Kelter P., Mosher M., Scott A. Chemistry. The Practical Science

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EXERCISE 1.8 Powers in Dimensional Analysis

A typical can of cola contains 355 mL of liquid. How many cubic meters would be

occupied by the liquid from a 12-pack of cola?

First Thoughts

Let’s map out how we will convert from milliliters into cubic meters. The conversion

from cubic centimeters to cubic meters will be a little more involved than a straight

conversion. We’ll have to break the cm

term down into cm × cm × cm in order to

get those units to cancel.

cans

cans to milliliters

−−−−−−−−−→mL

mL to cm

−−−−−−−→cm

to m

−−−−−−−→m

Solution

12 cans ×

355 mL

can

1cm

100 cm

= 0.00426 m

Further Insight

Note that in converting the unit cm

into m

, we completed the conversion from cm

to m three times. In the end, the units of cm

= cm × cm × cm, and the resulting

unit m

was obtained. This practice for converting units of multiple powers can be

used in any problem.

PRACTICE 1.8

A house requires 1200 yd

of carpet. How many square meters of carpet will it

require? How many square inches of carpet will it require?

See Problems 70 and 81.

1.6 Uncertainty, Precision,

Accuracy, and Signiﬁcant Figures

The density of the silicone tubes used in heart–lung machines is a good indicator

of the ﬂexibility and strength of the tubing. Strong and ﬂexible tubes typically

have relatively low densities. Judith Fairclough-Baity knows this, so she measures

densities to give an idea of the quality of a freshly made tube. Often she ﬁnds that

the density of her new tubing is quite similar to that of the tubing already in use

in hospitals. In some cases, the difference in density between good tubing and bad

tubing is very small (1.2011 g/mL versus 1.2005 g/mL). What degree of conﬁ-

dence does she have in her measurements? How can she be sure that the numbers

she obtains for her densities are correct? The conﬁdence that Fairclough-Baity

has in her measurements is based on the use of uncertainty and signiﬁ-

cant ﬁgures. This ensures that the numbers she calculates for the densities are

meaningful.

Uncertainty

There are a few things in science, and in life, that we can know for certain, with no

margin of error or room for doubt. For example, if you are asked how many U.S.

presidents’ faces are carved into Mt. Rushmore, you can be positively sure that the

answer is 4. This is an

exact number, a quantity that we know without any uncer-

tainty. Indeed, all data that are determined by counting are exact.

Measurement is different from merely counting, however, because every mea-

surement is associated with a certain degree of

uncertainty. There are no measure-

ments made in which we are absolutely certain of the answer because we, and our

28 Chapter 1 The World of Chemistry

measurement instruments, are imperfect. The uncertainty in a measurement, how

“sure” we are that our measurement is correct, depends on the method used to ob-

tain the measurement, on the quality of the measuring apparatus, and on the care

taken by the person making the measurement. For example, if you are asked to

measure the mass of an orange, you might obtain 151 g or 151.2 g or 151.20467 g,

depending on the balance you use and on how well you know how to use the bal-

ance. Each measured value will be associated with a particular level of uncer-

tainty. No measurement is ever exact.

How do scientists report the uncertainty in a measurement? One way is to use

the symbol ±, which means “plus or minus,” to indicate the limits within which

we conﬁdently expect the true value to lie. (This approach works only if we can

experimentally determine those limits.) Here are two examples:

If we write a mass of 151 ± 1 g, we mean that we are certain that the mass lies be-

tween 150 g and 152 g, but we are not certain of exactly where it lies between

these limits.

If we write a mass of 151.3 ± 0.2 g, we mean that we are certain the mass lies be-

tween 151.1 g and 151.5 g, but we are not certain of exactly where it lies between

these limits.

Even though scientists do their best to minimize the uncertainty of every

measurement, there is still a level of uncertainty in their answers. The two most

common sources of uncertainty in measurements for properly designed experi-

ments are

■

human error and variability. None of us is perfect, and we can make errors

from simple human clumsiness (spilling our reaction or improperly operating

a piece of equipment). But it is also true that our eyes and hands and brains

can manipulate labware, or read a balance, or interpret what we see only so

well.

