Unformatted text preview: Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 1 CHAPTER Chemistry: The Study of Change
CHEMISTRY IS AN ACTIVE, EVOLVING SCIENCE THAT HAS VITAL IMPOR- 1.1 CHEMISTRY: A SCIENCE FOR THE
TWENTY-FIRST CENTURY TANCE TO OUR WORLD, IN BOTH THE REALM OF NATURE AND THE REALM 1.2 THE STUDY OF CHEMISTRY
OF SOCIETY. ITS ROOTS ARE ANCIENT, BUT AS WE WILL SOON SEE, CHEM- 1.3 THE SCIENTIFIC METHOD
ISTRY IS EVERY BIT A MODERN SCIENCE. 1.4 CLASSIFICATIONS OF MATTER WE WILL BEGIN OUR STUDY OF CHEMISTRY AT THE MACROSCOPIC 1.5 THE THREE STATES OF MATTER
LEVEL, WHERE WE CAN SEE AND MEASURE THE MATERIALS OF WHICH OUR
WORLD IS MADE. IN 1.6 PHYSICAL AND CHEMICAL PROPERTIES OF
MATTER THIS CHAPTER WE WILL DISCUSS THE SCIENTIFIC METHOD, WHICH PROVIDES THE FRAMEWORK FOR RESEARCH NOT ONLY 1.7 MEASUREMENT IN CHEMISTRY BUT IN ALL OTHER SCIENCES AS WELL. 1.8 HANDLING NUMBERS NEXT WE WILL DIS- COVER HOW SCIENTISTS DEFINE AND CHARACTERIZE MATTER. THEN 1.9 THE FACTOR-LABEL METHOD OF SOLVING
PROBLEMS WE WILL FAMILIARIZE OURSELVES WITH THE SYSTEMS OF MEASUREMENT USED
IN THE LABORATORY. FINALLY, WE WILL SPEND SOME TIME LEARNING HOW TO HANDLE NUMERICAL RESULTS OF CHEMICAL MEASUREMENTS AND
HOW TO SOLVE NUMERICAL PROBLEMS. IN CHAPTER 2 WE WILL BEGIN TO EXPLORE THE MICROSCOPIC WORLD OF ATOMS AND MOLECULES. 3 Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 4 CHEMISTRY: THE STUDY OF CHANGE 1.1 The Chinese characters for chemistry mean “The study of
change.’’ CHEMISTRY: A SCIENCE FOR THE TWENTY-FIRST CENTURY Chemistry is the study of matter and the changes it undergoes. Chemistry is often called
the central science, because a basic knowledge of chemistry is essential for students
of biology, physics, geology, ecology, and many other subjects. Indeed, it is central to
our way of life; without it, we would be living shorter lives in what we would consider primitive conditions, without automobiles, electricity, computers, CDs, and many
other everyday conveniences.
Although chemistry is an ancient science, its modern foundation was laid in the
nineteenth century, when intellectual and technological advances enabled scientists to
break down substances into ever smaller components and consequently to explain many
of their physical and chemical characteristics. The rapid development of increasingly
sophisticated technology throughout the twentieth century has given us even greater
means to study things that cannot be seen with the naked eye. Using computers and
electron microscopes, for example, chemist can analyze the structure of atoms and molecules — the fundamental units on which the study of chemistry is based — and design
new substances with specific properties, such as drugs and environmentally friendly
As we prepare to leave the twentieth century, it is fitting to ask what part the central science will have in the next century. Almost certainly, chemistry will continue to
play a pivotal role in all areas of science and technology. Before plunging into the
study of matter and its transformation, let us consider some of the frontiers that chemists
are currently exploring (Figure 1.1). Whatever your reasons for taking introductory
chemistry, a good knowledge of the subject will better enable you to appreciate its impact on society and on you as an individual. Health and Medicine Three major advances in this century have enabled us to prevent and treat diseases.
They are: public health measures establishing sanitation systems to protect vast numbers of people from infectious disease; surgery with anesthesia, enabling physicians to
cure potentially fatal conditions, such as an inflamed appendix; and the introduction
of vaccines and antibiotics that make it possible to prevent diseases spread by microbes.
Gene therapy promises to be the fourth revolution in medicine. (A gene is the basic
unit of inheritance.) Several thousand known conditions, including cystic fibrosis and
hemophilia, are carried by inborn damage to a single gene. Many other ailments, such
as cancer, heart disease, AIDS, and arthritis, result to an extent from impairment of one
or more genes involved in the body’s defenses. In gene therapy, a selected healthy gene
is delivered to a patient’s cell to cure or ease such disorders. To carry out such a procedure, a doctor must have a sound knowledge of the chemical properties of the molecular components involved.
Chemists in the pharmaceutical industry are researching potent drugs with few or
no side effects to treat cancer, AIDS, and many other diseases as well as drugs to increase the number of successful organ transplants. On a broader scale, improved understanding of the mechanism of aging will lead to a longer and healthier lifespan for
the world’s population. Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 1.1 CHEMISTRY: A SCIENCE FOR THE TWENTY-FIRST CENTURY 5 FIGURE 1.1 (a) A chemical
research laboratory where new
drugs are synthesized. (b)
Photovoltaic cells. (c) A silicon
wafer being processed. (d) Effect
of a sex pheromone on gypsy
moths. (a) (c) (b) (d) Energy and the Environment Energy is a by-product of many chemical processes, and as the demand for energy continues to increase, both in technologically advanced countries like the United States
and in developing ones like China, chemists are actively trying to find new energy
sources. Currently the major sources of energy are fossil fuels (coal, petroleum, and
natural gas). The estimated reserves of these fuels will last us another 50–100 years,
at the present rate of consumption, so it is urgent that we find alternatives.
Solar energy promises to be a viable source of energy for the future. Every year
Earth’s surface receives about 10 times as much energy from sunlight as is contained
in all of the known reserves of coal, oil, natural gas, and uranium combined. But much
of this energy is “wasted’’ because it is reflected back into space. For the past thirty
years, intense research efforts have shown that solar energy can be harnessed effectively in two ways. One is the conversion of sunlight directly to electricity using devices called photovoltaic cells. The other is to use sunlight to obtain hydrogen from
water. The hydrogen can then be fed into a fuel cell to generate electricity. Although
our understanding of the scientific process of converting solar energy to electricity has
advanced, the technology has not yet improved to the point where we can produce electricity on a large scale at an economically acceptable cost. By 2050, however, it has
been predicted that solar energy will supply over 50 percent of our power needs.
Another potential source of energy is nuclear fission, but because of environmental
concerns about the radioactive wastes from fission processes, the future of the nuclear Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 6 CHEMISTRY: THE STUDY OF CHANGE industry in the United States is uncertain. Chemists can help to devise better ways to
dispose of nuclear waste. Nuclear fusion, the process that occurs in the sun and other
stars, generates huge amounts of energy without producing much dangerous radioactive waste. In another 50 years, nuclear fusion will likely be a significant source of
Energy production and energy utilization are closely tied to the quality of our environment. A major disadvantage of burning fossil fuels is that they give off carbon
dioxide, which is a greenhouse gas (that is, it promotes the heating of Earth’s atmosphere), along with sulfur dioxide and nitrogen oxides, which result in acid rain and
smog. (Harnessing solar energy has no such detrimental effects on the environment.)
By using fuel-efficient automobiles and more effective catalytic converters, we should
be able to drastically reduce harmful auto emissions and improve the air quality in areas with heavy traffic. In addition, electric cars, powered by durable, long-lasting batteries, should be more prevalent in the next century, and their use will help to minimize air pollution. Materials and Technology Chemical research and development in the twentieth century have provided us with
new materials that have profoundly improved the quality of our lives and helped to advance technology in countless ways. A few examples are polymers (including rubber
and nylon), ceramics (such as cookware), liquid crystals (like those in electronic displays), adhesives (used in your Post-It notes), and coatings (for example, latex paint).
What is in store for the near future? One likely possibility is room-temperature
superconductors. Electricity is carried by copper cables, which are not perfect conductors. Consequently, about 20 percent of electrical energy is lost in the form of heat
between the power station and our homes. This is a tremendous waste. Superconductors
are materials that have no electrical resistance and can therefore conduct electricity
with no energy loss. Although the phenomenon of superconductivity at very low temperatures (more than 400 degrees Fahrenheit below the freezing point of water) has
been known for over 80 years, a major breakthrough in the mid-1980s demonstrated
that it is possible to make materials that act as superconductors at or near room temperature. Chemists have helped to design and synthesize new materials that show
promise in this quest. The next 30 years will see high-temperature superconductors being applied on a large scale in magnetic resonance imaging (MRI), levitated trains, and
If we had to name one technological advance that has shaped our lives more than
any other, it would be the computer. The “engine’’ that drives the ongoing computer
revolution is the microprocessor — the tiny silicon chip that has inspired countless inventions, such as laptop computers and fax machines. The performance of a microprocessor is judged by the speed with which it carries out mathematical operations,
such as addition. The pace of progress is such that since their introduction, microprocessors have doubled in speed every 18 months. At this rate by the year 2030 one
desk computer will be as powerful as all those in California’s Silicon Valley in 1998!
The quality of any microprocessor depends on the purity of the silicon chip and on the
ability to add the desired amount of other substances, and chemists play an important
role in the research and development of silicon chips. For the future, scientists have
begun to explore the prospect of “molecular computing,’’ that is, replacing silicon with Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 1.2 THE STUDY OF CHEMISTRY 7 molecules. The advantages are that certain molecules can be made to respond to light,
rather than to electrons, so that we would have optical computers rather than electronic
computers. With proper genetic engineering, scientists can synthesize such molecules
using microorganisms instead of large factories. Optical computers also would have
much greater storage capacity than electronic computers.
Food and Agriculture How can the world’s rapidly increasing population be fed? In poor countries, agricultural activities occupy about 80 percent of the workforce, and half of an average family budget is spent on foodstuffs. This is a tremendous drain on a nation’s resources.
The factors that affect agricultural production are the richness of the soil, insects and
diseases that damage crops, and weeds that compete for nutrients. Besides irrigation,
farmers rely on fertilizers and pesticides to increase crop yield. Since the 1950s, treatment for crops suffering from pest infestations has sometimes been the indiscriminate
application of potent chemicals. Such measures have often had serious detrimental effects on the environment. Even the excessive use of fertilizers is harmful to the land,
water, and air.
