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Menu TOC Study Back Forward Main Guide TOC Textbook Website MHHE Website 1 CHAPTER Chemistry: The Study of Change INTRODUCTION CHEMISTRY IS AN ACTIVE, EVOLVING SCIENCE THAT HAS VITAL IMPOR- 1.1 CHEMISTRY: A SCIENCE FOR THE TWENTY-FIRST CENTURY TANCE TO OUR WORLD, IN BOTH THE REALM OF NATURE AND THE REALM 1.2 THE STUDY OF CHEMISTRY OF SOCIETY. ITS ROOTS ARE ANCIENT, BUT AS WE WILL SOON SEE, CHEM- 1.3 THE SCIENTIFIC METHOD ISTRY IS EVERY BIT A MODERN SCIENCE. 1.4 CLASSIFICATIONS OF MATTER WE WILL BEGIN OUR STUDY OF CHEMISTRY AT THE MACROSCOPIC 1.5 THE THREE STATES OF MATTER LEVEL, WHERE WE CAN SEE AND MEASURE THE MATERIALS OF WHICH OUR WORLD IS MADE. IN 1.6 PHYSICAL AND CHEMICAL PROPERTIES OF MATTER THIS CHAPTER WE WILL DISCUSS THE SCIENTIFIC METHOD, WHICH PROVIDES THE FRAMEWORK FOR RESEARCH NOT ONLY 1.7 MEASUREMENT IN CHEMISTRY BUT IN ALL OTHER SCIENCES AS WELL. 1.8 HANDLING NUMBERS NEXT WE WILL DIS- COVER HOW SCIENTISTS DEFINE AND CHARACTERIZE MATTER. THEN 1.9 THE FACTOR-LABEL METHOD OF SOLVING PROBLEMS WE WILL FAMILIARIZE OURSELVES WITH THE SYSTEMS OF MEASUREMENT USED IN THE LABORATORY. FINALLY, WE WILL SPEND SOME TIME LEARNING HOW TO HANDLE NUMERICAL RESULTS OF CHEMICAL MEASUREMENTS AND HOW TO SOLVE NUMERICAL PROBLEMS. IN CHAPTER 2 WE WILL BEGIN TO EXPLORE THE MICROSCOPIC WORLD OF ATOMS AND MOLECULES. 3 Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 4 CHEMISTRY: THE STUDY OF CHANGE 1.1 The Chinese characters for chemistry mean “The study of change.’’ CHEMISTRY: A SCIENCE FOR THE TWENTY-FIRST CENTURY Chemistry is the study of matter and the changes it undergoes. Chemistry is often called the central science, because a basic knowledge of chemistry is essential for students of biology, physics, geology, ecology, and many other subjects. Indeed, it is central to our way of life; without it, we would be living shorter lives in what we would consider primitive conditions, without automobiles, electricity, computers, CDs, and many other everyday conveniences. Although chemistry is an ancient science, its modern foundation was laid in the nineteenth century, when intellectual and technological advances enabled scientists to break down substances into ever smaller components and consequently to explain many of their physical and chemical characteristics. The rapid development of increasingly sophisticated technology throughout the twentieth century has given us even greater means to study things that cannot be seen with the naked eye. Using computers and electron microscopes, for example, chemist can analyze the structure of atoms and molecules — the fundamental units on which the study of chemistry is based — and design new substances with specific properties, such as drugs and environmentally friendly consumer 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 to play a pivotal role in all areas of science and technology. Before plunging into the study of matter and its transformation, let us consider some of the frontiers that chemists are currently exploring (Figure 1.1). Whatever your reasons for taking introductory chemistry, a good knowledge of the subject will better enable you to appreciate its impact on society and on you as an individual. Health and Medicine Three major advances in this century have enabled us to prevent and treat diseases. They are: public health measures establishing sanitation systems to protect vast numbers of people from infectious disease; surgery with anesthesia, enabling physicians to cure potentially fatal conditions, such as an inflamed appendix; and the introduction of vaccines and antibiotics that make it possible to prevent diseases spread by microbes. Gene therapy promises to be the fourth revolution in medicine. (A gene is the basic unit of inheritance.) Several thousand known conditions, including cystic fibrosis and hemophilia, are carried by inborn damage to a single gene. Many other ailments, such as cancer, heart disease, AIDS, and arthritis, result to an extent from impairment of one or more genes involved in the body’s defenses. In gene therapy, a selected healthy gene is delivered to a patient’s cell to cure or ease such disorders. To carry out such a procedure, a doctor must have a sound knowledge of the chemical properties of the molecular components involved. Chemists in the pharmaceutical industry are researching potent drugs with few or no side effects to treat cancer, AIDS, and many other diseases as well as drugs to increase the number of successful organ transplants. On a broader scale, improved understanding of the mechanism of aging will lead to a longer and healthier lifespan for the world’s population. Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 1.1 CHEMISTRY: A SCIENCE FOR THE TWENTY-FIRST CENTURY 5 FIGURE 1.1 (a) A chemical research laboratory where new drugs are synthesized. (b) Photovoltaic cells. (c) A silicon wafer being processed. (d) Effect of a sex pheromone on gypsy moths. (a) (c) (b) (d) Energy and the Environment Energy is a by-product of many chemical processes, and as the demand for energy continues to increase, both in technologically advanced countries like the United States and in developing ones like China, chemists are actively trying to find new energy sources. Currently the major sources of energy are fossil fuels (coal, petroleum, and natural gas). The estimated reserves of these fuels will last us another 50–100 years, at the present rate of consumption, so it is urgent that we find alternatives. Solar energy promises to be a viable source of energy for the future. Every year Earth’s surface receives about 10 times as much energy from sunlight as is contained in all of the known reserves of coal, oil, natural gas, and uranium combined. But much of this energy is “wasted’’ because it is reflected back into space. For the past thirty years, intense research efforts have shown that solar energy can be harnessed effectively in two ways. One is the conversion of sunlight directly to electricity using devices called photovoltaic cells. The other is to use sunlight to obtain hydrogen from water. The hydrogen can then be fed into a fuel cell to generate electricity. Although our understanding of the scientific process of converting solar energy to electricity has advanced, the technology has not yet improved to the point where we can produce electricity on a large scale at an economically acceptable cost. By 2050, however, it has been predicted that solar energy will supply over 50 percent of our power needs. Another potential source of energy is nuclear fission, but because of environmental concerns about the radioactive wastes from fission processes, the future of the nuclear Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 6 CHEMISTRY: THE STUDY OF CHANGE industry in the United States is uncertain. Chemists can help to devise better ways to dispose of nuclear waste. Nuclear fusion, the process that occurs in the sun and other stars, generates huge amounts of energy without producing much dangerous radioactive waste. In another 50 years, nuclear fusion will likely be a significant source of energy. Energy production and energy utilization are closely tied to the quality of our environment. A major disadvantage of burning fossil fuels is that they give off carbon dioxide, which is a greenhouse gas (that is, it promotes the heating of Earth’s atmosphere), along with sulfur dioxide and nitrogen oxides, which result in acid rain and smog. (Harnessing solar energy has no such detrimental effects on the environment.) By using fuel-efficient automobiles and more effective catalytic converters, we should be able to drastically reduce harmful auto emissions and improve the air quality in areas with heavy traffic. In addition, electric cars, powered by durable, long-lasting batteries, should be more prevalent in the next century, and their use will help to minimize air pollution. Materials and Technology Chemical research and development in the twentieth century have provided us with new materials that have profoundly improved the quality of our lives and helped to advance technology in countless ways. A few examples are polymers (including rubber and nylon), ceramics (such as cookware), liquid crystals (like those in electronic displays), adhesives (used in your Post-It notes), and coatings (for example, latex paint). What is in store for the near future? One likely possibility is room-temperature superconductors. Electricity is carried by copper cables, which are not perfect conductors. Consequently, about 20 percent of electrical energy is lost in the form of heat between the power station and our homes. This is a tremendous waste. Superconductors are materials that have no electrical resistance and can therefore conduct electricity with no energy loss. Although the phenomenon of superconductivity at very low temperatures (more than 400 degrees Fahrenheit below the freezing point of water) has been known for over 80 years, a major breakthrough in the mid-1980s demonstrated that it is possible to make materials that act as superconductors at or near room temperature. Chemists have helped to design and synthesize new materials that show promise in this quest. The next 30 years will see high-temperature superconductors being applied on a large scale in magnetic resonance imaging (MRI), levitated trains, and nuclear fusion. If we had to name one technological advance that has shaped our lives more than any other, it would be the computer. The “engine’’ that drives the ongoing computer revolution is the microprocessor — the tiny silicon chip that has inspired countless inventions, such as laptop computers and fax machines. The performance of a microprocessor is judged by the speed with which it carries out mathematical operations, such as addition. The pace of progress is such that since their introduction, microprocessors have doubled in speed every 18 months. At this rate by the year 2030 one desk computer will be as powerful as all those in California’s Silicon Valley in 1998! The quality of any microprocessor depends on the purity of the silicon chip and on the ability to add the desired amount of other substances, and chemists play an important role in the research and development of silicon chips. For the future, scientists have begun to explore the prospect of “molecular computing,’’ that is, replacing silicon with Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 1.2 THE STUDY OF CHEMISTRY 7 molecules. The advantages are that certain molecules can be made to respond to light, rather than to electrons, so that we would have optical computers rather than electronic computers. With proper genetic engineering, scientists can synthesize such molecules using microorganisms instead of large factories. Optical computers also would have much greater storage capacity than electronic computers. Food and Agriculture How can the world’s rapidly increasing population be fed? In poor countries, agricultural