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General, Organic, and Biological Chemistry: An Integrated Approach, Second Edition

Kenneth W. Raymond

John Wiley & Sons, Inc.

Every one of your students has the potential to make a difference. And realizing that potential starts right here, in your course. When students succeed in your coursewhen they stay on-task and make the breakthrough that turns confusion into confidencethey are empowered to realize the possibilities for greatness that lie within each of them. We know your goal is to create an environment where students reach their full potential and experience the exhilaration of academic success that will last them a lifetime. WileyPLUS can help you reach that goal.

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GENERAL, ORGANIC, AND BIOLOGICAL CHEMISTRY

An Integrated ApproachSECOND EDITION

GENERAL, ORGANIC, AND BIOLOGICAL CHEMISTRY

An Integrated ApproachSECOND EDITION

Kenneth W. Raymond

Eastern Washington University

John Wiley & Sons, Inc.

VICE PRESIDENT AND EXECUTIVE PUBLISHER PROJECT EDITOR PRODUCTION SERVICES MANAGER PRODUCTION EDITOR EXECUTIVE MARKETING MANAGER CREATIVE DIRECTOR ART DIRECTOR DESIGNER SENIOR PHOTO EDITOR EDITORIAL ASSISTANT SENIOR MEDIA EDITOR PRODUCTION MANAGEMENT COVER ILLUSTRATION/DESIGN BICENTENNIAL LOGO DESIGN COVER PHOTOS

Kaye Pace Jennifer Yee Dorothy Sinclair Janet Foxman Amanda Wygal Harry Nolan Hope Miller Brian Salisbury Lisa Gee Catherine Donovan Thomas Kulesa Suzanne Ingrao/Ingrao Associates Norm Christiansen Richard J. Pacifico Image of orange based on photo Stock Food/Punchstock (top) and Photodisc/Superstock (bottom)

This volume contains selected illustrations from the following texts, reprinted with permission by John Wiley and Sons, Inc. Boyer, Rodney, Concepts in Biochemistry, Second Edition, 2002. Hein, Morris; Best, Leo R.; Pattison, Scott; Arena, Susan, Introduction to General, Organic, and Biochemistry, Eighth Edition, 2005. Holum, John R., Fundamentals of General, Organic, and Biological Chemistry, Sixth Edition, 1998. Pratt, Charlotte W.; Cornely, Kathleen, Essential Biochemistry, 2004. Voet, Donald; Voet, Judith G.; Pratt, Charlotte W., Fundamentals of Biochemistry: Life at the Molecular Level, 2nd Edition, 2006.

This book was set in 10.5/12 Adobe Garamond by Prepar and printed and bound by Courier/Kendallville. The cover was printed by Courier/Kendallville. This book is printed on acid-free paper. Copyright 2008 John Wiley & Sons, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, website www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, (201) 748-6011, fax (201) 748-6008, website www.wiley.com/go/permissions. To order books or for customer service, please call 1-800-CALL WILEY (225-5945).

ISBN: 978-0-470-12927-2 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1

P R E F A C E

second edition of General, Organic, and Biochemistry: an Integrated Approach This dentalwritten fornutrition, preparingtechnology, andhealth-related fields such as has been students for careers in nursing, hygiene, medical occupational therapy. The text is also suitable for students majoring in other fields where it is important to have an understanding of chemistry and its relationship to living things. Students need have no previous background in chemistry, but should possess basic math skills. For those whose math is a bit rusty, the text provides reviews of the important material. While designed for use in one-semester or two-quarter General, Organic, and Biochemistry (GOB) courses, instructors have found that it also works well for one-year courses, especially when combined with the supplement Chemistry Case Studies For Allied Health Students by Colleen Kelley and Wendy Weeks. In a GOB course it is essential to show how the subject matter relates to the students future careers. For this reason, this text makes extensive use of real-life examples from the health sciences.

O R G A N I Z A T I O NIn most GOB texts, a group of chapters on general chemistry is followed by a series of organic chemistry chapters, which is followed by chapters devoted to biochemistry. Years of experience in teaching health science courses have shown the author that there is a drawback to this approach: in many cases there is a long time interval between when a topic is first presented and when it is used againenough of a break that students familiarity with the subject matter has often lapsed. In introducing GOB material, this text uses an integrated approach in which related general chemistry, organic chemistry, and biochemistry topics are presented in adjacent chapters. This approach helps students see the strong connections that exist between these three branches of chemistry and allows instructors to discuss these interrelationships while the material is still fresh in students minds. This integration involves the following sets of chapters: Chapter 3 (Compounds) and Chapter 4 (An Introduction to Organic Compounds). An introduction to bonding and compounds is followed by a look at the members of a few key organic families. Chapters 3 and 4 and Chapter 6 (Reactions). A study of inorganic and organic compounds is followed (after a look at gases, liquids, and solids in Chapter 5) by an introduction to their reactions. Chapter 7 (Solutions) and Chapter 8 (Lipids and Membranes). A discussion of solubility is followed by a look at the importance of solubility in biochemistry. Some reactions from Chapter 6 are reintroduced. Chapter 9 (Acids and Bases) and Chapter 10 (Carboxylic Acids, Phenols, and Amines). Principles of acid/base chemistry from an inorganic perspective are followed by a chapter on the organic and biochemical aspects of this topic.

x

PREFACE

Chapter 11 (Alcohols, Aldehydes, and Ketones) and Chapter 12 (Carbohydrates). An introduction to the chemistry of alcohols, aldehydes and ketones is followed by a presentation of related biochemical applications.K E Y F E AT U R E S OF THE SECOND EDITION

The many reviewers of this text have made helpful suggestions. The major changes to the second edition are: Newly introduced material: Molar mass (Chapter 2), step-by-step instructions for drawing molecules and polyatomic ions (Chapter 4), ionic equations and net ionic equations (Chapter 7), and naming esters and amides (Chapter 10). Revised material: Changed group naming from IA, IIA format to 1A, 2A format (Chapter 2), added details on naming binary molecules and introduced a table of prefixes used for naming them (Chapter 2), modified treatment of the combined gas law and the ideal gas law (Chapter 5), and updated discussion of waxes, fatty acids, phospholipids, and eicosanoids (Chapter 8). New Appendicies: Important families of organic compounds (Appendix B) and Naming ions, ionic compounds, binary molecules, and organic compounds (Appendix C). Addition of new chapter sections: Reaction types (Section 6.2), Maintaining the pH of blood serum (Section 9.10), and Oxidation of phenols (Section 10.5).

P R O B L E M

S O LV I N GLearning to do anything requires practice, and in chemistry this practice involves solving problems. This text offers students ample opportunities to do so.

102

CHAPTER 4 | AN INTRODUCTION

TO

ORGANIC COMPOUNDS

FIGURE |

4.3 H

H H H H C C C C H H H H F

CH3CH2CHCH3 F F

(Continued)

2-Fluorobutane

O H H C C

C C C H

O H C C

O H C H H

O HC HC

C C C H

OH C

O

O

OH O O

O C H

O CCH3

CH

Aspirin

Sample Problems and Practice Problems.

In skeletal structures (Figure 4.3), covalent bonds are represented by lines, carbon atoms are not shown, and hydrogen atoms are drawn only when attached to atoms other than carbon. To read a skeletal structure, you assume that a carbon atom appears where lines (bonds) meet and at the end of each line. To simplify matters, nonbonding electrons (Section 3.5) are sometimes omitted from skeletal and other structural formulas.S AMPLE P ROBLEM

4.4

Drawing condensed and skeletal structures Draw condensed and skeletal structures of diethyl ether, a compound once used as a general anesthetic. H H H H H C C O C C H H HStrategy

Each major topic is followed by a sample problem and a related practice problem. The solution to each sample problem is accompanied by a strategy to use when solving the problem. The answers to practice problems are given at the end of the chapter.

H H

To write the condensed formula, begin by thinking of the molecule as a chain of five atoms (CCOCC) and then add in the atoms attached to these five (CH3, etc.). The skeletal structure of diethyl ether is drawn by leaving out all of the carbon and hydrogen atoms, showing only the oxygen atom and the CC and CO bonds.Solution

CH3CH2OCH2CH3Condensed structure

OSkeletal structure

P RACTICE P ROBLEM

4.4

Research suggests that drinking green tea may help boost the immune system. Ethylamine (below), produced when one of the compounds in green tea is broken down in the liver, may be responsible for this immune response. Draw condensed and skeletal structures for the molecule. H H H C C N H H H H

PREFACE

xi

END

OF

CHAPTER PROBLEMS

131

8 Define the term functional group and describe the features

that distinguish hydrocarbons, alcohols, carboxylic acids, and esters from one another. Functional groups are atoms, groups of atoms, or bonds that give a molecule a particular set of chemical properties. The functional groups represented in hydrocarbons are the carboncarbon double bond (in alkenes), the carboncarbon triple bond (in alkynes), and alternating double and single bonds in a ring (in aromatic compounds). Alcohols contain the hydroxyl ( OH) functional group attached to an alkane-like carbon atom. Carboxylic acids contain the hydroxyl group attached to a carbonyl (C O) group, and esters contain a C O C linkage, with one of the carbon atoms belonging to a carbonyl group.

End of Chapter Problems. A large number ofEND OF CHAPTER PROBLEMSAnswers to problems whose numbers are printed in color are given in Appendix D. More challenging questions are marked with an asterisk. Problems within colored rules are paired. ILW = Interactive Learning Ware solution is available at www.wiley.com/college/raymond.|

4.1 S T R U C T U R A L F O R M U L A SFORMAL CHARGES

AND

4.9 What is the formal charge on each atom in the

following molecules or ions? a. H H S b. O C O C O2

4.1 Draw the line-bond structure of each molecule.

l l c. C N C l C

CH3a.

