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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
Take the confusion out of chemistry with hundreds of practice problems Chemistry Workbook For Dummies is your ultimate companion for introductory chemistry at the high school or college level. Packed with hundreds of practice problems, this workbook gives you the practice you need to internalize the essential concepts that form the foundations of chemistry. From matter and molecules to moles and measurements, these problems cover the full spectrum of topics you'll see in class--and each section includes key concept review and full explanations for every problem to quickly get you on the right track. This new third edition includes access to an online test bank, where you'll find bonus chapter quizzes to help you test your understanding and pinpoint areas in need of review. Whether you're preparing for an exam or seeking a start-to-finish study aid, this workbook is your ticket to acing basic chemistry. Chemistry problems can look intimidating; it's a whole new language, with different rules, new symbols, and complex concepts. The good news is that practice makes perfect, and this book provides plenty of it--with easy-to-understand coaching every step of the way. * Delve deep into the parts of the periodic table * Get comfortable with units, scientific notation, and chemical equations * Work with states, phases, energy, and charges * Master nomenclature, acids, bases, titrations, redox reactions, and more Understanding introductory chemistry is critical for your success in all science classes to follow; keeping up with the material now makes life much easier down the education road. Chemistry Workbook For Dummies gives you the practice you need to succeed!
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Veröffentlichungsjahr: 2017
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Chemistry Workbook For Dummies®, 3rd Edition with Online Practice
Published by: John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, www.wiley.com
Copyright © 2017 by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
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Library of Congress Control Number: 2017932047
ISBN 978-1-119-35745-2 (pbk); ISBN 978-1-119-35746-9 (ebk); ISBN 978-1-119-35747-6 (ebk)
Chemistry Workbook For Dummies®
To view this book's Cheat Sheet, simply go to www.dummies.com and search for “Chemistry Workbook For Dummies Cheat Sheet” in the Search box.
Table of Contents
Cover
Introduction
About This Book
Foolish Assumptions
Icons Used in This Book
Beyond the Book
Where to Go from Here
Part 1: Getting Cozy with Numbers, Atoms, and Elements
Chapter 1: Noting Numbers Scientifically
Using Exponential and Scientific Notation to Report Measurements
Multiplying and Dividing in Scientific Notation
Using Exponential Notation to Add and Subtract
Distinguishing between Accuracy and Precision
Expressing Precision with Significant Figures
Doing Arithmetic with Significant Figures
Answers to Questions on Noting Numbers Scientifically
Chapter 2: Using and Converting Units
Familiarizing Yourself with Base Units and Metric System Prefixes
Building Derived Units from Base Units
Converting between Units: The Conversion Factor
Letting the Units Guide You
Answers to Questions on Using and Converting Units
Chapter 3: Breaking Down Atoms
The Atom: Protons, Electrons, and Neutrons
Deciphering Chemical Symbols: Atomic and Mass Numbers
Accounting for Isotopes Using Atomic Masses
Answers to Questions on Atoms
Chapter 4: Surveying the Periodic Table of the Elements
Organizing the Periodic Table into Periods and Groups
Predicting Properties from Periodic and Group Trends
Seeking Stability with Valence Electrons by Forming Ions
Putting Electrons in Their Places: Electron Configurations
Measuring the Amount of Energy (or Light) an Excited Electron Emits
Answers to Questions on the Periodic Table
Part 2: Making and Remaking Compounds
Chapter 5: Building Bonds
Pairing Charges with Ionic Bonds
Sharing Electrons with Covalent Bonds
Occupying and Overlapping Molecular Orbitals
Polarity: Sharing Electrons Unevenly
Shaping Molecules: VSEPR Theory and Hybridization
Answers to Questions on Bonds
Chapter 6: Naming Compounds and Writing Formulas
Labeling Ionic Compounds and Writing Their Formulas
Getting a Grip on Ionic Compounds with Polyatomic Ions
Naming Molecular (Covalent) Compounds and Writing Their Formulas
Addressing Acids
Mixing the Rules for Naming and Formula Writing
Beyond the Basics: Naming Organic Carbon Chains
Answers to Questions on Naming Compounds and Writing Formulas
Chapter 7: Understanding the Many Uses of the Mole
The Mole Conversion Factor: Avogadro’s Number
