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F5Mastering Chemistry

Various interdisciplinary branches of knowledge with roots in chemistry have arisen, including:

molecular biology, the study of the chemical and physical basis of biological function and diversity, especially in relation to genes and proteins;

materials science, the study of the chemical structure and composition of materials; and

nanotechnology, the study of matter on the scale of nanometers, at which structures consisting of small number of atoms can be manipulated.

A newly emerging concern of chemistry is sustainable development, the economical utilization and renewal of resources coupled with hazardous waste reduction and concern for the environment. This sensitive approach

to the environment and our planetary inheritance is known colloquially as green chemistry. When it is appropriate to draw your attention to this important devel-opment, we display the small icon shown here.

All sciences, medicine, and many fields of commercial activity draw on chem-istry. You can be confident that whatever career you choose in a scientific or techni-cal field, it will make use of the concepts discussed in this text. Chemistry is truly central to science.

Mastering ChemistryYou might already have a strong background in chemistry. These blue-bordered introductory pages will provide you with a summary of a number of basic concepts and techniques. Your instructor will advise you on how to use these sections to prepare yourself for the chapters in the text itself.

If you have done little chemistry before, these pages are for you, too.They contain a brief but systematic summary of the basic concepts and calculations of chemistry that you should know before studying the chapters in the text. You can return to them as needed. If you need to review the mathematics required for chemistry, especially algebra and logarithms, Appendix 1 has a brief review of the important procedures.

A Matter and EnergyWhenever we touch, pour, or weigh something, we are working with matter. Chem-istry is concerned with the properties of matter and particularly the conversion of one form of matter into another kind. But what is matter? Matter is in fact difficult to define precisely without drawing on advanced ideas from elementary particle physics, but a straightforward working definition is that matter is anything that has mass and takes up space. Thus, gold, water, and flesh are forms of matter; electro-magnetic radiation (which includes light) and justice are not.

One characteristic of science is that it uses common words from our everyday language but gives them a precise meaning. In everyday language, a “substance” is just another name for matter. However, in chemistry, a substance is a single, pure form of matter. Thus, gold and water are distinct substances. Flesh is a mixture of many dif-ferent substances, and, in the technical sense used in chemistry, it is not a “substance.” Air is matter, but, because it is a mixture of several gases, it is not a single substance.

Substances, and matter in general, can take different forms, called states of matter. The three most common states of matter are solid, liquid, and gas.

A solid is a form of matter that retains its shape and does not fl ow.

A liquid is a fl uid form of matter that has a well-defi ned surface; it takes the shape of the part of the container it occupies.

A gas is a fl uid form of matter that fi lls any vessel containing it.

The term vapor denotes the gaseous form of a substance that is normally a solid or liquid. Thus, we speak of ice (the solid form of water), liquid water, and water vapor (steam).

A.1 PHYSICAL PROPERTIES

A.2 FORCE

A.3 ENERGY

G

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FIGURE A.1 shows how the states of matter can be distinguished by the arrange-ments and motions of atoms and molecules. In a solid, such as copper metal, the atoms are packed together closely; the solid is rigid because the atoms cannot move past one another. However, the atoms in a solid are not motionless: they oscillate around their average locations, and the oscillation becomes more vigorous as the tempera-ture is raised. The atoms (and molecules) of a liquid are packed together about as closely as they are in a solid, but they have enough energy to move past one another. As a result, a liquid, such as water or molten copper, flows in response to a force, such as gravity. In a gas, such as air (which is mostly nitrogen and oxygen) and water vapor, the molecules have achieved almost complete freedom from one another: they fly through empty space at close to the speed of sound, colliding when they meet and immediately flying off in another direction.

A.1 Physical PropertiesChemistry is concerned with the properties of matter, its distinguishing characteris-tics. A physical property of a substance is a characteristic that we can observe or measure without changing the identity of the substance. For example, two physical properties of a sample of water are its mass and its temperature. Physical properties include characteristics such as melting point (the temperature at which a solid turns into a liquid), hardness, color, state of matter (solid, liquid, or gas), and density. A chemical property refers to the ability of a substance to be changed into another substance. For example, a chemical property of the gas hydrogen is that it reacts with (burns in) oxygen to produce water; a chemical property of the metal zinc is that it reacts with acids to produce hydrogen gas. When a substance undergoes a physical change, the identity of the substance does not change; only its physical properties are different. For example, when water freezes, the solid ice is still water. However, when a substance undergoes a chemical change, it is transformed into a different substance altogether. In this section we review some important physical properties of matter.