To meet the food demands of the twenty-first century, new and novel approaches
in farming must be devised. It has already been demonstrated that, through biotechnology, it is possible to grow larger and better crops. These techniques can be applied
to many different farm products, not only for improved yields, but also for better frequency, that is, more crops every year. For example, it is known that a certain bacterium produces a protein molecule that is toxic to leaf-eating caterpillars. Incorporating
the gene that codes for the toxin into crops enables plants to protect themselves so that
pesticides are not necessary. Researchers have also found a way to prevent pesky insects from reproducing. Insects communicate with one another by emitting and reacting to special molecules called pheromones. By identifying and synthesizing
pheromones used in mating, it is possible to interfere with the normal reproductive cycle of common pests, for example, by inducing insects to mate too soon or tricking female insects into mating with sterile males. Moreover, chemists can devise ways to increase the production of fertilizers that are less harmful to the environment and
substances that would selectively kill weeds. 1.2 THE STUDY OF CHEMISTRY Compared with other subjects, chemistry is commonly believed to be more difficult,
at least at the introductory level. There is some justification for this perception; for one
thing, chemistry has a very specialized vocabulary. However, even if this is your first
course in chemistry, you already have more familiarity with the subject than you may
realize. In everyday conversations we hear words that have a chemical connection, although they may not be used in the scientifically correct sense. Examples are “electronic,’’ “quantum leap,’’ “equilibrium,’’ “catalyst,’’ “chain reaction,’’ and “critical
mass.’’ Moreover, if you cook, then you are a practicing chemist! From experience
gained in the kitchen, you know that oil and water do not mix and that boiling water
left on the stove will evaporate. You apply chemical and physical principles when you
use baking soda to leaven bread, choose a pressure cooker to shorten the time it takes
to prepare soup, add meat tenderizer to a pot roast, squeeze lemon juice over sliced Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 8 CHEMISTRY: THE STUDY OF CHANGE FIGURE 1.2 A badly rusted
car. Corrosion of iron costs the
U.S. economy tens of billions of
dollars every year. pears to prevent them from turning brown or over fish to minimize its odor, and add
vinegar to the water in which you are going to poach eggs. Every day we observe such
changes without thinking about their chemical nature. The purpose of this course is to
make you think like a chemist, to look at the macroscopic world — the things we can
see, touch, and measure directly — and visualize the particles and events of the microscopic world that we cannot experience without modern technology and our imaginations.
At first some students find it confusing that their chemistry instructor and textbook seem to be continually shifting back and forth between the macroscopic and microscopic worlds. Just keep in mind that the data for chemical investigations most often come from observations of large-scale phenomena, but the explanations frequently
lie in the unseen and partially imagined microscopic world of atoms and molecules. In
other words, chemists often see one thing (in the macroscopic world) and think another
(in the microscopic world). Looking at the rusted car in Figure 1.2, for example, a
chemist might think about the basic properties of individual atoms of iron and how
these units interact with other atoms and molecules to produce the observed change. 1.3 THE SCIENTIFIC METHOD All sciences, including the social sciences, employ variations of what is called the scientific method, a systematic approach to research. For example, a psychologist who
wants to know how noise affects people’s ability to learn chemistry and a chemist interested in measuring the heat given off when hydrogen gas burns in air would follow
roughly the same procedure in carrying out their investigations. The first step is to carefully define the problem. The next step includes performing experiments, making careful observations, and recording information, or data, about the system — the part of the
universe that is under investigation. (In the examples above, the systems are the group
of people the psychologist will study and a mixture of hydrogen and air.)
The data obtained in a research study may be both qualitative, consisting of general observations about the system, and quantitative, comprising numbers obtained by Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 1.3 FIGURE 1.3 The three levels of
studying chemistry and their
relationships. Observation deals
with events in the macroscopic
world; atoms and molecules
constitute the microscopic world.
Representation is a scientific
shorthand for describing an
experiment in symbols and
chemical equations. Chemists use
their knowledge of atoms and
molecules to explain an observed
phenomenon. Back Forward Main Menu Observation THE SCIENTIFIC METHOD Representation 9 Interpretation various measurements of the system. Chemists generally use standardized symbols and
equations in recording their measurements and observations. This form of representation not only simplifies the process of keeping records, but also provides a common
basis for communication with other chemists.
When the experiments have been completed and the data have been recorded, the
next step in the scientific method is interpretation, meaning that the scientist attempts
to explain the observed phenomenon. Based on the data that were gathered, the researcher formulates a hypothesis, a tentative explanation for a set of observations.
Further experiments are devised to test the validity of the hypothesis in as many ways
as possible, and the process begins anew. Figure 1.3 summarizes the main steps of the
After a large amount of data have been collected, it is often desirable to summarize the information in a concise way, as a law. In science, a law is a concise verbal
or mathematical statement of a relationship between phenomena that is always the
same under the same conditions. For example, Sir Isaac Newton’s second law of motion, which you may remember from high school science, says that force equals mass
times acceleration (F ma). What this law means is that an increase in the mass or in
the acceleration of an object will always increase its force proportionally, and a decrease in mass or acceleration will always decrease the force.
Hypotheses that survive many experimental tests of their validity may evolve into
theories. A theory is a unifying principle that explains a body of facts and/or those
laws that are based on them. Theories, too, are constantly being tested. If a theory is
disproved by experiment, then it must be discarded or modified so that it becomes consistent with experimental observations. Proving or disproving a theory can take years,
even centuries, in part because the necessary technology may not be available. Atomic
theory, which we will study in Chapter 2, is a case in point. It took more than 2000
years to work out this fundamental principle of chemistry proposed by Democritus, an
ancient Greek philosopher. A more contemporary example is the Big Bang theory of
the origin of the universe discussed on p. 28.
Scientific progress is seldom, if ever, made in a rigid, step-by-step fashion.
Sometimes a law precedes a theory; sometimes it is the other way around. Two scientists may start working on a project with exactly the same objective, but will end up
taking drastically different approaches. Scientists are, after all, human beings, and their
modes of thinking and working are very much influenced by their background, training, and personalities.
The development of science has been irregular and sometimes even illogical. Great
discoveries are usually the result of the cumulative contributions and experience of
many workers, even though the credit for formulating a theory or a law is usually given
to only one individual. There is, of course, an element of luck involved in scientific
discoveries, but it has been said that “chance favors the prepared mind.’’ It takes an
alert and well-trained person to recognize the significance of an accidental discovery
and to take full advantage of it. More often than not, the public learns only of spectacular scientific breakthroughs. For every success story, however, there are hundreds
of cases in which scientists have spent years working on projects that ultimately led to TOC Study Guide TOC Textbook Website MHHE Website 10 CHEMISTRY: THE STUDY OF CHANGE FIGURE 1.4 Separating iron
filings from a heterogeneous
mixture. The same technique is
used on a larger scale to
separate iron and steel from
nonmagnetic objects such as
aluminum, glass, and plastics. (a) (b) a dead end, and in which positive achievements came only after many wrong turns and
at such a slow pace that they went unheralded. Yet even the dead ends contribute something to the continually growing body of knowledge about the physical universe. It is
the love of the search that keeps many scientists in the laboratory. 1.4 CLASSIFICATIONS OF MATTER We defined chemistry at the beginning of the chapter as the study of matter and the
changes it undergoes. Matter is anything that occupies space and has mass. Matter includes things we can see and touch (such as water, earth, and trees), as well as things
we cannot (such as air). Thus, everything in the universe has a “chemical’’ connection.
Chemists distinguish among several subcategories of matter based on composition and properties. The classifications of matter include substances, mixtures, elements, and compounds, as well as atoms and molecules, which we will consider in
SUBSTANCES AND MIXTURES A substance is a form of matter that has a definite (constant) composition and distinct
properties. Examples are water, ammonia, table sugar (sucrose), gold, and oxygen.
Substances differ from one another in composition and can be identified by their appearance, smell, taste, and other properties.
A mixture is a combination of two or more substances in which the substances
retain their distinct identities. Some familiar examples are air, soft drinks, milk, and
cement. Mixtures do not have constant composition. Therefore, samples of air collected
in different cities would probably differ in composition because of differences in altitude, pollution, and so on.
Mixtures are either homogeneous or heterogeneous. When a spoonful of sugar
dissolves in water we obtain a homogeneous mixture in which the composition of the
mixture is the same throughout. If sand is mixed with iron filings, however, the sand
grains and the iron filings remain separate (Figure 1.4). This type of mixture is called
a heterogeneous mixture because the composition is not uniform. Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 1.4 CLASSIFICATIONS OF MATTER 11 Any mixture, whether homogeneous or heterogeneous, can be created and then
separated by physical means into pure components without changing the identities of
the components. Thus, sugar can be recovered from a water solution by heating the solution and evaporating it to dryness. Condensing the vapor will give us back the water component. To separate the iron-sand mixture, we can use a magnet to remove the
iron filings from the sand, because sand is not attracted to the magnet [see Figure
1.4(b)]. After separation, the components of the mixture will have the same composition and properties as they did to start with.
ELEMENTS AND COMPOUNDS Substances can be either elements or compounds. An element is a substance that cannot be separated into simpler substances by chemical means. To date, 112 elements
have been positively identified. Eighty-three of them occur naturally on Earth. The others have been created by scientists via nuclear processes, which are the subject of
Chapter 23 of this text.
For convenience, chemists use symbols of one, two, or three letters to represent
the elements. The first letter of a symbol is always capitalized, but any following letters are not. For example, Co is the symbol for the element cobalt, whereas CO is the
formula for the carbon monoxide molecule. Table 1.1 shows the names and symbols
of some of the more common elements; a complete list of the elements and their symbols appears inside the front cover of this book. The symbols of some elements are derived from their Latin names — for example, Au from aurum (gold), Fe from ferrum
(iron), and Na from natrium (sodium) — while most of them come from their English
names. Appendix 1 gives the origin of the names and lists the discoverers of most of
Most elements can interact with one or more other elements to form compounds.
Hydrogen gas, for example, burns in oxygen gas to form water, which has properties
that are distinctly different from those of the starting materials. Water is made up of
two parts hydrogen and one part oxygen. This composition does not change, regardless of whether the water comes from a faucet in the United States, a lake in Outer
Mongolia, or the ice caps on Mars. Thus, water is a compound, a substance composed
of atoms of two or more elements chemically united in fixed proportions. Unlike mixtures, compounds can be separated only by chemical means into their pure components.