Doing Mass and Volume Mole Conversions
Determining Percent Composition
Calculating Empirical Formulas
Using Empirical Formulas to Find Molecular Formulas
Answers to Questions on Moles
Chapter 8: Getting a Grip on Chemical Equations
Translating Chemistry into Equations and Symbols
Balancing Chemical Equations
Recognizing Reactions and Predicting Products
Canceling Spectator Ions: Net Ionic Equations
Answers to Questions on Chemical Equations
Chapter 9: Putting Stoichiometry to Work
Using Mole-Mole Conversions from Balanced Equations
Putting Moles at the Center: Conversions Involving Particles, Volumes, and Masses
Limiting Your Reagents
Counting Your Chickens after They’ve Hatched: Percent Yield Calculations
Answers to Questions on Stoichiometry
Part 3: Examining Changes in Terms of Energy
Chapter 10: Understanding States in Terms of Energy
Describing States of Matter with the Kinetic Molecular Theory
Make a Move: Figuring Out Phase Transitions and Diagrams
Answers to Questions on Changes of State
Chapter 11: Obeying Gas Laws
Boyle’s Law: Playing with Pressure and Volume
Charles’s Law and Absolute Zero: Looking at Volume and Temperature
The Combined and Ideal Gas Laws: Working with Pressure, Volume, and Temperature
Mixing It Up with Dalton’s Law of Partial Pressures
Diffusing and Effusing with Graham’s Law
Answers to Questions on Gas Laws
Chapter 12: Dissolving into Solutions
Seeing Different Forces at Work in Solubility
Concentrating on Molarity and Percent Solutions
Changing Concentrations by Making Dilutions
Altering Solubility with Temperature
Answers to Questions on Solutions
Chapter 13: Playing Hot and Cold: Colligative Properties
Portioning Particles: Molality and Mole Fractions
Too Hot to Handle: Elevating and Calculating Boiling Points
How Low Can You Go? Depressing and Calculating Freezing Points
Determining Molecular Masses with Boiling and Freezing Points
Answers to Questions on Colligative Properties
Chapter 14: Exploring Rates and Equilibrium
Measuring Rates
Focusing on Factors That Affect Rates
Measuring Equilibrium
Answers to Questions on Rates and Equilibrium
Chapter 15: Warming Up to Thermochemistry
Understanding the Basics of Thermodynamics
Working with Specific Heat Capacity and Calorimetry
Absorbing and Releasing Heat: Endothermic and Exothermic Reactions
Summing Heats with Hess’s Law
Answers to Questions on Thermochemistry
Part 4: Swapping Charges
Chapter 16: Working with Acids and Bases
Surveying Three Complementary Methods for Defining Acids and Bases
Measuring Acidity and Basicity: pH, pOH, and K
W
K
a
and K
b
: Finding Strength through Dissociation
Answers to Questions on Acids and Bases
Chapter 17: Achieving Neutrality with Titrations and Buffers
Concentrating on Titration to Figure Out Molarity
Maintaining Your pH with Buffers
Measuring Salt Solubility with
K
sp
Answers to Questions on Titrations and Buffers
Chapter 18: Accounting for Electrons in Redox
Oxidation Numbers: Keeping Tabs on Electrons
Balancing Redox Reactions under Acidic Conditions
Balancing Redox Reactions under Basic Conditions
Answers to Questions on Electrons in Redox
Chapter 19: Galvanizing Yourself to Do Electrochemistry
Identifying Anodes and Cathodes
Calculating Electromotive Force and Standard Reduction Potentials
Coupling Current to Chemistry: Electrolytic Cells
Answers to Questions on Electrochemistry
Chapter 20: Doing Chemistry with Atomic Nuclei
Decaying Nuclei in Different Ways
Measuring Rates of Decay: Half-Lives
Making and Breaking Nuclei: Fusion and Fission
Answers to Questions on Nuclear Chemistry
Part 5: The Part of Tens
Chapter 21: Ten Chemistry Formulas to Tattoo on Your Brain
The Combined Gas Law
Dalton’s Law of Partial Pressures
The Dilution Equation
Rate Laws
The Equilibrium Constant
Free Energy Change
Constant-Pressure Calorimetry
Hess’s Law
pH, pOH, and K
W
K
a
and K
b
Chapter 22: Ten Annoying Exceptions to Chemistry Rules
Hydrogen Isn’t an Alkali Metal
The Octet Rule Isn’t Always an Option
Some Electron Configurations Ignore the Orbital Rules
One Partner in a Coordinate Covalent Bond Giveth Electrons; the Other Taketh
All Hybridized Orbitals Are Created Equal
Use Caution When Naming Compounds with Transition Metals
You Must Memorize Polyatomic Ions
Liquid Water Is Denser than Ice
No Gas Is Truly Ideal
Common Names for Organic Compounds Hearken Back to the Old Days
About the Authors
Connect with Dummies
End User License Agreement
Guide
Cover
Table of Contents
Begin Reading
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Introduction
“The first essential in chemistry is that you should perform practical work and conduct experiments, for he who performs not practical work nor makes experiments will never attain the least degree of mastery.”