CH3CH2CHCH2CH3 CH2CH2NH2

S

b.

HC HC

C C H

4.10 What is the formal charge on each atom in the

CH CH

following molecules or ions?+

H Ha. D H C NH T

l 4 c. 3O C O

4.2 Draw the line-bond structure of each molecule.

H H O b. H C H 4.11 Draw each polyatomic ion and assign formal charges.

CH3a. CH3CCH2CH3

b. CH3CHCHCHCH2

CH34.3 What is the shape around the nitrogen and sulfur atoms

problems can be found and the end of each chapter, and Appendix D provides answers for the odd-numbered ones. Many of the end of chapter problems are paired and some, marked with an asterisk, are more challenging than others. Each chapter includes a set of Thinking It Through problems that ask students to go a bit further with one or more of the concepts presented in the chapter. Over two hundred and fifty new problems have been added to the second edition. Of these, more than half are multi-part questions and many are challenging.

in the ions shown in Figure 4.2?4.4 What is the shape around each of the carbon atoms in

Each atom, except for hydrogen, should have an octet of valence electrons. a. OH b. NH4 c. CN4.12 Draw each polyatomic ion and assign formal charges.

aspirin (Figure 4.3)?4.5 Draw each molecule. a. C2H6 b. C2H4 4.6 Draw each molecule. a. C3H8 b. C3H6 c. C2H2 c. C3H4

Each atom, except for hydrogen, should have an octet of valence electrons. a. PO43 b. HPO42 c. H2PO44.13 Draw each of the following and assign formal charges.

4.7 Draw each diatomic element. a. F2 b. O2 c. N2

Each atom should have an octet of valence electrons. a. SO3 b. SO324.14 Draw each molecule and assign formal charges. Each

* 4.8 Draw two different molecules that have the formula C2H6O.

atom should have an octet of valence electrons. a. CO b. SO2

SOLUTIONS

TO

PRACTICE PROBLEMS

59

H E A LT H L i n k | CT and MRI Imaging2.68 a. Cholesterol Marker describes using MRI to look

THINKING IT THROUGH 2.70 What are the pros and cons (both long-term and short-

for arterial plaque. Why is the presence of plaque in arteries a concern? b. What role does the particle similar to HDL play in the technique that is described?2.69 a. One of the two techniques described in this Health

term) of using radiation to treat cancer?2.71 A nurse is assisting a patient who has just undergone

Link is considered invasive. What do you suppose is meant by this term?b. To which technique does this term apply? c. In some cases, the images produced by CT and MRI

are quite similar. If given a choice, which would you rather have run?

Interactive Learning Ware Problems. The texts website (http://www.wiley.com/college/raymond) features Interactive Learning Ware (ILW), a step-by-step problem solving tutorial program that guides students through selected problems from the book. The ILW problems are representative of those that students frequently find most difficult and they reinforce students critical thinking and problem solving skills. An ILW icon identifies each ILW problem in the end-of-chapter question section.ILW

cancer treatment that involved exposure to gamma radiation from cobalt-60. Should the nurse be concerned that he will be exposed to gamma radiation given off by the patient? 2.72 In late 2006, a former Russian spy was poisoned when a small amount of polonium-210 was put in his food. He died a few weeks later. a. Polonium-210 emits alpha particles. Write a balanced nuclear equation for this process. b. This radioisotope has a half-life of 138 days. Of a 2 mg sample, how much would remain after 5 half-lives? c. If alpha particles can be blocked by a sheet of paper (Figure 2.13), why is polonium-210 so poisonous?

INTERACTIVE

LEARNING

PROBLEMS

ILW

2.73 How many atoms are contained in: a. 1.0 mol of calcium? b. 7.88 106 mol of calcium? c. 7.88 g of calcium? d. 5.2 mg of calcium?

2.74 Identify the missing product in each nuclear equation. ILW a. 20Mg ? + 0+ 12 1 b. 152Ho 148Tb + ? 67 650 c. 31Si ? + 1 14

SOLUTIONS

TO

PRACTICE

PROBLEMS

2.1 a. protons and neutrons; b. protons and electrons; c. protons and neutrons 2.2 a. atomic number = 8, mass number = 18; b. atomic number = 17, mass number = 37 2.331 15P

and 28P 15

2.4 10.8 amu 2.5 S 2.6 a. 3.7 1023 atoms; b. 4.8 1012 mol 2.7 a. 2.53 g; b. 0.860 g 2.8 2.9209 81Tl 192 77Ir

192 76Os

+ 0+ 1

2.10 132 days

xii

PREFACE

H E A LT H L I N K S A N D B I O C H E M I S T R Y118 CHAPTER 4 | AN INTRODUCTIONTO

L I N K S

ORGANIC COMPOUNDS

Prion Diseases

The conformation, or shape, that a molecule takes can greatly influence its biological action. This point is well illus-

trated by a particular class of proteins, called prions, that have been identified as the cause of mad cow disease (in cattle), scrapie (in sheep), chronic wasting disease (in deer and elk), and new variant Creutzfeldt-Jakob disease, or vCJD (in humans). Proteins are very large molecules formed from amino acid building blocks. Each protein has a favored conformation some with the protein chain twisted into spirals and bends and some with the chain zigzagged back and forth in a compact form. Prions, short for proteinaceous infection particles, are a type of protein found in the membranes of nerve cells. The prion diseases C mentioned above are caused 128 the H A P T E R 4 | A N I N T R O D U C T I O N T O O R G A N I C C O M P O U N D S when normal prion conformation (PrPc) is twisted into an abnormal shape (PrPsc) (Figure 4.14). When PrPsc comes into contact with PrPc, the PrPc proteins change conformation and become PrPsc. As PrPsc accumulates in affecNormal Prion Protein (PrPc) Disease-Causing Prion (PrPsc) ted animals or humans, sponge-like holes form in the brain, causing dizziness, seizuOdor and Flavor res, and death. FIGURE | 4.14 Prion diseases can be transferred from one he senses of smell and taste depend on specific receptors located in the nose and in the mouth, respectively. We detect an odor or species to another. Cattle are known to get Prions flavor when a compound attaches to these receptors and triggers nerve responses. How the compound interacts with a given recepc mad cow disease when fed parts of scrapie(a) The prion protein (PrP ) in its normal conformation. (b) The prion in its tor determines the particular odor or flavor that it has. In 2004, the Nobel Prize in Physiology or Medicine was awarded to two infected sheep, and vCJD in humans has been incorrectly folded (PrPsc) form. researchers who study the biochemistry of the sense of smell. linked to eating mad cowinfected beef. Source: Fred E. Cohen, M.D., D. Phil and Cedric Govaerts, Ph.D., Department of The odor and flavor of fruits is often due to a mixture of esters. The structure of a particular ester determines how it fits a given Cellular & Molecular Pharmacology, University of California San Francisco (UCSF). receptor, so esters containing a different number of carbon atoms are associated with different odors and flavors. For example, the pineapple and apricot esters differ by three CH2 groups (Figure 4.24). Constitutional isomers can also have different odors and flavors, as is the case for the apple-like and banana esters, each of which has the molecular formula C7H14O2.

T

4.7

CYCLOALKANES

O In some alkanes, called cycloalkanes, carbon atoms are joined into rings (Figure 4.15). Like CH3CH2CH2C OCH2CH3 their noncyclic counterparts, cycloalkanes are nonpolar molecules that are attracted to one Pineapple another by London forces. To simplify matters, cycloalkanes are usually drawn using skeletal structures, although side views can be useful when considering the orientation of O substituents attached to a ring. When naming cycloalkanes, the ring is usually designated as the parent, which CH3CH2CH2C OCH2CH2CH2CH2CH3 is named by combining cyclo with the appropriate numbering prefix (Table 4.5) and Apricot ane. When only one alkyl group is attached to a cycloalkane parent, the carbon atom O that holds that group is carbon 1 (Figure 4.16a), but the number is not included in the name. When a ring holds more than one alkyl group, the ring is numbered from the position and in the direction that gives the lowest numbers. Figure 4.16b shows how this CH3CH2CH2CH2C OCH2CH3works for the three dimethylcyclopentane constitutional isomers.Apple-like

Geometric IsomersThe limited rotation of the carboncarbon single bonds in cycloalkanes has an interesting side effect in that it allows for the existence of stereoisomers, molecules that have the same molecular formula have the same atomic connections have different three-dimensional shapes are interchanged only by breaking bonds

O CH3C

OCH2CH2CHCH3 CH3Banana

To emphasize the importance of chemistry to the health sciences and to living things, each chapter includes Health Links and Biochemistry Links. In the second edition, eight new Health Links have been added: Body Mass Index (Chapter 1), Dental Fillings (Chapter 3), Making Weight (Chapter 5), Saliva (Chapter 7), Omega-3 fatty acids (Chapter 8), Biofilms (Chapter 10), Drugs in the environment (Chapter 11), and RNA Interference (Chapter 14). In addition, six Health Links from the first edition have been updated: Body Temperature (Chapter 1), Dietary Reference Intakes (formerly Recommended Daily Allowances) (Chapter 2), CT and MRI (formerly CT and PET) (Chapter 2), Sunscreens (Chapter 4), Trans fats (Chapter 8), and Proteins in Medicine (formerly Enzymes in Medicine) (Chapter 13).O CH3C OCH2CH2CH2CH2CH2CH2CH2CH3Orange

O

CH3CH2CH2C

OCH2

Rose

O

CH3C OCH2Peach

O CH2C OCH2CH3

O CH3CH2C OCH2CHCH3 CH3Rum

Honey

O C OCH3 H2N

O H C OCH2CHCH3 CH3Raspberry FIGURE |

Grape Esters

4.24

Many esters have pleasing odors and flavors.