Each physical quantity is represented by an italic or sloping letter (thus, m for mass, not m). The result of a measurement, the “value” of a physical quantity, is reported as a multiple of a unit, such as reporting a mass as 15 kilograms, which is understood to be 15 times the unit “1 kilogram.” Scientists have reached international agreement on the units to use when reporting measurements, so their results can be used with confidence and checked by people anywhere in the world. You will find most of the symbols used in this textbook together with their units in Appendix 1.

A Note on Good Practice: All units are denoted by Roman letters, such as m for meter and s for second, which distinguishes them from the physical quan-tity to which they refer (such as l for length and t for time). ■

The Système International (SI) is the internationally accepted form and elabo-ration of the metric system. It defines seven base units in terms of which all physical quantities can be expressed. At this stage all we need are

meter, m The meter, the unit of length

kilogram, kg The kilogram, the unit of mass

second, s The second, the unit of time

All the units are defined in Appendix 1B. Each unit may be modified by a prefix. The full set is given in Appendix 1B; some common examples are

(a)

(b)

(c)

FIGURE A.1 A molecular

representation of the three states

of matter. In each case, the spheres

represent particles that may be atoms,

molecules, or ions. (a) In a solid, the

particles are packed tightly together

and held in place, but they continue

to oscillate. (b) In a liquid, the particles

are in contact, but they have enough

energy to move past one another. (c) In

a gas, the particles are far apart, move

almost completely freely, and are in

ceaseless random motion.

Prefi x Symbol Factor Example

kilo- k 103 (1000) 1 km ϭ 103 m (1 kilometer)centi- c 10Ϫ2 (1/100, 0.01) 1 cm ϭ 10Ϫ2 m (1 centimeter)milli- m 10Ϫ3 (1/1000, 0.001) 1 ms ϭ 10Ϫ3 s (1 millisecond)micro- 10Ϫ6 (1/1 000 000, 0.000 001) 1 g ϭ 10Ϫ6 g (1 microgram)nano- n 10Ϫ9 (1/1 000 000 000, 0.000 000 001) 1 nm ϭ 10Ϫ9 m (1 nanometer)


F7A.1 Physical Properties

Units may be combined together into derived units to express a property that is more complicated than mass, length, or time. For example, volume, V, the amount of space occupied by a substance, is the product of three lengths; therefore, the derived unit of volume is (meter)3, denoted m3. Similarly, density, the mass of a sample divided by its volume, is a derived unit expressed in terms of the base unit for mass divided by the derived unit for volume—namely, kilogram/(meter)3, denoted kg/m3 or, equivalently, kg�mϪ3.

A Note on Good Practice: The SI convention is that a power, such as the 3 in cm3, refers to the unit and its multiple. That is, cm3 should be interpreted as (cm)3 or 10Ϫ6 m3, not as c(m3) or 10Ϫ2 m3. ■

It is often necessary to convert measurements from another set of units into SI units. For example, when converting a length measured in inches into centimeters, we use the relation 1 in. ϭ 2.54 cm. In general,

Units given ϭ units required

Relations between common units can be found in Table 5 of Appendix 1B.We use these relations to construct a conversion factor of the form

Conversion factor ϭunits required

units given

which is then used as follows:

Information required ϭ information given ϫ conversion factor

When using a conversion factor, treat the units just like algebraic quantities: they can be multiplied or canceled in the normal way.

EXAMPLE A.1 Converting unitsSuppose you are in a store—perhaps in Canada or Europe—where paint is sold in liters. You know you need 1.7 qt of a particular paint. What is that volume in liters?

ANTICIPATE A glance at Table 5 in Appendix 1B shows that 1 L is slightly more than 1 qt, so you should expect a volume of slightly less than 1.7 L.

PLAN Identify the relation between the two units from Table 5 of Appendix 1B:

1 qt ϭ 0.946 352 5 L

Then set up the conversion factor from the units given (qt) to the units required (L).