—JĀBIR IBN HAYYĀN, 8TH CENTURY
“One of the wonders of this world is that objects so small can have such consequences: Any visible lump of matter — even the merest speck — contains more atoms than there are stars in our galaxy.”
—PETER W. ATKINS, 20TH CENTURY
Chemistry is at once practical and wondrous, humble and majestic. And for someone studying it for the first time, chemistry can be tricky.
That’s why we wrote this book. Chemistry is wondrous. Workbooks are practical. Practice makes perfect. This chemistry workbook will help you practice many types of chemistry problems with the solutions nicely laid out.
About This Book
When you’re fixed in the thickets of stoichiometry or bogged down by buffered solutions, you’ve got little use for rapturous poetry about the atomic splendor of the universe. What you need is a little practical assistance. Subject by subject, problem by problem, this book extends a helping hand to pull you out of the thickets and bogs.
The topics covered in this book are the topics most often covered in a first-year chemistry course in high school or college. The focus is on problems — problems like the ones you may encounter in homework or on exams. We give you just enough theory to grasp the principles at work in the problems. Then we tackle example problems. Then you tackle practice problems. The best way to succeed at chemistry is to practice. Practice more. And then practice even more. Watching your teacher do the problems or reading about them isn’t enough. Michael Jordan didn’t develop a jump shot by watching other people shoot a basketball. He practiced. A lot. Using this workbook, you can, too (but chemistry, not basketball).
This workbook is modular. You can pick and choose those chapters and types of problems that challenge you the most; you don’t have to read this book cover to cover if you don’t want to. If certain topics require you to know other topics in advance, we tell you so and point you in the right direction. Most importantly, we provide a worked-out solution and explanation for every problem.
Foolish Assumptions
We assume you have a basic facility with algebra and arithmetic. You should know how to solve simple equations for an unknown variable. You should know how to work with exponents and logarithms. That’s about it for the math. At no point do we ask you to, say, consider the contradictions between the Schrödinger equation and stochastic wavefunction collapse.
We assume you’re a high school or college student and have access to a secondary school-level (or higher) textbook in chemistry or some other basic primer, such as Chemistry For Dummies, 2nd Edition (written by John T. Moore, EdD, and published by Wiley). We present enough theory in this workbook for you to tackle the problems, but you’ll benefit from a broader description of basic chemical concepts. That way, you’ll more clearly understand how the various pieces of chemistry operate within a larger whole — you’ll see the compound for the elements, so to speak.
We assume you don’t like to waste time. Neither do we. Chemists in general aren’t too fond of time-wasting, so if you’re impatient for progress, you’re already part-chemist at heart.
Icons Used in This Book
You’ll find a selection of helpful icons nicely nestled along the margins of this workbook. Think of them as landmarks, familiar signposts to guide you as you cruise the highways of chemistry.
Within already pithy summaries of chemical concepts, passages marked by this icon represent the pithiest must-know bits of information. You’ll need to know this stuff to solve problems.
Sometimes there’s an easy way and a hard way. This icon alerts you to passages intended to highlight an easier way. It’s worth your while to linger for a moment. You may find yourself nodding quietly as you jot down a grateful note or two.