O N - L I N E124 CHAPTER 4 | AN INTRODUCTIONTO

V I D E O SFor one topic in each chapter, a special icon is used to indicate that an on-line ScienCentral article and video clip are available for viewing. These articles and video clips are of interest because they show how the chemistry being presented pertains to current events. Each set of end of chapter problems includes some related to the video content. The video titles include: Pork on the Run (Chapter 1), Cholesterol Marker (Chapter 2), Glowing Fish (Chapter 3), Tanning & Health (Chapter 4), Breath Of Life (Chapter 5), Hydrogen Cars (Chapter 6), Kidney Bones (Chapter 7), Teen Steroids (Chapter 8), Cystic Fibrosis Mucus (Chapter 9), Meth and the Brain (Chapter 10), Toxin Eaters (Chapter 11), Sweet Spot (Chapter 12), Young Hearts (Chapter 13), Cancer Screening (Chapter 14), Exercise Gene (Chapter 15).

ORGANIC COMPOUNDS

P RACTICE P ROBLEM

4.11

Designate each of the carboncarbon double bonds in bombykol, a moth pheromone, as cis or trans.H C CH3CH2CH2 H C C C CH2CH2CH2CH2CH2CH2CH2CH2CH2OHBombykol

H H

Sunscreensn addition to the visible light that is present in sunlight, a higher energy form of electromagnetic radiation called ultraviolet (UV) is also found. It is this UV radiation that makes spending too much time in the sun hazardous to your health. UV radiation is divided into three categories (arranged in order of increasing energy) UV-A, UV-B, and UV-C. Although all forms of UV radiation can be harmful, UV-C is the most damaging. We do not usually worry about exposure to UV-C from sunlight, however, because most is screened out by atmospheric ozone. The UV-A and UV-B in sunlight are not blocked by the atmosphere and it is exposure to UV-B that causes sunburns. This form of radiation has also been identified as one of the causes of skin cancer. While UV-A was once thought to be relatively harmless, there is now strong evidence that links wrinkles, other skin damage, and skin cancer to UV-A exposure. To some extent, your skin can protect itself from UV radiation. When sunlight hits the skin, a particular type of cells produce melanin, a black pigment that absorbs UV radiation. A suntan is the result of melanin production. Sunscreens can also provide some degree of protection from the sun. These contain aromatic compounds that block UV-A and UV-B light (Figure 4.22). Not all aromatic compounds are suitable for use as sunscreensmany do not absorb UV, and many are toxic. The SPF (sun protection factor) H O listed on the label of a sunscreen indicates how effective it is at C C Octyl blocking UV radiation. An SPF of C OCH2CHCH2CH2CH2CH3 methoxycinnamate 25 means that it takes 25 times H CH2CH3 longer to get sunburned with the sunscreen applied than without.

I

CH3O

O

OAvobenzone FIGURE |

CCH2C CH3O CH2SO3H H3C H3C O C H H C O CH3 C(CH3)3

4.22

UV-B and UV-A absorbing compounds in sunscreens

Ecamsule

CH3 CH2SO3H

Octyl methoxycinnamate is the UV-B blocker most commonly used in sunscreens. Avobenzone and Ecamsule are UV-A blockers. Ecamsule, which was recently approved for use in the United States, has been a sunscreen ingredient in Canada and Europe since 1993.

PREFACE

xiii

O T H E R

T E X T

F E A T U R E SChapter Opening Vignettes Each chapter begins with a story that focuses on the connection between chemistry and high-interest, everyday topics that students can relate to.

Macular degeneration is a disease of the eye with symptoms that includeloss of color vision and distortion, blurring, or complete loss of central vision. Peripheral vision is usually unaffected. People with this disease usually have trouble when it comes to reading or recognizing faces. There are a number of factors that increase the risk of getting macular degeneration, including

4

A

N

I N T R O D U C T I O N T O O R G A N I C C O M P O U N D S

advanced age, a history of smoking, and diabetes. Stargardts disease, an inherited form of macular degeneration that usually appears before age 30, results from damage to the retina caused by a malfunction in the recycling of an organic molecule essential to the visual process.Now that we have seen the basics of how atoms (Chapter 2) and compounds (Chapter 3) are put together, it is time to set the stage for the organic and biochemistry topics that we will encounter as we move through the text. This chapter will begin with an introduction to a range of diverse topics, all of which relate to how bonding patterns, the distribution of electrons, and the shape of a molecule influence the way that it interacts with others. In later sections of the chapter we will apply our knowledge of these interactions to understand the properties of a number of different families of organic compounds (contain carbon atoms). The shape that a molecule has and its interactions with others are important in determining its biological effects. Diseases ranging from Stargardts disease (mentioned on the facing page) to mad cow disease (Health Link: Prion Diseases) are directly related to these properties.

Objectives Each chapter begins with a list of goals for the student to achieve. These objectives identify key concepts within each chapter. A summary of how these objectives were met appears at the end of each chapter.

Photo source:

Science VU/NIH/Visual Unlimited.

92

objectivesAfter completing this chapter, you should be able to:1 Draw molecules and polyatomic ions using electron dot and line-bond structures.

Assign formal charges.2 Describe how condensed structural formulas and skeletal structures differ from

electron dot and line-bond structures.3 Define electronegativity and explain its relationship to polar covalent bonds. Give a

simple rule that can be used to predict whether or not a covalent bond is polar.4 List the five basic shapes about an atom in a molecule and describe the rules used

to predict shape. Explain how shape plays a role in determining overall polarity.5 Describe the noncovalent interactions that attract one compound to another. 6 Describe the four families of hydrocarbons. 7 Explain the difference between constitutional isomers, conformations, and the

stereoisomers known as geometric isomers. Give examples of two different families of hydrocarbons that can exist as geometric isomers.8 Define the term functional group and describe the features that distinguish

hydrocarbons, alcohols, carboxylic acids, and esters from one another.93

Student Web Site Within each chapter you will find an icon a indicating that there is a ScienCentral news video at the website with a news story related to chapter content. The web site also features practice quizzes and Interactive Learningware problems. Student Solutions Manual and Study Guide Written by Byron Howell, Tyler Junior College and Adeliza Flores, of Las Positas College, this supplement contains worked out solutions to the odd-numbered text problems; chapter summaries; sample problems, and practice problems. Laboratory Manual Written by David Macaulay, Joseph Bauer, and Molly Bloomfield. This lab manual is written for the one or two-term chemistry lab course for students in the allied health sciences and related fields. These experiments are presented in an integrated table of contents and contain chapter references from General, Organic, and Biological Chemistry: An Integrated Approach, Second Edition. Chemistry Case Studies For Allied Health Students Written by Colleen Kelley and Wendy Weeks. This manual was designed to bring relevance and critical thinking skills to the allied health chemistry course. Students are encouraged to become diagnosticians and apply their newly-acquired chemistry knowledge to solving real life health and environmental cases. The case manual also encourages a holistic approach by asking students to synthesize information across topics.

SUPPORT PACKAGE FOR STUDENTS

xiv

PREFACE

SUPPORT PA C K A G E F O R INSTRUCTORS

PowerPoint Lecture Slides Created by Colleen Kelley, Pima Community College, these slides contain lecture outlines and key topics from each chapter of the text, along with supporting artwork and figures from the text. The slides also contain assessment questions and questions for in-class discussion. WileyPlus Homework Management System WileyPlus is a powerful on-line tool that provides a completely integrated suite of teaching and learning resources in one easyto-use web site. WileyPlus integrates Wileys world-renowned content with media, including a multimedia version of the text, PowerPoint slides, on-line assessment, and more. Digital Image Archive The text web site includes downloadable files of text images in JPEG format. Test Bank Written by John Singer, Jackson Community College, the test bank includes multiple choice, true/false, and short answer questions. Computerized Test Bank The IBM and Macintosh compatible version of the entire Test Bank has full editing features to help the instructor customize tests. Instructors Manual Written by Colleen Kelley, Pima Community College, this supplement provides Chapter Summaries and lecture outlines. Instructors Solutions Manual Written by Adeliza Flores, of Las Positas College, this supplement contains worked-out solutions to all of the end-of-chapter problems.