■

instrument error and variability. Measurement devices are not perfect. Be-

cause of imperfections in their manufacture, faults, or limitations, instru-

ments themselves can contribute to the error in a measurement.

Accuracy and Precision

As we noted in the previous section, the quality of the balance we use to measure

mass is important in a measurement. More broadly, what is a high-quality mea-

surement? We deﬁne this via the accuracy and precision of the measurements

we make. To a chemist like Fairclough-Baity, these two terms mean completely

different things.

Accuracy relates how close a measurement is to its true value.

Precision relates how close repeated measurements are to each other, whether they

are accurate or not. A set of measurements can be accurate, can be precise, can ex-

hibit both of these properties, or can offer neither (see Figure 1.29). Fine instru-

ments tend to yield measurements that are both accurate and precise.

1.6 Uncertainty, Precision, Accuracy, and Signiﬁcant Figures 29

FIGURE 1.29

The application of precision and accuracy to a

game of darts.

Neither precise nor accurate Precise, but not accurate Accurate, but not precise Precise and accurate

Video Lesson: Precision and

Accuracy

Video Lesson: CIA

Demonstration: Precision and

Accuracy with Glassware

Suppose four students need to measure the mass of a sample of orange juice

prior to determining its vitamin C content. Let’s assume that the mass of the or-

ange juice is known to be 1.4683 g. The students all use the same sophisticated

balance that provides four ﬁgures after the decimal point, but they forget that the

balance must be set to zero before they use it. These students might get these

results:

Average mass 1.5674 g

Tr ue mass 1.4683 g

These are very precise answers because the masses are in close agreement

and are reported to four decimal places. Unfortunately, however, they are not

accurate answers, either individually or when averaged, because they all contain

the same instrument error, due to the students’ forgetfulness in not zeroing the

balance before they used it.

Now another group of students measures the mass of the orange juice sample,

and they remember to re-zero the balance before each use. Let’s assume that they

obtain these results:

Average mass 1.4684 g

True mass 1.4683 g

The results obtained by Group 2 are both precise and accurate. Each value

reported is in close agreement with the average, and all the values are accurate

because they are very close to the true value for the mass.

A third group of students remembers to zero the balance before use, but they

are less careful in making their measurements. This makes their measurements

subject to human error. Let’s assume this group of students obtains these results:

Average mass 1.4683 g

True mass 1.4683 g

The results they obtain are less precise than those of either Group 1 or Group2, be-

cause they show a greater degree of variability. Each result is individually less ac-

curate than the individual results obtained by Group 2, but they yield an average

Student Group 3

Zeb 1.4673 g

Jeff 1.4691 g

Elena 1.4675 g

Alice 1.4692 g

Student Group 2

Rebecca 1.4682 g

Maggie 1.4684 g

Winston 1.4685 g

Rob 1.4684 g

Student Group 1

Amy 1.5674 g

Jorge 1.5673 g

Barb 1.5673 g

Mike 1.5675 g

30 Chapter 1 The World of Chemistry

Application

value that is accurate. Taking the average value of a set of results subject to ran-

dom errors, such as many human errors, can yield a very accurate result. How-

ever, systematic instrument errors (caused by, for example, a balance that is

tilted) cannot be overcome by averaging, because all the results suffer from the

same instrument error.

What combination of precision and accuracy would the careless members of

Group 3 have produced if they had also forgotten to zero the balance? They

would have produced results that, compared to those of Group 2, were both

imprecise and inaccurate.

Why is it important for us to know about uncertainties in our measurements and

to worry about precision and accuracy?

Lives and jobs and a lot of money can be at

risk if our measurements don’t do what we want them to do. The dosage of drugs

must be measured carefully, within known limits, to avoid doing harm instead of

good. The amount of fuel loaded onto a plane before takeoff is critical if the plane

is to make it to its destination. Impure water puts lives at risk. And an accurate

and precise measurement of the density of heart–lung machine tubing could

mean the creation of a tube that doesn’t crack or break apart during a long

surgery.

