (l = 0 and 1) within the second principal energy level; there are three subshells (l = 0, 1, and 2) within the third principal energy level, and so on. KEY CONCEPT For any principal quantum number n, there will be n possible values for l, ranging from 0 to (n – 1). Spectroscopic notation refers to the shorthand representation of the principal and azimuthal quantum numbers. The principal quantum number remains a number, but the azimuthal quantum number is designated by a letter: the l = 0 subshell is called s; the l = 1 subshell is called p; the l = 2 subshell is called d; and the l = 3 subshell is called f. Thus, an electron in the shell n = 4 and subshell l = 2 is said to be in the 4d subshell. The spectroscopic notation for each subshell is demonstrated in Figure 1.9. Figure 1.9. Spectroscopic Notation for Every Subshell on the Periodic Table Within each subshell, there is a capacity to hold a certain number of electrons, given by: Maximum number of electrons within a subshell = 4l + 2 Equation 1.7 where l is the azimuthal quantum number. The energies of the subshells increase with increasing l value; however, the energies of subshells from different principal energy levels may overlap. For example, the 4s subshell will have a lower energy than the 3d subshell. Figure 1.10 provides an example of computer-generated probability maps of the first few electron clouds in a hydrogen atom. This provides a rough visual representation of the shapes of different subshells. Figure 1.10. Electron Clouds of Various Subshells Magnetic Quantum Number The third quantum number is the magnetic quantum number and is designated ml. The magnetic quantum number specifies the particular orbital within a subshell where an electron is most likely to be found at a given moment in time. Each orbital can hold a maximum of two electrons. The possible values of ml are the integers between –l and +l, including 0. For example, the s subshell, with l = 0, limits the possible ml values to 0, and because there is a single value of ml, there is only one orbital in the s subshell. The p subshell, with l = 1, limits the possible ml values to −1, 0, and +1, and because there are three values for ml, there are three orbitals in the p subshell. The d subshell has five orbitals (−2 to +2), and the f subshell has seven orbitals (−3 to +3). The shape of the orbitals, like the number of orbitals, is dependent on the subshell in which they are found. The orbitals in the s subshell are spherical, while the three orbitals in the p subshell are each dumbbell-shaped and align along the x-, y-, and z-axes. In fact, the p-orbitals are often referred to as px, py, and pz. The first five orbitals—1s, 2s, 2px, 2py, and 2pz—are demonstrated in Figure 1.11. Note the similarity to the images in Figure 1.10. Figure 1.11. The First Five Atomic Orbitals KEY CONCEPT For any value of l, there will be 2l + 1 possible values for ml. For any n, this produces n2 orbitals. For any value of n, there will be a maximum of 2n2 electrons (two per orbital). The shapes of the orbitals in the d and f subshells are much more complex, and the MCAT will not expect you to answer questions about their appearance. The shapes of orbitals are defined in terms of a concept called probability density, the likelihood that an electron will be found in a particular region of space. Take a look at the 2p block in the Periodic Table. As mentioned above, 2p contains three orbitals. If each orbital can contain two electrons, then six electrons can be added during the course of filling the 2p-orbitals. As atomic number increases, so does the number of electrons (assuming the species is neutral). Therefore, it should be no surprise that the p block contains six groups of elements. The s block contains two elements in each row of the Periodic Table, the d block contains ten elements, and the f block contains fourteen elements. Spin Quantum Number The fourth quantum number is called the spin quantum number and is denoted by ms. In classical mechanics, an object spinning about its axis has an infinite number of possible values for its angular momentum. However, this does not apply to the electron, which has two spin orientations designated and Whenever two electrons are in the same orbital, they must have opposite spins. In this case, they are often referred to as being paired. Electrons in different orbitals with the same ms values are said to have parallel spins. The quantum numbers for the orbitals in the second principal energy level, with their maximum number of electrons noted in parentheses, are shown in Table 1.2. n 2 (8) l 0 (2) 1 (6) ml 0 (2) +1 (2) 0 (2) −1(2) ms Table 1.2. Quantum Numbers for the Second Principal Energy Level ELECTRON CONFIGURATIONS For a given atom or ion, the pattern by which subshells are filled, as well as the number of electrons within each principal energy level and subshell, are designated by its electron configuration. Electron configurations use spectroscopic notation, wherein the first number denotes the principal energy level, the letter designates the subshell, and the superscript gives the number of electrons in that subshell. For example, 2p4 indicates that there are four electrons in the second (p) subshell of the second principal energy level. This also implies that the energy levels below 2p (that is, 1s and 2s) have already been filled, as shown in Figure 1.12. Figure 1.12. Electron Subshell Flow Diagram MCAT EXPERTISE Remember that the shorthand used to describe the electron configuration is derived directly from the quantum numbers. To write out an atom’s electron configuration, one needs to know the order in which subshells are filled. Electrons fill from lower- to higher-energy subshells, according to the building-up principle (also called the Aufbau