activities occupy about 80 percent of the workforce, and half of an average family budget is spent on foodstuffs. This is a tremendous drain on a nation’s resources. The factors that affect agricultural production are the richness of the soil, insects and diseases that damage crops, and weeds that compete for nutrients. Besides irrigation, farmers rely on fertilizers and pesticides to increase crop yield. Since the 1950s, treatment for crops suffering from pest infestations has sometimes been the indiscriminate application of potent chemicals. Such measures have often had serious detrimental effects on the environment. Even the excessive use of fertilizers is harmful to the land, water, and air. To meet the food demands of the twenty-first century, new and novel approaches in farming must be devised. It has already been demonstrated that, through biotechnology, it is possible to grow larger and better crops. These techniques can be applied to many different farm products, not only for improved yields, but also for better frequency, that is, more crops every year. For example, it is known that a certain bacterium produces a protein molecule that is toxic to leaf-eating caterpillars. Incorporating the gene that codes for the toxin into crops enables plants to protect themselves so that pesticides are not necessary. Researchers have also found a way to prevent pesky insects from reproducing. Insects communicate with one another by emitting and reacting to special molecules called pheromones. By identifying and synthesizing pheromones used in mating, it is possible to interfere with the normal reproductive cycle of common pests, for example, by inducing insects to mate too soon or tricking female insects into mating with sterile males. Moreover, chemists can devise ways to increase the production of fertilizers that are less harmful to the environment and substances that would selectively kill weeds. 1.2 THE STUDY OF CHEMISTRY Compared with other subjects, chemistry is commonly believed to be more difficult, at least at the introductory level. There is some justification for this perception; for one thing, chemistry has a very specialized vocabulary. However, even if this is your first course in chemistry, you already have more familiarity with the subject than you may realize. In everyday conversations we hear words that have a chemical connection, although they may not be used in the scientifically correct sense. Examples are “electronic,’’ “quantum leap,’’ “equilibrium,’’ “catalyst,’’ “chain reaction,’’ and “critical mass.’’ Moreover, if you cook, then you are a practicing chemist! From experience gained in the kitchen, you know that oil and water do not mix and that boiling water left on the stove will evaporate. You apply chemical and physical principles when you use baking soda to leaven bread, choose a pressure cooker to shorten the time it takes to prepare soup, add meat tenderizer to a pot roast, squeeze lemon juice over sliced Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 8 CHEMISTRY: THE STUDY OF CHANGE FIGURE 1.2 A badly rusted car. Corrosion of iron costs the U.S. economy tens of billions of dollars every year. pears to prevent them from turning brown or over fish to minimize its odor, and add vinegar to the water in which you are going to poach eggs. Every day we observe such changes without thinking about their chemical nature. The purpose of this course is to make you think like a chemist, to look at the macroscopic world — the things we can see, touch, and measure directly — and visualize the particles and events of the microscopic world that we cannot experience without modern technology and our imaginations. At first some students find it confusing that their chemistry instructor and textbook seem to be continually shifting back and forth between the macroscopic and microscopic worlds. Just keep in mind that the data for chemical investigations most often come from observations of large-scale phenomena, but the explanations frequently lie in the unseen and partially imagined microscopic world of atoms and molecules. In other words, chemists often see one thing (in the macroscopic world) and think another (in the microscopic world). Looking at the rusted car in Figure 1.2, for example, a chemist might think about the basic properties of individual atoms of iron and how these units interact with other atoms and molecules to produce the observed change. 1.3 THE SCIENTIFIC METHOD All sciences, including the social sciences, employ variations of what is called the scientific method, a systematic approach to research. For example, a psychologist who wants to know how noise affects people’s ability to learn chemistry and a chemist interested in measuring the heat given off when hydrogen gas burns in air would follow roughly the same procedure in carrying out their investigations. The first step is to carefully define the problem. The next step includes performing experiments, making careful observations, and recording information, or data, about the system — the part of the universe that is under investigation. (In the examples above, the systems are the group of people the psychologist will study and a mixture of hydrogen and air.) The data obtained in a research study may be both qualitative, consisting of general observations about the system, and quantitative, comprising numbers obtained by Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 1.3 FIGURE 1.3 The three levels of studying chemistry