SOLVE

Form the conversion factor as (units required)/(units given).

Conversion factor ϭ0.946 352 5 L

1 qt

Convert the measurement into the required units.

Volume 1L2 ϭ 11.7 qt2 ϫ0.946 352 5 L

1 qtϭ 1.6 L

Required

Given

× =

The Notes on Good Practice can also be found on the web site for this book, http://www.whfreeman.com/chemicalprinciples6e.

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It is often necessary to convert a unit that is raised to a power (including nega-tive powers). In such cases, the conversion factor is raised to the same power. For example, to convert a density of 11 700 kg�mϪ3 into grams per centimeter cubed (g�cmϪ3), we use the two relations

1 kg ϭ 103 g and 1 cm ϭ 10Ϫ2 m

as follows:

Density 1g�cmϪ32 ϭ 111 700 kg�mϪ32 ϫ103 g

1 kgϫ a 1 cm

10Ϫ2 mbϪ3

ϭ 111 700 kg�mϪ32 ϫ103 g

1 kgϫ

10Ϫ6 m3

1 cm3

ϭ 11.78

cm3 ϭ 11.7 g�cmϪ3

A Note on Good Practice: Units are treated like algebraic quantities and are multiplied and canceled just like numbers. For example, in the second line of this calculation we used the relationa 1 cm

10Ϫ2 mbϪ3

ϭ a10Ϫ2 m1 cm

b3

ϭ10Ϫ6 m3

1 cm3 ■

Self-Test A.2A Express a density of 6.5 g�mmϪ3 in micrograms per nanometer cubed (g�nmϪ3).

[Answer: 6.5 ϫ 10Ϫ12 g�nmϪ3]

Self-Test A.2B Express an acceleration of 9.81 m�sϪ2 in kilometers per hour squared. ■

Properties can be classified according to their dependence on the size of a sam-ple. An extensive property is a property that does depend on the size (“extent”) of the sample. More precisely, if a system is divided into parts and it is found that the property of the complete system has a value that is the sum of the values of the property of all the parts, then that property is extensive. If that is not the case, then the property is intensive. In short, an intensive property is independent of the size of the sample. Volume is an extensive property: 2 kg of water occupies twice the volume of 1 kg of water. Temperature is an intensive property, because whatever the size of the sample taken from a uniform bath of water, it has the same tempera-ture (FIG. A.2). The importance of the distinction is that we identify different sub-stances by their intensive properties. Thus, we might recognize a sample as water by noting its color, density (1.00 g�cmϪ3), melting point (0 ЊC), boiling point (100 ЊC), and the fact that it is a liquid.

Some intensive properties are ratios of two extensive properties. For example, the density, d, mentioned above, is a ratio of the mass, m, of a sample divided by its volume, V:

Density ϭmass

volume or d ϭ

mV

(1)

FIGURE A.2 Mass is an extensive

property, but temperature is intensive.

These two samples of iron(II) sulfate

solution were taken from the same

well-mixed supply; they have different

masses but the same temperature.

EVALUATE As expected, you need slightly less than 1.7 L. The answer has been rounded to two digits, as explained in Appendix 1.

Self-Test A.1A Express the height of a person 6.00 ft tall in centimeters.

[Answer: 183 cm]

Self-Test A.1B Express the mass in ounces of a 250.-g package of breakfast cereal.

Related Exercises A.13, A.14, A.31, A.32

Answers to all B self-tests are in the back of this book.


F9A.1 Physical Properties

The density of a substance is independent of the size of the sample because dou-bling the volume also doubles the mass, so the ratio of mass to volume remains the same. Density is therefore an intensive property.

Most properties of a substance depend on its state of matter and conditions, such as the temperature and pressure. For example, the density of water at 0 ЊC is 1.00 g�cmϪ3, but at 100 ЊC it is 0.96 g�cmϪ3. The density of ice at 0 ЊC is 0.92 g�cmϪ3, but the density of water vapor at 100 ЊC and atmospheric pressure is nearly 2000 times less, at 0.59 g�LϪ1. Most substances contract slightly and become more dense as they freeze, but water is unusual in that it expands slightly when it freezes; thus ice is less dense than water at 0 ЊC.

THINKING POINT When you heat a gas at constant pressure, it expands. Does the density of a gas increase, decrease, or stay the same as it expands?