principle), and each subshell will fill completely before electrons begin to enter the next one. The order need not be memorized because there are two very helpful ways of recalling this. The (n + l) rule can be used to rank subshells by increasing energy. This rule states that the lower the sum of the values of the first and second quantum numbers (n + l), the lower the energy of the subshell. This is a helpful rule to remember for Test Day. If two subshells possess the same (n + l) value, the subshell with the lower n value has a lower energy and will fill with electrons first. Example: Which will fill first, the 5d subshell or the 6s subshell? Solution: For 5d, n = 5 and l = 2, so (n + l) = 7. For 6s, n = 6 and l = 0, so (n + l) = 6. Therefore, the 6s subshell has lower energy and will fill first. An alternative way to approach electron configurations is through simply reading the Periodic Table. One must remember that the lowest s subshell is 1s, the lowest p subshell is 2p, the lowest d subshell is 3d, and the lowest f subshell is 4f. This can be seen in Figure 1.9 earlier. Then, we can simply read across the Periodic Table to get to the element of interest, filling subshells along the way. To do this, we must know the correct position of the lanthanide and actinide series (the f block), as shown in Figure 1.13. In most representations of the Periodic Table, the f block is pulled out and placed below the rest of the Table. This is purely an effect of graphic design—placing the f block in its correct location results in a lot of excess white space on a page. Figure 1.13. Periodic Table with Lanthanide and Actinide Series Inserted The f block fits between the s block and d block in the Periodic Table. MCAT EXPERTISE Many general chemistry courses teach the flow diagram in Figure 1.12 as a method to determine the order of subshell filling in electron configurations. However, on Test Day, it can be both time-consuming and error-prone, resulting in incorrect electron configurations. Learning to read the Periodic Table, as described here, is the best method. Electron configurations can be abbreviated by placing the noble gas that precedes the element of interest in brackets. For example, the electron configuration of any element in period four (starting with potassium) can be abbreviated by starting with [Ar]. Example: What is the electron configuration of osmium (Z = 76)? Solution: The noble gas that comes just before osmium is xenon (Z = 54). Therefore, the electron configuration can begin with [Xe]. Continuing across the Periodic Table, we pass through the 6s subshell (cesium and barium), the 4f subshell (the lanthanide series; remember its position on the Periodic Table!), and into the 5d subshell. Osmium is the sixth element in the 5d subshell, so the configuration is [Xe] 6s24f145d6 This method works for neutral atoms, but how does one write the electron configuration of an ion? Negatively charged ions (anions) have additional electrons that fill according to the same rules as above; for example, if fluorine’s electron configuration is [He] 2s22p5, then F– is [He] 2s22p6. Positively charged ions (cations) are a bit more complicated: start with the neutral atom, and remove electrons from the subshells with the highest value for n first. If multiple subshells are tied for the highest n value, then electrons are removed from the subshell with the highest l value among these. Example: What is the electron configuration of Fe3+? Solution: The electron configuration of iron is [Ar] 4s23d6. Electrons are removed from the 4s subshell before the 3d subshell because it has a higher principal quantum number. Therefore, Fe3+ has a configuration of [Ar] 3d5, not [Ar] 4s23d3. HUND’S RULE In subshells that contain more than one orbital, such as the 2p subshell with its three orbitals, the orbitals will fill according to Hund’s rule, which states that, within a given subshell, orbitals are filled such that there are a maximum number of half-filled orbitals with parallel spins. Like finding a seat on a crowded bus, electrons would prefer to have their own seat (orbital) before being forced to double up with another electron. Of course, the basis for this preference is electron repulsion: electrons in the same orbital tend to be closer to each other and thus repel each other more than electrons placed in different orbitals. Example: According to Hund’s rule, what are the orbital diagrams for nitrogen and iron? Solution: Nitrogen has an atomic number of 7. Thus, its electron configuration is 1s22s22p3. According to Hund’s rule, the two s-orbitals will fill completely, while the three p-orbitals will each contain one electron, all with parallel spins. Iron has an atomic number of 26. As determined earlier, its electron configuration is [Ar] 4s23d6. The electrons will fill all of the subshells except for the 3d, which will contain four orbitals with parallel (upward) spin and one orbital with electrons of both spin directions. Subshells may be listed either in the order in which they fill (4s before 3d) or with subshells of the same principal quantum number grouped together, as shown here. Both methods are correct. An important corollary from Hund’s rule is that half-filled and fully filled orbitals have lower energies (higher stability) than other states. This creates two notable exceptions to electron configuration that are often tested on the MCAT: chromium (and other elements in its group) and copper (and other elements in its group). Chromium (Z = 24) should have the electron configuration [Ar] 4s23d4 according to the rules established earlier. However, moving one electron from the 4s subshell to the 3d subshell allows the 3d subshell to be half-filled: [Ar] 4s13d5 (remember that s subshells can hold two electrons