and their relationships. Observation deals with events in the macroscopic world; atoms and molecules constitute the microscopic world. Representation is a scientific shorthand for describing an experiment in symbols and chemical equations. Chemists use their knowledge of atoms and molecules to explain an observed phenomenon. Back Forward Main Menu Observation THE SCIENTIFIC METHOD Representation 9 Interpretation various measurements of the system. Chemists generally use standardized symbols and equations in recording their measurements and observations. This form of representation not only simplifies the process of keeping records, but also provides a common basis for communication with other chemists. When the experiments have been completed and the data have been recorded, the next step in the scientific method is interpretation, meaning that the scientist attempts to explain the observed phenomenon. Based on the data that were gathered, the researcher formulates a hypothesis, a tentative explanation for a set of observations. Further experiments are devised to test the validity of the hypothesis in as many ways as possible, and the process begins anew. Figure 1.3 summarizes the main steps of the research 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 verbal or mathematical statement of a relationship between phenomena that is always the same under the same conditions. For example, Sir Isaac Newton’s second law of motion, which you may remember from high school science, says that force equals mass times acceleration (F ma). What this law means is that an increase in the mass or in the acceleration of an object will always increase its force proportionally, and a decrease in mass or acceleration will always decrease the force. Hypotheses that survive many experimental tests of their validity may evolve into theories. A theory is a unifying principle that explains a body of facts and/or those laws that are based on them. Theories, too, are constantly being tested. If a theory is disproved by experiment, then it must be discarded or modified so that it becomes consistent with experimental observations. Proving or disproving a theory can take years, even centuries, in part because the necessary technology may not be available. Atomic theory, which we will study in Chapter 2, is a case in point. It took more than 2000 years to work out this fundamental principle of chemistry proposed by Democritus, an ancient Greek philosopher. A more contemporary example is the Big Bang theory of the origin of the universe discussed on p. 28. Scientific progress is seldom, if ever, made in a rigid, step-by-step fashion. Sometimes a law precedes a theory; sometimes it is the other way around. Two scientists may start working on a project with exactly the same objective, but will end up taking drastically different approaches. Scientists are, after all, human beings, and their modes of thinking and working are very much influenced by their background, training, and personalities. The development of science has been irregular and sometimes even illogical. Great discoveries are usually the result of the cumulative contributions and experience of many workers, even though the credit for formulating a theory or a law is usually given to only one individual. There is, of course, an element of luck involved in scientific discoveries, but it has been said that “chance favors the prepared mind.’’ It takes an alert and well-trained person to recognize the significance of an accidental discovery and to take full advantage of it. More often than not, the public learns only of spectacular scientific breakthroughs. For every success story, however, there are hundreds of cases in which scientists have spent years working on projects that ultimately led to TOC Study Guide TOC Textbook Website MHHE Website 10 CHEMISTRY: THE STUDY OF CHANGE FIGURE 1.4 Separating iron filings from a heterogeneous mixture. The same technique is used on a larger scale to separate iron and steel from nonmagnetic objects such as aluminum, glass, and plastics. (a) (b) a dead end, and in which positive achievements came only after many wrong turns and at such a slow pace that they went unheralded. Yet even the dead ends contribute something to the continually growing body of knowledge about the physical universe. It is the love of the search that keeps many scientists in the laboratory. 1.4 CLASSIFICATIONS OF MATTER We defined chemistry at the beginning of the chapter as the study of matter and the changes it undergoes. Matter is anything that occupies space and has mass. Matter includes things we can see and touch (such as water, earth, and trees), as well as things we cannot (such as air). Thus, everything in the universe has a “chemical’’ connection. Chemists distinguish among several subcategories of matter based on composition and properties. The classifications of matter include substances, mixtures, elements, and compounds, as well as atoms and molecules, which we will consider in Chapter 2. SUBSTANCES AND MIXTURES A substance is a form of matter that has a definite (constant) composition and distinct properties. Examples are water, ammonia, table sugar (sucrose), gold, and oxygen. Substances differ from one another in composition and can be identified by their appearance, smell, taste, and other properties. A mixture is a combination of two or more substances in which the substances retain their distinct identities. Some familiar examples are air, soft drinks, milk, and cement. Mixtures do not have constant composition. Therefore, samples of air collected in different cities would probably differ in composition because of differences in altitude, pollution, and so on. Mixtures are either homogeneous or heterogeneous. When a spoonful of sugar dissolves in water we obtain a homogeneous mixture in which the composition of the mixture is the same throughout. If sand is mixed with iron filings, however, the sand grains and the iron filings remain separate (Figure 1.4). This type of mixture is called a heterogeneous mixture because the composition is not uniform. Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 1.4 CLASSIFICATIONS OF MATTER 11 Any mixture, whether homogeneous or heterogeneous, can be created and then separated by physical means into pure components without changing the identities of the components. Thus, sugar can be recovered from a water solution by heating the solution and evaporating it to dryness. Condensing the vapor will give us back the water component. To separate the iron-sand mixture, we can use a magnet to remove the iron filings from the sand, because sand is not attracted to the magnet [see Figure 1.4(b)]. After separation, the components of the mixture will have the same composition and properties as they did to start with. ELEMENTS AND COMPOUNDS Substances can be either elements or compounds. An element is a substance that cannot be separated into simpler substances by chemical means. To date, 112 elements have been positively identified. Eighty-three of them occur naturally on Earth. The others have been created by scientists via nuclear processes, which are the subject of Chapter 23 of this text. For convenience, chemists use symbols of one, two, or three letters to represent the elements. The first letter of a symbol is always capitalized, but any following letters are not. For example, Co is the symbol for the element cobalt, whereas CO is the formula for the carbon monoxide molecule. Table 1.1 shows the names and symbols of some of the more common elements; a complete list of the elements and their symbols appears inside the front cover of this book. The symbols of some elements are derived from their Latin names — for example, Au from aurum (gold), Fe from ferrum (iron), and Na from natrium (sodium) — while most of them come from their English names. Appendix 1 gives the origin of the names and lists the discoverers of most of the 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 properties that are distinctly different from those of the starting materials. Water is made up of two parts hydrogen and one part oxygen. This composition does not change, regardless of whether the water comes from a faucet in the United States, a lake in Outer Mongolia, or the ice caps on Mars. Thus, water is a compound, a substance composed of atoms of two or more elements chemically united in fixed proportions. Unlike mixtures, compounds can be separated only by chemical means into their pure components. TABLE 1.1 NAME Aluminum Arsenic Barium Bismuth Bromine Calcium Carbon Chlorine Chromium Cobalt Copper Back Forward Main Menu TOC Some Common Elements and Their Symbols SYMBOL Al As Ba Bi Br Ca C Cl Cr Co Cu NAME Fluorine Gold Hydrogen Iodine Iron Lead Magnesium Manganese Mercury Nickel Nitrogen SYMBOL F Au H I Fe Pb Mg Mn Hg Ni N Study Guide TOC NAME Oxygen Phosphorus Platinum Potassium Silicon Silver Sodium Sulfur Tin Tungsten Zinc SYMBOL O P Pt K Si Ag Na S Sn W Zn Textbook Website MHHE Website 12 CHEMISTRY: THE STUDY OF CHANGE Matter Separation by physical methods Mixtures Homogeneous mixtures Heterogeneous mixtures FIGURE 1.5 Classification of matter. 1.5 Pure substances Compounds Separation by chemical methods Elements The relationships among elements, compounds, and other categories of matter are summarized in Figure 1.5. THE THREE STATES OF MATTER All substances, at least in principle, can exist in three states: solid, liquid, and gas. As Figure 1.6 shows, gases differ from liquids and solids in the distances between the molecules. In a solid, molecules are held close together in an orderly fashion with little freedom of motion. Molecules in a liquid are close together but are not held so rigidly in position and can move past one another. In a gas, the molecules are separated by distances that are large compared with the size of the molecules. The three states of matter can be interconverted without changing the composition of the substance. Upon heating, a solid (for example, ice) will melt to form a liquid (water). (The temperature at which this transition occurs is called the melting point.) Further heating will convert the liquid into a gas. (This conversion takes place at the boiling point of the liquid.) On the other hand, cooling a gas will cause it to condense FIGURE 1.6 Microscopic views of a solid, a liquid, and a gas. Solid Back Forward Main Menu TOC Liquid Study Guide TOC Gas Textbook Website MHHE Website 1.6 PHYSICAL AND CHEMICAL PROPERTIES OF MATTER 13 FIGURE 1.7 The three states of matter. A hot poker changes ice into water and steam. into a liquid. When the liquid is cooled further, it will freeze into the solid form. Figure 1.7 shows the three states of water. 