Chemistry may be a practical science, but it also has its pitfalls. This icon raises a red flag to direct your attention to easily made errors or other tricky items. Pay attention to this material to save yourself from needless frustration.
Within each section of a chapter, this icon announces, “Here ends theory” and “Let the practice begin.” Alongside the icon is an example problem that employs the very concept covered in that section. An answer and explanation accompany each practice problem.
Beyond the Book
In addition to the topics we cover in this book, you can find even more information online. Check out the free Cheat Sheet for some quick and useful tips for solving the most common types of chemistry problems you’ll see. To get this Cheat Sheet, go to www.dummies.com and search for “Chemistry Workbook” in the Search box.
The online practice that comes free with this book contains extra practice questions that correspond with each chapter in the book. To gain access to the online practice, all you have to do is register. Just follow these simple steps:
Find your PIN access code located on the inside front cover of this book.
Go to Dummies.com and click
Activate Now.
Find your product
(Chemistry Workbook For Dummies with Online Practice)
and then follow the on-screen prompts to activate your PIN.
Now you’re ready to go! You can go back to the program at http://testbanks.wiley.com as often as you want — simply log on with the username and password you created during your initial login. No need to enter the access code a second time.
Tip: If you have trouble with your PIN or can’t find it, contact Wiley Product Technical Support at 877-762-2974 or go to http://support.wiley.com.
Where to Go from Here
Where you go from here depends on your situation and your learning style:
If you’re currently enrolled in a chemistry course, you may want to scan the table of contents to determine what material you’ve already covered in class and what you’re covering right now. Use this book as a supplement to clarify things you don’t understand or to practice concepts that you’re struggling with.
If you’re brushing up on forgotten chemistry, scan the chapters for example problems. As you read through them, you’ll probably have one of two responses: 1) “Ahhh, yes … I remember that” or 2) “Oooh, no … I so do
not
remember that.” Let your responses guide you.
If you’re just beginning a chemistry course, you can follow along in this workbook, using the practice problems to supplement your homework or as extra pre-exam practice. Alternatively, you can use this workbook to preview material before you cover it in class, sort of like a spoonful of sugar to help the medicine go down.
If you bought this book a week before your final exam and are just now trying to figure out what this whole “chemistry” thing is about, well, good luck. The best way to start in that case is to determine what exactly is going to be on your exam and to study only those parts of this book. Due to time constraints or the proclivities of individual teachers/professors, not everything is covered in every chemistry class.
No matter the reason you have this book in your hands now, there are three simple steps to remember:
Don’t just read it; do the practice problems.
Don’t panic.
Do more practice problems.
Anyone can do chemistry given enough desire, focus, and time. Keep at it, and you’ll get an element on the periodic table named after you soon enough.
Part 1
Getting Cozy with Numbers, Atoms, and Elements
IN THIS PART …
Discover how to deal with, organize, and use all the numbers that play a huge role in chemistry. In particular, find out about exponential and scientific notation as well as precision and accuracy.
Convert many types of units that exist across the scientific world. From millimeters to kilometers and back again, you find conversions here.
Determine the arrangement and structure of subatomic particles in atoms. Protons, neutrons, and electrons play a central role in everything chemistry, and you find their most basic properties in this part.
Get the scoop on the arrangement of the periodic table and the properties it conveys for each group of elements.
Chapter 1
Noting Numbers Scientifically
IN THIS CHAPTER
Crunching numbers in scientific and exponential notation
Telling the difference between accuracy and precision
Doing math with significant figures
Like any other kind of scientist, a chemist tests hypotheses by doing experiments. Better tests require more reliable measurements, and better measurements are those that have more accuracy and precision. This explains why chemists get so giggly and twitchy about high-tech instruments: Those instruments take better measurements!
How do chemists report their precious measurements? What’s the difference between accuracy and precision? And how do chemists do math with measurements? These questions may not keep you awake at night, but knowing the answers to them will keep you from making rookie mistakes in chemistry.
Using Exponential and Scientific Notation to Report Measurements
Because chemistry concerns itself with ridiculously tiny things like atoms and molecules, chemists often find themselves dealing with extraordinarily small or extraordinarily large numbers. Numbers describing the distance between two atoms joined by a bond, for example, run in the ten-billionths of a meter. Numbers describing how many water molecules populate a drop of water run into the trillions of trillions.