Units for physical quantities and temperature scales are discussed in Appendix 1B.

EXAMPLE A.2 Calculating the volume of a sampleMetal dealers need to know the volumes as well as the masses of their wares so that they can provide adequate packaging.

What is the volume occupied by 5.0 g of solid silver, given the density listed in Appendix 2D?

ANTICIPATE A glance at Appendix 2D shows that most metals have densities in the range 5 to 20 g�cmϪ3, with many close to 10 g�cmϪ3. Therefore, you should expect a mass of 1 g to correspond to a volume of about 0.1 cm3. For 5 g, you should expect an answer close to 0.5 cm3.

PLAN Rearrange Eq. 1 into V ϭ m/d, and then substitute the data.

SOLVE The density of silver is listed in Appendix 2D as 10.50 g�cmϪ3; so the volume of 5.0 g of solid silver is

From V ϭ m/d,

V ϭ5.0 g

10.50 g�cmϪ3 ϭ5.0

10.50 cm3 ϭ 0.48 cm3

EVALUATE The volume calculated, 0.48 cm3, is close to the expected value.

Self-Test A.3A The density of selenium is 4.79 g�cmϪ3. What is the mass of 6.5 cm3 of selenium?

[Answer: 31 g]

Self-Test A.3B The density of helium gas at 0 ЊC and 1.00 atm is 0.176 85 g�LϪ1. What is the volume of a balloon containing 10.0 g of helium under the same conditions?

Related Exercises A.17–A.21

All measured quantities have some uncertainty associated with them; in science it is important to convey the degree to which we are certain of not only the values we report but also the results of calculations using those values. Notice that in Example A.2 the result of dividing 5.0 by 10.50 is written as 0.48, not 0.47619.The number of digits reported in the result of a calculation must reflect the number of digits in the data provided.

0.78 cm

5.0 g


FundamentalsF10

The number of significant figures in a numerical value is the number of digits that can be justified by the data. Thus, the measurement 5.0 g has two significant figures (2 sf) and 10.50 g�cmϪ3 has four (4 sf). The number of significant figures in the result of a calculation cannot exceed the number in the data (you can’t generate reliability on a calculator!), so in Example A.2 we limited the result to 2 sf, the lower number of significant figures in the data. The full rules for counting the number of significant figures and determining the number of significant figures in the result of a calculation are given in Appendix 1C, together with the rules for rounding numerical values.

An ambiguity may arise when dealing with a whole number ending in a zero, because the number of significant figures in the number may be less than the num-ber of digits. For example, 400 could have 1, 2, or 3 sf. To avoid ambiguity, in this book, when all the digits in a number ending in zero are significant, the number is followed by a decimal point. Thus, the number 400. has 3 sf.

When scientists measure the properties of a substance, they monitor and report the accuracy and precision of the data. To make sure of their data, scientists usually repeat their measurements several times. The precision of a measurement is reflected in the number of significant figures justified by the procedure and depends on how close repeated measurements are to one another. The accuracy of a series of mea-surements is the closeness of their average value to the true value. The illustration in FIG. A.3 distinguishes precision from accuracy. As the illustration suggests, even precise measurements can give inaccurate values. For instance, if there is an unno-ticed speck of dust on the pan of a chemical balance that you are using to measure the mass of a sample of silver, then even though you might be justified in reporting your measurements to five significant figures (such as 5.0450 g), the reported mass of the sample will be inaccurate.

More often than not, measurements are accompanied by two kinds of error. A systematic error is an error that is present in every one of a series of repeated mea-surements. Systematic errors in a series of measurements always have the same sign and magnitude. An example is the effect of a speck of dust on a pan, which distorts the mass of each sample in the same direction (the speck makes each sample appear heavier than it is). In principle, systematic errors can be discovered and corrected (subtract the mass of the dust speck from the mass of each sample), but they often go unnoticed and in practice may be hard to determine. A random error is an error that varies in both sign and magnitude and can average to zero over a series of observations. An example is the effect of drafts of air from an open window mov-ing a balance pan either up or down a little, decreasing or increasing the mass measurements randomly. Scientists attempt to minimize random error by making many observations and taking the average of the results. Systematic errors are much harder to identify.