Copper Back Forward Main Menu TOC Some Common Elements and Their Symbols
Cu NAME Fluorine
Nitrogen SYMBOL F
N Study Guide TOC NAME Oxygen
Zinc SYMBOL O
Zn Textbook Website MHHE Website 12 CHEMISTRY: THE STUDY OF CHANGE Matter Separation by
physical methods Mixtures Homogeneous
mixtures FIGURE 1.5 Classification of
matter. 1.5 Pure
substances Compounds Separation by
chemical methods Elements The relationships among elements, compounds, and other categories of matter are
summarized in Figure 1.5. THE THREE STATES OF MATTER All substances, at least in principle, can exist in three states: solid, liquid, and gas. As
Figure 1.6 shows, gases differ from liquids and solids in the distances between the molecules. In a solid, molecules are held close together in an orderly fashion with little
freedom of motion. Molecules in a liquid are close together but are not held so rigidly
in position and can move past one another. In a gas, the molecules are separated by
distances that are large compared with the size of the molecules.
The three states of matter can be interconverted without changing the composition of the substance. Upon heating, a solid (for example, ice) will melt to form a liquid (water). (The temperature at which this transition occurs is called the melting point.)
Further heating will convert the liquid into a gas. (This conversion takes place at the
boiling point of the liquid.) On the other hand, cooling a gas will cause it to condense
FIGURE 1.6 Microscopic views
of a solid, a liquid, and a gas. Solid Back Forward Main Menu TOC Liquid Study Guide TOC Gas Textbook Website MHHE Website 1.6 PHYSICAL AND CHEMICAL PROPERTIES OF MATTER 13 FIGURE 1.7 The three states of
matter. A hot poker changes ice
into water and steam. into a liquid. When the liquid is cooled further, it will freeze into the solid form. Figure
1.7 shows the three states of water. 1.6 Hydrogen burning in air to form
water. Back Forward Main Menu PHYSICAL AND CHEMICAL PROPERTIES OF MATTER Substances are identified by their properties as well as by their composition. Color,
melting point, and boiling point are physical properties. A physical property can be
measured and observed without changing the composition or identity of a substance.
For example, we can measure the melting point of ice by heating a block of ice and
recording the temperature at which the ice is converted to water. Water differs from
ice only in appearance, not in composition, so this is a physical change; we can freeze
the water to recover the original ice. Therefore, the melting point of a substance is a
physical property. Similarly, when we say that helium gas is lighter than air, we are referring to a physical property.
On the other hand, the statement “Hydrogen gas burns in oxygen gas to form water ’’ describes a chemical property of hydrogen, because in order to observe this property we must carry out a chemical change, in this case burning. After the change, the
original chemical substance, the hydrogen gas, will have vanished, and all that will be
left is a different chemical substance — water. We cannot recover the hydrogen from
the water by means of a physical change, such as boiling or freezing.
Every time we hard-boil an egg, we bring about a chemical change. When subjected to a temperature of about 100 C, the yolk and the egg white undergo changes
that alter not only their physical appearance but their chemical makeup as well. When
eaten, the egg is changed again, by substances in our bodies called enzymes. This digestive action is another example of a chemical change. What happens during digestion depends on the chemical properties of both the enzymes and the food. TOC Study Guide TOC Textbook Website MHHE Website 14 CHEMISTRY: THE STUDY OF CHANGE All measurable properties of matter fall into one of two additional categories: extensive properties and intensive properties. The measured value of an extensive property depends on how much matter is being considered. Mass, which is the quantity of
matter in a given sample of a substance, is an extensive property. More matter means
more mass. Values of the same extensive property can be added together. For example, two copper pennies will have a combined mass that is the sum of the masses of
each penny, and the length of two tennis courts is the sum of the lengths of each tennis court. Volume, defined as length cubed, is another extensive property. The value
of an extensive quantity depends on the amount of matter.
The measured value of an intensive property does not depend on how much matter is being considered. Density, defined as the mass of an object divided by its volume, is an intensive property. So is temperature. Suppose that we have two beakers of
water at the same temperature. If we combine them to make a single quantity of water in a larger beaker, the temperature of the larger quantity of water will be the same
as it was in two separate beakers. Unlike mass, length, and volume, temperature and
other intensive properties are not additive. 1.7 MEASUREMENT The measurements chemists make are often used in calculations to obtain other related
quantities. Different instruments enable us to measure a substance’s properties: The
meter stick measures length or scale; the buret, the pipet, the graduated cylinder, and
the volumetric flask measure volume (Figure 1.8); the balance measures mass; the thermometer measures temperature. These instruments provide measurements of macroscopic properties, which can be determined directly. Microscopic properties, on the
atomic or molecular scale, must be determined by an indirect method, as we will see
in the next chapter.
FIGURE 1.8 Some common
measuring devices found in a
chemistry laboratory. These
devices are not drawn to scale
relative to one another. We will
discuss the uses of these
measuring devices in Chapter 4. mL
100 2 90 3 80 4 70 15
25 mL 60
17 50 18 40 19 30 20 20
10 Buret Back Forward Main Menu Pipet TOC Graduated cylinder Study Guide TOC 1 liter Volumetric flask Textbook Website MHHE Website 1.7 TABLE 1.2 NAME OF UNIT Length
Amount of substance
Luminous intensity Meter
Candela PREFIX TeraGigaMegaKiloDeciCentiMilliMicroNanoPico- 15 SI Base Units BASE QUANTITY TABLE 1.3 MEASUREMENT SYMBOL m
cd Prefixes Used with SI Units
SYMBOL MEANING EXAMPLE
m 1,000,000,000,000, or 10
1,000,000,000, or 109
1,000,000, or 106
1,000, or 103
1/10, or 10 1
1/100, or 10 2
1/1,000, or 10 3
1/1,000,000, or 10 6
1/1,000,000,000, or 10 9
1/1,000,000,000,000, or 10 n
p 12 1
1 terameter (Tm)
micrometer ( m)
picometer (pm) 1 1012 m
1 109 m
1 106 m
1 103 m
1 10 6 m
1 10 9 m
1 10 12 m A measured quantity is usually written as a number with an appropriate unit. To
say that the distance between New York and San Francisco by car along a certain route
is 5166 is meaningless. We must specify that the distance is 5166 kilometers. The same
is true in chemistry; units are essential to stating measurements correctly.
SI UNITS For many years scientists recorded measurements in metric units, which are related
decimally, that is, by powers of 10. In 1960, however, the General Conference of
Weights and Measures, the international authority on units, proposed a revised metric
system called the International System of Units (abbreviated SI, from the French
Système Internationale d’Unites). Table 1.2 shows the seven SI base units. All other
units of measurement can be derived from these base units. Like metric units, SI units
are modified in decimal fashion by a series of prefixes, as shown in Table 1.3. We will
use both metric and SI units in this book.
Measurements that we will utilize frequently in our study of chemistry include
time, mass, volume, density, and temperature.
MASS AND WEIGHT The terms “mass’’ and “weight’’ are often used interchangeably, although, strictly speaking, they are different quantities. Whereas mass is a measure of the amount of matter
in an object, weight, technically speaking, is the force that gravity exerts on an object.
An apple that falls from a tree is pulled downward by Earth’s gravity. The mass of the Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 16 CHEMISTRY: THE STUDY OF CHANGE apple is constant and does not depend on its location, but its weight does. For example, on the surface of the moon the apple would weigh only one-sixth what it does on
Earth, because the moon’s gravity is only one-sixth that of Earth. The moon’s smaller
gravity enables astronauts to jump about rather freely on its surface despite their bulky
suits and equipment. Chemists are interested primarily in mass, which can be
determined readily with a balance; the process of measuring mass, oddly, is called
The SI base unit of mass is the kilogram (kg), but in chemistry the smaller gram
(g) is more convenient:
1 kg 1000 g 103 g 1 VOLUME
An astronaut on the surface of
the moon. The SI unit of length is the meter (m), and the SI-derived unit for volume is the cubic
meter (m3). Generally, however, chemists work with much smaller volumes, such as
the cubic centimeter (cm3) and the cubic decimeter (dm3):
1 dm 3 (1
(1 10 2 m)3 10 1 3 m) 1
1 10 6 m3 10 3 m3 Another common unit of volume is the liter (L). A liter is the volume occupied by one
cubic decimeter. One liter of volume is equal to 1000 milliliters (mL) or 1000 cm3:
1L 1000 mL
1 dm3 and one milliliter is equal to one cubic centimeter:
Volume: 1000 cm3;
1L 1 cm3 Figure 1.9 compares the relative sizes of two volumes. Even though the liter is not an
SI unit, volumes are usually expressed in liters and milliliters.
DENSITY The equation for density is
d 1 cm
10 cm = 1 dm
Volume: 1 cm3;
FIGURE 1.9 Comparison of
two volumes, 1 mL and 1000 mL. Back Forward m
V (1.1) where d, m, and V denote density, mass, and volume, respectively. Because density is
an intensive property and does not depend on the quantity of mass present, for a given
material the ratio of mass to volume always remains the same; in other words, V increases as m does.
The SI-derived unit for density is the kilogram per cubic meter (kg/m3). This unit
is awkwardly large for most chemical applications. Therefore, grams per cubic centimeter (g/cm3) and its equivalent, grams per milliliter (g/mL), are more commonly
used for solid and liquid densities. Because gas densities are often very low, we express them in units of grams per liter (g/L): Main Menu TOC Study Guide TOC Textbook Website MHHE Website 1.7 1 g/cm3 1 g/mL 1 g/L MEASUREMENT 17 1000 kg/m3 0.001 g/mL The following examples show density calculations.
EXAMPLE 1.1 Gold is a precious metal that is chemically unreactive. It is used mainly in jewelry,
dentistry, and electronic devices. A piece of gold ingot with a mass of 301 g has a
volume of 15.6 cm3. Calculate the density of gold.
Answer The density of the gold metal is given by
d Gold bars. m
19.3 g/cm3 Similar problems: 1.21, 1.22.
PRACTICE EXERCISE A piece of platinum metal with a density of 21.5 g/cm3 has a volume of 4.49 cm3.
What is its mass? EXAMPLE 1.2 The density of ethanol, a colorless liquid that is commonly known as grain alcohol,
is 0.798 g/mL. Calculate the mass of 17.4 mL of the liquid.