A C K N O W L E D G M E N T S

I wish to thank my wife Susan and my son William for their encouragement, support, and patience. It is with great appreciation that I acknowledge the important contributions made by Jennifer Yee, Catherine Donovan, Suzanne Ingrao, Janet Foxman, Lisa Gee, Hope Miller, Thomas Kulesa, Gabriel Dillon, Amanda Wygal, and all of the others at Wiley who were involved in helping to prepare this second edition. Finally, I wish to acknowledge the important contributions made by the following reviewers of this text: Jeannie Collins University of Southern Indiana Myriam Cotton Pacific Lutheran University Stephen Dunham Moravian College Joseph Fassler Santa Rosa Junior College Louis Giacinti Milwaukee Area Technical College Christina Goode California State University, Fullerton Saifunnissa B. Hassam Santa Rosa Junior College Colleen Kelley Pima Community College Ira Krull Northeastern University Paul Moggach Georgian College Michael Myers California State University, Long Beach Lynette Rushton South Puget Sound Community College Shaun Schmidt Washburn University John Singer Jackson Community College Carnetta Skipworth Bowling Green Community College Steven Stefanides Wenatchee Valley College Maria Vogt Bloomfield College William Wagener West Liberty State College Wendy Weeks Pima Community College Lynda Peebles Texas Womans University Jennifer Powers Kennesaw State University Parris Powers Volunteer State Community College Rita Rhodes University of Tulsa Lenore Rodicio Miami-Dade College Lynette Rushton South Puget Sound Community College Sean Schmidt Washburn University Sara Selfe Edmonds Community College Anna Sequeira Forsyth Tech Community College Sonja Siewert West Shore Community College Carnetta Skipworth Western Kentucky University Robert St. Amand Union County College Richard Tarkka University of Central Arkansas Thottumkara Vinod Western Illinois University Tracy Whitehead Henderson State University Todd Wimpfheimer Salem State College

xv

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A B O U T T H E A U T H O R

Ken Raymond received a B.S. in Chemistry from Central Washington

University in 1975 and a Ph.D. in Organic Chemistry from the University of Washington in 1981. Since joining the faculty of Eastern Washington University in 1982, his primary teaching responsibilities have been in the general, organic, and biochemistry series for the health sciences and in the upper-division organic chemistry lecture and laboratory series. In 1990 he received EWUs annual award for excellence in teaching. He has been chair of the Department of Chemistry and Biochemistry since 2000. When not grading papers, he plays mandolin and button accordion in a local folk band.

xvii

B R I E F C O N T E N T S

The asterisks are color coded to indicate which chapters are integrated.

CHAPTER 1 CHAPTER 2

SCIENCE AT O M S

AND

MEASUREMENTS 1

AND

E L E M E N T S 26

* *

CHAPTER 3 CHAPTER 4

C O M P O U N D S 60 AN INTRODUCTION C O M P O U N D S 92 GASES, LIQUIDS, R E A C T I O N S 176 SOLUTIONS, COLLOIDS, S U S P E N S I O N S 212 LIPIDSAND AND TO

ORGANIC

CHAPTER 5

AND

S O L I D S 138

* * * * * * *

CHAPTER 6 CHAPTER 7

CHAPTER 8 CHAPTER 9

M E M B R A N E S 252AND

ACIDS, BASES, E Q U I L I B R I U M 286

CHAPTER 10

CARBOXYLIC ACIDS, PHENOLS, A M I N E S 320

AND

CHAPTER 11

ALCOHOLS, ETHERS, ALDEHYDES, A N D K E T O N E S 360 C A R B O H Y D R AT E S 396 PEPTIDES, PROTEINS, E N Z Y M E S 432 N U C L E I C A C I D S 468 M E TA B O L I S M 504AND

CHAPTER 12 CHAPTER 13

CHAPTER 14 CHAPTER 15

xviii

C O N T E N T S

CHAPTER

1

SCIENCE2

AND

MEASUREMENTS

1

1.1 1.2 1.3 1.4 1.5 1.6

The Scientific Method Matter and Energy4

H EALTH Link Science and MedicineUnits of Measurement6

4

Scientific Notation and Metric Prefixes Measurements and Significant Figures

9 11 15

H EALTH Link Body Mass Index H EALTH Link Body TemperatureCHAPTER

13 16

Conversion Factors and the Factor Label Method

228 29

ATOMS

AND

ELEMENTS

26

2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8

Atoms Elements

H EALTH Link Dietary Reference Intakes (DRIs)Atomic Number and Mass Number Periodic Table The Mole37 40 43 49 34 32

31

Radioactive Isotopes

Radioisotopes in Medicine

H EALTH Link CT and MRI ImagingFission and Fusion50

CHAPTER

362

COMPOUNDS65 70

60

3.1 3.2 3.3 3.4 3.5 3.6 3.7

Ions

The Arrangement of Electrons

B IOCHEMISTRY Link BioluminescenceThe Octet Rule Ionic Compounds Covalent Bonds Molecules78 80 71

B IOCHEMISTRY Link Ionophores and Biological Ion Transport74 77

73

H EALTH Link Dental Fillings

Formula Weight, Molecular Weight, and Molar Mass

81xix

B IOCHEMISTRY Link Ethylene, a Plant Hormone

84

xx

CONTENTSCHAPTER

4

AN INTRODUCTION COMPOUNDS 92

TO

ORGANIC

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9

Structural Formulas and Formal Charges Polar Covalent Bonds, Shape, and Polarity Noncovalent Interactions Alkanes110 115 118 117 118 108

94 103

Constitutional Isomers Conformations Cycloalkanes

H EALTH Link Prion Diseases

Alkenes, Alkynes, and Aromatic Compounds

120

H EALTH Link Sunscreens

124 125 128AND

Alcohols, Carboxylic Acids, and Esters

B IOCHEMISTRY Link Odor and FlavorCHAPTER

5

GASES, LIQUIDS,140 146 150

SOLIDS

138

5.1 5.2 5.3 5.4 5.5

States of Matter and Energy Gases and Pressure

H EALTH Link Blood PressureThe Gas Laws Partial Pressure Liquids161 150 158

H EALTH Link Making Weight 164 H EALTH Link Breathing 1665.6

Solids

167

CHAPTER

6

REACTIONS178 183 182

176

6.1 6.2 6.3 6.4 6.5 6.6 6.7

Chemical Equations Reaction Types

Oxidation and Reduction Reactions Involving Water

H EALTH Link Antiseptics and Oxidation189

187 191

Mole and Mass Relationships in Reactions Calculating the Yield of a Reaction Free Energy and Reaction Rate195 198

H EALTH Link Carbonic AnhydraseCHAPTER

201AND

7

SOLUTIONS, COLLOIDS, SUSPENSIONS 212214 216 220 221 222 222

7.1 7.2 7.3 7.4

Solutions

Reactions of Ions in Aqueous Solutions

Hard Water

Solubility of Gases in Water Organic Compounds

H EALTH Link Hyperbaric Medicine

CONTENTS

xxi

7.5 7.6 7.7 7.8 7.9

Biochemical Compounds

224

H EALTH Link ProdrugsConcentration Dilution236

227 228 237 240 242

Colloids and Suspensions

H EALTH Link Saliva

239

Diffusion and Osmosis

H EALTH Link Diffusion and the KidneysCHAPTER

8

LIPIDS254

AND

MEMBRANES

252

8.1 8.2 8.3

Fatty Acids Waxes258

H EALTH Link Omega-3 fatty acidsTriglycerides259

257

H EALTH Link Trans Fats 265 H EALTH Link Olestra 2668.4 8.5 8.6 8.7

Phospholipids and Glycolipids Steroids Eicosanoids Membranes270 272

266

H EALTH Link Anabolic Steroids275

275

CHAPTER

9

ACIDS, BASES, AND EQUILIBRIUM288 289

286

9.1 9.2 9.3 9.4 9.5 9.6

Acids and Bases Equilibrium290

BrnstedLowry Acids and Bases Le Chteliers Principle Ionization of Water The pH Scale297 293

B IOCHEMISTRY Link Diving Mammals, Oxygen, and Myoglobin296

295

Math SupportLogs and Antilogs 300 B IOCHEMISTRY Link Plants as pH Indicators9.7 9.8 9.9

301

Acid and Base Strength

301 303 305

Neutralizing Acids and Bases306

Effect of pH On Acid and Conjugate Base Concentrations308

9.10 Buffers

9.11 Maintaining the pH of Blood SerumCHAPTER

10

CARBOXYLIC ACIDS, PHENOLS, AND AMINES 320323 325 326 329

10.1 Carboxylic Acids 10.2 Phenols 324

H EALTH Link A Chili Pepper Painkiller

10.3 Carboxylic Acids and Phenols As Weak Organic Acids 10.4 Other Reactions of Carboxylic Acids

xxii

CONTENTS

10.5 Oxidation of Phenols 10.6 Amines 10.8 Amides 333

332 336

10.7 Amines As Weak Organic Bases 337

H EALTH Link Biofilms 339 B IOCHEMISTRY Link A Cure for Fleas10.9 Stereoisomers 341

340 346

H EALTH Link Adrenaline and Related CompoundsCHAPTER

11

ALCOHOLS, ETHERS, ALDEHYDES, AND KETONES 360363 367 370 373 374 376 376 379

11.1 Alcohols, Ethers, and Related Compounds 11.2 Preparation 11.3 Reactions

11.4 Aldehydes and Ketones 11.5 Oxidation of Aldehydes

H EALTH Link Aldehyde Dehydrogenase H EALTH Link Protective Enzymes378

11.6 Reduction of Aldehydes and Ketones

11.7 Reactions of Alcohols with Aldehydes and Ketones

H EALTH Link Drugs in the EnvironmentCHAPTER

382 396

12

C A R B O H Y D R AT E S398 404 406

12.1 Monosaccharides

12.2 Reactions of Monosaccharides 12.4 Oligosaccharides 410

12.3 Monosaccharides in Their Cyclic Form

H EALTH Link Relative Sweetness 415 H EALTH Link Indigestible Oligosaccharides12.5 Polysaccharides 418 422

417

H EALTH Link Blood TypeCHAPTER

13

PEPTIDES, PROTEINS, ENZYMES 432434 437 440 441

AND

13.1 Amino Acids

13.2 The Peptide Bond 13.4 Protein Structure

13.3 Peptides, Proteins, and pH

B IOCHEMISTRY Link Collagen and a-Keratin, Two Fibrous Proteins B IOCHEMISTRY Link Hemoglobin, a Globular Protein 44813.5 Denaturation 13.6 Enzymes 449 453 459 449

447

13.7 Control of Enzyme-Catalyzed Reactions

H EALTH Link Proteins in Medicine

CONTENTSCHAPTER

xxiii

14

NUCLEIC ACIDS470

468

14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9

Nucleic Acid Building Blocks Polynucleotides DNA Structure Denaturation DNA Replication RNA484 487 476 477 480