THINKING POINT What are some means that scientists can use to identify and eliminate systematic errors?

Chemical properties involve changing the identity of a substance; physical properties do not. Extensive properties depend on the mass of the sample; intensive properties do not. The precision of a measurement is an indication of how close together repeated measurements are; the accuracy of a measurement is its closeness to the true value.

A.2 ForceA force, F, is an influence that changes the state of motion of an object. For instance, we exert a force to open a door—to start the door swinging open—and we exert a force on a ball when we hit it with a bat. According to Newton’s second law of motion, when an object experiences a force, it is accelerated. The accelera-tion, a, of the object is the rate of change of its velocity and is proportional to the force that it experiences:

Acceleration r force or a r F

FIGURE A.3 The holes in these

targets represent measurements

that are (a) precise and accurate,

(b) precise but inaccurate, (c) imprecise

but accurate on average, and (d) both

imprecise and inaccurate.

(a) (b)

(c) (d)


F11A.3 Energy

The constant of proportionality between the force and the acceleration it produces is the mass, m, of the object experiencing the force:

Force ϭ mass ϫ acceleration or F ϭ ma (2)

What Does This Equation Tell Us? This expression, in the form a ϭ F/m, tells us that a stronger force is required to accelerate a heavy object by a given amount than to accelerate a lighter object by the same amount. ■

Velocity, the rate of change of position, has both magnitude and direction; so, when a force acts, it can change the magnitude alone, the direction alone, or both simultaneously (FIG. A.4). The magnitude of the velocity of an object—the rate of change of position, regardless of the direction of the motion—is called its speed, v. When we accelerate a car in a straight line, we change its speed, but not its direc-tion, by applying a force through the rotation of the wheels and their contact with the road. To stop a car, we apply a force that opposes the motion. However, a force can also act without changing the speed: if a body is forced to travel in a different direction at the same speed, it undergoes acceleration because velocity includes direction as well as magnitude. For example, when a ball bounces on the floor, the force exerted by the floor reverses the ball’s direction of travel without affecting its speed very much.

Forces that are important in chemistry include the electrostatic forces of attrac-tion and repulsion between charged particles and the weaker forces between mol-ecules. Atomic nuclei exert forces on the electrons that surround them, and it takes energy to move those electrons from one place to another in a molecule. Rather than considering the forces directly, chemists normally focus on the energy needed to overcome them. One major exception, discussed in Major Technique 1, follow-ing Chapter 3, is in the vibrations of molecules, where atoms in bonds behave as though they are joined by springs that exert forces when the bonds are stretched and compressed.

Acceleration, the rate of change of velocity, is proportional to applied force.

A.3 EnergySome chemical changes give off a lot of energy (FIG. A.5); others absorb energy. An understanding of the role of energy is the key to understanding chemical phenom-ena and the structures of atoms and molecules. But just what is energy?

The word energy is so common in everyday language that most people have a general sense of what it means; however, a technical answer to this question would require using the theory of relativity, which is far beyond the scope of this book. In chemistry, we use a practical definition of energy as the capacity to do work, with work defined as the process of moving an object against an opposing force.

Work done ϭ force ϫ distance

Thus, energy is needed to do the work of raising a weight a given height or the work of forcing an electric current through a circuit. The greater the energy of an object, the greater is its capacity to do work.

The SI unit for energy is the joule (J). As explained in Appendix 1B,

1 J ϭ 1 kg�m2�sϪ2

Each beat of the human heart uses about 1 J of energy, and to raise this book (of mass close to 2.0 kg) from the floor to a tabletop about 0.97 m above the floor

The joule is named for James Joule, the nineteenth-century English scientist who made many contributions to the study of heat.

(a)

(b)FIGURE A.4 (a) When a force acts along the direction of travel, the speed (the magnitude of the

velocity) changes, but the direction of motion does not. (b) The direction of travel can be changed

without affecting the speed if the force is applied in an appropriate direction. Both changes in

velocity correspond to acceleration.

FIGURE A.5 When bromine is poured

onto red phosphorus, a chemical

change takes place in which a lot of

energy is released as heat and light.