The mass of ethanol is found by rearranging the density equation d
as follows: Answer m d V 0.798
Ethanol is produced during the
fermentation of bread. It evaporates during baking and produces the fragrant aroma. Similar problems: 1.21, 1.22. m/V g
mL 17.4 mL 13.9 g
PRACTICE EXERCISE The density of sulfuric acid in a certain car battery is 1.41 g/mL. Calculate the mass
of 242 mL of the liquid. TEMPERATURE SCALES Note that the kelvin scale does
not have the degree sign. Also,
temperatures expressed in kelvin
can never be negative. Back Forward Main Menu Three temperature scales are currently in use. Their units are F (degrees Fahrenheit),
°C (degrees Celsius), and K (kelvin). The Fahrenheit scale, which is the most commonly used scale in the United States outside the laboratory, defines the normal freezing and boiling points of water to be exactly 32 F and 212 F, respectively. The Celsius
scale divides the range between the freezing point (0 C) and boiling point (100 C) of
water into 100 degrees. As Table 1.2 shows, the kelvin is the SI base unit of temperature; it is the absolute temperature scale. By absolute we mean that the zero on the
kelvin scale, denoted by 0 K, is the lowest temperature that can be attained theoreti- TOC Study Guide TOC Textbook Website MHHE Website 18 CHEMISTRY: THE STUDY OF CHANGE cally. On the other hand, 0 F and 0 C are based on the behavior of an arbitrarily chosen substance, water. Figure 1.10 compares the three temperature scales.
The size of a degree on the Fahrenheit scale is only 100/180, or 5/9, of a degree
on the Celsius scale. To convert degrees Fahrenheit to degrees Celsius, we write
?C (F 5C
9F 32 F) (1.2) The following equation is used to convert degrees Celsius to degrees Fahrenheit
5C ( C) 32 F (1.3) Both the Celsius and the Kelvin scales have units of equal magnitude; that is, one
degree Celsius is equivalent to one kelvin. Experimental studies have shown that absolute zero on the kelvin scale is equivalent to 273.15°C on the Celsius scale. Thus
we can use the following equation to convert degrees Celsius to kelvin:
?K (C 273.15 C) 1K
1C (1.4) We will frequently find it necessary to convert between degrees Celsius and degrees Fahrenheit and between degrees Celsius and kelvin. The following example illustrates these conversions.
EXAMPLE 1.3 (a) Solder is an alloy made of tin and lead that is used in electronic circuits. A
certain solder has a melting point of 224 C. What is its melting point in degrees
Fahrenheit? (b) Helium has the lowest boiling point of all the elements at 452 F.
Convert this temperature to degrees Celsius. (c) Mercury, the only metal that exists
as a liquid at room temperature, melts at 38.9 C. Convert its melting point to
Answer (a) This conversion is carried out by writing
5C (224 C) 32 F 32 F) 5C
9F 435 F (b) Here we have
( 452 F
Solder is used extensively in the
construction of electronic circuits. 269 C (c) The melting point of mercury in kelvins is given by
( 38.9 C
Similar problems: 1.24, 1.25, 1.26. 273.15 C) 1K
1C 234.3 K PRACTICE EXERCISE Convert (a) 327.5 C (the melting point of lead) to degrees Fahrenheit; (b) 172.9 F
(the boiling point of ethanol) to degrees Celsius; and (c) 77 K, the boiling point of
liquid nitrogen, to degrees Celsius. Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 1.8 FIGURE 1.10 Comparison of
the three temperature scales:
Celsius, Fahrenheit, and the
absolute (Kelvin) scales. Note that
there are 100 divisions, or 100
degrees, between the freezing
point and the boiling point of
water on the Celsius scale, and
there are 180 divisions, or 180
degrees, between the same two
temperature limits on the
Fahrenheit scale. 373 K 100°C 310 K 37°C 298 K 25°C Room
temperature 0°C Freezing point
of water 32°F Kelvin 1.8 19 77°F 273 K HANDLING NUMBERS Boiling point
of water Body
temperature Celsius 212°F 98.6°F Fahrenheit HANDLING NUMBERS Having surveyed some of the units used in chemistry, we now turn to techniques for
handling numbers associated with measurements: scientific notation and significant figures.
SCIENTIFIC NOTATION Chemists often deal with numbers that are either extremely large or extremely small.
For example, in 1 g of the element hydrogen there are roughly
602,200,000,000,000,000,000,000 hydrogen atoms. Each hydrogen atom has a mass of only
0.00000000000000000000000166 g These numbers are cumbersome to handle, and it is easy to make mistakes when using them in arithmetic computations. Consider the following multiplication:
0.0000000056 0.00000000048 0.000000000000000002688 It would be easy for us to miss one zero or add one more zero after the decimal point.
Consequently, when working with very large and very small numbers, we use a system called scientific notation. Regardless of their magnitude, all numbers can be expressed in the form
N 10n where N is a number between 1 and 10 and n, the exponent, is a positive or negative
integer (whole number). Any number expressed in this way is said to be written in scientific notation.
Suppose that we are given a certain number and asked to express it in scientific
notation. Basically, this assignment calls for us to find n. We count the number of places Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 20 CHEMISTRY: THE STUDY OF CHANGE that the decimal point must be moved to give the number N (which is between 1 and
10). If the decimal point has to be moved to the left, then n is a positive integer; if it
has to be moved to the right, n is a negative integer. The following examples illustrate
the use of scientific notation:
(a) Express 568.762 in scientific notation:
568.762 102 5.68762 Note that the decimal point is moved to the left by two places and n
(b) Express 0.00000772 in scientific notation:
0.00000772 Any number raised to the power
zero is equal to one. 7.72 2. 6 10 Here the decimal point is moved to the right by six places and n
Keep in mind the following two points. First, n 0 is used for numbers that are
not expressed in scientific notation. For example, 74.6 100 (n 0) is equivalent to
74.6. Second, the usual practice is to omit the superscript when n 1. Thus the scientific notation for 74.6 is 7.46 10 and not 7.46 101.
Next, we consider how scientific notation is handled in arithmetic operations.
Addition and Subtraction To add or subtract using scientific notation, we first write each quantity — say N1 and
N2 — with the same exponent n. Then we combine N1 and N2; the exponents remain
the same. Consider the following examples:
103) (7.4 4 (4.31 10 ) (2.1
(3.9 103) 103 9.5 3 10 ) 104) (4.31 104 4.70
(2.22 2 10 ) (4.10 3 10 ) 104) (0.39 10 2) (2.22
1.81 10 10 2) (0.41 2 Multiplication and Division To multiply numbers expressed in scientific notation, we multiply N1 and N2 in the
usual way, but add the exponents together. To divide using scientific notation, we divide N1 and N2 as usual and subtract the exponents. The following examples show how
these operations are performed:
(8.0 104) (5.0 102) (8.0 5.0)(104 2) 40
(4.0 10 5) (7.0 103) 106
107 (4.0 7.0)(10 28 Back Forward Main Menu TOC 5 104
109 Study Guide TOC 6.9
3.0 107 ) 1012 8.5
5.0 104 1.7 8.5
10 10 2.3 6.9
3.0 10 2.8
7 53 2 10 1
( 5) 9
5 Textbook Website MHHE Website 1.8 FIGURE 1.11
balance. HANDLING NUMBERS 21 A single-pan SIGNIFICANT FIGURES Except when all the numbers involved are integers (for example, in counting the number of students in a class), it is often impossible to obtain the exact value of the quantity under investigation. For this reason, it is important to indicate the margin of error
in a measurement by clearly indicating the number of significant figures, which are
the meaningful digits in a measured or calculated quantity. When significant figures
are used, the last digit is understood to be uncertain. For example, we might measure
the volume of a given amount of liquid using a graduated cylinder with a scale that
gives an uncertainty of 1 mL in the measurement. If the volume is found to be 6 mL,
then the actual volume is in the range of 5 mL to 7 mL. We represent the volume of
the liquid as (6 1) mL. In this case, there is only one significant figure (the digit 6)
that is uncertain by either plus or minus 1 mL. For greater accuracy, we might use a
graduated cylinder that has finer divisions, so that the volume we measure is now uncertain by only 0.1 mL. If the volume of the liquid is now found to be 6.0 mL, we may
express the quantity as (6.0 0.1) mL, and the actual value is somewhere between 5.9
mL and 6.1 mL. We can further improve the measuring device and obtain more significant figures, but in every case, the last digit is always uncertain; the amount of this
uncertainty depends on the particular measuring device we use.
Figure 1.11 shows a modern balance. Balances such as this one are available in
many general chemistry laboratories; they readily measure the mass of objects to four
decimal places. Therefore the measured mass typically will have four significant figures (for example, 0.8642 g) or more (for example, 3.9745 g). Keeping track of the
number of significant figures in a measurement such as mass ensures that calculations
involving the data will reflect the precision of the measurement.
Guidelines for Using Significant Figures We must always be careful in scientific work to write the proper number of significant
figures. In general, it is fairly easy to determine how many significant figures a number has by following these rules: Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 22 CHEMISTRY: THE STUDY OF CHANGE Any digit that is not zero is significant. Thus 845 cm has three significant figures,
1.234 kg has four significant figures, and so on.
Zeros between nonzero digits are significant. Thus 606 m contains three significant
figures, 40,501 kg contains five significant figures, and so on.
Zeros to the left of the first nonzero digit are not significant. Their purpose is to indicate the placement of the decimal point. For example, 0.08 L contains one significant figure, 0.0000349 g contains three significant figures, and so on.
If a number is greater than 1, then all the zeros written to the right of the decimal
point count as significant figures. Thus 2.0 mg has two significant figures, 40.062
mL has five significant figures, and 3.040 dm has four significant figures. If a number is less than 1, then only the zeros that are at the end of the number and the zeros that are between nonzero digits are significant. This means that 0.090 kg has
two significant figures, 0.3005 L has four significant figures, 0.00420 min has three
significant figures, and so on.
For numbers that do not contain decimal points, the trailing zeros (that is, zeros after the last nonzero digit) may or may not be significant. Thus 400 cm may have
one significant figure (the digit 4), two significant figures (40), or three significant
figures (400). We cannot know which is correct without more information. By using scientific notation, however, we avoid this ambiguity. In this particular case, we
can express the number 400 as 4 102 for one significant figure, 4.0 102 for two
significant figures, or 4.00 102 for three significant figures. •
• • • The following example shows the determination of significant figures.