and d subshells can hold ten). While moving the 4s electron up to the 3d-orbital is energetically unfavorable, the extra stability from making the 3d subshell half-filled outweighs that cost. Similarly, copper (Z = 29) has the electron configuration [Ar] 4s13d10, rather than [Ar] 4s23d9; a full d subshell outweighs the cost of moving an electron out of the 4s subshell. Other elements in the same group have similar behavior, moving one electron from the highest s subshell to the highest d subshell. Similar shifts can be seen with f subshells, but they are never observed for the p subshell; the extra stability doesn’t outweigh the cost. The presence of paired or unpaired electrons affects the chemical and magnetic properties of an atom or molecule. Materials composed of atoms with unpaired electrons will orient their spins in alignment with a magnetic field, and the material will thus be weakly attracted to the magnetic field. These materials are considered paramagnetic. An example is shown in Figure 1.14 where a ferrofluid (colloidal liquid containing a surfactant and paramagnetic particles) is influenced by the magnet beneath a glass slide. The spikes emanating from the fluid contain magnetite (an iron oxide) which is orienting along the magnetic field lines. This is similar to a typical iron filing and magnet demonstration. Figure 1.14. Paramagnetic Ferrofluid MNEMONIC Remember that paramagnetic means that a magnetic field will cause parallel spins in unpaired electrons and therefore cause an attraction. Materials consisting of atoms that have all paired electrons will be slightly repelled by a magnetic field and are said to be diamagnetic. In Figure 1.15, a piece of pyrolytic graphite is suspended in the air over strong neodymium magnets. All the electrons in this allotrope (configuration) of carbon are paired because of covalent bonding between layers of the material, and are thus opposed to being reoriented. Given sufficiently strong magnetic fields beneath an object, any diamagnetic substance can be made to levitate. Figure 1.15. Diamagnetic Pyrolytic Graphite REAL WORLD The concept behind “maglev” or magnetic levitation is no longer science fiction. Using powerful magnetic fields and strongly diamagnetic materials, some transportation systems have developed frictionless, high speed rail networks such as Japan’s SCMaglev. VALENCE ELECTRONS The valence electrons of an atom are those electrons that are in its outermost energy shell, are most easily removed, and are available for bonding. In other words, the valence electrons are the “active” electrons of an atom and to a large extent dominate the chemical behavior of the atom. For elements in Groups IA and IIA (Groups 1 and 2), only the highest s subshell electrons are valence electrons. For elements in Groups IIIA through VIIIA (Groups 13 through 18), the highest s and p subshell electrons are valence electrons. For transition elements, the valence electrons are those in the highest s and d subshells, even though they do not have the same principal quantum number. For the lanthanide and actinide series, the valence electrons are those in the highest s and f subshells, even though they have different principal quantum numbers. All elements in period three (starting with sodium) and below may accept electrons into their d subshell, which allows them to hold more than eight electrons in their valence shell. This allows them to violate the octet rule, as discussed in Chapter 3 of MCAT General Chemistry Review. MCAT EXPERTISE The valence electron configuration of an atom helps us understand its properties and is ascertainable from the Periodic Table (the only “cheat sheet” available on the MCAT!). The “EXHIBIT” button on the bottom of the screen on Test Day will bring up a window with the Periodic Table. Use it as needed! Example: Which electrons are the valence electrons of elemental vanadium, elemental selenium, and the sulfur atom in a sulfate ion? Solution: Vanadium has five valence electrons: two in its 4s subshell and three in its 3d subshell. Selenium has six valence electrons: two in its 4s subshell and four in its 4p subshell. Selenium’s 3d electrons are not part of its valence shell. Sulfur in a sulfate ion has 12 valence electrons: its original six plus six more from the oxygens to which it is bonded. Sulfur’s 3s and 3p subshells can contain only eight of these 12 electrons; the other four electrons have entered the sulfur atom’s 3d subshell, which is normally empty in elemental sulfur. MCAT Concept Check 1.4: Before you move on, assess your understanding of the material with these questions. 1. If given the following quantum numbers, which element(s) do they likely refer to? (Note: Assume that these quantum numbers describe the valence electrons in the element.) n l Possible Elements 2 1 3 0 5 3 4 2 2. Write out and compare an orbital diagram for a neutral oxygen (O) atom and an O2– ion. 3. Magnetic resonance angiography (MRA) is a technique that can resolve defects like stenotic arteries. A contrast agent like gadolinium or manganese injected into the blood stream interacts with the strong magnetic fields of the MRI device to produce such images. Based on their orbital configurations, are these contrast agents paramagnetic or diamagnetic? 