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Unformatted text preview: BackForwardMain MenuTOCStudy Guide TOCTextbook WebsiteMHHE Website1CHAPTERChemistry: The Study of ChangeINTRODUCTIONCHEMISTRYIS AN ACTIVE, EVOLVING SCIENCE THAT HAS VITAL IMPOR-1.1 CHEMISTRY: A SCIENCE FOR THETWENTY-FIRST CENTURYTANCE TO OUR WORLD, IN BOTH THE REALM OF NATURE AND THE REALM1.2 THE STUDY OF CHEMISTRYOF SOCIETY. ITS ROOTS ARE ANCIENT, BUT AS WE WILL SOON SEE, CHEM-1.3 THE SCIENTIFIC METHODISTRY IS EVERY BIT A MODERN SCIENCE.1.4 CLASSIFICATIONS OF MATTERWEWILL BEGIN OUR STUDY OF CHEMISTRY AT THE MACROSCOPIC1.5 THE THREE STATES OF MATTERLEVEL, WHERE WE CAN SEE AND MEASURE THE MATERIALS OF WHICH OURWORLD IS MADE.IN1.6 PHYSICAL AND CHEMICAL PROPERTIES OFMATTERTHIS CHAPTER WE WILL DISCUSS THE SCIENTIFICMETHOD, WHICH PROVIDES THE FRAMEWORK FOR RESEARCH NOT ONLY1.7 MEASUREMENTIN CHEMISTRY BUT IN ALL OTHER SCIENCES AS WELL.1.8 HANDLING NUMBERSNEXTWE WILL DIS-COVER HOW SCIENTISTS DEFINE AND CHARACTERIZE MATTER.THEN1.9 THE FACTOR-LABEL METHOD OF SOLVINGPROBLEMSWEWILL FAMILIARIZE OURSELVES WITH THE SYSTEMS OF MEASUREMENT USEDIN THE LABORATORY.FINALLY,WE WILL SPEND SOME TIME LEARNINGHOW TO HANDLE NUMERICAL RESULTS OF CHEMICAL MEASUREMENTS ANDHOW TO SOLVE NUMERICAL PROBLEMS.IN CHAPTER2 WE WILL BEGINTO EXPLORE THE MICROSCOPIC WORLD OF ATOMS AND MOLECULES.3BackForwardMain MenuTOCStudy Guide TOCTextbook WebsiteMHHE Website4CHEMISTRY: THE STUDY OF CHANGE1.1The Chinese characters for chemistry mean The study ofchange.CHEMISTRY: A SCIENCE FOR THE TWENTY-FIRST CENTURYChemistry is the study of matter and the changes it undergoes. Chemistry is often calledthe central science, because a basic knowledge of chemistry is essential for studentsof biology, physics, geology, ecology, and many other subjects. Indeed, it is central toour way of life; without it, we would be living shorter lives in what we would consider primitive conditions, without automobiles, electricity, computers, CDs, and manyother everyday conveniences.Although chemistry is an ancient science, its modern foundation was laid in thenineteenth century, when intellectual and technological advances enabled scientists tobreak down substances into ever smaller components and consequently to explain manyof their physical and chemical characteristics. The rapid development of increasinglysophisticated technology throughout the twentieth century has given us even greatermeans to study things that cannot be seen with the naked eye. Using computers andelectron microscopes, for example, chemist can analyze the structure of atoms and molecules the fundamental units on which the study of chemistry is based and designnew substances with specific properties, such as drugs and environmentally friendlyconsumer products.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 toplay a pivotal role in all areas of science and technology. Before plunging into thestudy of matter and its transformation, let us consider some of the frontiers that chemistsare currently exploring (Figure 1.1). Whatever your reasons for taking introductorychemistry, a good knowledge of the subject will better enable you to appreciate its impact on society and on you as an individual.Health and MedicineThree 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 tocure potentially fatal conditions, such as an inflamed appendix; and the introductionof 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 basicunit of inheritance.) Several thousand known conditions, including cystic fibrosis andhemophilia, are carried by inborn damage to a single gene. Many other ailments, suchas cancer, heart disease, AIDS, and arthritis, result to an extent from impairment of oneor more genes involved in the bodys defenses. In gene therapy, a selected healthy geneis delivered to a patients 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 orno 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 forthe worlds population.BackForwardMain MenuTOCStudy Guide TOCTextbook WebsiteMHHE Website1.1CHEMISTRY: A SCIENCE FOR THE TWENTY-FIRST CENTURY5FIGURE 1.1 (a) A chemicalresearch laboratory where newdrugs are synthesized. (b)Photovoltaic cells. (c) A siliconwafer being processed. (d) Effectof a sex pheromone on gypsymoths.(a)(c)(b)(d)Energy and the EnvironmentEnergy 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 Statesand in developing ones like China, chemists are actively trying to find new energysources. Currently the major sources of energy are fossil fuels (coal, petroleum, andnatural gas). The estimated reserves of these fuels will last us another 50100 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 yearEarths surface receives about 10 times as much energy from sunlight as is containedin all of the known reserves of coal, oil, natural gas, and uranium combined. But muchof this energy is wasted because it is reflected back into space. For the past thirtyyears, 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 fromwater. The hydrogen can then be fed into a fuel cell to generate electricity. Althoughour understanding of the scientific process of converting solar energy to electricity hasadvanced, 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 hasbeen predicted that solar energy will supply over 50 percent of our power needs.Another potential source of energy is nuclear fission, but because of environmentalconcerns about the radioactive wastes from fission processes, the future of the nuclearBackForwardMain MenuTOCStudy Guide TOCTextbook WebsiteMHHE Website6CHEMISTRY: THE STUDY OF CHANGEindustry in the United States is uncertain. Chemists can help to devise better ways todispose of nuclear waste. Nuclear fusion, the process that occurs in the sun and otherstars, generates huge amounts of energy without producing much dangerous radioactive waste. In another 50 years, nuclear fusion will likely be a significant source ofenergy.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 carbondioxide, which is a greenhouse gas (that is, it promotes the heating of Earths atmosphere), along with sulfur dioxide and nitrogen oxides, which result in acid rain andsmog. (Harnessing solar energy has no such detrimental effects on the environment.)By using fuel-efficient automobiles and more effective catalytic converters, we shouldbe 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 TechnologyChemical research and development in the twentieth century have provided us withnew materials that have profoundly improved the quality of our lives and helped to advance technology in countless ways. A few examples are polymers (including rubberand 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-temperaturesuperconductors. Electricity is carried by copper cables, which are not perfect conductors. Consequently, about 20 percent of electrical energy is lost in the form of heatbetween the power station and our homes. This is a tremendous waste. Superconductorsare materials that have no electrical resistance and can therefore conduct electricitywith no energy loss. Although the phenomenon of superconductivity at very low temperatures (more than 400 degrees Fahrenheit below the freezing point of water) hasbeen known for over 80 years, a major breakthrough in the mid-1980s demonstratedthat 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 showpromise 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, andnuclear fusion.If we had to name one technological advance that has shaped our lives more thanany other, it would be the computer. The engine that drives the ongoing computerrevolution 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 onedesk computer will be as powerful as all those in Californias Silicon Valley in 1998!The quality of any microprocessor depends on the purity of the silicon chip and on theability to add the desired amount of other substances, and chemists play an importantrole in the research and development of silicon chips. For the future, scientists havebegun to explore the prospect of molecular computing, that is, replacing silicon withBackForwardMain MenuTOCStudy Guide TOCTextbook WebsiteMHHE Website1.2THE STUDY OF CHEMISTRY7molecules. 