EXAMPLE 1.4 Determine the number of significant figures in the following measurements: (a)
478 cm, (b) 6.01 g, (c) 0.825 m, (d) 0.043 kg, (e) 1.310 1022 atoms, (f) 7000
(a) Three, (b) Three, (c) Three, (d) Two, (e) Four, (f) This is an ambiguous case. The number of significant figures may be four (7.000 103), three (7.00
103), two (7.0 103), or one (7 103). Answer Similar problems: 1.33, 1.34. PRACTICE EXERCISE Determine the number of significant figures in each of the following measurements:
(a) 24 mL, (b) 3001 g, (c) 0.0320 m3, (d) 6.4 104 molecules, (e) 560 kg.
A second set of rules specifies how to handle significant figures in calculations.
• In addition and subtraction, the number of significant figures to the right of the decimal point in the final sum or difference is determined by the smallest number of
significant figures to the right of the decimal point in any of the original numbers.
Consider these examples:
01.100 m88 one significant figure after the decimal point
90.432 m88 round off to 90.4
0.12 0m88 two significant figures after the decimal point
1.977 m88 round off to 1.98 Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 1.8 HANDLING NUMBERS 23 The rounding-off procedure is as follows. To round off a number at a certain point
we simply drop the digits that follow if the first of them is less than 5. Thus 8.724
rounds off to 8.72 if we want only two figures after the decimal point. If the first
digit following the point of rounding off is equal to or greater than 5, we add 1 to
the preceding digit. Thus 8.727 rounds off to 8.73, and 0.425 rounds off to 0.43.
• In multiplication and division, the number of significant figures in the final product or quotient is determined by the original number that has the smallest number
of significant figures. The following examples illustrate this rule: • 4.5039 12.61092 m88 round off to 13 6.85
112.04 2.8 0.0611388789 m88 round off to 0.0611 Keep in mind that exact numbers obtained from definitions or by counting numbers of objects can be considered to have an infinite number of significant figures.
If an object has a mass of 0.2786 g, then the mass of eight such objects is
0.2786 g 8 2.229 g We do not round off this product to one significant figure, because the number 8 is
8.00000 . . . , by definition. Similarly, to take the average of the two measured
lengths 6.64 cm and 6.68 cm, we write
6.64 cm 6.68 cm
2 6.66 cm because the number 2 is 2.00000 . . . , by definition.
The following example shows how significant figures are handled in arithmetic
EXAMPLE 1.5 Carry out the following arithmetic operations: (a) 11,254.1 g 0.1983 g, (b) 66.59
L 3.113 L, (c) 8.16 m 5.1355, (d) 0.0154 kg 88.3 mL, (e) 2.64 103 cm
3.27 102 cm.
Answer (a) 11,254.1 g
11,254.2983 g m88 round off to 11,254.3 g (b) 66.59 L
63.477 L m88 round off to 63.48 L (c) 8.16 m
(d) Similar problems: 1.35, 1.36. Back Forward Main Menu 5.1355 0.0154 kg
88.3 mL 41.90568 m m88 round off to 41.9 m 0.000174405436 kg/mL m88 round off to 0.000174 kg/mL
or 1.74 10 4 kg/mL (e) First we change 3.27 102 cm to 0.327 103 cm and then carry out the addition (2.64 cm 0.327 cm) 103. Following the procedure in (a), we find the answer is 2.97 103 cm. TOC Study Guide TOC Textbook Website MHHE Website 24 CHEMISTRY: THE STUDY OF CHANGE PRACTICE EXERCISE Carry out the following arithmetic operations and round off the answers to the
appropriate number of significant figures: (a) 26.5862 L 0.17 L, (b) 9.1 g 4.682
g, (c) 7.1 104 dm 2.2654 102, (d) 6.54 g 86.5542 mL, (e) (7.55 104 m)
(8.62 103 m).
The above rounding-off procedure applies to one-step calculations. In chain calculations, that is, calculations involving more than one step, we use a modified procedure. Consider the following two-step calculation:
First step: A B C Second step: C D E Let us suppose that A 3.66, B 8.45, and D 2.11. Depending on whether we
round off C to three or four significant figures, we obtain a different number for E:
Method 1 Method 2 3.66 8.45 30.9 3.66 30.9 2.11 65.2 30.93 8.45
65.3 However, if we had carried out the calculation as 3.66 8.45 2.11 on a calculator
without rounding off the intermediate result, we would have obtained 65.3 as the answer for E. In general, we will show the correct number of significant figures in each
step of the calculation. However, in some worked examples, only the final answer is
rounded off to the correct number of significant figures. The answers for all intermediate calculations will be carried to one extra figure.
Accuracy and Precision In discussing measurements and significant figures it is useful to distinguish between
accuracy and precision. Accuracy tells us how close a measurement is to the true value
of the quantity that was measured. To a scientist there is a distinction between accuracy and precision. Precision refers to how closely two or more measurements of the
same quantity agree with one another (Figure 1.12).
The difference between accuracy and precision is a subtle but important one.
Suppose, for example, that three students are asked to determine the mass of a piece
of copper wire. The results of two successive weighings by each student are
STUDENT A STUDENT C 1.964 g
Average value STUDENT B 1.972 g
1.968 g 2.000 g
2.002 g 1.971 g 1.970 g 2.001 g The true mass of the wire is 2.000 g. Therefore, Student B’s results are more precise
than those of Student A (1.972 g and 1.968 g deviate less from 1.970 g than 1.964 g
and 1.978 g from 1.971 g), but neither set of results is very accurate. Student C’s results are not only the most precise, but also the most accurate, since the average value
is closest to the true value. Highly accurate measurements are usually precise too. On
the other hand, highly precise measurements do not necessarily guarantee accurate results. For example, an improperly calibrated meter stick or a faulty balance may give
precise readings that are in error. Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 1.9 FIGURE 1.12 The distribution
of darts on a dart board shows
the difference between precise
and accurate. (a) Good accuracy
and good precision. (b) Poor
accuracy and good precision. (c)
Poor accuracy and poor
precision. THE FACTOR-LABEL METHOD OF SOLVING PROBLEMS 10 10 30 30 30 60 60 60 100 100 100 (a) 1.9 10 (b) 25 (c) THE FACTOR-LABEL METHOD OF SOLVING PROBLEMS Careful measurements and the proper use of significant figures, along with correct calculations, will yield accurate numerical results. But to be meaningful, the answers also
must be expressed in the desired units. The procedure we will use to convert between
units in solving chemistry problems is called the factor-label method, or dimensional
analysis. A simple technique requiring little memorization, the factor-label method is
based on the relationship between different units that express the same physical quantity.
We know, for example, that the unit “dollar ’’ for money is different from the unit
“penny.’’ However, we say that 1 dollar is equivalent to 100 pennies because they both
represent the same amount of money. This equivalence allows us to write
1 dollar 100 pennies Because 1 dollar is equal to 100 pennies, it follows that their ratio has a value of 1;
100 pennies 1 This ratio can be read as 1 dollar per 100 pennies. The fraction is called a unit factor
(equal to 1) because the numerator and denominator describe the same amount of
We can also write the ratio as 100 pennies per dollar:
1 dollar 1 This fraction is also a unit factor. We see that the reciprocal of any unit factor is also
a unit factor. The usefulness of unit factors is that they allow us to carry out conversions between different units that measure the same quantity. Suppose that we want to
convert 2.46 dollars into pennies. This problem may be expressed as
? pennies 2.46 dollars Since this is a dollar-to-penny conversion, we choose the unit factor that has the unit
“dollar ’’ in the denominator (to cancel the “dollars’’ in 2.46 dollars) and write
2.46 dollars Back Forward Main Menu TOC 100 pennies
1 dollar Study Guide TOC 246 pennies Textbook Website MHHE Website 26 CHEMISTRY: THE STUDY OF CHANGE Note that the unit factor 100 pennies/1 dollar contains exact numbers, so it does not
affect the number of significant figures in the final answer.
Next let us consider the conversion of 57.8 meters to centimeters. This problem
may be expressed as
? cm 57.8 m By definition,
1 cm 1 2 10 m Since we are converting “m’’ to “cm,’’ we choose the unit factor that has meters in the
10 2 m 1 1 and write the conversion as
? cm 57.8 m 1 cm
10 2 m 1 5780 cm
5.78 103 cm Note that scientific notation is used to indicate that the answer has three significant
figures. The unit factor 1 cm/1 10 2 m contains exact numbers; therefore, it does
not affect the number of significant figures.
In the factor-label method the units are carried through the entire sequence of calculations. Therefore, if the equation is set up correctly, then all the units will cancel
except the desired one. If this is not the case, then an error must have been made somewhere, and it can usually be spotted by reviewing the solution.
The following examples illustrate the use of the factor-label method. EXAMPLE 1.6
A hydrogen molecule. The distance between two hydrogen atoms in a hydrogen molecule is 74 pm. Convert
this distance to meters.
Answer The problem is
?m 74 pm By definition,
1 pm 1 10 12 m The unit factor is
10 12 m
1 pm 1 1 Therefore we write
?m Similar problem: 1.37(a). 74 pm 1 10 12 m
1 pm 7.4 10 11 m PRACTICE EXERCISE Convert 197 pm, the radius of a calcium (Ca) atom, to centimeters. Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 1.9 THE FACTOR-LABEL METHOD OF SOLVING PROBLEMS 27 EXAMPLE 1.7
Conversion factors for some of the
English system units commonly
used in the United States for nonscientific measurements (for example,
pounds and inches) are provided inside the back cover of this book. A person’s average daily intake of glucose (a form of sugar) is 0.0833 pound (lb).
What is this mass in milligrams (mg)? (1 lb 453.6 g)
Answer The problem can be expressed as
? mg 0.0833 lb so the unit factor is
1 lb 1 and
1 mg 1 10 3 g so we must also include the unit factor
10 3 g 1 1 Thus
? mg Similar problem: 1.43. 0.0833 lb 453.6 g
1 lb 1 1 mg
10 3 g 104 mg 3.78 PRACTICE EXERCISE A roll of aluminum foil has a mass of 1.07 kg. What is its mass in pounds?