4. Determine how many valence electrons come from each subshell in the following atoms: Conclusion Congratulations! You’ve made it through the first chapter! Now that we have covered topics related to the most fundamental unit of matter—the atom—you’re set to advance your understanding of the physical world in more complex ways. This chapter described the characteristics and behavior of the three subatomic particles: the proton, neutron, and electron. In addition, it compared and contrasted two models of the atom. The Bohr model is adequate for describing the structure of one-electron systems, such as the hydrogen atom or the helium ion, but fails to describe adequately the structure of more complex atoms. The quantum mechanical model theorizes that electrons are found not in discrete orbits, but in “clouds of probability,” or orbitals, by which we can predict the likelihood of finding electrons within given regions of space surrounding the nucleus. Both theories tell us that the energy levels available to electrons are not infinite but discrete and that the energy difference between levels is a precise amount called a quantum. The four quantum numbers completely describe the position and energy of any electron within a given atom. Finally, we learned two simple recall methods for the order in which electrons fill the shells and subshells of an atom and that the valence electrons are the reactive electrons in an atom. In the next chapter, we’ll take a look at how the elements are organized on the Periodic Table and will then turn our attention to their bonding behavior —based on valence electrons—in Chapter 3 of MCAT General Chemistry Review. Concept Summary Subatomic Particles A proton has a positive charge and mass around 1 amu; a neutron has no charge and mass around 1 amu; an electron has a negative charge and negligible mass. The nucleus contains the protons and neutrons, while the electrons move around the nucleus. The atomic number is the number of protons in a given element. The mass number is the sum of an element’s protons and neutrons. Atomic Mass vs. Atomic Weight Atomic mass is essentially equal to the mass number, the sum of an element’s protons and neutrons. Isotopes are atoms of a given element (same atomic number) that have different mass numbers. They differ in number of neutrons. Most isotopes are identified by the element followed by the mass number (such as carbon-12, carbon-13, and carbon-14). The three isotopes of hydrogen go by different names: protium, deuterium, and tritium. Atomic weight is the weighted average of the naturally occurring isotopes of an element. The Periodic Table lists atomic weights, not atomic masses. Rutherford, Planck, and Bohr Rutherford first postulated that the atom had a dense, positively charged nucleus that made up only a small fraction of the volume of the atom. In the Bohr model of the atom, a dense, positively charged nucleus is surrounded by electrons revolving around the nucleus in orbits with distinct energy levels. The energy difference between energy levels is called a quantum, first described by Planck. Quantization means that there is not an infinite range of energy levels available to an electron; electrons can exist only at certain energy levels. The energy of an electron increases the farther it is from the nucleus. The atomic absorption spectrum of an element is unique; for an electron to jump from a lower energy level to a higher one, it must absorb an amount of energy precisely equal to the energy difference between the two levels. When electrons return from the excited state to the ground state, they emit an amount of energy that is exactly equal to the energy difference between the two levels; every element has a characteristic atomic emission spectrum, and sometimes the electromagnetic energy emitted corresponds to a frequency in the visible light range. Quantum Mechanical Model of Atoms The quantum mechanical model posits that electrons do not travel in defined orbits but rather are localized in orbitals; an orbital is a region of space around the nucleus defined by the probability of finding an electron in that region of space. The Heisenberg uncertainty principle states that it is impossible to know both an electron’s position and its momentum exactly at the same time. There are four quantum numbers; these numbers completely describe any electron in an atom. The principal quantum number, n, describes the average energy of a shell. The azimuthal quantum number, l, describes the subshells within a given principal energy level (s, p, d, and f). The magnetic quantum number, ml, specifies the particular orbital within a subshell where an electron is likely to be found at a given moment in time. The spin quantum number, ms, indicates the spin orientation of an electron in an orbital. The electron configuration uses spectroscopic notation (combining the n and l values as a number and letter, respectively) to designate the location of electrons. For example, 1s22s22p63s2 is the electron configuration for magnesium: a neutral magnesium atom has 12 electrons—two in the s subshell of the first energy level, two in the s subshell of the second energy level, six in the p subshell of the second energy level, and two in the s subshell of the third energy level; the two electrons in the 3s subshell are the valence electrons for the magnesium atom. Electrons fill the principal energy levels and subshells according to increasing energy, which can be determined by the (n + l) rule. Electrons fill orbitals according to Hund’s rule, which states that subshells with multiple orbitals (p, d, and f) fill electrons so that every orbital in a subshell gets one electron before any of them gets a second. Paramagnetic materials have unpaired electrons that align with magnetic fields, attracting the material to a magnet. Diamagnetic materials have all paired electrons, which cannot easily be realigned; they are repelled by magnets. Valence electrons are those electrons in the outermost shell available for interaction (bonding) with other atoms. For the representative elements (those in Groups 1, 2, and 13−18), the valence electrons are found in s- and/or p-orbitals. For the transition elements, the valence electrons are found in s- and either d- or f-orbitals. Many atoms interact with other atoms to form bonds that complete an octet in the valence shell. Answers to Concept Checks 1.1 1. Charge is determined by the number of electrons present. Atomic number is determined by the number of protons. Isotope is determined by the number of neutrons (while protons make up part of the mass number, it is the number of neutrons that explains the variability between isotopes). 