LAB VIDEO FIGURE A.5


FundamentalsF12

requires about 19 J (FIG. A.6). Because energy changes in chemical reactions tend to be of the order of thousands of joules for the amounts usually studied, it is more common in chemistry to use the kilojoule (kJ, where 1 kJ ϭ 103 J).

A Note on Good Practice: Names of units derived from the names of people are always lowercase (as for joule), but their abbreviations are always upper-case (as in J for joule). ■

There are three contributions to energy: kinetic energy, potential energy, and electromagnetic energy. Kinetic energy, Ek, is the energy that a body pos-sesses due to its motion. For a body of mass m traveling at a speed v, the kinetic energy is

Ek ϭ 12 mv2 (3)*

A heavy body traveling rapidly has a high kinetic energy. A body at rest (stationary, v ϭ 0) has zero kinetic energy.

A star next to an equation number signals that it appears in the list of Key Equations on the Web site for this book: www.whfreeman.com/chemicalprinciples6e.

CHEMISTRY

CCHEMCHEMCHEMCHEMCHEMCHEMCHEMCHEMCHEM STSTRSTRISTRISTRISTRISTRISTRISTRISTRYYYYYYYYYCHEMISTRY

0.97 m

2.0 kg

Potential energy

0

19 J

FIGURE A.6 The energy required

to raise the book that you are now

reading from the floor to the tabletop

is approximately 19 J. The same energy

would be released if the book fell from

the tabletop to the floor.

The potential energy, Ep, of an object is the energy that it possesses on account of its position in a field of force. There is no single formula for the potential energy of an object, because the potential energy depends on the nature of the forces that it experiences. However, two simple cases are important in chemistry: gravitational

Potential energy is also commonly denoted V. A fi eld is a region where a force acts.

EXAMPLE A.3 Calculating kinetic energyAthletes can expend a lot of energy in a race, not only in running but also in the process of starting to run. Suppose you are working as a sports physiologist. You would need to know the energy involved in each phase of a race.

How much energy does it take to accelerate a person and a bicycle of total mass 75 kg to 20. mph (8.9 m�sϪ1), starting from rest and ignoring friction and wind resistance?

PLAN A stationary cyclist has zero kinetic energy; a moving cyclist has a kinetic energy. You need to decide how much energy must be supplied to reach the kinetic energy of the cyclist corresponding to the fi nal speed.

SOLVE

From Ek ϭ 12 mv2,

Ek ϭ 12 ϫ 175 kg2 ϫ 18.9 m�sϪ122

ϭ 3.0 ϫ 103 kg�m2�sϪ2 ϭ 3.0 kJ

EVALUATE A minimum of 3.0 kJ is needed. More energy is needed to achieve that speed when friction and wind resistance are taken into account.

Self-Test A.4A Calculate the kinetic energy of a ball of mass 0.050 kg traveling at 25 m�sϪ1.

[Answer: 16 J]

Self-Test A.4B Calculate the kinetic energy of a 1.5-kg book just before it lands on your foot after falling off a table, when it is traveling at 3.0 m�sϪ1.

Related Exercises A.37, A.38

75 kg

3.0 kJ

8.9 m·sϪ1

123

k14243

J


F13A.3 Energy

Mass, m

Hei

ght,

h

Potentialenergy

0

mgh

FIGURE A.7 The potential energy

of a mass m in a gravitational field is

proportional to its height h above a

point (here, the surface of the Earth),

which is taken to correspond to zero

potential energy.

potential energy (for a particle in a gravitational field) and Coulomb potential energy (for a charged particle in an electrostatic field).

A body of mass m at a height h above the surface of the Earth has a gravita-tional potential energy

Ep ϭ mgh (4)*

relative to its potential energy on the surface itself (FIG. A.7), where g is the accel-eration of free fall (and, commonly, the “acceleration of gravity”). The value of g depends on location, but in most typical locations on the surface of the Earth g has close to its “standard value” of 9.81 m�sϪ2, and we shall use this value in all cal-culations. Equation 4 shows that the greater the altitude of an object, the greater is its gravitational potential energy. For instance, a book on a table has a greater capacity to do work than one on the floor, and so we can say that it has a greater potential energy on the table than on the floor. To raise it from the floor to the table and thereby increase its potential energy, work has to be done.