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 electroniccomputers. With proper genetic engineering, scientists can synthesize such moleculesusing microorganisms instead of large factories. Optical computers also would havemuch greater storage capacity than electronic computers.Food and AgricultureHow can the worlds 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 nations resources.The factors that affect agricultural production are the richness of the soil, insects anddiseases 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 indiscriminateapplication 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 approachesin 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 appliedto 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. Incorporatingthe gene that codes for the toxin into crops enables plants to protect themselves so thatpesticides 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 synthesizingpheromones 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 andsubstances that would selectively kill weeds.1.2THE STUDY OF CHEMISTRYCompared 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 onething, chemistry has a very specialized vocabulary. However, even if this is your firstcourse in chemistry, you already have more familiarity with the subject than you mayrealize. 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 criticalmass. Moreover, if you cook, then you are a practicing chemist! From experiencegained in the kitchen, you know that oil and water do not mix and that boiling waterleft on the stove will evaporate. You apply chemical and physical principles when youuse baking soda to leaven bread, choose a pressure cooker to shorten the time it takesto prepare soup, add meat tenderizer to a pot roast, squeeze lemon juice over slicedBackForwardMain MenuTOCStudy Guide TOCTextbook WebsiteMHHE Website8CHEMISTRY: THE STUDY OF CHANGEFIGURE 1.2 A badly rustedcar. Corrosion of iron costs theU.S. economy tens of billions ofdollars every year.pears to prevent them from turning brown or over fish to minimize its odor, and addvinegar to the water in which you are going to poach eggs. Every day we observe suchchanges without thinking about their chemical nature. The purpose of this course is tomake you think like a chemist, to look at the macroscopic world the things we cansee, 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 frequentlylie in the unseen and partially imagined microscopic world of atoms and molecules. Inother 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, achemist might think about the basic properties of individual atoms of iron and howthese units interact with other atoms and molecules to produce the observed change.1.3THE SCIENTIFIC METHODAll sciences, including the social sciences, employ variations of what is called the scientific method, a systematic approach to research. For example, a psychologist whowants to know how noise affects peoples ability to learn chemistry and a chemist interested in measuring the heat given off when hydrogen gas burns in air would followroughly 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 theuniverse that is under investigation. (In the examples above, the systems are the groupof 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 byBackForwardMain MenuTOCStudy Guide TOCTextbook WebsiteMHHE Website1.3FIGURE 1.3 The three levels ofstudying chemistry and theirrelationships. Observation dealswith events in the macroscopicworld; atoms and moleculesconstitute the microscopic world.Representation is a scientificshorthand for describing anexperiment in symbols andchemical equations. Chemists usetheir knowledge of atoms andmolecules to explain an observedphenomenon.BackForwardMain MenuObservationTHE SCIENTIFIC METHODRepresentation9Interpretationvarious measurements of the system. Chemists generally use standardized symbols andequations in recording their measurements and observations. This form of representation not only simplifies the process of keeping records, but also provides a commonbasis for communication with other chemists.When the experiments have been completed and the data have been recorded, thenext step in the scientific method is interpretation, meaning that the scientist attemptsto 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 waysas possible, and the process begins anew. Figure 1.3 summarizes the main steps of theresearch process.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 verbalor mathematical statement of a relationship between phenomena that is always thesame under the same conditions. For example, Sir Isaac Newtons second law of motion, which you may remember from high school science, says that force equals masstimes acceleration (F ma). What this law means is that an increase in the mass or inthe 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 intotheories. A theory is a unifying principle that explains a body of facts and/or thoselaws that are based on them. Theories, too, are constantly being tested. If a theory isdisproved 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. Atomictheory, which we will study in Chapter 2, is a case in point. It took more than 2000years to work out this fundamental principle of chemistry proposed by Democritus, anancient Greek philosopher. A more contemporary example is the Big Bang theory ofthe 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 uptaking drastically different approaches. Scientists are, after all, human beings, and theirmodes 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. Greatdiscoveries are usually the result of the cumulative contributions and experience ofmany workers, even though the credit for formulating a theory or a law is usually givento only one individual. There is, of course, an element of luck involved in scientificdiscoveries, but it has been said that chance favors the prepared mind. It takes analert and well-trained person to recognize the significance of an accidental discoveryand 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 hundredsof cases in which scientists have spent years working on projects that ultimately led toTOCStudy Guide TOCTextbook WebsiteMHHE Website10CHEMISTRY: THE STUDY OF CHANGEFIGURE 1.4 Separating ironfilings from a heterogeneousmixture. The same technique isused on a larger scale toseparate iron and steel fromnonmagnetic objects such asaluminum, glass, and plastics.(a)(b)a dead end, and in which positive achievements came only after many wrong turns andat 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 isthe love of the search that keeps many scientists in the laboratory.1.4CLASSIFICATIONS OF MATTERWe defined chemistry at the beginning of the chapter as the study of matter and thechanges 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 thingswe 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 inChapter 2.SUBSTANCES AND MIXTURESA substance is a form of matter that has a definite (constant) composition and distinctproperties. 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 substancesretain their distinct identities. Some familiar examples are air, soft drinks, milk, andcement. Mixtures do not have constant composition. Therefore, samples of air collectedin 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 sugardissolves in water we obtain a homogeneous mixture in which the composition of themixture is the same throughout. If sand is mixed with iron filings, however, the sandgrains and the iron filings remain separate (Figure 1.4). This type of mixture is calleda heterogeneous mixture because the composition is not uniform.BackForwardMain MenuTOCStudy Guide TOCTextbook WebsiteMHHE Website1.4CLASSIFICATIONS OF MATTER11Any mixture, whether homogeneous or heterogeneous, can be created and thenseparated by physical means into pure components without changing the identities ofthe 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 theiron filings from the sand, because sand is not attracted to the magnet [see Figure1.4(b)]. After separation, the components of the mixture will have the same composition and properties as they did to start with.ELEMENTS AND COMPOUNDSSubstances can be either elements or compounds. An element is a substance that cannot be separated into simpler substances by chemical means. To date, 112 elementshave 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 ofChapter 23 of this text.For convenience, chemists use symbols of one, two, or three letters to representthe 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 theformula for the carbon monoxide molecule. Table 1.1 shows the names and symbolsof 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 Englishnames. Appendix 1 gives the origin of the names and lists the discoverers of most ofthe elements.