Note that unit factors may be squared or cubed, because 12
such factors is illustrated in Examples 1.8 and 1.9. 13 1. The use of EXAMPLE 1.8 An average adult has 5.2 liters of blood. What is the volume of blood in m3?
Since 1 L
lem can be stated as
Answer 1000 cm3, 5.2 L is equivalent to 5.2
? m3 103 cm3. The prob- 103 cm3 5.2 By definition
1m 100 cm The unit factor is
100 cm 1 It follows that
100 cm 3 13 1 Therefore we write
? m3 Back Forward Main Menu TOC 5.2 103 cm3 Study Guide TOC 1m
100 cm 3 5.2 10 3 m3 Textbook Website MHHE Website 28 CHEMISTRY: THE STUDY OF CHANGE Chemistry in Action Chemistry in Action Chemistry in Action Chemistry in Action Chemistry in Action Chemistry in Action Chemistry Chemistry in Action Chemistry in Action Chemistry in Action Chemistry in Action Chemistry in Action Chemistry Back Primordial Helium and The Big Bang Theory
Where did we come from? How did the universe begin? Humans have asked these questions for as long
as we have been able to think. The search for answers
provides an example of the scientific method.
In the 1940s the Russian-American physicist
George Gamow hypothesized that our universe burst
into being billions of years ago in a gigantic explosion, or Big Bang. In its earliest moments, the universe
occupied a tiny volume and was unimaginably hot.
This blistering fireball of radiation mixed with microscopic particles of matter gradually cooled enough for
atoms to form. Under the influence of gravity, these
atoms clumped together to make billions of galaxies
including our own Milky Way Galaxy.
Gamow’s idea is interesting and highly provocative. It has been tested experimentally in a number of
ways. First, measurements showed that the universe is
expanding; that is, galaxies are all moving away from
one another at high speeds. This fact is consistent with
the universe’s explosive birth. By imagining the expansion running backwards, like a movie in reverse,
astronomers have deduced that the universe was born
about 15 billion years ago. The second observation
that supports Gamow’s hypothesis is the detection of
cosmic background radiation. Over billions of years,
the searingly hot universe has cooled down to a mere
3 K (or 270 C)! At this temperature, most energy is
in the microwave region. Because the Big Bang would
have occurred simultaneously throughout the tiny volume of the forming universe, the radiation it generated should have filled the entire universe. Thus the
radiation should be the same in any direction that we
observe. Indeed, the microwave signals recorded by
astronomers are independent of direction.
The third piece of evidence supporting Gamow’s
hypothesis is the discovery of primordial helium.
Scientists believe that helium and hydrogen (the lightest elements) were the first elements formed in the early
stages of cosmic evolution. (The heavier elements, like
carbon, nitrogen, and oxygen, are thought to have
originated later via nuclear reactions involving hydrogen and helium in the center of stars.) If so, a dif- Forward Main Menu TOC fuse gas of hydrogen and helium would have spread
through the early universe before much of the galaxies formed. In 1995 astronomers analyzed ultraviolet
light from a distant quasar (a strong source of light
and radio signals that is thought to be an exploding
galaxy at the edge of the universe) and found that
some of the light was absorbed by helium atoms on
the way to Earth. Since this particular quasar is more
than 10 billion light years away (a light year is the
distance traveled by light in a year), the light reaching Earth reveals events that took place 10 billion
years ago. Why wasn’t the more abundant hydrogen
detected? A hydrogen atom has only one electron,
which is stripped by the light from a quasar in a
process known as ionization. Ionized hydrogen atoms
cannot absorb any of the quasar’s light. A helium
atom, on the other hand, has two electrons. Radiation
may strip a helium atom of one electron, but not always both. Singly ionized helium atoms can still absorb light and are therefore detectable.
Proponents of Gamow’s explanation rejoiced at
the detection of helium in the far reaches of the universe. In recognition of all the supporting evidence,
scientists now refer to Gamow’s hypothesis as the Big
Bang theory. Photo showing some distant galaxy, including the position
of a quasar. Study Guide TOC Textbook Website MHHE Website SUMMARY OF KEY EQUATIONS 29 Notice that in cubing the quantity [1 m/(100 cm)] we cube both the numbers and the units. Comment Similar problem: 1.48(d). PRACTICE EXERCISE 108 dm3. What is the volume in m3? The volume of a room is 1.08
EXAMPLE 1.9 The density of silver is 10.5 g/cm3. Convert the density to units of kg/m3.
The problem can be stated as Answer ? kg/m3
A silver coin. 10.5 g/cm3 We need two unit factors — one to convert g to kg and the other to convert cm3 to
m3. We know that
1 kg 1000 g so
1000 g Second, since 1 cm 1 10 2 1 cm
1 10 2 m 1 m, the following unit factors can be generated:
1 and 1 cm
1 10 2 m 3 1 Finally we can calculate the density in the desired units as follows:
? kg/m3 10.5 g
1 cm3 1 kg
1000 g 1 1 cm
10 2 m 3 10,500 kg/m3
1.05 Similar problem: 1.49. Comment 104 kg/m3 The units kg/m3 give inconveniently large values for density. PRACTICE EXERCISE The density of the lightest metal, lithium (Li), is 5.34
density to g/cm3. SUMMARY OF
KEY EQUATIONS m
V •d (1.1) Equation for density • ?C Main Menu 32 F) 9F
5C ( C) • ?K Forward (F • ?F Back (C TOC 102 kg/m3. Convert the 5C
9F (1.2) Converting F to C 32 F (1.3) Converting C to F 273.15 C) 1K
1C (1.4) Study Guide TOC Converting C to K Textbook Website MHHE Website 30 CHEMISTRY: THE STUDY OF CHANGE SUMMARY OF FACTS
AND CONCEPTS 1. The study of chemistry involves three basic steps: observation, representation, and interpretation. Observation refers to measurements in the macroscopic world; representation involves the use of shorthand notation symbols and equations for communication; interpretations are based on atoms and molecules, which belong to the microscopic world.
2. The scientific method is a systematic approach to research that begins with the gathering of
information through observation and measurements. In the process, hypotheses, laws, and
theories are devised and tested.
3. Chemists study matter and the changes it undergoes. The substances that make up matter
have unique physical properties that can be observed without changing their identity and
unique chemical properties that, when they are demonstrated, do change the identity of the
substances. Mixtures, whether homogeneous or heterogeneous, can be separated into pure
components by physical means.
4. The simplest substances in chemistry are elements. Compounds are formed by the chemical combination of atoms of different elements in fixed proportions.
5. All substances, in principle, can exist in three states: solid, liquid, and gas. The interconversion between these states can be effected by changing the temperature.
6. SI units are used to express physical quantities in all sciences, including chemistry.
7. Numbers expressed in scientific notation have the form N 10n, where N is between 1
and 10, and n is a positive or negative integer. Scientific notation helps us handle very
large and very small quantities. KEY WORDS
Accuracy, p. 24
Chemical property, p. 13
Chemistry, p. 4
Compound, p. 11
Density, p. 14
Element, p. 11
Extensive property, p. 14
Heterogeneous mixture, p. 10 Homogeneous mixture, p. 10
Hypothesis, p. 9
Intensive property, p. 14
International System of Units
(SI), p. 15
Kelvin, p. 17
Law, p. 9
Liter, p. 16 Macroscopic property, p. 14
Mass, p. 14
Matter, p. 10
Microscopic property, p. 14
Mixture, p. 10
Physical property, p. 13
Precision, p. 24
Qualitative, p. 8 Quantitative, p. 8
Scientific method, p. 8
Significant figures, p. 21
Substance, p. 10
Theory, p. 9
Volume, p. 14
Weight, p. 15 QUESTIONS AND PROBLEMS
THE SCIENTIFIC METHOD
Review Questions 1.1 Explain what is meant by the scientific method.
1.2 What is the difference between qualitative data and
quantitative data? tion to music would have been much greater if he had
married. (b) An autumn leaf gravitates toward the
ground because there is an attractive force between the
leaf and Earth. (c) All matter is composed of very small
particles called atoms.
CLASSIFICATION AND PROPERTIES OF MATTER
Review Questions Problems 1.3 Classify the following as qualitative or quantitative
statements, giving your reasons. (a) The sun is approximately 93 million miles from Earth. (b) Leonardo
da Vinci was a better painter than Michelangelo. (c)
Ice is less dense than water. (d) Butter tastes better than
margarine. (e) A stitch in time saves nine.
1.4 Classify each of the following statements as a hypothesis, a law, or a theory. (a) Beethoven’s contribu- Back Forward Main Menu TOC 1.5 Give an example for each of the following terms: (a)
matter, (b) substance, (c) mixture.
1.6 Give an example of a homogeneous mixture and an
example of a heterogeneous mixture.
1.7 Using examples, explain the difference between a
physical property and a chemical property?
1.8 How does an intensive property differ from an extensive property? Which of the following properties are Study Guide TOC Textbook Website MHHE Website QUESTIONS AND PROBLEMS intensive and which are extensive? (a) length, (b) volume, (c) temperature, (d) mass.
1.9 Give an example of an element and a compound. How
do elements and compounds differ?
1.10 What is the number of known elements?
Problems 1.11 Do the following statements describe chemical or
physical properties? (a) Oxygen gas supports combustion. (b) Fertilizers help to increase agricultural production. (c) Water boils below 100°C on top of a mountain. (d) Lead is denser than aluminum. (e) Sugar tastes
1.12 Does each of the following describe a physical change
or a chemical change? (a) The helium gas inside a balloon tends to leak out after a few hours. (b) A flashlight beam slowly gets dimmer and finally goes out.
(c) Frozen orange juice is reconstituted by adding water to it. (d) The growth of plants depends on the sun’s
energy in a process called photosynthesis. (e) A spoonful of table salt dissolves in a bowl of soup.
1.13 Give the names of the elements represented by the
chemical symbols Li, F, P, Cu, As, Zn, Cl, Pt, Mg, U,
Al, Si, Ne. (See Table 1.1 and the inside front cover.)
1.14 Give the chemical symbols for the following elements:
(a) potassium, (b) tin, (c) chromium, (d) boron, (e) barium, (f) plutonium, (g) sulfur, (h) argon, (i) mercury.
(See Table 1.1 and the inside front cover.)