To make working with such extreme numbers easier, chemists turn to scientific notation, which is a special kind of exponential notation. Exponential notation simply means writing a number in a way that includes exponents. In scientific notation, every number is written as the product of two numbers, a coefficient and a power of 10. In plain old exponential notation, a coefficient can be any value of a number multiplied by a power with a base of 10 (such as 104). But scientists have rules for coefficients in scientific notation. In scientific notation, the coefficient is always at least 1 and always less than 10. For example, the coefficient could be 7, 3.48, or 6.0001.
To convert a very large or very small number to scientific notation, move the decimal point so it falls between the first and second digits. Count how many places you moved the decimal point to the right or left, and that’s the power of 10. If you moved the decimal point to the left, the exponent on the 10 is positive; to the right, it’s negative. (Here’s another easy way to remember the sign on the exponent: If the initial number value is greater than 1, the exponent will be positive; if the initial number value is between 0 and 1, the exponent will be negative.)
To convert a number written in scientific notation back into decimal form, just multiply the coefficient by the accompanying power of 10.
Q. Convert 47,000 to scientific notation.
A.. First, imagine the number as a decimal:
Next, move the decimal point so it comes between the first two digits:
Then count how many places to the left you moved the decimal (four, in this case) and write that as a power of 10: .
Q. Convert 0.007345 to scientific notation.
A.. First, put the decimal point between the first two nonzero digits:
Then count how many places to the right you moved the decimal (three, in this case) and write that as a power of 10: .
1 Convert 200,000 into scientific notation.
2 Convert 80,736 into scientific notation.
3 Convert 0.00002 into scientific notation.
4 Convert from scientific notation into decimal form.
Multiplying and Dividing in Scientific Notation
A major benefit of presenting numbers in scientific notation is that it simplifies common arithmetic operations. The simplifying abilities of scientific notation are most evident in multiplication and division. (As we note in the next section, addition and subtraction benefit from exponential notation but not necessarily from strict scientific notation.)
To multiply two numbers written in scientific notation, multiply the coefficients and then add the exponents. To divide two numbers, simply divide the coefficients and then subtract the exponent of the denominator (the bottom number) from the exponent of the numerator (the top number).
Q. Multiply using the shortcuts of scientific notation: .
A.. First, multiply the coefficients:
Next, add the exponents of the powers of 10:
Finally, join your new coefficient to your new power of 10:
Q. Divide using the shortcuts of scientific notation: .
A.. First, divide the coefficients:
Next, subtract the exponent in the denominator from the exponent in the numerator:
Then join your new coefficient to your new power of 10:
5 Multiply .
6 Divide .
7 Using scientific notation, multiply .
8 Using scientific notation, divide .
Using Exponential Notation to Add and Subtract
Addition or subtraction gets easier when you express your numbers as coefficients of identical powers of 10. To wrestle your numbers into this form, you may need to use coefficients less than 1 or greater than 10. So scientific notation is a bit too strict for addition and subtraction, but exponential notation still serves you well.
To add two numbers easily by using exponential notation, first express each number as a coefficient and a power of 10, making sure that 10 is raised to the same exponent in each number. Then add the coefficients. To subtract numbers in exponential notation, follow the same steps but subtract the coefficients.
Q. Use exponential notation to add these numbers: .
A.. First, convert both numbers to the same power of 10:
Next, add the coefficients:
Finally, join your new coefficient to the shared power of 10:
Q. Use exponential notation to subtract: .
A.. First, convert both numbers to the same power of 10:
Next, subtract the coefficients:
Then join your new coefficient to the shared power of 10:
9 Add .
10 Subtract .
11 Use exponential notation to add .
12 Use exponential notation to subtract .
Expressing Precision with Significant Figures
When you know how to express your numbers in scientific notation and how to distinguish between precision and accuracy (we cover both topics earlier in this chapter), you can bask in the glory of a new skill: using scientific notation to express precision. The beauty of this system is that simply by looking at a measurement, you know just how precise that measurement is.