1.6 Hydrogen burning in air to form water. Back Forward Main Menu PHYSICAL AND CHEMICAL PROPERTIES OF MATTER Substances are identified by their properties as well as by their composition. Color, melting point, and boiling point are physical properties. A physical property can be measured and observed without changing the composition or identity of a substance. For example, we can measure the melting point of ice by heating a block of ice and recording the temperature at which the ice is converted to water. Water differs from ice only in appearance, not in composition, so this is a physical change; we can freeze the water to recover the original ice. Therefore, the melting point of a substance is a physical property. Similarly, when we say that helium gas is lighter than air, we are referring to a physical property. On the other hand, the statement “Hydrogen gas burns in oxygen gas to form water ’’ describes a chemical property of hydrogen, because in order to observe this property we must carry out a chemical change, in this case burning. After the change, the original chemical substance, the hydrogen gas, will have vanished, and all that will be left is a different chemical substance — water. We cannot recover the hydrogen from the water by means of a physical change, such as boiling or freezing. Every time we hard-boil an egg, we bring about a chemical change. When subjected to a temperature of about 100 C, the yolk and the egg white undergo changes that alter not only their physical appearance but their chemical makeup as well. When eaten, the egg is changed again, by substances in our bodies called enzymes. This digestive action is another example of a chemical change. What happens during digestion depends on the chemical properties of both the enzymes and the food. TOC Study Guide TOC Textbook Website MHHE Website 14 CHEMISTRY: THE STUDY OF CHANGE All measurable properties of matter fall into one of two additional categories: extensive properties and intensive properties. The measured value of an extensive property depends on how much matter is being considered. Mass, which is the quantity of matter in a given sample of a substance, is an extensive property. More matter means more mass. Values of the same extensive property can be added together. For example, two copper pennies will have a combined mass that is the sum of the masses of each penny, and the length of two tennis courts is the sum of the lengths of each tennis court. Volume, defined as length cubed, is another extensive property. The value of an extensive quantity depends on the amount of matter. The measured value of an intensive property does not depend on how much matter is being considered. Density, defined as the mass of an object divided by its volume, is an intensive property. So is temperature. Suppose that we have two beakers of water at the same temperature. If we combine them to make a single quantity of water in a larger beaker, the temperature of the larger quantity of water will be the same as it was in two separate beakers. Unlike mass, length, and volume, temperature and other intensive properties are not additive. 1.7 MEASUREMENT The measurements chemists make are often used in calculations to obtain other related quantities. Different instruments enable us to measure a substance’s properties: The meter stick measures length or scale; the buret, the pipet, the graduated cylinder, and the volumetric flask measure volume (Figure 1.8); the balance measures mass; the thermometer measures temperature. These instruments provide measurements of macroscopic properties, which can be determined directly. Microscopic properties, on the atomic or molecular scale, must be determined by an indirect method, as we will see in the next chapter. FIGURE 1.8 Some common measuring devices found in a chemistry laboratory. These devices are not drawn to scale relative to one another. We will discuss the uses of these measuring devices in Chapter 4. mL 0 1 mL 100 2 90 3 80 4 70 15 25 mL 60 16 17 50 18 40 19 30 20 20 10 Buret Back Forward Main Menu Pipet TOC Graduated cylinder Study Guide TOC 1 liter Volumetric flask Textbook Website MHHE Website 1.7 TABLE 1.2 NAME OF UNIT Length Mass Time Electrical current Temperature Amount of substance Luminous intensity Meter Kilogram Second Ampere Kelvin Mole Candela PREFIX TeraGigaMegaKiloDeciCentiMilliMicroNanoPico- 15 SI Base Units BASE QUANTITY TABLE 1.3 MEASUREMENT SYMBOL m kg s A K mol cd Prefixes Used with SI Units SYMBOL MEANING EXAMPLE 12 T G M k d c m 1,000,000,000,000, or 10 1,000,000,000, or 109 1,000,000, or 106 1,000, or 103 1/10, or 10 1 1/100, or 10 2 1/1,000, or 10 3 1/1,000,000, or 10 6 1/1,000,000,000, or 10 9 1/1,000,000,000,000, or 10 n p 12 1 1 1 1 1 1 1 1 1 1 terameter (Tm) gigameter (Gm) megameter (Mm) kilometer (km) decimeter (dm) centimeter (cm) millimeter (mm) micrometer ( m) nanometer (nm) picometer (pm) 1 1012 m 1 109 m 1 106 m 1 103 m 0.1 m 0.01 m 0.001 m 1 10 6 m 1 10 9 m 1 10 12 m A measured quantity is usually written as a number with an appropriate unit. To say that the distance between New York and San Francisco by car along a certain route is 5166 is meaningless. We must specify that the distance is 5166 kilometers. The same is true in chemistry; units are essential to stating measurements correctly. SI UNITS For many years scientists recorded measurements in metric units, which are related decimally, that is, by powers of 10. In 1960, however, the General Conference of Weights and Measures, the international authority on units, proposed a revised metric system called the International System of Units (abbreviated SI, from the French Système Internationale d’Unites). Table 1.2 shows the seven SI base units. All other units of measurement can be derived