A Note on Good Practice: You will sometimes see kinetic energy denoted KE and potential energy denoted PE. Modern practice is to denote all physical quantities by a single letter (accompanied, if necessary, by subscripts). ■

EXAMPLE A.4 Calculating the gravitational potential energyA skier of mass 65 kg boards a ski lift at a resort in eastern British Columbia and is lifted 1164 m above the starting point. What is the change in potential energy of the skier?

ANTICIPATE When a mass of 1 kg is raised by 1 m on the surface of the Earth, it gains nearly 10 J of potential energy. In this example, 65 kg is raised over 1000 m, so you should expect the gain in potential energy to be greater than 650 kJ.

PLAN To calculate the change, suppose that the potential energy of the skier at the bottom of the lift is zero, then calculate the potential energy at the height at the top of the lift.

SOLVE The potential energy of a skier at the top of the lift relative to the bottom of the lift is

From Ep ϭ mgh,

Ep ϭ 165 kg2 ϫ 19.81 m�sϪ22 ϫ 11164 m2 ϭ 7.4 ϫ 105 kg�m2�sϪ2 ϭ ϩ740 kJ

EVALUATE As expected, the potential energy difference is greater than 650 kJ.

Self-Test A.5A What is the gravitational potential energy of this book (mass 1.5 kg) when it is on a table of height 0.82 m, relative to its potential energy when it is on the fl oor?

[Answer: 12 J]

Self-Test A.5B How much energy has to be expended to raise a can of soda (mass 0.350 kg) to the top of the Willis Tower in Chicago (height 443 m)?

Related Exercises A.39–A.41

1164 m

ϩ740 kJ

The energy due to attractions and repulsions between electric charges is of great importance in chemistry, which deals with electrons, atomic nuclei, and ions,


FundamentalsF14

all of which are charged. The Coulomb potential energy of a particle of charge Q1 at a distance r from another particle of charge Q2 is proportional to the two charges and inversely proportional to the distance between them:

Ep ϭQ1Q2

4�e0r (5)*

In this expression, which applies when the two charges are separated by a vacuum, e0 (epsilon zero) is a fundamental constant called the vacuum permittivity; its value is 8.854 ϫ 10Ϫ12 JϪ1�C2�mϪ1. The Coulomb potential energy is obtained in joules when the charges are in coulombs (C, the SI unit of charge) and their separation is in meters (m). The charge on an electron is Ϫe, with e ϭ 1.602 ϫ 10Ϫ19 C, the “fun-damental charge.”

What Does This Equation Tell Us? The Coulomb potential energy approaches zero as the distance between two particles approaches infinity. If the particles have the same charge—if they are two electrons, for instance—then the numerator, Q1Q2, and therefore Ep itself, is positive, and the potential energy rises (becomes more strongly positive) as the particles approach each other (r decreases). If the particles have opposite charges—an electron and an atomic nucleus, for instance—then the numerator, and therefore Ep, is negative and the potential energy decreases (in this case, becomes more negative) as the particles approach each other (FIG. A.8). ■

What we termed “electromagnetic energy” at the beginning of Section A.3 is the energy of the electromagnetic field, such as the energy carried through space by radio waves, light waves, and x-rays (very-high-energy electromagnetic radiation). An electromagnetic field is generated by the acceleration of charged particles and consists of an oscillating electric field and an oscillating magnetic field (FIG. A.9). The crucial distinction is that an electric field affects charged particles whether they are stationary or moving, whereas a magnetic field affects only moving charged particles.

The total energy, E, of a particle is the sum of its kinetic and potential energies:

Total energy ϭ kinetic energy ϩ potential energy or E ϭ Ek ϩ Ep (6)*

A very important feature of the total energy of an object is that, provided there are no outside influences, it is constant. This observation is summarized by saying that energy is conserved. Kinetic energy and potential energy can change into each other, but their sum for a given object, whether as large as a planet or as tiny as an atom, is constant. For instance, a ball thrown up into the air initially has high kinetic energy and zero potential energy. At the top of its flight, it has zero kinetic energy and high potential energy. However, as it returns to Earth, its kinetic energy rises and its potential energy approaches zero again. At each stage, its total energy is the same as it was when it was initially launched (FIG. A.10). When it strikes the Earth, the ball is no longer isolated, and its energy is dissipated as thermal motion, the chaotic, random motion of atoms and molecules. If we added up all the kinetic and potential energies, we would find that the total energy of the Earth had increased by exactly the same amount as that lost by the ball. No one has ever observed any exception to the law of conservation of energy, the observation that energy can be neither created nor destroyed. One region of the universe—an individual atom, for instance—can lose energy, but another region must gain that energy.