2. 18O: 8p+, 10 n0, 8 e–. 18F: 9p+, 9 n0, 9 e–. 1.2 1. Atomic mass is (just slightly less than) the sum of the masses of protons and neutrons in a given atom of an element. Atoms of the same element with different mass numbers are isotopes of each other. The atomic weight is the weighted average of the naturally occurring isotopes of an element. 2. This ratio is an equivalent concept. It is therefore acceptable, as long as units can be cancelled in dimensional analysis. 3. Isotope Protons Neutrons Electrons 19O 8 11 8 16O 8 8 8 17O 8 9 8 19 19F 9 10 9 16F 9 7 9 238U 92 146 92 240F 92 148 92 1.3 1. 2. 3. 1.4 1. n l Possible Elements 2 1 2p: B, C, N, O, F, Ne 3 0 3s: Na, Mg 5 3 5f: Actinide series 4 2 4d: Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd 2. Both O and O2– have fully filled 1s- and 2s-orbitals. O has four electrons in the 2p subshell; two are paired, and the other two each have their own orbital. O2– has six electrons in the 2p subshell, all of which are paired in the three p-orbitals. 3. Both these molecules have unfilled valence electron shells with relatively few paired electrons; therefore, they are paramagnetic. 4. Equations to Remember (1.1) Planck relation (frequency): E = hf (1.2) Angular momentum of an electron (Bohr model): (1.3) Energy of an electron (Bohr model): (1.4) Planck relation (wavelength): (1.5) Energy of electron transition (Bohr model): (1.6) Maximum number of electrons within a shell: 2n 2 (1.7) Maximum number of electrons within a subshell: 4l + 2 Shared Concepts General Chemistry Chapter 2 The Periodic Table General Chemistry Chapter 3 Bonding and Chemical Interactions Organic Chemistry Chapter 3 Bonding Physics and Math Chapter 2 Work and Energy Physics and Math Chapter 8 Light and Optics Physics and Math Chapter 9 Atomic and Nuclear Phenomena Practice Questions 1. Which of the following is the correct electron configuration for Zn2+? (A) 1s22s22p63s23p64s03d10 (B) 1s22s22p63s23p64s23d8 (C) 1s22s22p63s23p64s23d10 (D) 1s22s22p63s23p64s03d8 2. Which of the following quantum number sets is possible? (A) n = 2; l = 2; ml = 1; (B) n = 2; l = 1; ml = −1; (C) n = 2; l = 0; ml = −1; (D) n = 2; l = 0; ml = 1; 3. What is the maximum number of electrons allowed in a single atomic energy level in terms of the principal quantum number n? (A) 2n (B) 2n + 2 (C) 2n 2 (D) 2n 2 + 2 4. Which of the following equations describes the maximum number of electrons that can fill a subshell? (A) 2l + 2 (B) 4l + 2 (C) 2l 2 (D) 2l 2 + 2 5. Which of the following atoms only has paired electrons in its ground state? (A) Sodium (B) Iron (C) Cobalt (D) Helium 6. An electron returns from an excited state to its ground state, emitting a photon at λ = 500 nm. What would be the magnitude of the energy change if one mole of these photons were emitted? (Note: h = 6.626 × 10−34 J⋅s) (A) 3.98 × 10−21 J (B) 3.98 × 10−19 J (C) 2.39 × 103 J (D) 2.39 × 105 J 7. Suppose an electron falls from n = 4 to its ground state, n = 1. Which of the following effects is most likely? (A) A photon is absorbed. (B) A photon is emitted. (C) The electron moves into a p-orbital. (D) The electron moves into a d-orbital. 8. Which of the following isotopes of carbon is LEAST likely to be found in nature? (A) 6C (B) 12C (C) 13C (D) 14C 9. Which of the following best explains the inability to measure position and momentum exactly and simultaneously according to the Heisenberg uncertainty principle? (A) Imprecision in the definition of the meter and kilogram (B) Limits on accuracy of existing scientific instruments (C) Error in one variable is increased by attempts to measure the other (D) Discrepancies between the masses of nuclei and of their component particles 10. Which of the following electronic transitions would result in the greatest gain in energy for a single hydrogen electron? (A) An electron moves from n = 6 to n = 2. (B) An electron moves from n = 2 to n = 6. (C) An electron moves from n = 3 to n = 4. (D) An electron moves from n = 4 to n = 3. 11. Suppose that an atom fills its orbitals as shown: Such an electron configuration most clearly illustrates which of the following laws of atomic physics? (A) Hund’s rule (B) Heisenberg uncertainty principle (C) Bohr model (D) Rutherford model 12. How many total electrons are in a 133Cs cation? (A) 54 (B) 55 (C) 78 (D) 133 13. The atomic weight of hydrogen is 1.008 amu. What is the percent composition of hydrogen by isotope, assuming that hydrogen’s only isotopes are 1H and 2D? (A) 92% H, 8% D (B) 99.2% H, 0.8% D (C) 99.92% H, 0.08% D (D) 99.992% H, 0.008% D 14. Consider the two sets of quantum numbers shown in the table, which describe two different electrons in the same atom. n l ml ms 2 1 1 3 1 −1 Which of the following terms best describes these two electrons? (A) Parallel (B) Opposite (C) Antiparallel (D) Paired 15. Which of the following species is represented by the electron configuration 1s22s22p63s23p64s13d5? I. Cr + II. Mn+ III. Fe2+ (A) I only (B) I and II only (C) II and III only (D) I, II, and III PRACTICE QUESTIONS Answers and Explanations 1. A Remember that when electrons are removed from an element, forming a cation, they will be removed from the subshell with the highest n value first. Zn0 has 30 electrons, so it would have an electron configuration of 1s22s22p63s23p64s23d10. The 4s subshell has the highest principal quantum number, so it is emptied first, forming 1s22s22p63s23p64s03d10. Choice (B) implies that electrons are pulled out of the d orbital, choice (C) presents the configuration of the uncharged zinc atom, and choice (D) shows the configuration that would exist if four electrons were removed. 