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 propertiesthat are distinctly different from those of the starting materials. Water is made up oftwo 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 OuterMongolia, or the ice caps on Mars. Thus, water is a compound, a substance composedof 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.TABLE 1.1NAMEAluminumArsenicBariumBismuthBromineCalciumCarbonChlorineChromiumCobaltCopperBackForwardMain MenuTOCSome Common Elements and Their SymbolsSYMBOLAlAsBaBiBrCaCClCrCoCuNAMEFluorineGoldHydrogenIodineIronLeadMagnesiumManganeseMercuryNickelNitrogenSYMBOLFAuHIFePbMgMnHgNiNStudy Guide TOCNAMEOxygenPhosphorusPlatinumPotassiumSiliconSilverSodiumSulfurTinTungstenZincSYMBOLOPPtKSiAgNaSSnWZnTextbook WebsiteMHHE Website12CHEMISTRY: THE STUDY OF CHANGEMatterSeparation byphysical methodsMixturesHomogeneousmixturesHeterogeneousmixturesFIGURE 1.5 Classification ofmatter.1.5PuresubstancesCompoundsSeparation bychemical methodsElementsThe relationships among elements, compounds, and other categories of matter aresummarized in Figure 1.5.THE THREE STATES OF MATTERAll substances, at least in principle, can exist in three states: solid, liquid, and gas. AsFigure 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 littlefreedom of motion. Molecules in a liquid are close together but are not held so rigidlyin position and can move past one another. In a gas, the molecules are separated bydistances 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 theboiling point of the liquid.) On the other hand, cooling a gas will cause it to condenseFIGURE 1.6 Microscopic viewsof a solid, a liquid, and a gas.SolidBackForwardMain MenuTOCLiquidStudy Guide TOCGasTextbook WebsiteMHHE Website1.6PHYSICAL AND CHEMICAL PROPERTIES OF MATTER13FIGURE 1.7 The three states ofmatter. A hot poker changes iceinto water and steam.into a liquid. When the liquid is cooled further, it will freeze into the solid form. Figure1.7 shows the three states of water.1.6Hydrogen burning in air to formwater.BackForwardMain MenuPHYSICAL AND CHEMICAL PROPERTIES OF MATTERSubstances are identified by their properties as well as by their composition. Color,melting point, and boiling point are physical properties. A physical property can bemeasured 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 andrecording the temperature at which the ice is converted to water. Water differs fromice only in appearance, not in composition, so this is a physical change; we can freezethe water to recover the original ice. Therefore, the melting point of a substance is aphysical 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, theoriginal chemical substance, the hydrogen gas, will have vanished, and all that will beleft is a different chemical substance water. We cannot recover the hydrogen fromthe 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 changesthat alter not only their physical appearance but their chemical makeup as well. Wheneaten, 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.TOCStudy Guide TOCTextbook WebsiteMHHE Website14CHEMISTRY: THE STUDY OF CHANGEAll 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 ofmatter in a given sample of a substance, is an extensive property. More matter meansmore 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 ofeach 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 valueof 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 ofwater 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 sameas it was in two separate beakers. Unlike mass, length, and volume, temperature andother intensive properties are not additive.1.7MEASUREMENTThe measurements chemists make are often used in calculations to obtain other relatedquantities. Different instruments enable us to measure a substances properties: Themeter stick measures length or scale; the buret, the pipet, the graduated cylinder, andthe 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 theatomic or molecular scale, must be determined by an indirect method, as we will seein the next chapter.FIGURE 1.8 Some commonmeasuring devices found in achemistry laboratory. Thesedevices are not drawn to scalerelative to one another. We willdiscuss the uses of thesemeasuring devices in Chapter 4.mL01mL1002903804701525 mL6016175018401930202010BuretBackForwardMain MenuPipetTOCGraduated cylinderStudy Guide TOC1 literVolumetric flaskTextbook WebsiteMHHE Website1.7TABLE 1.2NAME OF UNITLengthMassTimeElectrical currentTemperatureAmount of substanceLuminous intensityMeterKilogramSecondAmpereKelvinMoleCandelaPREFIXTeraGigaMegaKiloDeciCentiMilliMicroNanoPico-15SI Base UnitsBASE QUANTITYTABLE 1.3MEASUREMENTSYMBOLmkgsAKmolcdPrefixes Used with SI UnitsSYMBOLMEANINGEXAMPLE12TGMkdcm1,000,000,000,000, or 101,000,000,000, or 1091,000,000, or 1061,000, or 1031/10, or 10 11/100, or 10 21/1,000, or 10 31/1,000,000, or 10 61/1,000,000,000, or 10 91/1,000,000,000,000, or 10np121111111111terameter (Tm)gigameter (Gm)megameter (Mm)kilometer (km)decimeter (dm)centimeter (cm)millimeter (mm)micrometer ( m)nanometer (nm)picometer (pm)1 1012 m1 109 m1 106 m1 103 m0.1 m0.01 m0.001 m1 10 6 m1 10 9 m1 10 12 mA measured quantity is usually written as a number with an appropriate unit. Tosay that the distance between New York and San Francisco by car along a certain routeis 5166 is meaningless. We must specify that the distance is 5166 kilometers. The sameis true in chemistry; units are essential to stating measurements correctly.SI UNITSFor many years scientists recorded measurements in metric units, which are relateddecimally, that is, by powers of 10. In 1960, however, the General Conference ofWeights and Measures, the international authority on units, proposed a revised metricsystem called the International System of Units (abbreviated SI, from the FrenchSystme Internationale dUnites). Table 1.2 shows the seven SI base units. All otherunits of measurement can be derived from these base units. Like metric units, SI unitsare modified in decimal fashion by a series of prefixes, as shown in Table 1.3. We willuse both metric and SI units in this book.Measurements that we will utilize frequently in our study of chemistry includetime, mass, volume, density, and temperature.MASS AND WEIGHTThe terms mass and weight are often used interchangeably, although, strictly speaking, they are different quantities. Whereas mass is a measure of the amount of matterin 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 Earths gravity. The mass of theBackForwardMain MenuTOCStudy Guide TOCTextbook WebsiteMHHE Website16CHEMISTRY: THE STUDY OF CHANGEapple 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 onEarth, because the moons gravity is only one-sixth that of Earth. The moons smallergravity enables astronauts to jump about rather freely on its surface despite their bulkysuits and equipment. Chemists are interested primarily in mass, which can bedetermined readily with a balance; the process of measuring mass, oddly, is calledweighing.The SI base unit of mass is the kilogram (kg), but in chemistry the smaller gram(g) is more convenient:1 kg1000 g103 g1VOLUMEAn astronaut on the surface ofthe moon.The SI unit of length is the meter (m), and the SI-derived unit for volume is the cubicmeter (m3). Generally, however, chemists work with much smaller volumes, such asthe cubic centimeter (cm3) and the cubic decimeter (dm3):1 cm31 dm3(1(1102m)31013m)11106m3103m3Another common unit of volume is the liter (L). A liter is the volume occupied by onecubic decimeter. One liter of volume is equal to 1000 milliliters (mL) or 1000 cm3:1L1000 mL1000 cm31 dm3and one milliliter is equal to one cubic centimeter:1 