Chemists often refer to two other kinds of energy. The term chemical energy is used to refer to the change in energy when a chemical reaction takes place, as in the combustion of a fuel. “Chemical energy” is not a special form of energy: it is simply a shorthand name for the sum of the potential and kinetic energies of the sub-stances participating in the reaction, including the potential and kinetic energies of

Mass is a measure of the energy present in a region: the two are related by Einstein’s famous equation, E ϭ mc2, where c is the speed of light.

0

Pote

ntia

l ene

rgy,

Ep

Separation, r

FIGURE A.8 The variation of the

Coulomb potential energy of two

opposite charges (one represented by

the red sphere, the other by the green

sphere) with their separation. Notice

that the potential energy decreases as

the charges approach each other.

Electric field

Magneticfield

FIGURE A.9 An electromagnetic

field oscillates in time and space.

The magnetic field (shown in blue) is

perpendicular to the electric field (shown

in red). The length of an arrow at any

point represents the strength of the field

at that point, and its orientation denotes

its direction. Both fields are perpendicular

to the direction of travel of the radiation.


F15Exercises

Pote

ntia

l ene

rgy,

Ep

Kin

etic

ene

rgy,

Ek

Tota

l ene

rgy,

E

FIGURE A.10 Kinetic energy (represented by the height of the light green bar) and potential

energy (the dark green bar) are interconvertible, but their sum (the total height of the bar) is a

constant in the absence of external influences, such as air resistance. A ball thrown up from the

ground loses kinetic energy as it slows, but it gains potential energy. The reverse happens as it falls

back to Earth.

What have you learned in this section?

You have learned how to use and report measurements. You have also been introduced to force and energy, and you have learned how to distinguish kinetic and potential energy.

Specifi cally, you can now:

❑ 1 Identify properties as chemical or physical, intensive or extensive.

❑ 2 Use the density of a substance in calculations (Example A.1).

❑ 3 Calculate the kinetic energy of an object (Example A.2).

❑ 4 Calculate the gravitational potential energy of an object (Example A.3).

❑ 5 Distinguish the different forms of energy described in this section.

Skills You Should Have Mastered

A.1 Laws and hypotheses were distinguished in the Introduction and Orientation Section. Which of the following statements are best described as laws?(a) The volume of a gas increases as it is heated at constant pressure.(b) Sodium reacts with chlorine to produce sodium chloride.(c) The universe is infi nite in extent.(d) All animal life on Earth requires water to survive.(e) The burning of coal is a cause of global warming.

A.2 Which of the statements in Exercise A.1 are best described as hypotheses?

A.3 Classify the following properties as chemical or physical: (a) objects made of silver become tarnished; (b) the red color of rubies is due to the presence of chromium ions; (c) the boiling point of ethanol is 78 ЊC.

A.4 A chemist investigates the transparency, boiling point, and fl ammability of hexane, a component of mineral spirits. Which of these properties are physical properties and which are chemical properties?

A.5 Identify all the physical properties and changes in the following statement: “The camp nurse measured the temperature of the injured camper and ignited a propane burner; when the water began to boil, some of the water vapor condensed on the cold window.”

A.6 Identify all the chemical properties and changes in the following statement: “Copper is a red-brown element

obtained from copper sulfi de ores by heating them in air, which forms copper oxide. Heating the copper oxide with carbon produces impure copper, which is purifi ed by electrolysis.”

A.7 In the containers below, the green spheres represent atoms of one element, the red spheres the atoms of a second element. In each case, the pictures show either a physical or chemical change; identify the type of change.

(a)

(b)

(c)

Exercises

their electrons. The term thermal energy is another shorthand term. In this case it is shorthand for the sum of the potential and kinetic energies arising from the ther-mal motion of atoms, ions, and molecules.

Kinetic energy results from motion, potential energy from position. An electromagnetic fi eld carries energy through space; work is motion against an opposing force.


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