Nucleoside di-and Triphosphates, Cyclic Nucleotides

475

Nucleic Acids and Information Flow482

481

Translation

H EALTH Link Viruses 489 14.10 Control of Gene Expression H EALTH Link RNA Interference14.11 Mutation 491

489 491 492 494 504 506

H EALTH Link Breast Cancer Genes14.12 Recombinant DNA 492

B IOCHEMISTRY Link DNA FingerprintingCHAPTER

15

M E TA B O L I S M507

15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9

Metabolic Pathways, Energy, and Coupled Reactions Overview of Metabolism Digestion Glycolysis512 514 519 521 522

B IOCHEMISTRY Link The Origin of Mitochondria

512

Gluconeogenesis Citric Acid Cycle

Glycogen Metabolism

Electron Transport Chain and Oxidative Phosphorylation

524

H EALTH Link Brown FatLipid Metabolism

527 528 532

15.10 Amino Acid Metabolism

Appendix A Appendix B Appendix C Appendix D Appendix E Index I-1

Scientific Calculators

A-1 A-5

Important Families of Organic Compounds

Naming Ions, Ionic Compounds, Binary Molecules, and Organic Compound A-8 Answers to Odd-Numbered Problems Glossary A-51 A-23

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GENERAL, ORGANIC, AND BIOLOGICAL CHEMISTRY

An Integrated ApproachSECOND EDITION

After their first chemistry lecture

a group of students walks

across campus together. One student says, I want to be a nurse. I can see how we might need to study chemistry, but why does the textbook have to start with a chapter on math? What does math have to do with the health sciences? The rest of the group voices their agreement. A nursing student walking past the group in the other direction overhears this comment and smiles. They have no idea how much math they will use, she thinks to herself.

Photo source:

Rick Madonik/Toronto Star/Zuma Press.

1

S

C I E N C E A N D M E A S U R E M E N T S

In this first chapter of the text we will take a look at science, chemistry, and mathematics, and will see the important role that each plays in the health sciences.

objectivesAfter completing this chapter, you should be able to:1 Explain the terms scientific method, law, theory, hypothesis, and experiment. 2 Define the terms matter and energy. Describe the three states of matter and the two

forms of energy.3 Describe and give examples of physical properties and physical change. 4 Convert from one unit of measurement into another. 5 Express values using scientific notation and metric prefixes. 6 Explain the difference between the terms accurate and precise. 7 Use the correct number of significant figures to report the results of calculations

involving measured quantities.

1

2

CHAPTER 1 | SCIENCE AND MEASUREMENTS

1.1

THE

SCIENTIFIC

METHOD

Experiments test hypotheses.

(a)

(b) FIGURE |

1.1

Medical imaging

(a) The first x ray of the human body was taken in 1895 by Wilhelm Roentgen, the discoverer of x rays. In this x ray, you can see the bones of his wifes hand and her wedding ring. (b) With the improvements that have been made to x-ray equipment, clinicians can now obtain sharper and more detailed images, as in this scan of a patients vertebrae.Source:

(a) SPL/Photoresearchers; (b) Gondelon/Photo Researchers, Inc.

Science is an approach that is used to try to make sense out of how the universe operates, ranging in scale from the very large (understanding how stars form) to the very small (understanding the behavior of the tiny particles from which everything is made). The knowledge gained from scientific studies has impacted our lives in many positive ways, including our ever-improving ability to treat diseases. For example, the medical scanners (including CT and MRI) and many of the therapeutic drugs (including antibiotics and anti-cancer drugs) used today are available as a result of the careful work of scientists (Figure 1.1). In doing science, the scientific method is the process used to gather and interpret information. Observation is part of this process. One well-known story regarding the importance of observation involves the English scientist Isaac Newton (16421727). Reportedly, seeing an apple fall out of a tree led him to formulate the law of gravity, which states that there is an attractive force between any two objects (in this case, between the earth and an apple). This and other scientific laws are statements that describe things that are consistently and reproducibly observed. While a law does not explain why things happen, it can be used to predict what might happen in the future. For example, the law of gravity does not explain why things fall, but it does allow you to predict what will happen if you jump off of a ladder. Explaining observations is a key component of the scientific method. The process begins with the construction of a hypothesis, a tentative explanation (educated guess) that is based on presently known facts. Clinicians, for example, make educated guesses when treating patients. If a patient complains of stomach pains, the clinician will ask a few questions and make a few observations before coming up with a hypothesis (diagnosis) as to the nature of the problem. This hypothesis is based on knowledge of symptoms and diseases. The most important part of the scientific method is what happens once a hypothesis has been constructedit must be tested by doing careful experiments. To test a hypothesis, a clinician might call for a series of medical tests (experiments) to be run. If the test results support the diagnosis, treatment can begin. If they invalidate the diagnosis, the clinician must revise the hypothesis and look for another cause of the illness. Experiments must be designed so that the observations made are directly related to the question at hand. For example, if a patient has stomach pains, taking an x ray of his or her big toe will probably not help find the cause of the illness. Once a hypothesis has survived repeated testing, it may become a theoryan experimentally tested explanation of an observed behavior. For a theory to survive, it must be consistent with existing experimental evidence, must accurately predict the results of future experiments, and must explain future observations. Figure 1.2 shows the interconnections of the various parts of the scientific method making an observation, forming a hypothesis, performing experiments, and creating a theory. Scientists do not necessarily follow these steps in order, nor do they always use all of the steps. It may be that an existing law suggests a new experiment or that a set of published experiments suggests a radically new hypothesis. Creativity is an important part of science; sometimes new theories arise when someone discovers an entirely new way of interpreting experimental results that hundreds of others had looked at before, but could not explain. In addition to creativity, a scientist must have sufficient knowledge of the field to be able to interpret experimental results and to evaluate hypotheses and experiments. The fact that theories are based on experimental observations means that they sometimes change. In Section 2.1 two theories of the atom, the fundamental particle from which matter is created, are discussed. One of these theories dates back to the early 1800s, when technology was not very advanced and experiments provided much less information than is obtainable today (Figure 1.3). While the earliest theory of the atom accounted for the observations made up until the early 1800s, once better experimental results were obtained, errors were revealed. Whether scientists study atoms or inherited diseases, theories must be continually reevaluated and, if necessary, revised as new experiments provide additional information. This change is an expected part of science.

1.1 THE SCIENTIFIC METHOD

3

Observations

FIGURE |

1.2

The scientific method

Form new hypothesis

In the scientific method, experiments provide the information used to discard, revise, or accept hypotheses.Source:

Experiments

From Biochemistry: A Foundation 1st edition by Ritter. 1996. Reprinted with permission of Brooks/Cole, a division of Thomson Learning: www.thomsonrights.com. Fax 800 730 2215.

Fails

Does fairly well Passes

Discard hypothesis

Revise hypothesis

Accept hypothesisRepeated testing

Theory

(a) FIGURE |

(b)

1.3

Modifying theories

Theories are sometimes revised when improved scientific equipment allows better experimental results to be obtained.Source: (a) Hulton-Deutsch Collection/Corbis; (b) James Holmes/ Thomson Laboratories/Photo Researchers Inc.

4

CHAPTER 1 | SCIENCE AND MEASUREMENTS

Science and Medicine

The level of glucose (blood sugar) in the body is controlled by a hormone called insulin. Diabetes is the diseasethat occurs when insulin is not produced in sufficient amounts or when the body is not sensitive to its effects. As science has progressed over the years, so has our understanding of this disease and our ability to treat it. In the mid 1800s, before it was known that high levels of glucose cause the symptoms of diabetes, some physicians recommended that their diabetic patients eat lots of sugar. Others recommended starvation. Scientific studies in the late 1800s and early 1900s led to an understanding of the role that the pancreas plays in glucose metabolism and to the discovery of insulin, which is produced by the pancreas. Insulin was first used in 1922 to treat diabetes in humans. Because the insulin used then was not very pure, patients were given injectionsoften painfulof up to 2 teaspoons (10 milliliters) at a time. As the science of isolating and purifying insulin improved, dosages dropped to less than one-tenth of that size. Other advances in the treatment of diabetes included the use of oral drugs to control insulin levels (introduced in 1955), the use of genetically engineered human insulin (introduced in (a) 1982) in place of that isolated from cattle and pigs, FIGURE | 1.4 (b) and the development of Glucose testing new methods to test blood It is important for diabetics to monitor their blood glucose levels. (a) When these test strips are glucose levels (Figure 1.4).

dipped in a urine sample, the array of colors produced indicates the amount of glucose present. (b) Blood glucose monitors that require just a small drop of blood are alternatives to test strips.Source:

(a) Saturn Stills/Photo Researchers, Inc.; (b) Yoav Levy/Phototake.

1.2

MATTER

AND

ENERGY

Now that we have been introduced to some of the basic aspects of science, let us see how chemistry fits into the picture. Chemistry is the study of matter and the changes it undergoes. Matter is defined as anything that has mass and occupies space. In everyday terms, this definition includes your body, the air that you breathe, this book, and all of the other material around you. We can describe matter in terms of physical properties, those characteristics that can be determined without changing the chemical composition of matter (what it is made of). For example, a cube of sugar is white, tastes sweet, and is odorless. The act of measuring these and other physical properties, including melting point (melting temperature), does not change the sugar into anything elseit is still sugar. Matter is typically found in one of three different physical states or phasesas a solid, a liquid, or a gas. From our direct experience we know that Solids have fixed shapes and volumes. Liquids have variable shapes and fixed volumes. Gases have variable shapes and volumes.