mLVolume: 1000 cm3;1000 mL;1 dm3;1L1 cm3Figure 1.9 compares the relative sizes of two volumes. Even though the liter is not anSI unit, volumes are usually expressed in liters and milliliters.DENSITYThe equation for density isdensitymassvolumeord1 cm10 cm = 1 dmVolume: 1 cm3;1 mL1 cmFIGURE 1.9 Comparison oftwo volumes, 1 mL and 1000 mL.BackForwardmV(1.1)where d, m, and V denote density, mass, and volume, respectively. Because density isan intensive property and does not depend on the quantity of mass present, for a givenmaterial 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 unitis awkwardly large for most chemical applications. Therefore, grams per cubic centimeter (g/cm3) and its equivalent, grams per milliliter (g/mL), are more commonlyused for solid and liquid densities. Because gas densities are often very low, we express them in units of grams per liter (g/L):Main MenuTOCStudy Guide TOCTextbook WebsiteMHHE Website1.71 g/cm31 g/mL1 g/LMEASUREMENT171000 kg/m30.001 g/mLThe following examples show density calculations.EXAMPLE 1.1Gold 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 avolume of 15.6 cm3. Calculate the density of gold.AnswerThe density of the gold metal is given bydGold bars.mV301 g15.6 cm319.3 g/cm3Similar problems: 1.21, 1.22.PRACTICE EXERCISEA piece of platinum metal with a density of 21.5 g/cm3 has a volume of 4.49 cm3.What is its mass?EXAMPLE 1.2The 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 das follows:AnswermdV0.798Ethanol is produced during thefermentation of bread. It evaporates during baking and produces the fragrant aroma.Similar problems: 1.21, 1.22.m/VgmL17.4 mL13.9 gPRACTICE EXERCISEThe density of sulfuric acid in a certain car battery is 1.41 g/mL. Calculate the massof 242 mL of the liquid.TEMPERATURE SCALESNote that the kelvin scale doesnot have the degree sign. Also,temperatures expressed in kelvincan never be negative.BackForwardMain MenuThree 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 Celsiusscale divides the range between the freezing point (0 C) and boiling point (100 C) ofwater 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 thekelvin scale, denoted by 0 K, is the lowest temperature that can be attained theoreti-TOCStudy Guide TOCTextbook WebsiteMHHE Website18CHEMISTRY: THE STUDY OF CHANGEcally. 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 degreeon the Celsius scale. To convert degrees Fahrenheit to degrees Celsius, we write?C(F5C9F32 F)(1.2)The following equation is used to convert degrees Celsius to degrees Fahrenheit?F9F5C( C)32 F(1.3)Both the Celsius and the Kelvin scales have units of equal magnitude; that is, onedegree Celsius is equivalent to one kelvin. Experimental studies have shown that absolute zero on the kelvin scale is equivalent to 273.15C on the Celsius scale. Thuswe can use the following equation to convert degrees Celsius to kelvin:?K(C273.15 C)1K1C(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. Acertain solder has a melting point of 224 C. What is its melting point in degreesFahrenheit? (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 existsas a liquid at room temperature, melts at 38.9 C. Convert its melting point tokelvins.Answer(a) This conversion is carried out by writing9F5C(224 C)32 F32 F)5C9F435 F(b) Here we have( 452 FSolder is used extensively in theconstruction of electronic circuits.269 C(c) The melting point of mercury in kelvins is given by( 38.9 CSimilar problems: 1.24, 1.25, 1.26.273.15 C)1K1C234.3 KPRACTICE EXERCISEConvert (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 ofliquid nitrogen, to degrees Celsius.BackForwardMain MenuTOCStudy Guide TOCTextbook WebsiteMHHE Website1.8FIGURE 1.10 Comparison ofthe three temperature scales:Celsius, Fahrenheit, and theabsolute (Kelvin) scales. Note thatthere are 100 divisions, or 100degrees, between the freezingpoint and the boiling point ofwater on the Celsius scale, andthere are 180 divisions, or 180degrees, between the same twotemperature limits on theFahrenheit scale.373 K100C310 K37C298 K25CRoomtemperature0CFreezing pointof water32FKelvin1.81977F273 KHANDLING NUMBERSBoiling pointof waterBodytemperatureCelsius212F98.6FFahrenheitHANDLING NUMBERSHaving surveyed some of the units used in chemistry, we now turn to techniques forhandling numbers associated with measurements: scientific notation and significant figures.SCIENTIFIC NOTATIONChemists often deal with numbers that are either extremely large or extremely small.For example, in 1 g of the element hydrogen there are roughly602,200,000,000,000,000,000,000hydrogen atoms. Each hydrogen atom has a mass of only0.00000000000000000000000166 gThese numbers are cumbersome to handle, and it is easy to make mistakes when using them in arithmetic computations. Consider the following multiplication:0.00000000560.000000000480.000000000000000002688It 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 formN10nwhere N is a number between 1 and 10 and n, the exponent, is a positive or negativeinteger (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 scientificnotation. Basically, this assignment calls for us to find n. We count the number of placesBackForwardMain MenuTOCStudy Guide TOCTextbook WebsiteMHHE Website20CHEMISTRY: THE STUDY OF CHANGEthat the decimal point must be moved to give the number N (which is between 1 and10). If the decimal point has to be moved to the left, then n is a positive integer; if ithas to be moved to the right, n is a negative integer. The following examples illustratethe use of scientific notation:(a) Express 568.762 in scientific notation:568.7621025.68762Note that the decimal point is moved to the left by two places and n(b) Express 0.00000772 in scientific notation:0.00000772Any number raised to the powerzero is equal to one.7.722.610Here the decimal point is moved to the right by six places and n6.Keep in mind the following two points. First, n 0 is used for numbers that arenot expressed in scientific notation. For example, 74.6 100 (n 0) is equivalent to74.6. 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 SubtractionTo add or subtract using scientific notation, we first write each quantity say N1 andN2 with the same exponent n. Then we combine N1 and N2; the exponents remainthe same. Consider the following examples:103)(7.44(4.3110 )(2.1(3.9103)1039.5310 )104)(4.311044.70(2.22210 )(4.10310 )104)(0.3910 2)(2.221.811010 2)(0.412Multiplication and DivisionTo multiply numbers expressed in scientific notation, we multiply N1 and N2 in theusual 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 howthese operations are performed:(8.0104)(5.0102)(8.05.0)(104 2)404.0(4.010 5)(7.0103)106107(4.07.0)(1028BackForwardMain MenuTOC5104109Study Guide TOC6.93.0107)10128.55.01041.78.55.01010102.36.93.0102.87532101( 5)95Textbook WebsiteMHHE Website1.8FIGURE 1.11balance.HANDLING NUMBERS21A single-panSIGNIFICANT FIGURESExcept 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 errorin a measurement by clearly indicating the number of significant figures, which arethe meaningful digits in a measured or calculated quantity. When significant figuresare used, the last digit is understood to be uncertain. For example, we might measurethe volume of a given amount of liquid using a graduated cylinder with a scale thatgives 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 ofthe 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 agraduated 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 mayexpress the quantity as (6.0 0.1) mL, and the actual value is somewhere between 5.9mL 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 thisuncertainty depends on the particular measuring device we use.Figure 1.11 shows a modern balance. Balances such as this one are available inmany general chemistry laboratories; they readily measure the mass of objects to fourdecimal 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 thenumber of significant figures in a measurement such as mass ensures that calculationsinvolving the data will reflect the precision of the measurement.Guidelines for Using Significant FiguresWe must always be careful in scientific work to write the proper number of significantfigures. In general, it is fairly easy to determine how many significant figures a number has by following these rules:BackForwardMain MenuTOCStudy Guide TOCTextbook WebsiteMHHE Website22CHEMISTRY: THE STUDY OF CHANGEAny 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 significantfigures, 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 decimalpoint count as significant figures. Thus 2.0 mg has two significant figures, 40.062mL 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 hastwo significant figures, 0.3005 L has four significant figures, 0.00420 min has threesignificant 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 haveone significant figure (the digit 4), two significant figures (40), or three significantfigures (400). We cannot know which is correct without more information. By using scientific notation, however, we avoid this ambiguity. In this particular case, wecan express the number 400 as 4 102 for one significant figure, 4.0 102 for twosignificant figures, or 4.00 102 for three significant figures.The following example shows the determination of significant figures.EXAMPLE 1.4Determine 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) 7000mL.