Signiﬁcant Figures

As we have just seen, it is useful to be able to assess the precision and accuracy of

different values. Furthermore, we cannot claim that our answers are more precise

than any of the measurements we used to obtain the answer. In practice, the re-

sults of calculations must contain at least as much uncertainty as is present in the

measured values we used to obtain these results. This means that when we per-

form calculations, we cannot accept all of the numbers shown on the calculator

display, because doing so would imply that we know the result to a degree of cer-

tainty that is not justiﬁed. A temperature of 325 K can be divided by 3 on a cal-

culator, which might display an answer of 108.33333333333. However, we do not

know the temperature to 14 digits, only to 3. Some of the numbers in the calcu-

lator’s display are “not signiﬁcant,” in the sense that we simply cannot trust them;

in other words, some of the numbers in the display have no meaning, so we

should not use them. We can deal with this problem through the use of

signiﬁcant

ﬁgures

,speciﬁc numbers in a measurement whose values we can trust.

Let’s follow Judith Fairclough-Baity as she measures the mass of a new piece

of tubing she prepared. She uses a rough balance to obtain a mass of the little

piece of tube. The balance’s display says 5 g. What is the quality of that measure-

ment? Speciﬁcally, the number means that the mass is closer to 5 g than it is to 4 g

or to 6 g. This value has just one signiﬁcant ﬁgure. Fairclough-Baity then uses a

higher-quality balance to measure the mass. This balance says the mass of the

tubing is 5.125 g. This number has four signiﬁcant ﬁgures. The balance’s dis-

play indicates that the mass of our sample is closer to 5.125 g than it is to either

5.124 g or 5.126 g. Some uncertainty about the value still exists, but there is less

uncertainty than before. The more signiﬁcant ﬁgures there are in any measure-

ment, the less uncertainty there is about the measurement.

When Fairclough-Baity writes down any value in her notebook, all of the

numbers other than zero are always implied to be signiﬁcant. When a zero is en-

countered in a measurement, determining its signiﬁcance is less straightforward.

All zeros that come before the nonzero digits in a number are used to locate the

position of the decimal point, so they do not count as signiﬁcant ﬁgures. For ex-

ample, 0.005 has only one signiﬁcant ﬁgure, not four, because the zeros on the left

just hold the position of the decimal point. She clears up any ambiguity by writ-

ing the value in scientiﬁc notation. For example, she writes 0.005 as 5 × 10

–3

show that there is only one signiﬁcant ﬁgure.

Zeros that lie between nonzero digits, which are called “captive zeros,” are al-

ways signiﬁcant. Therefore, the number 505, for example, has three signiﬁcant

1.6 Uncertainty, Precision, Accuracy, and Signiﬁcant Figures 31

When we divide 5.125 by 4.6 on a

calculator, not all of the digits in its

answer are signiﬁcant.

Video Lesson: Signiﬁcant

Figures

Video Lesson: Scientiﬁc

(Exponential) Notation

ﬁgures. The number 0.00505 also has only three signiﬁcant ﬁgures. We can write

the latter of these two numbers in exponential notation as 5.05 × 10

–3

Zeros that come at the end of a number, which are sometimes called “trailing

zeros,” are truly ambiguous. For instance, if a technician reports a mass of 200 g,

we don’t know whether he or she means 2 × 10

or 2.0 × 10

or 2.00 × 10

.We

can take the most careful possible view and say the value is closer to 200 g than it

is to either 300 g or 100 g. That’s a fairly wide range of uncertainty, but we have no

evidence to allow us to assume that the measurement is more precise. The only

way to resolve the ambiguity is to write a measurement with ambiguous trailing

zeros in scientiﬁc notation. If the technician records the value as 2.0 × 10

, then

the zero is after the decimal point, which makes it signiﬁcant. This measurement

unambiguously has two signiﬁcant ﬁgures. If the value is written as 2.00 × 10

then the measurement has three signiﬁcant ﬁgures. In this case, we would know

that the actual value is between 199 g and 201 g. Table 1.7 summarizes the rules

for determining the number of signiﬁcant ﬁgures in a measured number.

Finally, note that counting numbers (such as the number of people in a room)

and certain deﬁned conversion factors and equalities (such as 4 qt = 1 gal) are

considered to have an inﬁnite number of signiﬁcant ﬁgures. They are exact.