1.2 MATTER AND ENERGY

5

FIGURE |

1.5

Gas, liquid, and solid

A paint can (a solid), paint (a liquid), and paint fumes (a gas) illustrate the three physical states of matter.

Think about what happens if an opened can of paint gets spilled (Figure 1.5). Whether it is standing upright or lying on its side, the can (a solid) has the same shape and occupies the same volume of space. The paint (a liquid) keeps its original 1 gallon volume but changes its shape as it spreads out across the floor. The paint fumes (a gas) quickly change their shape and volume as they spread through the air in the room. Converting matter between each of these states is an example of physical change, change in which the chemical composition of matter is not altered (Figure 1.6). Crushing a cube of sugar, boiling water to make steam, and melting an iron rod are examples of physical change. Any time that matter is changed in any way, work has been done. This includes the physical changes just mentioned, as well as walking, running, or turning the pages of this book. All of these activities involve energy, which is defined as the ability to do work and to transfer heat. Energy can be found in two forms, as potential energy (stored energy) or as kinetic energy (the energy of motion). The water sitting behind a dam has potential energy. When the floodgates are opened and the water begins to pour through, potential energy is converted into kinetic energy. All matter contains energy, so changes in matter (work) and changes in energy (potential or kinetic) are connected to one another. For example, if you drive a car, some of the potential energy of gasoline is converted into the kinetic energy used to move the pistons in the engine (doing work) and some is converted into heat, a form of kinetic energy related to the motion of the particles from which things are made.

Matter can exist in the solid, liquid, and gas states.

Potential energy is stored energy. Kinetic energy is the energy of motion.

FIGURE |

1.6

Physical change

When snow melts in the spring, rivers fill with water. The conversion of snow into water is a physical change.Source:

Peter Van Rijn/Superstock.

6

CHAPTER 1 | SCIENCE AND MEASUREMENTS

S AMPLE P ROBLEM

1.1

Potential versus kinetic energy Which are mainly examples of potential energy and which are mainly examples of kinetic energy? a. A mountain climber sits at the top of a peak. b. A mountain climber rappels down a cliff. c. A hamburger sits on a plate. d. A nurse inflates a blood pressure cuff.Strategy

Recall that potential energy is stored energy and that kinetic energy is the energy of motion.Solution a. potential energy b. kinetic energy c. potential energy d. kinetic energy

P RACTICE P ROBLEM

1.1

a. Describe changes in the kinetic energy and the potential energy of a barbell when a

weightlifter picks it up.b. Describe changes in the kinetic energy and the potential energy of a weightlifter when

a barbell is picked up.

1.3

UNITS

OF

MEASUREMENT

Making measurements is part of our everyday lives. Every time that you look at your watch to see how many minutes of class remain, tell a friend about your 5 mile run this morning, or save money by buying products with the lowest unit price, you are using measurements. Measurements are also a key part of the job of health professionals. A nurse might measure your pulse, blood pressure, and temperature, a dental hygienist might measure the depth of your gum pockets, or an occupational therapist might measure your hand strength to gauge the degree of recovery from an injury (Figure 1.7). Measurements consist of two parts: a number and a unit. Saying that you swam for 3 is not very informativewas it 3 minutes, 3 hours, or 3 miles? The number must be accompanied by a unit, a quantity that is used as a standard of measurement (of time, of length, of volume, etc.). The metric system is the measurement system used most often worldwide. In this text we will use metric units and the common units used in the United States (Table 1.1). Occasionally, SI units (an international system of units related to the metric system) will be introduced. Table 1.2 lists some of the additional units that are commonly used in medical applications. FIGURE |

1.7

Measuring hand strength

MassMass is related to the amount of matter in a materialthe more matter that it contains, the greater its mass. Units commonly used to measure mass are the gram (g), kilogram (kg), and pound (lb). A mass of 454 g is equivalent to 1 lb and 2.205 lb is equivalent to 1 kg (Figure 1.8).

A dynamometer is used to measure a patients hand strength.Source:

Keith Brofsky/Photodisc Green/Getty Images.

1.3 UNITS OF MEASUREMENT

7

(a) FIGURE |

(b)

(c)

1.8

Comparing units

(a) One kilogram weighs a little more than two pounds. (b) One meter (bottom) is slightly longer than one yard (top). (c) One quart is slightly smaller than one liter.Source:

(a), (b) Andy Washnik/Wiley Archive; (c) Michael Dalton/Fundamental Photographs.

TABLE |

1.1

MEASUREMENT UNITS

Quantity

Common Unit

Metric Unit

SI Unit

Relationships

Mass Length Volume Energy Temperature

Pound (lb) Foot (ft) Quart (qt) calorie (cal) Degree Fahrenheit (F)

Gram (g) Meter (m) Liter (L) calorie (cal) Degree Celsius (C)

Kilogram (kg) Meter (m) Cubic meter (m3) Joule (J) Kelvin (K)

1 kg = 2.205 lb 1 kg = 1000 g 1 m = 3.281 ft 0.946 L = 1 qt 1 m3 = 1000 L 4.184 J = 1 cal F = (1.8 C) + 32 F 32 C = 1.8 K = C + 273.15

TABLE |

1.2

SOME MEASUREMENT UNITS USED

IN

MEDICINE

Quantity

Relationship

Mass

1 milligram (mg) = 1000 micrograms (mcg or g)a 1 grain (gr) = 65 milligrams (mg) 1 cubic centimeter (cc or cm3) = 1 milliliter (mL) 15 drops (gtt) = 1 milliliter (mL) 1 teaspoon (tsp) = 5 milliliters (mL) 1 tablespoon (T or tbsp) = 15 milliliters (mL) 2 tablespoons (T or tbsp) = 1 ounce (oz)

Volume

a

The prefixes micro and milli are explained in Section 1.4.

8

CHAPTER 1 | SCIENCE AND MEASUREMENTS

Length

454 g = 1 lb; 2.205 lb = 1 kg 1 m = 3.281 ft = 39.37 in 0.946 L = 1 qt 32F = 0C = 273.15 K 1 cal = 4.184 J

The meter (m), which is slightly longer than a yard, is the metric unit of length. One meter is equal to 3.281 ft and 39.37 in.

VolumeThe liter (L) and the quart (qt) are two units commonly used to measure volume (the amount of space occupied by a material). One quart is a bit smaller than a liter (1 qt = 0.946 L).

TemperatureThe metric system uses the Celsius (C) scale to measure temperature. On this scale, water freezes at 0C and boils at 100C. On the Fahrenheit (F) scale, still used in the United States, water freezes at 32F and boils at 212F (Figure 1.9). Besides having different numerical values for the freezing and boiling points of water, these two temperature scales have degrees of different sizes. On the Fahrenheit scale there are 180 degrees between the temperatures where water boils and freezes (212F 32F = 180F). On the Celsius scale, however, there are only 100 degrees over this same range (100C 0C = 100C). This means that the boiling to freezing range for water has almost twice as many Fahrenheit degrees as Celsius degrees (180/100 = 1.8). Scientists often measure temperature using the SI unit called the kelvin (K). A temperature of 0 K, known as absolute zero, is the temperature at which all heat energy has been removed from a sample. On the Kelvin temperature scale, the difference between the freezing point (273.15 K) and the boiling point (373.15 K) of water is 100 degrees, the same as that for the Celsius scale, so a kelvin is the same size as a Celsius degree.

EnergyThe metric unit for energy, the calorie (cal), is defined as the amount of energy required to raise the temperature of 1 g of water from 14.5C to 15.5C. The SI energy unit, the joule (J), which is approximately equal to the energy expended by a human heart each time that it beats, is about one-fourth as large as a calorie (1 cal = 4.184 J). When you hear the word calorie, it might bring food to mind. One food Calorie (Cal) is equal to 1000 cal, which means that an 80 Cal cookie contains 80,000 cal of potential energy.

FIGURE |

1.9

212 F200 190 180

100 C

100

373.15 K

370

water boils

90

360

Temperature units

80 170 160 150 140 130 120 110 100 90 30 80 70 60 50 40 10 20 40 60 70

Water freezes and boils at different temperature values in the Fahrenheit, Celsius, and Kelvin scales.

350

340

330

180

50

100

320

100

310

300

290

280

32 F

30 20 10 0

0 C

0

273.15 K

270

water freezes

10

260

1.4 SCIENTIFIC NOTATION AND METRIC PREFIXES

9

S AMPLE P ROBLEM

1.2

Comparing units Which is larger? a. 1 g or 1 lbStrategy b. 1 lb or 1 kg c. 1 L or 1 qt d. 1 cal or 1 J

Refer to the Relationships column in Table 1.1 to get a feel for the relative sizes of these units.Solution a. 1 lb b. 1 kg c. 1 L d. 1 cal

P RACTICE P ROBLEM

1.2

Which is a warmer temperature?a. 273C or 273 K? b. 32F or 32C? c. 0F or 0 K?