(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 (7.00103), two (7.0 103), or one (7 103).AnswerSimilar problems: 1.33, 1.34.PRACTICE EXERCISEDetermine 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 ofsignificant figures to the right of the decimal point in any of the original numbers.Consider these examples:89.33201.100 m88 one significant figure after the decimal point90.432 m88 round off to 90.42.0970.12 0m88 two significant figures after the decimal point1.977 m88 round off to 1.98BackForwardMain MenuTOCStudy Guide TOCTextbook WebsiteMHHE Website1.8HANDLING NUMBERS23The rounding-off procedure is as follows. To round off a number at a certain pointwe simply drop the digits that follow if the first of them is less than 5. Thus 8.724rounds off to 8.72 if we want only two figures after the decimal point. If the firstdigit following the point of rounding off is equal to or greater than 5, we add 1 tothe 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 numberof significant figures. The following examples illustrate this rule:4.503912.61092 m88 round off to 136.85112.042.80.0611388789 m88 round off to 0.0611Keep 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 is0.2786 g82.229 gWe do not round off this product to one significant figure, because the number 8 is8.00000 . . . , by definition. Similarly, to take the average of the two measuredlengths 6.64 cm and 6.68 cm, we write6.64 cm6.68 cm26.66 cmbecause the number 2 is 2.00000 . . . , by definition.The following example shows how significant figures are handled in arithmeticoperations.EXAMPLE 1.5Carry out the following arithmetic operations: (a) 11,254.1 g 0.1983 g, (b) 66.59L 3.113 L, (c) 8.16 m 5.1355, (d) 0.0154 kg 88.3 mL, (e) 2.64 103 cm3.27 102 cm.Answer(a)11,254.1 g0.1983 g11,254.2983 g m88 round off to 11,254.3 g(b)66.59 L3.113 L63.477 L m88 round off to 63.48 L(c) 8.16 m(d)Similar problems: 1.35, 1.36.BackForwardMain Menu5.13550.0154 kg88.3 mL41.90568 m m88 round off to 41.9 m0.000174405436 kg/mL m88 round off to 0.000174 kg/mLor 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.TOCStudy Guide TOCTextbook WebsiteMHHE Website24CHEMISTRY: THE STUDY OF CHANGEPRACTICE EXERCISECarry out the following arithmetic operations and round off the answers to theappropriate number of significant figures: (a) 26.5862 L 0.17 L, (b) 9.1 g 4.682g, (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:ABCSecond step:CDELet us suppose that A 3.66, B 8.45, and D 2.11. Depending on whether weround off C to three or four significant figures, we obtain a different number for E:Method 1Method 23.668.4530.93.6630.92.1165.230.938.452.1130.9365.3However, if we had carried out the calculation as 3.66 8.45 2.11 on a calculatorwithout 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 eachstep of the calculation. However, in some worked examples, only the final answer isrounded off to the correct number of significant figures. The answers for all intermediate calculations will be carried to one extra figure.Accuracy and PrecisionIn discussing measurements and significant figures it is useful to distinguish betweenaccuracy and precision. Accuracy tells us how close a measurement is to the true valueof 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 thesame 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 pieceof copper wire. The results of two successive weighings by each student areSTUDENT ASTUDENT C1.964 g1.978 gAverage valueSTUDENT B1.972 g1.968 g2.000 g2.002 g1.971 g1.970 g2.001 gThe true mass of the wire is 2.000 g. Therefore, Student Bs results are more precisethan those of Student A (1.972 g and 1.968 g deviate less from 1.970 g than 1.964 gand 1.978 g from 1.971 g), but neither set of results is very accurate. Student Cs results are not only the most precise, but also the most accurate, since the average valueis closest to the true value. Highly accurate measurements are usually precise too. Onthe other hand, highly precise measurements do not necessarily guarantee accurate results. For example, an improperly calibrated meter stick or a faulty balance may giveprecise readings that are in error.BackForwardMain MenuTOCStudy Guide TOCTextbook WebsiteMHHE Website1.9FIGURE 1.12 The distributionof darts on a dart board showsthe difference between preciseand accurate. (a) Good accuracyand good precision. (b) Pooraccuracy and good precision. (c)Poor accuracy and poorprecision.THE FACTOR-LABEL METHOD OF SOLVING PROBLEMS1010303030606060100100100(a)1.910(b)25(c)THE FACTOR-LABEL METHOD OF SOLVING PROBLEMSCareful measurements and the proper use of significant figures, along with correct calculations, will yield accurate numerical results. But to be meaningful, the answers alsomust be expressed in the desired units. The procedure we will use to convert betweenunits in solving chemistry problems is called the factor-label method, or dimensionalanalysis. A simple technique requiring little memorization, the factor-label method isbased 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 unitpenny. However, we say that 1 dollar is equivalent to 100 pennies because they bothrepresent the same amount of money. This equivalence allows us to write1 dollar100 penniesBecause 1 dollar is equal to 100 pennies, it follows that their ratio has a value of 1;that is,1 dollar100 pennies1This 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 ofmoney.We can also write the ratio as 100 pennies per dollar:100 pennies1 dollar1This fraction is also a unit factor. We see that the reciprocal of any unit factor is alsoa 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 toconvert 2.46 dollars into pennies. This problem may be expressed as? pennies2.46 dollarsSince this is a dollar-to-penny conversion, we choose the unit factor that has the unitdollar in the denominator (to cancel the dollars in 2.46 dollars) and write2.46 dollarsBackForwardMain MenuTOC100 pennies1 dollarStudy Guide TOC246 penniesTextbook WebsiteMHHE Website26CHEMISTRY: THE STUDY OF CHANGENote that the unit factor 100 pennies/1 dollar contains exact numbers, so it does notaffect the number of significant figures in the final answer.Next let us consider the conversion of 57.8 meters to centimeters. This problemmay be expressed as? cm57.8 mBy definition,1 cm1210mSince we are converting m to cm, we choose the unit factor that has meters in thedenominator,1 cm10 2 m11and write the conversion as? cm57.8 m1 cm10 2 m15780 cm5.78103 cmNote that scientific notation is used to indicate that the answer has three significantfigures. The unit factor 1 cm/1 10 2 m contains exact numbers; therefore, it doesnot 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 cancelexcept 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 1.6A hydrogen molecule.The distance between two hydrogen atoms in a hydrogen molecule is 74 pm. Convertthis distance to meters.AnswerThe problem is?m74 pmBy definition,1 pm11012mThe unit factor is10 12 m1 pm11Therefore we write?mSimilar problem: 1.37(a).74 pm110 12 m1 pm7.41011mPRACTICE EXERCISEConvert 197 pm, the radius