from these base units. Like metric units, SI units are modified in decimal fashion by a series of prefixes, as shown in Table 1.3. We will use both metric and SI units in this book. Measurements that we will utilize frequently in our study of chemistry include time, mass, volume, density, and temperature. MASS AND WEIGHT The terms “mass’’ and “weight’’ are often used interchangeably, although, strictly speaking, they are different quantities. Whereas mass is a measure of the amount of matter in an object, weight, technically speaking, is the force that gravity exerts on an object. An apple that falls from a tree is pulled downward by Earth’s gravity. The mass of the Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 16 CHEMISTRY: THE STUDY OF CHANGE apple is constant and does not depend on its location, but its weight does. For example, on the surface of the moon the apple would weigh only one-sixth what it does on Earth, because the moon’s gravity is only one-sixth that of Earth. The moon’s smaller gravity enables astronauts to jump about rather freely on its surface despite their bulky suits and equipment. Chemists are interested primarily in mass, which can be determined readily with a balance; the process of measuring mass, oddly, is called weighing. The SI base unit of mass is the kilogram (kg), but in chemistry the smaller gram (g) is more convenient: 1 kg 1000 g 103 g 1 VOLUME An astronaut on the surface of the moon. The SI unit of length is the meter (m), and the SI-derived unit for volume is the cubic meter (m3). Generally, however, chemists work with much smaller volumes, such as the cubic centimeter (cm3) and the cubic decimeter (dm3): 1 cm3 1 dm 3 (1 (1 10 2 m)3 10 1 3 m) 1 1 10 6 m3 10 3 m3 Another common unit of volume is the liter (L). A liter is the volume occupied by one cubic decimeter. One liter of volume is equal to 1000 milliliters (mL) or 1000 cm3: 1L 1000 mL 1000 cm3 1 dm3 and one milliliter is equal to one cubic centimeter: 1 mL Volume: 1000 cm3; 1000 mL; 1 dm3; 1L 1 cm3 Figure 1.9 compares the relative sizes of two volumes. Even though the liter is not an SI unit, volumes are usually expressed in liters and milliliters. DENSITY The equation for density is density mass volume or d 1 cm 10 cm = 1 dm Volume: 1 cm3; 1 mL 1 cm FIGURE 1.9 Comparison of two volumes, 1 mL and 1000 mL. Back Forward m V (1.1) where d, m, and V denote density, mass, and volume, respectively. Because density is an intensive property and does not depend on the quantity of mass present, for a given material the ratio of mass to volume always remains the same; in other words, V increases as m does. The SI-derived unit for density is the kilogram per cubic meter (kg/m3). This unit is awkwardly large for most chemical applications. Therefore, grams per cubic centimeter (g/cm3) and its equivalent, grams per milliliter (g/mL), are more commonly used for solid and liquid densities. Because gas densities are often very low, we express them in units of grams per liter (g/L): Main Menu TOC Study Guide TOC Textbook Website MHHE Website 1.7 1 g/cm3 1 g/mL 1 g/L MEASUREMENT 17 1000 kg/m3 0.001 g/mL The following examples show density calculations. EXAMPLE 1.1 Gold is a precious metal that is chemically unreactive. It is used mainly in jewelry, dentistry, and electronic devices. A piece of gold ingot with a mass of 301 g has a volume of 15.6 cm3. Calculate the density of gold. Answer The density of the gold metal is given by d Gold bars. m V 301 g 15.6 cm3 19.3 g/cm3 Similar problems: 1.21, 1.22. PRACTICE EXERCISE A piece of platinum metal with a density of 21.5 g/cm3 has a volume of 4.49 cm3. What is its mass? EXAMPLE 1.2 The density of ethanol, a colorless liquid that is commonly known as grain alcohol, is 0.798 g/mL. Calculate the mass of 17.4 mL of the liquid. The mass of ethanol is found by rearranging the density equation d as follows: Answer m d V 0.798 Ethanol is produced during the fermentation of bread. It evaporates during baking and produces the fragrant aroma. Similar problems: 1.21, 1.22. m/V g mL 17.4 mL 13.9 g PRACTICE EXERCISE The density of sulfuric acid in a certain car battery is 1.41 g/mL. Calculate the mass of 242 mL of the liquid. TEMPERATURE SCALES Note that the kelvin scale does not have the degree sign. Also, temperatures expressed in kelvin can never be negative. Back Forward Main Menu Three temperature scales are currently in use. Their units are F (degrees Fahrenheit), °C (degrees Celsius), and K (kelvin). The Fahrenheit scale, which is the most commonly used scale in the United States outside the laboratory, defines the normal freezing and boiling points of water to be exactly 32 F and 212 F, respectively. The Celsius scale divides the range between the freezing point (0 C) and boiling point (100 C) of water into 100 degrees. As Table 1.2 shows, the kelvin is the SI base unit of temperature; it is the absolute temperature scale. By absolute we mean that the zero on the kelvin scale, denoted by 0 K, is the lowest temperature that can be attained theoreti- TOC Study Guide TOC Textbook Website MHHE Website 18 CHEMISTRY: THE STUDY OF CHANGE cally. On the other hand, 0 F and 0 C are based on the behavior of an arbitrarily chosen substance, water. Figure 1.10 compares the three temperature scales. The size of a degree on the Fahrenheit scale is only 100/180, or 5/9, of a degree on the Celsius scale. To convert degrees Fahrenheit to degrees Celsius, we write ?C (F 5C 9F 32 F) (1.2) The following equation is used to