1.4

SCIENTIFIC NOTATION AND METRIC PREFIXES

Scientific NotationWhen making measurements, particularly in the sciences, there are many times when you must deal with very large or very small numbers. For example, a typical red blood cell has a diameter of about 0.0000075 m. In scientific notation (exponential notation) this diameter is written 7.5 106 m. Values expressed in scientific notation are written as a number between 1 and 10 multiplied by a power of ten. The superscripted number to the right of the ten is called an exponent. 7.5 106A number between 1 and 10 Exponent

An exponent with a positive value tells you how many times to multiply a number by 10, 3.5 104 = 3.5 10 10 10 10 = 35000 6.22 102 = 6.22 10 10 = 622 while an exponent with a negative value tells you how many times to divide a number by 10. 3.5 = 0.00035 10 10 10 10 6.22 102 = 6.22 = 0.0622 10 10 An easy way to convert a number into scientific notation is to shift the decimal point. For a number that is equal to or greater than 10, shift the decimal point to the left until you get a number between 1 and 10. The number of spaces that you moved the decimal place is the new exponent (see Table 1.3). 3.5 104 = 35000 = 3.5 104 285.2 = 2.852 102 8300000 = 8.3 106

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CHAPTER 1 | SCIENCE AND MEASUREMENTS

TABLE |

1.3

S C I E N T I F I C N O TAT I O N

Number

Scientific Notation

Exponent

0.0001 0.001 0.01 0.1 1 10 100 1000 10000

1 104 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 103 2 1 0 1 2 3 4

4 3 2 1 0 1 2 3 4

For a number less than 1, shift the decimal point to the right until you get a number between 1 and 10. Put a negative sign in front of the number of spaces that you moved the decimal place and make this the new exponent. 0.00035 = 3.5 104 0.0445 = 4.45 102 0.00000003554 = 3.554 108

Metric PrefixesUnits larger and smaller than the metric units introduced in Section 1.3 can be created by attaching a prefix that indicates how the new unit relates to the original (see Table 1.4). For example, drugs are often administered in milliliter (mL) volumes. The prefix milli indicates that the original unit, in this case the liter, has been multiplied by 103. 1 milliliter (mL) = 1 103 L Similarly, distance can be measured in kilometers. The prefix kilo indicates that the meter unit of length has been multiplied by 103. 1 kilometer (km) = 1 103 m TABLE |

1.4

SI

AND

METRIC PREFIXES

Prefix

Symbol

Multiplier

giga mega kilo hecto deka deci centi milli micro nano

G M k h da d c m n

1,000,000,000 1,000,000 1000 100 10 1 0.1 0.01 0.001 0.000001

= 109 = 106 = 103 = 102 = 101 = 100 = 101 = 102 = 103 = 106

0.000000001 = 109

1.5 MEASUREMENTS AND SIGNIFICANT FIGURES

11

S AMPLE P ROBLEM

1.3

Using scientific notation Convert each number into scientific notation. a. 0.0144 b. 144 c. 36.32Strategy d. 0.0000098

The decimal point is shifted to the left for numbers equal to or greater than 10 and shifted to the right for numbers less than 1.Solution a. 1.44 102 b. 1.44 102 c. 3.632 101 d. 9.8 106

P RACTICE P ROBLEM

1.3

One-millionth of a liter of blood contains about 5 million red blood cells. Express this volume of blood using a metric prefix and this number of cells using scientific notation.

1.5

MEASUREMENTS AND SIGNIFICANT FIGURES

We have just examined some of the units used to report the measured properties of a material. In this section we will address three of the important factors to consider when making measurements: accuracy, precision, and significant figures. Accuracy is related to how close a measured value is to a true value. Suppose that a patients temperature is taken twice and values of 98F and 102F are obtained. If the patients actual temperature is 103F, the second measurement is more accurate because it is closer to the true value. Precision is a measure of reproducibility. The closer that separate measurements come to one another, the more precise they are. Suppose that a patients temperature is taken three times and values of 98F, 99F, and 97F are obtained. Another set of temperature measurements gives 90F, 100F, and 96F. The first three measurements are more in agreement with one another, so they are more precise than the second set. A set of precise measurements is not necessarily accurate and a set of accurate measurements is not necessarily precise. This is illustrated in Figure 1.10, using the game of darts as an example. Figure 1.10a shows the results of three shots that are precise, but not accuratethe shots fall close together, but they not are centered on the bulls-eye. In Figure 1.10b, the shots are accurate, but not precise, because the shots fall near the bulls-eye but not close together. Figure 1.10c shows three shots that are both accurate and precise.

Accurate measurements fall near the true value.

Precise measurements are grouped together.

(a) FIGURE |

(b)

(c)

1.10

Accuracy and precision

(a) The darts were thrown precisely (they are all close to one another) but not accurately. (b) The darts were thrown accurately (they fall near the bulls-eye) but not precisely. (c) The darts were thrown precisely and accurately.

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CHAPTER 1 | SCIENCE AND MEASUREMENTS

Significant FiguresThe quality of the equipment used to make a measurement is one factor in obtaining accurate and precise results. For example, balances similar to the one shown in Figure 1.11 come in different models. A lower priced model might report masses to within 0.1 g, and a higher priced one to within 0.001 g. Suppose that the precision of a balance is such that repeated measurements always agree to within 0.1 g. On this balance, a U.S. quarter (25 cent coin) might have a reported mass of 5.6 g. This number, 5.6, has two significant figures (those digits in a measurement that are reproducible when the measurement is repeated, plus the first doubtful digit). Here the 6 in 5.6 is doubtful, because the balance reports mass with an error of 0.1 g. Assuming that the balance is accurate, the actual mass of the quarter may be a little bit more or a little bit less than 5.6 grams. On a different balance that reports masses with a precision of 0.001 g, the reported mass of the same quarter might be 5.563 g. Using this measuring device, the mass of the quarter is reported with four significant figures. For the numbers above (5.6 and 5.563), determining significant figures is straightforward: all of the digits written are significant. Things get a bit trickier when zeros are involved, because zeros that are part of the measurement are significant, while those that only specify the position of the decimal point are not. Table 1.5 summarizes the rules for determining when a digit is significant. It is important to note that significant figures apply only to measurements, because measurements always contain some degree of error. Numbers have no error when they are obtained by an exact count (there are seven patients sitting in the waiting room) or are defined (12 eggs = 1 dozen, 1 km = 1000 m). These exact numbers have an unlimited number of significant figures.

FIGURE |

1.11

Balances

Top-loading balances give a digital readout of the mass of an object.Source:

BSIP/Photo Researchers, Inc.

TABLE |

1.5

SIGNIFICANT FIGURES

Examples

Number of Significant Figures

Numbers are significant if they are: a. Nonzero digits b. Zeros between nonzero digits c. Zeros at the end of a number when a decimal point is written d. Digits in a number written in scientific notation (not including the power of ten) Numbers are not significant if they are: a. Zeros at the beginning of a number b. Zeros at the end of a number when no decimal point is written 0.543 0.0006 200 1,500,000 3 1 1 2 3.4 25.85 308 97.0002 5.010 200. 7.0 105 6.02 1023 2 4 3 6 4 3 2 3

1.5 MEASUREMENTS AND SIGNIFICANT FIGURES

13

S AMPLE P ROBLEM

1.4

Determining significant figures Specify the number of significant figures in each measured value. a. 30.1C b. 0.00730 m c. 7.30 103 mStrategy d. 44.50 mL

All nonzero digits are significant. Zeros, however, are significant only under certain conditions (see Table 1.5).Solution a. 3 b. 3 c. 3 d. 4

P RACTICE P ROBLEM

1.4

Write each measured value in exponential notation, being sure to give the correct number of significant figures.a. 7032 cal b. 88.0 L c. 0.00005 g d. 0.06430 lb

Body Mass Index

In early 2006, the Harris Poll released a report titled, Obesity Epidemic Continues to Worsen in the United States.According to this report, the percentage of Americans who are overweight or obese continues to rise. Based on Body Mass Index (discussed below), 66% of U.S. adults are overweight, and 27% are also obese. These numbers, which echo those given in other reports, are of concern to health professionals because being overweight or obese increases a persons risk of developing health problems. Among the identified overweight- and obesity-related diseases are type II diabetes, heart disease, high blood pressure, high cholesterol levels, stroke, cancer (colon, breast, and endometrial), and asthma. For years, determining whether someone was overweight involved using height and weight charts. These charts were of limited usefulness because, when it comes to assessing the risk of overweight- and obesity-related disease, body weight is not the main the issue. The primary factor to consider is the percentage of body weight that is due to fat. What body fat percentage is considered healthy? There is no single answer to this question because recommended body fat levels depend on a variety of factors. Table 1.6 lists the gender- and age-based recommendations for adults. Health professionals can determine percentage body fat using a variety of techniques. One of these is the skinfold measurement, in which calipers are used to test the thickness of folds of skin at various places on the body

TABLE |

1.6

R E C O M M E N D E D P E R C E N T B O D Y F AT

Age

Underweight

Recommended weight

Overweight

Obese

Female

2039 4059 6079

29

Male

2039 4059 6079

Values also depend upon ethnicity. The values reported here are averages for the ethnic groups studied in Gallagher et al., American Journal of Clinical Nutrition, 2000; 72:694701.

14

CHAPTER 1 | SCIENCE AND MEASUREMENTS

(Figure 1.12). A calculation using the measured values gives body fat percentage. Underwater weighing is another method used to determine body fat levels. Because fat has a lower density than muscle and bone, the more fat that a person has, the less the person will weigh underwater. Once measurements have been made, a set of equations is used to calculate percent body fat. In a different technique called bioelectrical impedance, electrodes are placed on different parts of the body and a low electrical current is applied. Fat is a poorer conductor of electricity than muscle and bone, so the higher the percent body fat, the greater the resistance or impedance to the current. Although it is not based on direct measurements of percent body fat, Body Mass Index (BMI) is a good predictor of an individuals risk for overweight- or obesity-related disease. BMI is calculated from a persons weight and height, using the equation BMI = 703 weight (lb) height (in)2

A 5 foot 1 inch (61.0 inch) tall person weighing 145 lbs is calculated to have a BMI of 27.4. BMI = 703 weight (lb) height (in)2 = 703 1452 = 27.4 61.0

According to adult BMI standards (Table 1.7), a person with a BMI of 27.4 is overweight. BMI is calculated in the same way for children and teens, but the interpretation of BMI differs.