Calculations Involving Signiﬁcant Figures

Judith Fairclough-Baity’s mass for her piece of tubing can be used to determine

the density of the tubing. She places the tubing into a graduated cylinder and

notes the displacement of water. In the end, she determines that the volume dis-

placed by the 5.125-g piece of tubing was 4.6 mL. She then divides the mass by the

volume to obtain the density, which she reads from the calculator display as

1.1141304 g/mL.

Density =

mass

volume

5.125 g

4.6mL

= 1.1141304

g/mL

How many of the digits displayed on her calculator are signiﬁcant? The rules

we use to determine this (see Table 1.8), depend on whether the number is the

result of addition, subtraction, multiplication, or division. These rules ensure

that Fairclough-Baity’s answer is no more precise than either of her two

measurements.

Using these rules, Fairclough-Baity writes 1.1 g/mL in her notebook. This an-

swer contains only two signiﬁcant ﬁgures and is just as precise as the volume

measurement that she obtained. If she needed to measure the density to four sig-

niﬁcant ﬁgures, she would have to measure more precisely the volume of water

displaced by the piece of tubing, or she could use a different strategy for deter-

mining the density.

32 Chapter 1 The World of Chemistry

Rules for Signiﬁcant Figures

Nonzero digits are always signiﬁcant. 123 has three signiﬁcant ﬁgures.

Zeros before the nonzero digits are never signiﬁcant. 0.0123 has three signiﬁcant ﬁgures.

Zeros between nonzero digits are always signiﬁcant. 1.023 has four signiﬁcant ﬁgures.

Zeros at the end of a number that does not contain 1230 has three signiﬁcant ﬁgures.

a decimal point are ambiguous.

When in doubt, write the number using 1230 written as 1.230  10

has four

exponential notation. signiﬁcant ﬁgures.

Counting numbers have inﬁnite signiﬁcant ﬁgures. 200 pencils is an exact number because it came

from counting rather than measuring.

TABLE 1.7

When to Round Off

If you are performing a series of calculations on a calculator, you should carry all

the extra digits through until you obtain the ﬁnal answer and then do the round-

ing off at the end. You should not round off at intermediate stages, because in doing

so you might lose ﬁgures that affect the accuracy of the ﬁnal result. This rule can

sometimes cause problems—for example, if you perform in one step a calcula-

tion that a textbook or multimedia package has performed in two or more steps.

If you get answers that differ very slightly from those in a textbook or multime-

dia package’s solutions, don’t automatically assume it is wrong. The problem may

lie in the different approaches taken or in rounding off at different stages.

We’ll emphasize this important rule about not rounding off during a calcula-

tion throughout this textbook. For instance, if we are working on a problem that

involves many steps before the answer is obtained, we will not drop the next in-

signiﬁcant ﬁgure. Instead, the ﬁrst insigniﬁcant ﬁgure will be highlighted in color,

or otherwise noted at the end of the number. This will serve as a reminder that

one shouldn’t round off until the end of the calculation.

For example, let’s consider the calculation of the density of a piece of metal. If

we measured the volume of water initially as 25.25 mL and then added a 53.375-g

chunk of metal, we note that the volume of water changes to 32.1 mL. To solve

this problem, we determine the difference in the volumes and divide that into the

mass of the metal. Mathematically, here are the steps we take:

Density = 53.375 g ÷ (32.1 mL − 25.25 mL)

= 53.375 g ÷ (6.85 mL)

At this step, we’ve highlighted the insigniﬁcant digit in the subtraction so that we

can easily count the number of signiﬁcant ﬁgures for our next step. We haven’t

rounded anything yet because we are not ﬁnished with the calculation.

53.375 g ÷ (6.85 mL) = 7.79197 g/mL

= 7.8 g/mL

Here, approaching our ﬁnal answer, we highlighted the insigniﬁcant ﬁgures, and

then, because this was the ﬁnal calculation, we rounded the ﬁnal answer.

1.6 Uncertainty, Precision, Accuracy, and Signiﬁcant Figures 33

Calculations Using Signiﬁcant Figures

Addition/ The result has the same number of digits after 21.3  1.045  22.3

subtraction the decimal point as the measurement with the

least precision.

Multiplication/ The result contains the same number of 1.2  4.2613  5.1

division signiﬁcant ﬁgures as the measurement with the

smallest number of signiﬁcant ﬁgures.