1.15 Classify each of the following substances as an element or a compound: (a) hydrogen, (b) water, (c) gold,
1.16 Classify each of the following as an element, a compound, a homogeneous mixture, or a heterogeneous
mixture: (a) seawater, (b) helium gas, (c) sodium chloride (table salt), (d) a bottle of soft drink, (e) a milkshake, (f) air, (g) concrete.
MEASUREMENT 31 Problems 1.21 Bromine is a reddish-brown liquid. Calculate its density (in g/mL) if 586 g of the substance occupies 188
1.22 Mercury is the only metal that is a liquid at room temperature. Its density is 13.6 g/mL. How many grams
of mercury will occupy a volume of 95.8 mL?
1.23 Convert the following temperatures to degrees Celsius:
(a) 95 F, the temperature on a hot summer day; (b)
12 F, the temperature on a cold winter day; (c) a 102 F
fever; (d) a furnace operating at 1852 F.
1.24 (a) Normally the human body can endure a temperature of 105 F for only short periods of time without
permanent damage to the brain and other vital organs.
What is this temperature in degrees Celsius? (b)
Ethylene glycol is a liquid organic compound that is
used as an antifreeze in car radiators. It freezes at
11.5 C. Calculate its freezing temperature in degrees
Fahrenheit. (c) The temperature on the surface of the
sun is about 6300 C. What is this temperature in degrees Fahrenheit?
1.25 Convert the following temperatures to Kelvin: (a)
113 C, the melting point of sulfur, (b) 37 C, the normal body temperature, (c) 357 C, the boiling point of
1.26 Convert the following temperatures to degrees Celsius:
(a) 77 K, the boiling point of liquid nitrogen, (b) 4.2
K, the boiling point of liquid helium, (c) 601 K, the
melting point of lead.
Review Questions 1.27 What is the advantage of using scientific notation over
1.28 Define significant figure. Discuss the importance of
using the proper number of significant figures in measurements and calculations. Review Questions Back Problems 1.17 Name the SI base units that are important in chemistry.
Give the SI units for expressing the following: (a)
length, (b) volume, (c) mass, (d) time, (e) energy, (f)
1.18 Write the numbers represented by the following prefixes:
(a) mega-, (b) kilo-, (c) deci-, (d) centi-, (e) milli-,
(f) micro-, (g) nano-, (h) pico-.
1.19 What units do chemists normally use for density of liquids and solids? For gas density? Explain the difference?
1.20 Describe the three temperature scales used in the laboratory and in every day life: the Fahrenheit scale, the
Celsius scale, and the Kelvin scale. 1.29 Express the following numbers in scientific notation:
(a) 0.000000027, (b) 356, (c) 47,764, (d) 0.096.
1.30 Express the following numbers as decimals: (a) 1.52
10 2, (b) 7.78 10 8.
1.31 Express the answers to the following calculations in
(a) 145.75 (2.3 10 1)
(b) 79,500 (2.5 102)
(c) (7.0 10 3) (8.0 10 4)
(d) (1.0 104) (9.9 106)
1.32 Express the answers to the following calculations in
(a) 0.0095 (8.5 10 3) Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 32 1.33 1.34 1.35 1.36 CHEMISTRY: THE STUDY OF CHANGE (b) 653 (5.75 10 8)
(c) 850,000 (9.0 105)
(d) (3.6 10 4) (3.6 106)
What is the number of significant figures in each of
the following measurements?
(a) 4867 mi
(b) 56 mL
(c) 60,104 ton
(d) 2900 g
(e) 40.2 g/cm3
(f) 0.0000003 cm
(g) 0.7 min
(h) 4.6 1019 atoms
How many significant figures are there in each of the
following? (a) 0.006 L, (b) 0.0605 dm, (c) 60.5 mg,
(d) 605.5 cm2, (e) 960 10 3 g, (f) 6 kg, (g) 60 m.
Carry out the following operations as if they were calculations of experimental results, and express each answer in the correct units with the correct number of
(a) 5.6792 m 0.6 m 4.33 m
(b) 3.70 g 2.9133 g
(c) 4.51 cm 3.6666 cm
Carry out the following operations as if they were calculations of experimental results, and express each answer in the correct units with the correct number of
(a) 7.310 km 5.70 km
(b) (3.26 10 3 mg) (7.88 10 5 mg)
(c) (4.02 106 dm) (7.74 107 dm) THE FACTOR-LABEL METHOD
Problems 1.37 Carry out the following conversions: (a) 22.6 m to
decimeters, (b) 25.4 mg to kilograms.
1.38 Carry out the following conversions: (a) 242 lb to milligrams, (b) 68.3 cm3 to cubic meters.
1.39 The price of gold on November 3, 1995, was $384 per
ounce. How much did 1.00 g of gold cost that day? (1
ounce 28.4 g.)
1.40 How many seconds are there in a solar year (365.24
1.41 How many minutes does it take light from the sun to
reach Earth? (The distance from the sun to Earth is 93
million mi; the speed of light 3.00 108 m/s.)
1.42 A slow jogger runs a mile in 13 min. Calculate the
speed in (a) in/s, (b) m/min, (c) km/h. (1 mi 1609
m; 1 in 2.54 cm.)
1.43 A 6.0-ft person weighs 168 lb. Express this person’s
height in meters and weight in kilograms. (1 lb
453.6 g; 1 m 3.28 ft.) Back Forward Main Menu TOC 1.44 The current speed limit in some states in the U.S. is
55 miles per hour. What is the speed limit in kilometers per hour? (1 mi 1609 m.)
1.45 For a fighter jet to take off from the deck of an aircraft carrier, it must reach a speed of 62 m/s. Calculate
the speed in mph.
1.46 The “normal’’ lead content in human blood is about
0.40 part per million (that is, 0.40 g of lead per million grams of blood). A value of 0.80 part per million
(ppm) is considered to be dangerous. How many grams
of lead are contained in 6.0 103 g of blood (the
amount in an average adult) if the lead content is 0.62
1.47 Carry out the following conversions: (a) 1.42 lightyears to miles (a light-year is an astronomical measure
of distance — the distance traveled by light in a year,
or 365 days; the speed of light is 3.00 108 m/s), (b)
32.4 yd to centimeters, (c) 3.0 1010 cm/s to ft/s.
1.48 Carry out the following conversions: (a) 47.4 F to degrees Celsius, (b) 273.15 C (the lowest attainable
temperature) to degrees Fahrenheit, (c) 71.2 cm3 to m3,
(d) 7.2 m3 to liters.
1.49 Aluminum is a lightweight metal (density 2.70
g/cm3) used in aircraft construction, high-voltage
transmission lines, beverage cans, and foils. What is
its density in kg/m3?
1.50 The density of ammonia gas under certain conditions
is 0.625 g/L. Calculate its density in g/cm3.
ADDITIONAL PROBLEMS 1.51 Give one qualitative and one quantitative statement
about each of the following: (a) water, (b) carbon, (c)
iron, (d) hydrogen gas, (e) sucrose (cane sugar), (f) table
salt (sodium chloride), (g) mercury, (h) gold, (i) air.
1.52 Which of the following statements describe physical
properties and which describe chemical properties? (a)
Iron has a tendency to rust. (b) Rainwater in industrialized regions tends to be acidic. (c) Hemoglobin molecules have a red color. (d) When a glass of water is
left out in the sun, the water gradually disappears. (e)
Carbon dioxide in air is converted to more complex
molecules by plants during photosynthesis.
1.53 In 1995, 95.4 billion pounds of sulfuric acid were produced in the United States. Convert this quantity to
1.54 In determining the density of a rectangular metal bar,
a student made the following measurements: length,
8.53 cm; width, 2.4 cm; height, 1.0 cm; mass, 52.7064
g. Calculate the density of the metal to the correct number of significant figures.
1.55 Calculate the mass of each of the following: (a) a
sphere of gold with a radius of 10.0 cm [the volume Study Guide TOC Textbook Website MHHE Website QUESTIONS AND PROBLEMS 1.56 1.57 1.58 1.59 1.60 1.61
1.62 1.63 1.64 1.65 1.66 Back of a sphere with a radius r is V (4/3) r3; the density of gold 19.3 g/cm3], (b) a cube of platinum of
edge length 0.040 mm (the density of platinum 21.4
g/cm3), (c) 50.0 mL of ethanol (the density of ethanol
A cylindrical glass tube 12.7 cm in length is filled with
mercury. The mass of mercury needed to fill the tube
is 105.5 g. Calculate the inner diameter of the tube.
(The density of mercury 13.6 g/mL.)
The following procedure was used to determine the
volume of a flask. The flask was weighed dry and then
filled with water. If the masses of the empty flask and
filled flask were 56.12 g and 87.39 g, respectively, and
the density of water is 0.9976 g/cm3, calculate the volume of the flask in cm3.
The speed of sound in air at room temperature is about
343 m/s. Calculate this speed in miles per hour (mph).
(1 mi 1609 m.)
A piece of silver (Ag) metal weighing 194.3 g is placed
in a graduated cylinder containing 242.0 mL of water.
The volume of water now reads 260.5 mL. From these
data calculate the density of silver.
The experiment described in Problem 1.59 is a crude
but convenient way to determine the density of some
solids. Describe a similar experiment that would allow
you to measure the density of ice. Specifically, what
would be the requirements for the liquid used in your
A lead sphere has a mass of 1.20 104 g, and its volume is 1.05 103 cm3. Calculate the density of lead.
Lithium is the least dense metal known (density: 0.53
g/cm3). What is the volume occupied by 1.20 103 g
The medicinal thermometer commonly used in homes
can be read
0.1 F, while those in the doctor ’s office may be accurate to
0.1 C. In degrees Celsius,
express the percent error expected from each of these
thermometers in measuring a person’s body temperature of 38.9 C.
Vanillin (used to flavor vanilla ice cream and other
foods) is the substance whose aroma the human nose
detects in the smallest amount. The threshold limit is
2.0 10 11 g per liter of air. If the current price of 50
g of vanillin is $112, determine the cost to supply
enough vanillin so that the aroma could be detected in
a large aircraft hangar with a volume of 5.0 107 ft3.
At what temperature does the numerical reading on a
Celsius thermometer equal that on a Fahrenheit thermometer?
Suppose that a new temperature scale has been devised
on which the melting point of ethanol ( 117.3 C) and
the boiling point of ethanol (78.3 C) are taken as 0 S Forward Main Menu TOC 1.67 1.68 1.69 1.70 1.71 1.72 1.73 1.74 33 and 100 S, respectively, where S is the symbol for the
new temperature scale. Derive an equation relating a
reading on this scale to a reading on the Celsius scale.
