Chemistry Workbook For Dummies®, 3rd Edition with Online Practice
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“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.
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.
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.
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.
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.
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Your registration is good for one year from the day you activate your PIN.
Where you go from here depends on your situation and your learning style:
No matter the reason you have this book in your hands now, there are three simple steps to remember:
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
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
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.
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 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.
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.)
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 .
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.
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 .
The two most common measurements related to accuracy are error and percent error:
Being off by 1 meter isn’t such a big deal when measuring the altitude of a mountain, but it’s a shameful amount of error when measuring the height of an individual mountain climber.
Q. A police officer uses a radar gun to clock a passing Ferrari at 131 miles per hour (mph). The Ferrari was really speeding at 127 mph. Calculate the error in the officer’s measurement.
A. . First, determine which value is the actual value and which is the measured value:
Then calculate the error by subtracting the measured value from the actual value:
Q. Calculate the percent error in the officer’s measurement of the Ferrari’s speed.
A. 3.15%. First, divide the error’s absolute value (the size, as a positive number) by the actual value:
Next, multiply the result by 100 to obtain the percent error:
13 Two people, Reginald and Dagmar, measure their weight in the morning by using typical bathroom scales, instruments that are famously unreliable. The scale reports that Reginald weighs 237 pounds, though he actually weighs 256 pounds. Dagmar’s scale reports her weight as 117 pounds, though she really weighs 129 pounds. Whose measurement incurred the greater error? Who incurred a greater percent error?
14 Two jewelers were asked to measure the mass of a gold nugget. The true mass of the nugget is 0.856 grams (g). Each jeweler took three measurements. The average of the three measurements was reported as the “official” measurement with the following results:
Which jeweler’s official measurement was more accurate? Which jeweler’s measurements were more precise? In each case, what was the error and percent error in the official measurement?
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 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.)
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:
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 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.
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.
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:
The following are the answers to the practice problems in this chapter.
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%.
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.”
inches. Here, you have to recall that defined quantities (1 foot is defined as 12 inches) have unlimited significant figures. So your calculation is limited only by the number of significant figures in the measurement 345.6 feet. When you multiply 345.6 feet by 12 inches per foot, the feet cancel, leaving units of inches:
The raw calculation yields 4,147.2 inches, which rounds properly to four significant figures as 4,147 inches, or inches in scientific notation.
2.81 feet. Following standard order of operations, you can do this problem in two main steps, first performing multiplication and division and then performing addition and subtraction.
Following the rules of significant-figure math, the first step yields . Each product or quotient contains the same number of significant figures as the number in the calculation with the fewest number of significant figures.
After completing the first step, divide by 10.0 feet to finish the problem:
You write the answer with three sig figs because the measurement 10.0 feet contains three sig figs, which is the smallest available between the two numbers.
Chapter 2
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.
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 |
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?
Chemists aren’t satisfied with measuring length, mass, temperature, and time alone. On the contrary, chemistry often deals in calculated quantities. These kinds of quantities are expressed with derived units, which are built from combinations of base units.
Volume (of a reaction vessel, for example): You calculate volume by using the familiar formula . Because length, width, and height are all length units, you end up with , or a length cubed (for example, cubic meters, or m3).
The most common way of representing volume in chemistry is by using liters (L). You can treat the liter like you would any other metric base unit by adding prefixes to it, such as milli- or deci-.
Density (of an unidentified substance): Density, arguably the most important derived unit to a chemist, is built by using the basic formula .
In the SI system, mass is measured in kilograms. The standard SI units for mass and length were chosen by the Scientific Powers That Be because many objects that you encounter in everyday life have masses between 1 and 100 kilograms and have dimensions on the order of 1 meter. Chemists, however, are most often concerned with very small masses and dimensions; in such cases, grams and centimeters are much more convenient. Therefore, the standard unit of density in chemistry is grams per cubic centimeter (g/cm3) rather than kilograms per cubic meter.
The cubic centimeter is exactly equal to 1 milliliter, so densities are also often expressed in grams per milliliter (g/mL).
Q. A physicist measures the density of a substance to be 20 kg/m3. His chemist colleague, appalled with the excessively large units, decides to change the units of the measurement to the more familiar grams per cubic centimeter. What is the new expression of the density?
A. 0.02 g/cm3. A kilogram contains 1,000 (103) grams, so 20 kg equals 20,000 g. Well, 100 cm = 1 m; therefore, . In other words, there are 1003 (or 106) cubic centimeters in 1 cubic meter. Doing the division gives you 0.02 g/cm3. You can write out the conversion as follows:
3 The pascal, a unit of pressure, is equivalent to 1 newton per square meter. If the newton, a unit of force, is equal to a kilogram-meter per second squared, what is the pascal expressed entirely in basic units?
4 A student measures the length, width, and height of a sample to be 10 mm, 15 mm, and 5 mm, respectively. If the sample has a mass of 0.9 Dg, what is the sample’s density in grams per milliliter?