When you report a measurement, you should include digits only if you’re really confident about their values. Including a lot of digits in a measurement means something — it means that you really know what you’re talking about — so we call the included digits significant figures. The more significant figures (sig figs) in a measurement, the more accurate that measurement must be. The last significant figure in a measurement is the only figure that includes any uncertainty, because it’s an estimate. Here are the rules for deciding what is and what isn’t a significant figure:
Any nonzero digit is significant.
So 6.42 contains three significant figures.
Zeros sandwiched between nonzero digits are significant.
So 3.07 contains three significant figures.
Zeros on the left side of the first nonzero digit are
not
significant.
So 0.0642 and 0.00307 each contain three significant figures.
One or more
final zeros
(zeros that end the measurement) used after the decimal point are significant.
So 1.760 has four significant figures, and 1.7600 has five significant figures. The number
has only four significant figures because the first zeros are not final.
When a number has no decimal point, any zeros after the last nonzero digit may or may not be significant. So in a measurement reported as 1,370, you can’t be certain whether the 0 is a certain value or is merely a placeholder.
Be a good chemist. Report your measurements in scientific notation to avoid such annoying ambiguities. (See the earlier section “Using Exponential and Scientific Notation to Report Measurements” for details on scientific notation.)
If a number is already written in scientific notation, then all the digits in the coefficient are significant.
So the number
has five significant figures due to the five digits in the coefficient.
Numbers from counting (for example, 1 kangaroo, 2 kangaroos, 3 kangaroos) or from defined quantities (say, 60 seconds per 1 minute) are understood to have an unlimited number of significant figures.
In other words, these values are completely certain.
The number of significant figures you use in a reported measurement should be consistent with your certainty about that measurement. If you know your speedometer is routinely off by 5 miles per hour, then you have no business protesting to a policeman that you were going only 63.2 mph in a 60 mph zone.
Q. How many significant figures are in the following three measurements?
A.a) Five, b) three, and c) four significant figures. In the first measurement, all digits are nonzero, except for a 0 that’s sandwiched between nonzero digits, which counts as significant. The coefficient in the second measurement contains only nonzero digits, so all three digits are significant. The coefficient in the third measurement contains a 0, but that 0 is the final digit and to the right of the decimal point, so it’s significant.
15 Identify the number of significant figures in each measurement:
0.000769 meters
769.3 meters
16 In chemistry, the potential error associated with a measurement is often reported alongside the measurement, as in grams. This report indicates that all digits are certain except the last, which may be off by as much as 0.2 grams in either direction. What, then, is wrong with the following reported measurements?
Doing Arithmetic with Significant Figures
Doing chemistry means making a lot of measurements. The point of spending a pile of money on cutting-edge instruments is to make really good, really precise measurements. After you’ve got yourself some measurements, you roll up your sleeves, hike up your pants, and do some math.
When doing math in chemistry, you need to follow some rules to make sure that your sums, differences, products, and quotients honestly reflect the amount of precision present in the original measurements. You can be honest (and avoid the skeptical jeers of surly chemists) by taking things one calculation at a time, following a few simple rules. One rule applies to addition and subtraction, and another rule applies to multiplication and division.
Adding or subtracting:
Round the sum or difference to the same number of decimal places as the measurement with the fewest decimal places. Rounding like this is honest, because you’re acknowledging that your answer can’t be any more precise than the least-precise measurement that went into it.
Multiplying or dividing:
Round the product or quotient so that it has the same number of significant figures as the least-precise measurement — the measurement with the fewest significant figures.
Notice the difference between the two rules. When you add or subtract, you assign significant figures in the answer based on the number of decimal places in each original measurement. When you multiply or divide, you assign significant figures in the answer based on the smallest number of significant figures from your original set of measurements.
Caught up in the breathless drama of arithmetic, you may sometimes perform multi-step calculations that include addition, subtraction, multiplication, and division, all in one go. No problem. Follow the normal order of operations, doing multiplication and division first, followed by addition and subtraction. At each step, follow the simple significant-figure rules, and then move on to the next step.
Q. Express the following sum with the proper number of significant figures:
A.671.1 miles. Adding the three values yields a raw sum of 671.05 miles. However, the 35.7 miles measurement extends only to the tenths place. Therefore, you round the answer to the tenths place, from 671.05 to 671.1 miles.