Rounding The ﬁnal answer is rounded to the nearest 5.35  2.68  1.996  2.00

signiﬁcant digit. The digit is rounded down if the 8.26 rounds to 8.3

next digit is less than 5; it is rounded up if the next 8.32 rounds to 8.3

digit is greater than 5. If the last signiﬁcant digit is 8.25 rounds to 8.2

odd and the next digit is exactly 5, the digit is 8.15 rounds to 8.2

rounded up; if the last signiﬁcant digit is even and 8.251 rounds to 8.3

the next digit is exactly 5, the digit is not rounded. 8.151 rounds to 8.2

Final answer The ﬁnal answer is the only number in a (3.9684167  1.8)

calculation that is rounded.  7.14315

Intermediate calculations are never rounded.  1.50  4.7621  4.8

TABLE 1.8

EXERCISE 1.9 Calculations

Provide the answer to this calculation. Be sure to indicate the appropriate number

of signiﬁcant ﬁgures.

288 ×1.445

7.9 ×10

− 0.064 =

Solution

To start, let’s complete the multiplication on the numerator. We retain at least one

insigniﬁcant ﬁgure (the 2 in 416.2) in the intermediate calculation:

288 × 1.445 = 416.2

Then we’ll do the division. If this were our ﬁnal computation, we would keep only

two signiﬁcant ﬁgures. But because we have more calculating to do, we retain a

third, insigniﬁcant ﬁgure, highlighted in red:

416.2

7.9 ×10

= 0.527

Finally, we’ll subtract the two numbers. We don’t round at all until all calculations

are ﬁnished. The presence of the highlighted digit represents all of the insigniﬁcant

ﬁgures we retain.

0.527 − 0.064 = 0.463, which rounds to 0.46

Our answer only has two signiﬁcant ﬁgures. If we had rounded at the previous step,

0.527 would have become 0.53. This would have led to an incorrect answer in the

ﬁnal step (0.53 − 0.064 = 0.466), because 0.466 rounds to 0.47. Remember, never

round until you are completely done with a calculation.

PRACTICE 1.9

How many signiﬁcant ﬁgures are there in each of these numbers?

a. 1.3090 b. 3450 c. 0.0020 d. 2.000

How many signiﬁcant ﬁgures will there be in the answer to this problem?

2.3 +0.88

79.4

See Problems 87–98.

1.7 The Chemical Challenges of the Future

The chemist’s ability to raise questions about everything around us, to design ex-

periments, to make measurements, and to derive theories and laws via this

process we call the scientiﬁc method has taught us a great deal about our world

and the role of chemistry in all of its changes. The future is built by these changes,

and they present many chemical challenges to us. Some of these challenges are

problems caused by our use of chemistry in the past; others involve our continu-

ing efforts to make life better, more enjoyable, and more fulﬁlling. Some infor-

mation about a few of the future challenges for chemists follows.

■

The frontiers of medicine. Chemists will continue to search for new and more

effective medicines to treat cancer, AIDS, heart disease, Alzheimer’s disease,

rheumatoid arthritis, and many other diseases. They will also be urgently try-

ing to create new antibiotics that enable us to “stay ahead” of the pace at which

disease-causing organisms become resistant to existing antibiotics.

34 Chapter 1 The World of Chemistry

Application

1.7 The Chemical Challenges of the Future 35

■

New challenges in agriculture. Chemists have already transformed agriculture

once, through their development of artiﬁcial fertilizers and pesticides. They

are now heavily involved in a new and controversial transformation involving

the creation of genetically modiﬁed crops. This may enable us to create new

“engineered” plants with larger and more reliable yields. Nevertheless, many

people are concerned about the legal, ethical, and safety issues associated with

genetically modiﬁed crops.

■

The challenge of pollution. Oil spills, smog, and pollution in general are nega-

tive aspects of our use of chemical processes—aspects that often predominate

in public perceptions of chemistry. Pollution of our environment has been the

price we have paid for many of the comforts and conveniences of modern life.

Chemists are working hard to reduce that price by developing alternative

“green” technologies and by learning how to use chemistry more effectively to

clean up the problems that still arise.