What would this thermometer read at 25 C?
A resting adult requires about 240 mL of pure oxygen/min and breathes about 12 times every minute. If
inhaled air contains 20 percent oxygen by volume and
exhaled air 16 percent, what is the volume of air per
breath? (Assume that the volume of inhaled air is equal
to that of exhaled air.)
(a) Referring to Problem 1.67, calculate the total volume (in liters) of air an adult breathes in a day. (b) In
a city with heavy traffic, the air contains 2.1 10 6
L of carbon monoxide (a poisonous gas) per liter.
Calculate the average daily intake of carbon monoxide in liters by a person.
The total volume of seawater is 1.5 1021 L. Assume
that seawater contains 3.1 percent sodium chloride by
mass and that its density is 1.03 g/mL. Calculate the
total mass of sodium chloride in kilograms and in tons.
(1 ton 2000 lb; 1 lb 453.6 g)
Magnesium (Mg) is a valuable metal used in alloys,
in batteries, and in the manufacture of chemicals. It is
obtained mostly from seawater, which contains about
1.3 g of Mg for every kilogram of seawater. Referring
to Problem 1.69, calculate the volume of seawater (in
liters) needed to extract 8.0 104 tons of Mg, which
is roughly the annual production in the United States.
A student is given a crucible and asked to prove
whether it is made of pure platinum. She first weighs
the crucible in air and then weighs it suspended in water (density 0.9986 g/mL). The readings are 860.2
g and 820.2 g, respectively. Based on these measurements and given that the density of platinum is 21.45
g/cm3, what should her conclusion be? (Hint: An object suspended in a fluid is buoyed up by the mass of
the fluid displaced by the object. Neglect the buoyance
The surface area and average depth of the Pacific Ocean
are 1.8 108 km2 and 3.9 103 m, respectively.
Calculate the volume of water in the ocean in liters.
The unit “troy ounce’’ is often used for precious
metals such as gold (Au) and platinum (Pt). (1 troy
ounce 31.103 g) (a) A gold coin weighs 2.41 troy
ounces. Calculate its mass in grams. (b) Is a troy ounce
heavier or lighter than an ounce. (1 lb 16 oz; 1 lb
Osmium (Os) is the densest element known (density
22.57 g/cm3). Calculate the mass in pounds and in
kilograms of an Os sphere 15 cm in diameter (about
the size of a grapefruit). See Problem 1.55 for volume
of a sphere. Study Guide TOC Textbook Website MHHE Website 34 CHEMISTRY: THE STUDY OF CHANGE 1.75 Percent error is often expressed as the absolute value
of the difference between the true value and the experimental value, divided by the true value:
percent error true value experimental value
true value 100% 1.85 The vertical lines indicate absolute value. Calculate the
percent error for the following measurements: (a) The
density of alcohol (ethanol) is found to be 0.802 g/mL.
(True value: 0.798 g/mL.) (b) The mass of gold in an
earring is analyzed to be 0.837 g. (True value: 0.864 g.) 1.76 The natural abundances of elements in the human
body, expressed as percent by mass, are: oxygen (O),
65%; carbon (C), 18%; hydrogen (H), 10%; nitrogen
(N), 3%; calcium (Ca), 1.6%; phosphorus (P), 1.2%;
all other elements, 1.2%. Calculate the mass in grams
of each element in the body of a 62-kg person.
1.77 The men’s world record for running a mile outdoors
(as of 1997) is 3 minutes 44.39 seconds. At this rate,
how long would it take to run a 1500-m race? (1 mi
1.78 Venus, the second closest planet to the sun, has a surface temperature of 7.3 102 K. Convert this temperature to C and F.
1.79 Chalcopyrite, the principal ore of copper (Cu), contains 34.63% Cu by mass. How many grams of Cu can
be obtained from 5.11 103 kg of the ore?
1.80 It has been estimated that 8.0 104 tons of gold (Au)
have been mined. Assume gold costs $350 per ounce.
What is the total worth of this quantity of gold?
1.81 A 1.0-mL volume of seawater contains about 4.0
10 12 g of gold. The total volume of ocean water is
1.5 1021 L. Calculate the total amount of gold (in
grams) that is present in seawater, and the worth of the
gold in dollars (see Problem 1.80). With so much gold
out there, why hasn’t someone become rich by mining gold from the ocean?
1.82 Measurements show that 1.0 g of iron (Fe) contains
1.1 1022 Fe atoms. How many Fe atoms are in 4.9
g of Fe, which is the total amount of iron in the body
of an average adult?
1.83 The thin outer layer of Earth, called the crust, contains
only 0.50% of Earth’s total mass and yet is the source
of almost all the elements (the atmosphere provides elements such as oxygen, nitrogen, and a few other
gases). Silicon (Si) is the second most abundant element in Earth’s crust (27.2% by mass). Calculate the
mass of silicon in kilograms in Earth’s crust. (The mass
of Earth is 5.9 1021 tons. 1 ton 2000 lb; 1 lb
1.84 The diameter of a copper (Cu) atom is roughly 1.3
10 12 m. How many times can you divide evenly a Back Forward Main Menu TOC 1.86 1.87 1.88 1.89 1.90 piece of 10-cm copper wire until it is reduced to two
separate copper atoms? (Assume there are appropriate
tools for this procedure and that copper atoms are lined
up in a straight line, in contact with each other.) Round
off your answer to an integer.)
One gallon of gasoline in an automobile’s engine produces on the average 9.5 kg of carbon dioxide, which
is a greenhouse gas, that is, it promotes the warming
of Earth’s atmosphere. Calculate the annual production of carbon dioxide in kilograms if there are 40 million cars in the United States and each car covers a
distance of 5000 miles at a consumption rate of 20
miles per gallon.
A sheet of aluminum (Al) foil has a total area of 1.000
ft2 and a mass of 3.636 g. What is the thickness of the
foil in millimeters? (Density of Al 2.699 g/cm3.)
Comment on whether each of the following is a homogeneous mixture or a heterogeneous mixture: (a) air
in a closed bottle and (b) air over New York City.
It has been proposed that dinosaurs and many other organisms became extinct 65 million years ago because
Earth was struck by a large asteroid. The idea is that
dust from the impact was lofted into the upper atmosphere all around the globe, where it lingered for at
least several months and blocked the sunlight from
reaching Earth’s surface. In the dark and cold conditions that temporarily resulted, many forms of life became extinct. Available evidence suggests that about
20% of the asteroid’s mass turned to dust and spread
uniformly over Earth after eventually settling out of
the upper atmosphere. This dust amounted to about
0.02 g/cm2 of Earth’s surface. The asteroid very likely
had a density of about 2 g/cm3. Calculate the mass (in
kilograms and tons) of the asteroid and its radius in
meters, assuming that it was a sphere. (The area of
Earth is 5.1 1014 m2; 1 lb 453.6 g.) (Source:
Consider a Spherical Cow — A Course in
Environmental Problem Solving by J. Harte,
University Science Books, Mill Valley, CA, 1988.
Used with permission.)
The world’s total petroleum reserve is estimated at 2.0
1022 J (Joule is the unit of energy where 1 J 1 kg
m /s ). At the present rate of consumption, 1.8 1020
J/yr, how long would it take to exhaust the supply?
Chlorine is used to disinfect swimming pools. The accepted concentration for this purpose is 1 ppm chlorine, or one gram of chlorine per million grams of water. Calculate the volume of a chlorine solution (in
milliliters) a homeowner should add to her swimming
pool if the solution contains 6.0% chlorine by mass
and there are 2.0 104 gallons of water in the pool.
(1 gallon 3.79 L; density of liquids 1.0 g/mL.) Study Guide TOC Textbook Website MHHE Website QUESTIONS AND PROBLEMS 1.91 Fluoridation is the process of adding fluorine compounds to drinking water to help fight tooth decay. A
concentration of 1 ppm of fluorine is sufficient for the
purpose. (1 ppm means one part per million, or 1 g of
fluorine per one million grams of water.) The compound normally chosen for fluoridation is sodium fluoride, which is also added to some toothpastes.
Calculate the quantity of sodium fluoride in kilograms
needed per year for a city of 50,000 people if the daily
consumption of water per person is 150 gallons. What
percent of the sodium fluoride is “wasted’’ if each person uses only 6.0 L of water a day for drinking and
cooking? (Sodium fluoride is 45.0% fluorine by mass.
1 gallon 3.79 L; 1 year 365 days; 1 ton 2000
lb; 1 lb 453.6 g; density of water 1.0 g/mL.)
1.92 In water conservation, chemists spread a thin film of
certain inert material over the surface of water to cut
down the rate of evaporation of water in reservoirs.
This technique was pioneered by Benjamin Franklin
two centuries ago. Franklin found that 0.10 mL of oil
could spread over the surface of about 40 m2 of water. Assuming that the oil forms a monolayer, that is, Back Forward Main Menu TOC 35 a layer that is only one molecule thick, estimate the
length of each oil molecule in nanometers. (1 nm 1
10 9 m.)
1.93 Pheromones are compounds secreted by females of
many insect species to attract mates. Typically, 1.0
10 8 g of a pheromone is sufficient to reach all targeted males within a radius of 0.50 mi. Calculate the
density of the pheromone (in grams per liter) in a cylindrical air space having a radius of 0.50 mi and a height
of 40 ft.
1.94 A gas company in Massachusetts charges $1.30 for
15.0 ft3 of natural gas. (a) Convert this rate to dollars
per liter of gas. (b) It takes 0.304 ft3 of gas to boil a
liter of water, starting at room temperature (25 C), how
much would it cost to boil a 2.1-liter kettle of water? Answers to Practice Exercises: 1.1 96.5 g. 1.2 341 g. 1.3 (a) 621.5 F, (b) 78.3 C, (c) 196 C. 1.4 (a) Two, (b) four, (c)
three, (d) two, (e) three or two. 1.5 (a) 26.76 L, (b) 4.4 g, (c)
1.6 107 dm, (d) 0.0756 g/mL, (e) 6.69 104 m. 1.6 1.97
10 8 cm. 1.7 2.36 lb. 1.8 1.08 105 m3. 1.9 0.534 g/cm3. Study Guide TOC Textbook Website MHHE Website ...
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