Q. Express the following product with the proper number of significant figures:
A.. Of the two measurements, one has two significant figures (27 feet) and the other has four significant figures (13.45 feet). The answer is therefore limited to two significant figures. You need to round the raw product, 363.15 feet2. You could write 360 feet2, but doing so may imply that the final 0 is significant and not just a placeholder. For clarity, express the product in scientific notation, as feet2.
17 Express this difference using the appropriate number of significant figures:
18 Express the answer to this calculation using the appropriate number of significant figures:
19 Report the difference using the appropriate number of significant figures:
20 Express the answer to this multi-step calculation using the appropriate number of significant figures:
Answers to Questions on Noting Numbers Scientifically
The following are the answers to the practice problems in this chapter.
.
Move the decimal point immediately after the 2 to create a coefficient between 1 and 10. Because you’re moving the decimal point five places to the left, multiply the coefficient, 2, by the power 10
5
.
.
Move the decimal point immediately after the 8 to create a coefficient between 1 and 10. You’re moving the decimal point four places to the left, so multiply the coefficient, 8.0736, by the power 10
4
.
.
Move the decimal point immediately after the 2 to create a coefficient between 1 and 10. You’re moving the decimal point five spaces to the right, so multiply the coefficient, 2, by the power 10
–5
.
690.3.
You need to understand scientific notation to change the number back to regular decimal form. Because 10
2
equals 100, multiply the coefficient, 6.903, by 100. This moves the decimal point two spaces to the right.
.
First, multiply the coefficients:
. Then multiply the powers of 10 by adding the exponents:
. The raw calculation yields
, which converts to the given answer when you express it in scientific notation.
.
The ease of math with scientific notation shines through in this problem. Dividing the coefficients yields a coefficient quotient of
, and dividing the powers of 10 (by subtracting their exponents) yields a quotient of
. Marrying the two quotients produces the given answer, already in scientific notation.
1.8.
First, convert each number to scientific notation:
and
. Next, multiply the coefficients:
. Then add the exponents on the powers of 10:
. Finally, join the new coefficient with the new power:
. Expressed in scientific notation, this answer is
. Looking back at the original numbers, you see that both factors have only two significant figures; therefore, you have to round your answer to match that number of sig figs, making it 1.8.
.
First, convert each number to scientific notation:
and
. Then divide the coefficients:
. Next, subtract the exponent on the denominator from the exponent of the numerator to get the new power of 10:
. Join the new coefficient with the new power:
. Finally, express gratitude that the answer is already conveniently expressed in scientific notation.
.
Because the numbers are each already expressed with identical powers of 10, you can simply add the coefficients:
. Then join the new coefficient with the original power of 10.
.
Because the numbers are each expressed with the same power of 10, you can simply subtract the coefficients:
. Then join the new coefficient with the original power of 10.
(or an equivalent expression).
First, convert the numbers so they each use the same power of 10:
and
. Here, we use 10
–3
, but you can use a different power as long as the power is the same for each number. Next, add the coefficients:
. Finally, join the new coefficient with the shared power of 10.
(or an equivalent expression).
First, convert the numbers so each uses the same power of 10:
and
. Here, we’ve picked 10
2
, but any power is fine as long as the two numbers have the same power. Then subtract the coefficients:
. Finally, join the new coefficient with the shared power of 10.
Reginald’s measurement incurred the greater magnitude of error, and Dagmar’s measurement incurred the greater percent error.
Reginald’s scale reported with an error of
, and Dagmar’s scale reported with an error of
. Comparing the
magnitudes
of error, you see that 19 pounds is greater than 12 pounds. However, Reginald’s measurement had a percent error of
, while Dagmar’s measurement had a percent error of
.
Jeweler A’s official average measurement was 0.864 grams, and Jeweler B’s official measurement was 0.856 grams. You determine these averages by adding up each jeweler’s measurements and then dividing by the total number of measurements, in this case 3. Based on these averages, Jeweler B’s official measurement is more accurate because it’s closer to the actual value of 0.856 grams.
However, Jeweler A’s measurements were more precise because the differences between A’s measurements were much smaller than the differences between B’s measurements. Despite the fact that Jeweler B’s average measurement was closer to the actual value, the range of his measurements (that is, the difference between the largest and the smallest measurements) was 0.041 grams (). The range of Jeweler A’s measurements was 0.010 grams ().