TABLE |

1.7

A D U LT B O D Y M A S S I N D E X

BMI FIGURE |

Condition

1.12

Below 18.5 18.524.9 25.029.9 30.0 or higher

Underweight Recommended weight Overweight Obese

Skin fold calipers

Skinfold measurements can be used to determine percent body fat.Source:

Courtesy of Accu-Measure, LLC.

Calculations Involving Significant FiguresReporting answers with too many or too few significant figures is a problem commonly encountered with calculations involving measured values. The important thing to remember is that calculations should not change the degree of uncertainty in a value. When doing multiplication or division with measured values, the answer should have the same number of significant figures as the quantity with the fewest. Suppose that you are asked to determine the area of a rectangle. According to your measurements, its width is 5.3 cm and its length is 6.1 cm. Since area = width length, you use your calculator to multiply the two, and obtain 5.3 6.1 32.33 (32 cm cm cm2 cm2) Two significant figures Two significant figures Calculator answer (four significant figures) Correct answer (two significant figures)

The result given by your calculator has too many significant figures. Each of the original numbers (5.3 and 6.1) has just two significant figures, but the calculator has given an answer with four. Rewriting a number with the proper number of significant figures means that we have to drop the digits that are not significant (in this case, the two to the right of the decimal point) and round off the last digit of the number. We will use the following rules when rounding numbers:

1.6 CONVERSION FACTORS AND THE FACTOR LABEL METHOD

15

If the first digit to be removed is 0, 1, 2, 3, or 4, leave the last reported digit unchanged. (57.42 rounds off to 57.4 if three significant figures are needed and to 57 if two significant figures are needed.) If the first digit to be removed is 5, 6, 7, 8, or 9, increase the last reported digit by 1. (57.69 rounds off to 57.7 if three significant figures are needed and to 58 if two significant figures are needed.) When doing addition or subtraction with measured values, the answer should have the same number of decimal places as the quantity with the fewest decimal places. Suppose that you are given three mass measurements and are asked to calculate the total mass: 13.5 g One decimal place 2.335 g Three decimal places +653 g Zero decimal places 668.835 g Calculator answer (three decimal places) (669 g) Correct answer (Zero decimal places)S AMPLE P ROBLEM

1.5

Calculations involving significant figures Each of the numbers below is measured. Solve the calculations and give the answer with the correct number of significant figures. a. 0.12 1.77 c. 5.444 0.44 b. 690.4 12 d. 16.5 + 0.114 + 3.55Strategy

You must apply a different rule to carry significant figures through multiplication or division than to carry them through addition or subtraction.Solution a. 0.21 b. 58 c. 5.00 d. 20.2

P RACTICE P ROBLEM

1.5

Each of the numbers below is measured. Solve the calculations and give the answer with the correct number of significant figures.a. 53.4 489.6 b. 6.333 104 5.77 103 c. (5 989.5) 16.3 d. (0.45 6) + 3.14

1.6

CONVERSION FACTORS AND THE FACTOR LABEL METHOD

What is your height in inches and in centimeters? What is the volume of a cup of coffee in milliliters? Answering these questions requires that you convert from one unit into another. Some unit conversions are simple enough that you can probably do them in your headsix eggs are half a dozen and twenty-four inches are two feet. Solving other conversions may require a systematic approach called the factor label method, which uses conversion factors to transform one unit into another. Conversion factors are derived from the numerical relationship between two units. Suppose that a 185 lb patient is prescribed a drug whose recommended dosage is listed in terms of kilograms of body weight. To administer the correct dose, you must convert

Although the terms mass and weight are often used interchangeably, they do not mean the same thing. Mass is related to the amount of matter in an object, while weight depends on gravity. An astronaut weighs much less in space than on the surface of the earth, but his or her mass does not change.

16

CHAPTER 1 | SCIENCE AND MEASUREMENTS

Body Temperaturehen you go in for a medical checkup, a health professional will almost always begin by taking your temperature. This is done because running a fever is a sign of illness. What should your temperature be? A temperature of 98.6F (37.0C), measured orally, is considered normal. This normal temperature is actually an average of the typical range of oral body temperatures (97.2 99.9F) recorded for healthy people. The human body is divided into two different temperature zones, the core and the shell, so temperature readings will vary depending on which part of your body is measured. The bodys internal core, which holds the organs of the abdomen, chest, and head, is held at a constant temperature. The outer shell, that part of the body nearest the skin, is used to insulate the core. Shell temperatures fluctuate, depending on the whether the body is trying to keep or to lose heat, and typically shell temperatures run about 1F lower than core temperatures. Rectal temperature measurements are a good way to determine the core body temperature. While oral measurements can indicate core temperature, readings may be incorrect if the thermometer is not placed correctly in the mouth. Hot or cold drinks can also affect the results of oral temperature measurements. Tympanic membrane (eardrum) measurements give an indication of the core temperature of the brain, while axillary (armpit) and temporal artery (an artery in the head that runs near the temple) give the shell temperature. Like oral measurements, these three methods are prone to error.

W

FIGURE |

1.13

Temporal artery thermometer

A temporal artery thermometer measures temperature by detecting infrared (IR) energy released at the temporal artery.Source: Courtesy Exergen Corporation.

How are temperatures measured?A variety of methods can be used to take someones temperature. The low tech method used by countless parents is touchdoes your childs forehead feel hot? As you might expect, this is not the most reliable technique. For centuries the mercury thermometer has been used to measure temperature. Its operation is based on the fact that mercury expands as it gets warmerthe higher the temperature, the longer the column of mercury in a thermometer. These thermometers, used for rectal, oral, and axillary temperature measurements, have fallen out of favor because they can be difficult to read, can transmit infection when not cleaned properly, and, if broken, can expose people to toxic mercury. The digital thermometer is one alternative to the mercury thermometer. The operation of this thermometer is based on a thermistor, a device that conducts electricity better the higher the temperature. Digital thermometers, like mercury thermometers, are used to measure rectal, oral, and axillary temperatures. A digital thermometer pacifier has been developed for infant use. A third type of thermometer measures temperature by detecting infrared (IR) energy (Section 2.6), a form of energy that is associated with heat. Tympanic membrane and temporal artery thermometers (Figure 1.13), which operate using IR energy, are quick to use but, in the case of the tympanic thermometers, can give false readings. FIGURE | 1.14 In an interesting application of IR-based temperature measurement, some airports have installed automated Remote temperature sensing In an attempt to slow the spread of SARS (severe acute respiratory remote temperature sensors to scan people for fever syndrome), some airports have installed automated IR sensors to (Figure 1.14). These devices, originally installed to help identify travelers who are running a fever. control the spread of SARS (severe acute respiratory syndrome), may be used to help fight avian flu. Source: Courtesy of Infrared Solutions Inc. www.infraredsolutions.com

1.6 CONVERSION FACTORS AND THE FACTOR LABEL METHOD

17

the patients pound weight into kilograms. Converting from pounds to kilograms makes use of the equality 2.205 lb = 1 kg (Table 1.1). Two different conversion factors can be created from this relationship, the first of which is produced by dividing both sides of the equality by 1 kg. This and all other conversion factors are equal to 1. 2.205 lb = 1 kg 2.205 lb 1 kg = =1 1 kg 1 kg conversion factor: 2.205 lb 1 kg

The second conversion factor is created by dividing both sides of the equality by 2.205 lb 1 kg = 2.205 lb 1 kg 2.205 lb = =1 2.205 lb 2.205 lb conversion factor: 1 kg 2.205 lb

What is the kilogram weight of a 185 lb patient? To answer this question using the factor label method, we multiply 185 lb by the appropriate conversion factor (equal to 1). In this case the conversion factor to use is the one that has the desired new unit in the numerator. This allows the original units to cancel one another (Figure 1.15). 185 lb 1 kg = 83.9 kg 2.205 lb

Looking at this answer, you might wonder why it is reported with three significant figures. In the equality 1 kg = 2.205 lb, the 1 is an exact number and has an unlimited number of significant figures. The value with the fewest significant figures is 185 lb. Let us try another one. A vial contains 15 mL of blood serum. Convert this volume into liters. Converting from mL into L uses the equality 1 mL = 1 103 L (Table 1.4). The two conversion factors derived from this relationship are 1 mL 1 103 L and 1 103 L 1 mL

and the conversion factor to use is the one with the new unit (L) in the numerator.3 15 mL 1 10 L = 1.5 102 L 1 mL

FIGURE |

1.15

A problem with unit conversions

In September of 1999, the Mars Climate Orbiter (a $168 million weather satellite) fired its main engine to drop into orbit around Mars. Unfortunately, due to a mix-up in unitsthe computer on the orbiter used SI units, but NASA scientists sent it information in common unitsthe orbiter crashed into the planet.Source:

NASA.

18

CHAPTER 1 | SCIENCE AND MEASUREMENTS

If you do not have access to a direct relationship between two different units, making a unit conversion may require more than one step. Suppose that you are asked to convert the average volume of blood pumped by one beat of your heart (0.070 L) from liters into cups. What is this volume in cups? You may not know the direct relationship between liters and cups, but 0.946 L = 1 qt (Table 1.1). This gives the conversion factors 1 qt 0.946 L which means that 0.070 L 1 qt = 0.074 qt 0.946 L and 0.946 L 1 qt

Knowing that there are 4 cups in one quart gives the equation 0.074 qt 4 cups = 0.30 cup 1 qt

so 0.070 L is the same volume as 0.30 cup. The two steps of this conversion can be taken care of at once by incorporating both conversion factors into one equation