of a calcium (Ca) atom, to centimeters.BackForwardMain MenuTOCStudy Guide TOCTextbook WebsiteMHHE Website1.9THE FACTOR-LABEL METHOD OF SOLVING PROBLEMS27EXAMPLE 1.7Conversion factors for some of theEnglish system units commonlyused in the United States for nonscientific measurements (for example,pounds and inches) are provided inside the back cover of this book.A persons 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)AnswerThe problem can be expressed as? mg0.0833 lbso the unit factor is453.6 g1 lb1and1 mg1103gso we must also include the unit factor1 mg10 3 g11Thus? mgSimilar problem: 1.43.0.0833 lb453.6 g1 lb11 mg10 3 g104 mg3.78PRACTICE EXERCISEA 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 12such factors is illustrated in Examples 1.8 and 1.9.131. The use ofEXAMPLE 1.8An average adult has 5.2 liters of blood. What is the volume of blood in m3?Since 1 Llem can be stated asAnswer1000 cm3, 5.2 L is equivalent to 5.2? m3103 cm3. The prob-103 cm35.2By definition1m100 cmThe unit factor is1m100 cm1It follows that1m100 cm3131Therefore we write? m3BackForwardMain MenuTOC5.2103 cm3Study Guide TOC1m100 cm35.2103m3Textbook WebsiteMHHE Website28CHEMISTRY: THE STUDY OF CHANGEChemistry in Action Chemistry in Action Chemistry in Action Chemistry in Action Chemistry in Action Chemistry in Action ChemistryChemistry in Action Chemistry in Action Chemistry in Action Chemistry in Action Chemistry in Action ChemistryBackPrimordial Helium and The Big Bang TheoryWhere did we come from? How did the universe begin? Humans have asked these questions for as longas we have been able to think. The search for answersprovides an example of the scientific method.In the 1940s the Russian-American physicistGeorge Gamow hypothesized that our universe burstinto being billions of years ago in a gigantic explosion, or Big Bang. In its earliest moments, the universeoccupied a tiny volume and was unimaginably hot.This blistering fireball of radiation mixed with microscopic particles of matter gradually cooled enough foratoms to form. Under the influence of gravity, theseatoms clumped together to make billions of galaxiesincluding our own Milky Way Galaxy.Gamows idea is interesting and highly provocative. It has been tested experimentally in a number ofways. First, measurements showed that the universe isexpanding; that is, galaxies are all moving away fromone another at high speeds. This fact is consistent withthe universes explosive birth. By imagining the expansion running backwards, like a movie in reverse,astronomers have deduced that the universe was bornabout 15 billion years ago. The second observationthat supports Gamows hypothesis is the detection ofcosmic background radiation. Over billions of years,the searingly hot universe has cooled down to a mere3 K (or 270 C)! At this temperature, most energy isin the microwave region. Because the Big Bang wouldhave occurred simultaneously throughout the tiny volume of the forming universe, the radiation it generated should have filled the entire universe. Thus theradiation should be the same in any direction that weobserve. Indeed, the microwave signals recorded byastronomers are independent of direction.The third piece of evidence supporting Gamowshypothesis is the discovery of primordial helium.Scientists believe that helium and hydrogen (the lightest elements) were the first elements formed in the earlystages of cosmic evolution. (The heavier elements, likecarbon, nitrogen, and oxygen, are thought to haveoriginated later via nuclear reactions involving hydrogen and helium in the center of stars.) If so, a dif-ForwardMain MenuTOCfuse gas of hydrogen and helium would have spreadthrough the early universe before much of the galaxies formed. In 1995 astronomers analyzed ultravioletlight from a distant quasar (a strong source of lightand radio signals that is thought to be an explodinggalaxy at the edge of the universe) and found thatsome of the light was absorbed by helium atoms onthe way to Earth. Since this particular quasar is morethan 10 billion light years away (a light year is thedistance traveled by light in a year), the light reaching Earth reveals events that took place 10 billionyears ago. Why wasnt the more abundant hydrogendetected? A hydrogen atom has only one electron,which is stripped by the light from a quasar in aprocess known as ionization. Ionized hydrogen atomscannot absorb any of the quasars light. A heliumatom, on the other hand, has two electrons. Radiationmay 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 Gamows explanation rejoiced atthe detection of helium in the far reaches of the universe. In recognition of all the supporting evidence,scientists now refer to Gamows hypothesis as the BigBang theory.Photo showing some distant galaxy, including the positionof a quasar.Study Guide TOCTextbook WebsiteMHHE WebsiteSUMMARY OF KEY EQUATIONS29Notice that in cubing the quantity [1 m/(100 cm)] we cube both the numbers and the units.CommentSimilar problem: 1.48(d).PRACTICE EXERCISE108 dm3. What is the volume in m3?The volume of a room is 1.08EXAMPLE 1.9The density of silver is 10.5 g/cm3. Convert the density to units of kg/m3.The problem can be stated asAnswer? kg/m3A silver coin.10.5 g/cm3We need two unit factors one to convert g to kg and the other to convert cm3 tom3. We know that1 kg1000 gso1 kg1000 gSecond, since 1 cm11021 cm1 10 2 m1m, the following unit factors can be generated:1and1 cm1 10 2 m31Finally we can calculate the density in the desired units as follows:? kg/m310.5 g1 cm31 kg1000 g11 cm10 2 m310,500 kg/m31.05Similar problem: 1.49.Comment104 kg/m3The units kg/m3 give inconveniently large values for density.PRACTICE EXERCISEThe density of the lightest metal, lithium (Li), is 5.34density to g/cm3.SUMMARY OFKEY EQUATIONSmVd(1.1)Equation for density ?CMain Menu32 F)9F5C( C) ?KForward(F ?FBack(CTOC102 kg/m3. Convert the5C9F(1.2)Converting F to C32 F (1.3)Converting C to F273.15 C)1K1C(1.4)Study Guide TOCConverting C to KTextbook WebsiteMHHE Website30CHEMISTRY: THE STUDY OF CHANGESUMMARY OF FACTSAND CONCEPTS1. 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 ofinformation through observation and measurements. In the process, hypotheses, laws, andtheories are devised and tested.3. Chemists study matter and the changes it undergoes. The substances that make up matterhave unique physical properties that can be observed without changing their identity andunique chemical properties that, when they are demonstrated, do change the identity of thesubstances. Mixtures, whether homogeneous or heterogeneous, can be separated into purecomponents 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 1and 10, and n is a positive or negative integer. Scientific notation helps us handle verylarge and very small quantities.KEY WORDSAccuracy, p. 24Chemical property, p. 13Chemistry, p. 4Compound, p. 11Density, p. 14Element, p. 11Extensive property, p. 14Heterogeneous mixture, p. 10Homogeneous mixture, p. 10Hypothesis, p. 9Intensive property, p. 14International System of Units(SI), p. 15Kelvin, p. 17Law, p. 9Liter, p. 16Macroscopic property, p. 14Mass, p. 14Matter, p. 10Microscopic property, p. 14Mixture, p. 10Physical property, p. 13Precision, p. 24Qualitative, p. 8Quantitative, p. 8Scientific method, p. 8Significant figures, p. 21Substance, p. 10Theory, p. 9Volume, p. 14Weight, p. 15QUESTIONS AND PROBLEMSTHE SCIENTIFIC METHODReview Questions1.1 Explain what is meant by the scientific method.1.2 What is the difference between qualitative data andquantitative data?tion to music would have been much greater if he hadmarried. (b) An autumn leaf gravitates toward theground because there is an attractive force between theleaf and Earth. (c) All matter is composed of very smallparticles called atoms.CLASSIFICATION AND PROPERTIES OF MATTERReview QuestionsProblems1.3 Classify the following as qualitative or quantitativestatements, giving your reasons. (a) The sun is approximately 93 million miles from Earth. (b) Leonardoda Vinci was a better painter than Michelangelo. (c)Ice is less dense than water. (d) Butter tastes better thanmargarine. (e) A stitch in time saves nine.1.4 Classify each of the following statements as a hypothesis, a