This example shows how low-precision measurements can yield highly accurate results through averaging of repeated measurements. In the case of Jeweler A, the error in the official measurement was . The corresponding percent error was . In the case of Jeweler B, the error in the official measurement was . Accordingly, the percent error was 0%.
The correct number of significant figures is as follows for each measurement:
a) 5, b) 3,
and
c) 4.
a) “ gram” is an improperly reported measurement because the reported value, 893.7, suggests that the measurement is certain to within a few tenths of a gram. The reported error is known to be greater, at gram. The measurement should be reported as “ gram.”
b) “ gram” is improperly reported because the reported value, 342, gives the impression that the measurement becomes uncertain at the level of grams. The reported error makes clear that uncertainty creeps into the measurement only at the level of hundredths of a gram. The measurement should be reported as “ gram.”
114.36 seconds.
The trick here is remembering to convert all measurements to the same power of 10 before comparing decimal places for significant figures. Doing so reveals that
seconds goes to the hundredths of a second, despite the fact that the measurement contains only two significant figures. The raw calculation yields 114.359 seconds, which rounds properly to the hundredths place (taking significant figures into account) as 114.36 seconds, or
seconds in scientific notation.
inches.
Chapter 2
Using and Converting Units
IN THIS CHAPTER
Embracing the International System of Units
Relating base units and derived units
Converting between units
Have you ever been asked for your height in centimeters, your weight in kilograms, or the speed limit in kilometers per hour? These measurements may seem a bit odd to those folks who are used to feet, pounds, and miles per hour, but the truth is that scientists sneer at feet, pounds, and miles. Because scientists around the globe constantly communicate numbers to each other, they prefer a highly systematic, standardized system. The International System of Units, abbreviated SI from the French term Système International, is the unit system of choice in the scientific community.
In this chapter, you find that the SI system offers a very logical and well-organized set of units. Scientists, despite what many of their hairstyles may imply, love logic and order, so SI is their system of choice.
As you work with SI units, try to develop a good sense for how big or small the various units are. That way, as you’re doing problems, you’ll have a sense for whether your answer is reasonable.
Familiarizing Yourself with Base Units and Metric System Prefixes
The first step in mastering the SI system is to figure out the base units. Much like the atom, the SI base units are building blocks for more-complicated units. In later sections of this chapter, you find out how more-complicated units are built from the SI base units. The five SI base units that you need to do chemistry problems (as well as their familiar, non-SI counterparts) are in Table 2-1.
Table 2-1 SI Base Units
Measurement
SI Unit
Symbol
Non-SI Unit
Amount of a substance
mole
mol
no non-SI unit
Length
meter
m
foot, inch, yard, mile
Mass
kilogram
kg
pound
Temperature
kelvin
K
degree Celsius, degree Fahrenheit
Time
second
s
minute, hour
Chemists routinely measure quantities that run the gamut from very small (the size of an atom, for example) to extremely large (such as the number of particles in one mole). Nobody, not even chemists, likes dealing with scientific notation (which we cover in Chapter 1) if they don’t have to. For these reasons, chemists often use a metric system prefix (a word part that goes in front of the base unit to indicate a numerical value) in lieu of scientific notation. For example, the size of the nucleus of an atom is roughly 1 nanometer across, which is a nicer way of saying meters across. The most useful of these prefixes are in Table 2-2.
Table 2-2 Metric System Prefixes
Prefix
Symbol
Meaning
Example
kilo-
k
103
deca-
D or da
101
base unit
varies
1
1 m
deci-
d
centi-
c
milli-
m
micro-
nano-
n
Feel free to refer to Table 2-2 as you do your problems. You may want to earmark this page because after this chapter, we simply assume that you know how many meters are in 1 kilometer, how many grams are in 1 microgram, and so on.
Q. You measure a length to be 0.005 m. How can this be better expressed using a metric system prefix?
A.5 mm. 0.005 is , or 5 mm.
1 How many nanometers are in 1 cm?
2 Your lab partner has measured the mass of your sample to be 2,500 g. How can you record this more nicely (without scientific notation) in your lab notebook using a metric system prefix?