2. B The azimuthal quantum number l cannot be higher than n – 1, ruling out choice (A). The ml number, which describes the chemical’s magnetic properties, can only be an integer value between –l and l. It cannot be equal to 1 if l = 0; this would imply that an s orbital has three subshells (−1, 0, and 1) when we know it can only have one. This rules out choices (C) and (D). 3. C For any value of n there will be a maximum of 2n2 electrons; that is, two per orbital. This can also be determined from the Periodic Table. There are only two elements (H and He) that have valence electrons in the n = 1 shell. Eight elements (Li to Ne) have valence electrons in the n = 2 shell. This is the only equation that matches this pattern. 4. B This formula describes the number of electrons in terms of the azimuthal quantum number l, which ranges from 0 to n – 1, with n being the principal quantum number. A table of the maximum number of electrons per subshell is provided here: Subshell Azimuthal Quantum Number (l) Number of Electrons s 0 2 p 1 6 d 2 10 f 3 14 5. D The only answer choice without unpaired electrons in its ground state is helium. Recall from the chapter that a diamagnetic substance is identified by the lack of unpaired electrons in its shell. A substance without unpaired electrons, like helium, cannot be magnetized by an external magnetic field and is actually slightly repelled. Elements that come at the end of a block (Group IIA, the group containing Zn, and the noble gases, most notably) have only paired electrons. 6. D While daunting at first, the problem requires the MCAT favorite equation where h = 6.626 × 10−34 J·s (Planck’s constant), is the speed of light, and λ is the wavelength of the light. This question asks for the energy of one mole of photons, so we must multiply by Avogadro’s number, N A = 6.02 × 1023 mol−1. The setup is: 7. B Because the electron is moving into the n = 1 shell, the only subshell available is the 1s subshell, which eliminates choices (C) and (D). There will be some energy change, however, as the electron must lose energy to return to the minimum-energy ground state. That will require emitting radiation in the form of a photon. 8. A Recall that the superscript refers to the mass number of an atom, which is equal to the number of protons plus the number of neutrons present in an element. Sometimes a text will list the atomic number, Z, as a subscript under the mass number, A. According to the Periodic Table, carbon contains six protons; therefore, its atomic number is 6. Isotopes all have the same number of protons, but differ in number of neutrons. Almost all atoms with Z > 1 have at least one neutron. Carbon is most likely to have a mass number of 12, for six protons and six neutrons, as in choice (B). Choices (C) and (D) are possible isotopes that would have more neutrons than 12C. The 6C isotope is unlikely. It would mean that there are 6 protons and 0 neutrons. As shown in Figure 1.4, this would be a highly unstable isotope. 9. C The limitations placed by the Heisenberg uncertainty principle are caused by limitations inherent in the measuring process: if a particle is moving, it has momentum, but trying to measure that momentum necessarily creates uncertainty in the position. Even if we had an exact definition of the meter, as in choice (A), or perfect measuring devices, as in choice (B), we still wouldn’t be able to measure position and momentum simultaneously and exactly. 10. B For the electron to gain energy, it must absorb energy from photons to jump up to a higher energy level. There is a bigger jump between n = 2 and n = 6 than there is between n = 3 and n = 4. 11. A The MCAT covers the topics in this chapter qualitatively more often than quantitatively. It is critical to be able to distinguish the fundamental principles that determine electron organization, which are usually known by the names of the scientists who discovered or postulated them. The Heisenberg uncertainty principle, choice (B), refers to the inability to know the momentum and position of a single electron simultaneously. The Bohr model, choice (C), was an early attempt to describe the behavior of the single electron in a hydrogen atom. The Rutherford model, choice (D), described a dense, positively charged nucleus. The element shown here, nitrogen, is often used to demonstrate Hund’s rule because it is the smallest element with a half-filled p subshell. Hund’s rule explains that electrons fill empty orbitals first before doubling up electrons in the same orbital. 12. A The quickest way to solve this problem is to use the Periodic Table and find out how many protons are in Cs atoms; there are 55. Neutral Cs atoms would also have 55 electrons. A stable Cs cation will have a single positive charge because it has one unpaired s-electron. This translates to one fewer electron than the number of protons, or 54 electrons. 13. B The easiest way to approach this problem is to set up a system of two algebraic equations, where H and D are the percentages of H (mass = 1 amu) and D (mass = 2 amu), respectively. Your setup should look like the following system: H + D = 1 (percent H + percent D = 100%) 1 H + 2 D = 1.008 (atomic weight calculation) Rearranging the first equation and substituting into the second yields (1 – D) + 2D = 1.008, or D = 0.008. 0.008 is 0.8%, so there is 0.8% D. 14. A The terms in the answer choices refer to the magnetic spin of the two electrons. The quantum number ms represents this property as a measure of an electron’s intrinsic spin. These electrons’ spins are parallel, in that their spins are aligned in the same direction ( for both species). 