law, or a theory. (a) Beethovens contribu-BackForwardMain MenuTOC1.5 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 anexample of a heterogeneous mixture.1.7 Using examples, explain the difference between aphysical property and a chemical property?1.8 How does an intensive property differ from an extensive property? Which of the following properties areStudy Guide TOCTextbook WebsiteMHHE WebsiteQUESTIONS AND PROBLEMSintensive and which are extensive? (a) length, (b) volume, (c) temperature, (d) mass.1.9 Give an example of an element and a compound. Howdo elements and compounds differ?1.10 What is the number of known elements?Problems1.11 Do the following statements describe chemical orphysical properties? (a) Oxygen gas supports combustion. (b) Fertilizers help to increase agricultural production. (c) Water boils below 100C on top of a mountain. (d) Lead is denser than aluminum. (e) Sugar tastessweet.1.12 Does each of the following describe a physical changeor 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 sunsenergy 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 thechemical 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,(d) sugar.1.16 Classify each of the following as an element, a compound, a homogeneous mixture, or a heterogeneousmixture: (a) seawater, (b) helium gas, (c) sodium chloride (table salt), (d) a bottle of soft drink, (e) a milkshake, (f) air, (g) concrete.MEASUREMENT31Problems1.21 Bromine is a reddish-brown liquid. Calculate its density (in g/mL) if 586 g of the substance occupies 188mL.1.22 Mercury is the only metal that is a liquid at room temperature. Its density is 13.6 g/mL. How many gramsof 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 Ffever; (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 withoutpermanent damage to the brain and other vital organs.What is this temperature in degrees Celsius? (b)Ethylene glycol is a liquid organic compound that isused as an antifreeze in car radiators. It freezes at11.5 C. Calculate its freezing temperature in degreesFahrenheit. (c) The temperature on the surface of thesun 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 ofmercury.1.26 Convert the following temperatures to degrees Celsius:(a) 77 K, the boiling point of liquid nitrogen, (b) 4.2K, the boiling point of liquid helium, (c) 601 K, themelting point of lead.HANDLING NUMBERSReview Questions1.27 What is the advantage of using scientific notation overdecimal notation?1.28 Define significant figure. Discuss the importance ofusing the proper number of significant figures in measurements and calculations.Review QuestionsBackProblems1.17 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)temperature.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, theCelsius 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) 1.5210 2, (b) 7.78 10 8.1.31 Express the answers to the following calculations inscientific notation:(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 inscientific notation:(a) 0.0095 (8.5 10 3)ForwardMain MenuTOCStudy Guide TOCTextbook WebsiteMHHE Website321.331.341.351.36CHEMISTRY: 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 ofthe 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 atomsHow many significant figures are there in each of thefollowing? (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 ofsignificant figures:(a) 5.6792 m 0.6 m 4.33 m(b) 3.70 g 2.9133 g(c) 4.51 cm 3.6666 cmCarry out the following operations as if they were calculations of experimental results, and express each answer in the correct units with the correct number ofsignificant figures:(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 METHODProblems1.37 Carry out the following conversions: (a) 22.6 m todecimeters, (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 perounce. How much did 1.00 g of gold cost that day? (1ounce 28.4 g.)1.40 How many seconds are there in a solar year (365.24days)?1.41 How many minutes does it take light from the sun toreach Earth? (The distance from the sun to Earth is 93million mi; the speed of light 3.00 108 m/s.)1.42 A slow jogger runs a mile in 13 min. Calculate thespeed in (a) in/s, (b) m/min, (c) km/h. (1 mi 1609m; 1 in 2.54 cm.)1.43 A 6.0-ft person weighs 168 lb. Express this personsheight in meters and weight in kilograms. (1 lb453.6 g; 1 m 3.28 ft.)BackForwardMain MenuTOC1.44 The current speed limit in some states in the U.S. is55 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. Calculatethe speed in mph.1.46 The normal lead content in human blood is about0.40 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 gramsof lead are contained in 6.0 103 g of blood (theamount in an average adult) if the lead content is 0.62ppm?1.47 Carry out the following conversions: (a) 1.42 lightyears to miles (a light-year is an astronomical measureof 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 attainabletemperature) to degrees Fahrenheit, (c) 71.2 cm3 to m3,(d) 7.2 m3 to liters.1.49 Aluminum is a lightweight metal (density 2.70g/cm3) used in aircraft construction, high-voltagetransmission lines, beverage cans, and foils. What isits density in kg/m3?1.50 The density of ammonia gas under certain conditionsis 0.625 g/L. Calculate its density in g/cm3.ADDITIONAL PROBLEMS1.51 Give one qualitative and one quantitative statementabout each of the following: (a) water, (b) carbon, (c)iron, (d) hydrogen gas, (e) sucrose (cane sugar), (f) tablesalt (sodium chloride), (g) mercury, (h) gold, (i) air.1.52 Which of the following statements describe physicalproperties 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 isleft out in the sun, the water gradually disappears. (e)Carbon dioxide in air is converted to more complexmolecules by plants during photosynthesis.1.53 In 1995, 95.4 billion pounds of sulfuric acid were produced in the United States. Convert this quantity totons.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, 52.7064g. Calculate the density of the metal to the correct number of significant figures.1.55 Calculate the mass of each of the following: (a) asphere of gold with a radius of 10.0 cm [the volumeStudy Guide TOCTextbook WebsiteMHHE WebsiteQUESTIONS AND PROBLEMS1.561.571.581.591.601.611.621.631.641.651.66Backof a sphere with a radius r is V (4/3) r3; the density of gold 19.3 g/cm3], (b) a cube of platinum ofedge length 0.040 mm (the density of platinum 21.4g/cm3), (c) 50.0 mL of ethanol (the density of ethanol0.798 g/mL).A cylindrical glass tube 12.7 cm in length is filled withmercury. The mass of mercury needed to fill the tubeis 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 thevolume of a flask. The flask was weighed dry and thenfilled with water. If the masses of the empty flask andfilled flask were 56.12 g and 87.39 g, respectively, andthe 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 about343 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 placedin a graduated cylinder containing 242.0 mL of water.The volume of water now reads 260.5 mL. From thesedata calculate the density of silver.The experiment described in Problem 1.59 is a crudebut convenient way to determine the density of somesolids. Describe a similar experiment that would allowyou to measure the density of ice. Specifically, whatwould be the requirements for the liquid used in yourexperiment?