■

Global warming and ozone depletion. Our desire for comforts and conveniences

has created two major problems in the chemistry of the atmosphere. A rise in

levels of carbon dioxide and other greenhouse gases has been implicated in

global warming. And the destruction of the protective ozone layer by chemi-

cals called chloroﬂuorocarbons, or CFCs, has contributed to increases in skin

cancer. Chemists will continue to research both issues to determine the causes

of, and solutions to, these environmental concerns. In addition, the develop-

ment of new chemical technologies will help us learn more about the hazards

that caused these problems, with the goal of reducing or eliminating them.

■

Better materials. Materials are the chemicals we use to make things, such as

clothes, cars, aircraft, homes, televisions, and computers. Every material has its

own set of advantages and limitations for a given application. Chemists are

continually trying to enhance the advantages, such as durability, ﬂexibility,

and efﬁciency as electrical conductors or insulators. They are also working to

overcome the limitations of some materials, such as susceptibility to corro-

sion, high cost, inability to recycle and reuse, and so on. That work will con-

tinue indeﬁnitely, hopefully yielding a steady supply of new and more versatile

materials to make the things we need and want.

■

New ways to supply energy. The modern world is sustained by huge supplies of

materials—such as coal, oil, and gas—that can provide usable energy. Unfor-

tunately, the chemical reserves of energy are limited. Moreover, their use

contributes to environmental pollution and global warming. Chemists are

learning how to get the energy we need in more sustainable and less polluting

ways. Many alternative ways of supplying energy already exist, such as solar

and wind power. But these ways need to be made more efﬁcient, cost-effective,

and powerful in order to ﬁnd use in today’s energy-hungry world.

The frontiers of medicine involve ﬁnding

the viruses that cause disease and identi-

fying the compounds that make them.

Pollution in Mexico City.

■

Nanotechnology. In the 1970s people began to use the term nanotechnology to

describe the manipulation and machining of matter at very small scales. Some

developments in this ﬁeld can be described as “molecular manufacturing,” in-

volving attempts to build tiny machines, materials, and medical devices by

manipulating very small assemblies of matter, even molecule by molecule or

atom by atom. Traditional chemistry works with huge numbers of particles.

The twenty-ﬁrst century might see a new industrial revolution, in which the

precise manipulation of tiny numbers of atoms, molecules, and ions becomes

a routine part of our technology. Many of the ﬁrst steps toward that new rev-

olution have already been taken (Figure 1.30).

■

Understanding life. We understand a great deal about the chemistry of life, but

many processes are not fully understood. Indeed, the chemistry of what we re-

ally are—the chemistry of consciousness—is still a complete mystery to us.

We have uncovered the general chemical mechanisms at the heart of all life,

but there are endless intricate details still to be learned. As we learn these de-

tails, and therefore learn more about the workings of life, we will be in a much

better position to ﬁx things when the chemistry of life goes wrong and makes

us ill.

These are just a few of the “hot” chemical topics that will tap the creative en-

ergy of chemists tomorrow and into the distant future. Chemists will also be

involved in the operation of oil reﬁneries, plastics factories, pharmaceutical com-

panies, food manufacturers, cosmetics companies, makers of paints, glues, and

varnish, semiconductor plants, and much, much more (see Table 1.9). Their op-

eration depends on the application of chemical knowledge, continuously, day

and night, to keep the modern world running.

36 Chapter 1 The World of Chemistry

Some Career Opportunities in Chemistry

TABLE 1.9

Agronomist

Anesthesiologist

Biochemist

Ceramics engineer

Chemical engineer

Consumer protection

specialist

Dentist

Dietitian

Educator

Food and drug analyst

Food technologist

Geneticist

Geologist

Industrial health

engineer

Internist

Laboratory analyst

Medicinal chemist

Metallurgist

Nuclear scientist

Patent examiner

Pharmacist

Pharmacologist

Pharmacologist sales

representative

Physician

Professor

Sanitarian

Science technician

Technical writer

Toxicologist

Wood scientist

FIGURE 1.30

Nanotubes, nanospheres, nanogears, and

nanolevers. Such things might be the

building blocks of a new industrial

revolution in “nanotechnology.”