15. B When dealing with ions, you cannot directly approach electronic configurations based on the number of electrons they currently hold. First examine the neutral atom’s configuration, and then determine which electrons are removed. Neutral Atom’s Configuration Ion’s Configuration Cr0: [Ar] 4s13d5 — Mn0: [Ar] 4s23d5 Mn+: [Ar] 4s13d5 Fe0: [Ar] 4s23d6 Fe2+: [Ar] 4s03d6 Due to the stability of half-filled d-orbitals, neutral chromium assumes the electron configuration of [Ar] 4s13d5. Mn must lose one electron from its initial configuration to become the Mn+ cation. That electron would come from the 4s subshell, according to the rule that the first electron removed comes from the highest-energy shell. Fe must lose two electrons to become Fe2+. They’ll both be lost from the same orbital; the only way Fe2+ could hold the configuration in the question stem would be if one d-electron and one s-electron were lost together. In This Chapter 2.1 The Periodic Table 2.2 Types of Elements Metals Nonmetals Metalloids 2.3 Periodic Properties of the Elements Atomic and Ionic Radii Ionization Energy Electron Affinity Electronegativity 2.4 The Chemistry of Groups Alkali Metals (IA) Alkaline Earth Metals (IIA) Chalcogens (VIA) Halogens (VIIA) Noble Gases (VIIIA) Transition Metals (B) Concept Summary Introduction The pharmacological history of lithium is an interesting window into the scientific and medical communities’ attempts to take advantage of the chemical and physical properties of an element for human benefit. By the mid-1800s, the medical community was showing great interest in theories that linked uric acid to a myriad of maladies. When it was discovered that solutions of lithium carbonate dissolved uric acid, therapeutic preparations containing lithium carbonate salt became popular. Even nonmedical companies tried to profit from lithium’s reputation as a cure-all by adding it to their soft drinks. Eventually, fascination with theories of uric acid wore off, and lithium’s time in the spotlight seemed to be coming to an end. Then, in the 1940s, doctors began to recommend salt-restricted diets for cardiac patients. Lithium chloride was made commercially available as a sodium chloride (table salt) substitute. Unfortunately, lithium is quite toxic at fairly low concentrations, and when medical literature in the late 1940s reported several incidents of severe poisonings and multiple deaths—some associated with only minor lithium overdosing—U.S. companies voluntarily withdrew all lithium salts from the market. Right around this time, the Australian psychiatrist John Cade proposed the use of lithium salts for the treatment of mania. Cade’s clinical trials were quite successful. In fact, his use of lithium salts to control mania was the first instance of successful medical treatment of a mental illness, and lithium carbonate became commonly prescribed in Europe for manic behavior. Not until 1970 did the U.S. Food and Drug Administration finally approve the use of lithium carbonate for manic illnesses. Lithium (Li) is the element with the atomic number 3. It is a very soft alkali metal, and under standard conditions, it is the least dense solid element (specific gravity = 0.53). Lithium is so reactive that it does not naturally occur on earth in its elemental form and is found only in various salt compounds. Why would medical scientists pay attention to this particular element? What would make doctors believe that lithium chloride would be a good substitute for sodium chloride for patients on salt-restricted diets? The answers lie in the Periodic Table. 2.1 The Periodic Table In 1869, the Russian chemist Dmitri Mendeleev published the first version of his Periodic Table of the Elements, which showed that ordering the known elements according to atomic weight revealed a pattern of periodically recurring physical and chemical properties. Since then, the Periodic Table has been revised, using the work of physicist Henry Moseley, to organize the elements based on increasing atomic number (the number of protons in an element) rather than atomic weight. Using this revised table, many properties of elements that had not yet been discovered could be predicted. The Periodic Table creates a visual representation of the periodic law, which states: the chemical and physical properties of the elements are dependent, in a periodic way, upon their atomic numbers. The modern Periodic Table arranges the elements into periods (rows) and groups or families (columns), based on atomic number. There are seven periods, representing the principal quantum numbers n = 1 through n = 7 for the s- and p-block elements. Each period is filled sequentially, and each element in a given period has one more proton and one more electron than the element to its left (in their neutral states). Groups contain elements that have the same electronic configuration in their valence shell and share similar chemical properties. BRIDGE Recall from Chapter 1 of MCAT General Chemistry Review that periods (rows) graphically represent the principal quantum number, and groups (columns) help to determine the valence electron configuration. The electrons in the valence shell, known as the valence electrons, are the farthest from the nucleus and have the greatest amount of potential energy. Their higher potential energy and the fact that they are held less tightly by the nucleus allows them to become involved in chemical bonds with the valence electrons of other atoms; thus, the valence shell electrons largely determine the chemical reactivity and properties of the element. MCAT EXPERTISE Relating valence electrons to reactivity is important. Elements with similar