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: 0.53g/cm3). What is the volume occupied by 1.20 103 gof lithium?The medicinal thermometer commonly used in homescan be read0.1 F, while those in the doctor s office may be accurate to0.1 C. In degrees Celsius,express the percent error expected from each of thesethermometers in measuring a persons body temperature of 38.9 C.Vanillin (used to flavor vanilla ice cream and otherfoods) is the substance whose aroma the human nosedetects in the smallest amount. The threshold limit is2.0 10 11 g per liter of air. If the current price of 50g of vanillin is $112, determine the cost to supplyenough vanillin so that the aroma could be detected ina large aircraft hangar with a volume of 5.0 107 ft3.At what temperature does the numerical reading on aCelsius thermometer equal that on a Fahrenheit thermometer?Suppose that a new temperature scale has been devisedon which the melting point of ethanol ( 117.3 C) andthe boiling point of ethanol (78.3 C) are taken as 0 SForwardMain MenuTOC1.671.681.691.701.711.721.731.7433and 100 S, respectively, where S is the symbol for thenew temperature scale. Derive an equation relating areading 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. Ifinhaled air contains 20 percent oxygen by volume andexhaled air 16 percent, what is the volume of air perbreath? (Assume that the volume of inhaled air is equalto 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) Ina city with heavy traffic, the air contains 2.1 10 6L 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. Assumethat seawater contains 3.1 percent sodium chloride bymass and that its density is 1.03 g/mL. Calculate thetotal 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 isobtained mostly from seawater, which contains about1.3 g of Mg for every kilogram of seawater. Referringto Problem 1.69, calculate the volume of seawater (inliters) needed to extract 8.0 104 tons of Mg, whichis roughly the annual production in the United States.A student is given a crucible and asked to provewhether it is made of pure platinum. She first weighsthe crucible in air and then weighs it suspended in water (density 0.9986 g/mL). The readings are 860.2g and 820.2 g, respectively. Based on these measurements and given that the density of platinum is 21.45g/cm3, what should her conclusion be? (Hint: An object suspended in a fluid is buoyed up by the mass ofthe fluid displaced by the object. Neglect the buoyanceof air.)The surface area and average depth of the Pacific Oceanare 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 preciousmetals such as gold (Au) and platinum (Pt). (1 troyounce 31.103 g) (a) A gold coin weighs 2.41 troyounces. Calculate its mass in grams. (b) Is a troy ounceheavier or lighter than an ounce. (1 lb 16 oz; 1 lb453.6 g)Osmium (Os) is the densest element known (density22.57 g/cm3). Calculate the mass in pounds and inkilograms of an Os sphere 15 cm in diameter (aboutthe size of a grapefruit). See Problem 1.55 for volumeof a sphere.Study Guide TOCTextbook WebsiteMHHE Website34CHEMISTRY: THE STUDY OF CHANGE1.75 Percent error is often expressed as the absolute valueof the difference between the true value and the experimental value, divided by the true value:percent errortrue valueexperimental valuetrue value100%1.85The vertical lines indicate absolute value. Calculate thepercent error for the following measurements: (a) Thedensity of alcohol (ethanol) is found to be 0.802 g/mL.(True value: 0.798 g/mL.) (b) The mass of gold in anearring is analyzed to be 0.837 g. (True value: 0.864 g.)1.76 The natural abundances of elements in the humanbody, 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 gramsof each element in the body of a 62-kg person.1.77 The mens 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 mi1609 m.)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 canbe 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 4.010 12 g of gold. The total volume of ocean water is1.5 1021 L. Calculate the total amount of gold (ingrams) that is present in seawater, and the worth of thegold in dollars (see Problem 1.80). With so much goldout there, why hasnt someone become rich by mining gold from the ocean?1.82 Measurements show that 1.0 g of iron (Fe) contains1.1 1022 Fe atoms. How many Fe atoms are in 4.9g of Fe, which is the total amount of iron in the bodyof an average adult?1.83 The thin outer layer of Earth, called the crust, containsonly 0.50% of Earths total mass and yet is the sourceof almost all the elements (the atmosphere provides elements such as oxygen, nitrogen, and a few othergases). Silicon (Si) is the second most abundant element in Earths crust (27.2% by mass). Calculate themass of silicon in kilograms in Earths crust. (The massof Earth is 5.9 1021 tons. 1 ton 2000 lb; 1 lb453.6 g.)1.84 The diameter of a copper (Cu) atom is roughly 1.310 12 m. How many times can you divide evenly aBackForwardMain MenuTOC1.861.871.881.891.90piece of 10-cm copper wire until it is reduced to twoseparate copper atoms? (Assume there are appropriatetools for this procedure and that copper atoms are linedup in a straight line, in contact with each other.) Roundoff your answer to an integer.)One gallon of gasoline in an automobiles engine produces on the average 9.5 kg of carbon dioxide, whichis a greenhouse gas, that is, it promotes the warmingof Earths atmosphere. Calculate the annual production of carbon dioxide in kilograms if there are 40 million cars in the United States and each car covers adistance of 5000 miles at a consumption rate of 20miles per gallon.A sheet of aluminum (Al) foil has a total area of 1.000ft2 and a mass of 3.636 g. What is the thickness of thefoil 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) airin 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 becauseEarth was struck by a large asteroid. The idea is thatdust from the impact was lofted into the upper atmosphere all around the globe, where it lingered for atleast several months and blocked the sunlight fromreaching Earths surface. In the dark and cold conditions that temporarily resulted, many forms of life became extinct. Available evidence suggests that about20% of the asteroids mass turned to dust and spreaduniformly over Earth after eventually settling out ofthe upper atmosphere. This dust amounted to about0.02 g/cm2 of Earths surface. The asteroid very likelyhad a density of about 2 g/cm3. Calculate the mass (inkilograms and tons) of the asteroid and its radius inmeters, assuming that it was a sphere. (The area ofEarth is 5.1 1014 m2; 1 lb 453.6 g.) (Source:Consider a Spherical Cow A Course inEnvironmental Problem Solving by J. Harte,University Science Books, Mill Valley, CA, 1988.Used with permission.)The worlds total petroleum reserve is estimated at 2.01022 J (Joule is the unit of energy where 1 J 1 kg22m /s ). At the present rate of consumption, 1.8 1020J/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 (inmilliliters) a homeowner should add to her swimmingpool if the solution contains 6.0% chlorine by massand 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 TOCTextbook WebsiteMHHE WebsiteQUESTIONS AND PROBLEMS1.91 Fluoridation is the process of adding fluorine compounds to drinking water to help fight tooth decay. Aconcentration of 1 ppm of fluorine is sufficient for thepurpose. (1 ppm means one part per million, or 1 g offluorine 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 kilogramsneeded per year for a city of 50,000 people if the dailyconsumption of water per person is 150 gallons. Whatpercent of the sodium fluoride is wasted if each person uses only 6.0 L of water a day for drinking andcooking? (Sodium fluoride is 45.0% fluorine by mass.1 gallon 3.79 L; 1 year 365 days; 1 ton 2000lb; 1 lb 453.6 g; density of water 1.0 g/mL.)1.92 In water conservation, chemists spread a thin film ofcertain inert material over the surface of water to cutdown the rate of evaporation of water in reservoirs.This technique was pioneered by Benjamin Franklintwo centuries ago. Franklin found that 0.10 mL of oilcould spread over the surface of about 40 m2 of water. Assuming that the oil forms a monolayer, that is,BackForwardMain MenuTOC35a layer that is only one molecule thick, estimate thelength of each oil molecule in nanometers. (1 nm 110 9 m.)1.93 Pheromones are compounds secreted by females ofmany insect species to attract mates. Typically, 1.010 8 g of a pheromone is sufficient to reach all targeted males within a radius of 0.50 mi. Calculate thedensity of the pheromone (in grams per liter) in a cylindrical air space having a radius of 0.50 mi and a heightof 40 ft.1.94 A gas company in Massachusetts charges $1.30 for15.0 ft3 of natural gas. (a) Convert this rate to dollarsper liter of gas. (b) It takes 0.304 ft3 of gas to boil aliter of water, starting at room temperature (25 C), howmuch 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 1.9710 8 cm. 1.7 2.36 lb. 1.8 1.08 105 m3. 1.9 0.534 g/cm3.Study Guide TOCTextbook WebsiteMHHE Website...
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