Beverage companies

Centers for Disease Control

Chemical companies

Chemical manufacturing ﬁrms

Colleges and universities

Cosmetics companies

Department of Agriculture

Department of Defense

Engineering ﬁrms

Environmental Protection Agency

Food companies

Food and Drug Administration

Hospitals

Journals

Local government

Medical laboratories

Medical libraries

Medical supply companies

Mining companies

National Institutes of Health

Newspapers and magazines

Petroleum reﬁneries

Pharmaceutical companies

Research ﬁrms

State and federal government

Technical libraries

Textile manufacturers

Possible Employers of Chemistry Majors

Key Words 37

The Bottom Line

■

Our universe and everything in it are made of chem-

icals. Chemicals are involved in all of the changes

that affect and sustain us. (Section 1.1)

■

Atoms are the most fundamental particles of the

chemical world. A substance containing only one

kind of atom is called an element. The particles of

chemistry—atoms and molecules—are incredibly

tiny compared to the objects we see in the everyday

world. (Section 1.2)

■

Molecules are composed of two or more atoms

chemically bonded together. A chemical compound

is any substance that contains different elements

chemically bonded together. (Section 1.2)

■

Chemical changes occur when chemicals undergo

reactions in which new chemical products are

formed from the initial chemical reactants. Physical

changes occur when chemicals undergo changes in

their state. (Section 1.2)

■

Scientists ﬁnd out about nature, and learn how to

change it, using the scientiﬁc method. (Section 1.3)

■

The International System (SI) deﬁnes the fundamen-

tal base units, and a variety of derived units, that are

used to measure physical quantities. (Section 1.4)

■

The calculations in chemistry include the conversion

of units by using factors that relate identical quanti-

ties. This can be done via a method known as dimen-

sional analysis. (Section 1.5)

■

Precision and accuracy are important to the discus-

sion of chemistry. They relate the uncertainties in

measurements. The number of signiﬁcant digits a

number contains is related to the precision of that

number. (Section 1.6)

■

Our understanding of chemistry can be used to

solve problems in many ﬁelds, including medicine,

agriculture, pollution control, and nanotechnology.

In addition, we can broaden our understanding of

many issues, including global warming, materials,

meeting our energy needs, and life itself.

(Section 1.7)

Key Words

accuracy The closeness of a measurement to the actual

value. (p. 29)

ampere (A) The SI base unit of electric current. (p. 20)

atoms The smallest identifying unit of an element.

(p. 5)

base units The set of seven fundamental units of the In-

ternational System (SI). (p. 17)

candela (cd) The SI base unit of luminous intensity.

(p. 20)

chemical See matter.

chemical changes Changes that involve chemical reac-

tions in which existing chemicals, the reactants, are

changed into different chemicals, the products. (p. 6)

chemical property A characteristic of a substance that

can be determined as it undergoes a change in its

chemical composition. (p. 6)

chemical reaction The combination or reorganization of

chemicals to produce different chemicals. (p. 6)

chemistry The systematic study of the composition,

structure, and properties of the matter of our uni-

verse. (p. 4)

composition The relative proportions of the elements in

a compound. (p. 5)

compound A substance containing different elements

chemically bonded together. (p. 5)

conversion factor A mathematical expression of the ratio

of one unit to another, used to convert quantities

from one system of units to another. (p. 25)

cubic decimeter (dm

) The derived unit commonly

used to measure volumes in the laboratory. See liter.

(p. 22)

cubic meter (m

) The derived SI unit used for volume.

(p. 22)

degree Celsius (°C) The unit of temperature on the Cel-

sius scale. (p. 19)

degree Fahrenheit (°F) The unit of temperature on the

Fahrenheit scale. (pp. 18–19)

density The mass of a substance that is present in a

given volume of the substance. The SI unit for mea-

suring density is kilograms per cubic meter (kg/m

(p. 22)

derived units Units formed by the combination of SI

base units. (p. 22)

desalination The process that removes dissolved salts

from seawater to make potable water. (p. 10)

dimensional analysis An extremely useful method for

performing calculations by using appropriate con-

version factors and allowing units (dimensions) to

cancel out, leaving only the desired answer in the de-

sired units. (p. 26)