valence electron configurations generally behave in similar ways, as long as they are the same type (metal, nonmetal, or metalloid). The Roman numeral above each group represents the number of valence electrons elements in that group have in their neutral state. The Roman numeral is combined with the letter A or B to separate the elements intotwo larger classes. The A elements are known as the representative elements and include groups IA through VIIIA. The elements in these groups have their valence electrons in the orbitals of either s or p subshells. The B elements are known as the nonrepresentative elements and include both the transition elements, which have valence electrons in the s and d subshells, and the lanthanide and actinide series, which have valence electrons in the s and f subshells. For therepresentative elements, the Roman numeral and the letter designation determine the electron configuration. For example, an element in Group VA has five valence electrons with the configuration s2p3. As described in Chapter 1 of MCAT General Chemistry Review, the nonrepresentative elements may have unexpected electron configurations, such as chromium (4s1 3d 5) and copper (4s1 3d10). In the modern IUPAC identification system, the groups are numbered 1 to 18 and are not subdivided into Group A and Group B elements. MCAT Concept Check 2.1: Before you move on, assess your understanding of the material with these questions. 1. Mendeleev’s table was arranged by atomic weight, but the modern Periodic Table is arranged by: 2. Which of the following are representative elements (A), and which are nonrepresentative (B)? 2.2 Types of Elements When we consider the trends of chemical reactivity and physical properties together, we can begin to identify groups of elements with similar characteristics. These larger collections are divided into three categories: metals, nonmetals, and metalloids (also called semimetals). METALS Metals are found on the left side and in the middle of the Periodic Table. They include the active metals, the transition metals, and the lanthanide and actinide series of elements. Metals are lustrous (shiny) solids, except for mercury, which is a liquid under standard conditions. They generally have high melting points and densities, but there are exceptions, such as lithium, which has a density about half that of water. Metals have the ability to be deformed without breaking; the ability of metal to be hammered into shapes is called malleability, and its ability to be pulled or drawn into wires is called ductility. At the atomic level, a metal is defined by a low effective nuclear charge, low electronegativity (high electropositivity), large atomic radius, small ionic radius, and low ionization energy. All of these characteristics are manifestations of the ability of metals to easily give up electrons. Many of the transition metals (Group B elements) have two or more oxidation states (charges when forming bonds with other atoms). Because the valence electrons of all metals are only loosely held to their atoms, they are free to move, which makes metals good conductors of heat and electricity. The valence electrons of the active metals are found in the s subshell; those of the transition metals are found in the d subshell; and those of the lanthanide and actinide series elements are in the f subshell. Some transition metals—copper, nickel, silver, gold, palladium, and platinum—are relatively nonreactive, a property that makes them ideal for the production of coins and jewelry. KEY CONCEPT Alkali and alkaline earth metals are both metallic in nature because they easily lose electrons from the s subshell of their valence shells. An example of a metal is shown in Figure 2.1 with an indium wire. The wire exhibits luster, malleability, and ductility. It is used as a wire because it also exhibits good heat and electrical conductivity. Figure 2.1. Indium (In) Metal Wire NONMETALS Nonmetals are found predominantly on the upper right side of the Periodic Table. Nonmetals are generally brittle in the solid state and show little or no metallic luster. They have high ionization energies, electron affinities, and electronegativities, as well as small atomic radii and large ionic radii. They are usually poor conductors of heat and electricity. All of these characteristics are manifestations of the inability of nonmetals to easily give up electrons. Nonmetals are less unified in their chemical and physical properties than the metals. Carbon, shown in Figure 2.2, is a stereotypical nonmetal that retains a solid structure but is brittle, nonlustrous, and generally a poor conductor of heat and electricity. Figure 2.2. Activated Charcoal, Composed of the Nonmetal Carbon (C) METALLOIDS Separating the metals and nonmetals are a stair-step group of elements called the metalloids. The metalloids are also called semimetals because they share some characteristics with both metals and nonmetals. The electronegativities and ionization energies of the metalloids lie between those of metals and nonmetals. Their physical properties—densities, melting points, and boiling points—vary widely and can be combinations of metallic and nonmetallic characteristics. For example, silicon (Si) has a metallic luster but is brittle and a poor conductor. The reactivities of the metalloids are dependent on the elements with which they are reacting. Boron (B), for example, behaves like a nonmetal when reacting with sodium (Na) and like a metal when reacting with fluorine (F). The elements classified as metalloids form a “staircase” on the Periodic Table and include boron, silicon, germanium (Ge), arsenic (As), antimony (Sb), tellurium (Te), polonium (Po), and astatine (At). While there

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