convert degrees Celsius to degrees Fahrenheit ?F 9°F 5C ( C) 32 F (1.3) Both the Celsius and the Kelvin scales have units of equal magnitude; that is, one degree Celsius is equivalent to one kelvin. Experimental studies have shown that absolute zero on the kelvin scale is equivalent to 273.15°C on the Celsius scale. Thus we can use the following equation to convert degrees Celsius to kelvin: ?K (C 273.15 C) 1K 1C (1.4) We will frequently find it necessary to convert between degrees Celsius and degrees Fahrenheit and between degrees Celsius and kelvin. The following example illustrates these conversions. EXAMPLE 1.3 (a) Solder is an alloy made of tin and lead that is used in electronic circuits. A certain solder has a melting point of 224 C. What is its melting point in degrees Fahrenheit? (b) Helium has the lowest boiling point of all the elements at 452 F. Convert this temperature to degrees Celsius. (c) Mercury, the only metal that exists as a liquid at room temperature, melts at 38.9 C. Convert its melting point to kelvins. Register to View AnswerThis conversion is carried out by writing 9F 5C (224 C) 32 F 32 F) 5C 9F 435 F (b) Here we have ( 452 F Solder is used extensively in the construction of electronic circuits. 269 C (c) The melting point of mercury in kelvins is given by ( 38.9 C Similar problems: 1.24, 1.25, 1.26. 273.15 C) 1K 1C 234.3 K PRACTICE EXERCISE Convert (a) 327.5 C (the melting point of lead) to degrees Fahrenheit; (b) 172.9 F (the boiling point of ethanol) to degrees Celsius; and (c) 77 K, the boiling point of liquid nitrogen, to degrees Celsius. Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 1.8 FIGURE 1.10 Comparison of the three temperature scales: Celsius, Fahrenheit, and the absolute (Kelvin) scales. Note that there are 100 divisions, or 100 degrees, between the freezing point and the boiling point of water on the Celsius scale, and there are 180 divisions, or 180 degrees, between the same two temperature limits on the Fahrenheit scale. 373 K 100°C 310 K 37°C 298 K 25°C Room temperature 0°C Freezing point of water 32°F Kelvin 1.8 19 77°F 273 K HANDLING NUMBERS Boiling point of water Body temperature Celsius 212°F 98.6°F Fahrenheit HANDLING NUMBERS Having surveyed some of the units used in chemistry, we now turn to techniques for handling numbers associated with measurements: scientific notation and significant figures. SCIENTIFIC NOTATION Chemists often deal with numbers that are either extremely large or extremely small. For example, in 1 g of the element hydrogen there are roughly 602,200,000,000,000,000,000,000 hydrogen atoms. Each hydrogen atom has a mass of only 0.00000000000000000000000166 g These numbers are cumbersome to handle, and it is easy to make mistakes when using them in arithmetic computations. Consider the following multiplication: 0.0000000056 0.00000000048 0.000000000000000002688 It would be easy for us to miss one zero or add one more zero after the decimal point. Consequently, when working with very large and very small numbers, we use a system called scientific notation. Regardless of their magnitude, all numbers can be expressed in the form N 10n where N is a number between 1 and 10 and n, the exponent, is a positive or negative integer (whole number). Any number expressed in this way is said to be written in scientific notation. Suppose that we are given a certain number and asked to express it in scientific notation. Basically, this assignment calls for us to find n. We count the number of places Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 20 CHEMISTRY: THE STUDY OF CHANGE that the decimal point must be moved to give the number N (which is between 1 and 10). If the decimal point has to be moved to the left, then n is a positive integer; if it has to be moved to the right, n is a negative integer. The following examples illustrate the use of scientific notation: (a) Express 568.762 in scientific notation: 568.762 102 5.68762 Note that the decimal point is moved to the left by two places and n (b) Express 0.00000772 in scientific notation: 0.00000772 Any number raised to the power zero is equal to one. 7.72 2. 6 10 Here the decimal point is moved to the right by six places and n 6. Keep in mind the following two points. First, n 0 is used for numbers that are not expressed in scientific notation. For example, 74.6 100 (n 0) is equivalent to 74.6. Second, the usual practice is to omit the superscript when n 1. Thus the scientific notation for 74.6 is 7.46 10 and not 7.46 101. Next, we consider how scientific notation is handled in arithmetic operations. Addition and Subtraction To add or subtract using scientific notation, we first write each quantity — say N1 and N2 — with the same exponent n. Then we combine N1 and N2; the exponents remain the same. Consider the following examples: 103) (7.4 4 (4.31 10 ) (2.1 (3.9 103) 103 9.5 3 10 ) 104) (4.31 104 4.70 (2.22 2 10 ) (4.10 3 10 ) 104) (0.39 10 2) (2.22 1.81 10 10 2) (0.41 2 Multiplication and Division To multiply numbers expressed in scientific notation, we multiply N1 and N2 in the usual way, but add the exponents together. To divide using scientific notation, we divide N1 and N2 as usual and subtract the exponents. The following examples show how these operations are performed: (8.0 104) (5.0 102) (8.0 5.0)(104 2) 40 4.0 (4.0 10 5) (7.0 103) 106 107 (4.0 7.0)(10 28 Back Forward Main Menu TOC 5 104 109 Study Guide TOC 6.9 3.0 107 ) 1012 8.5 5.0 104 1.7 8.5 5.0 10 10 10 2.3 6.9 3.0 10 2.8 7 53 2 10 1 ( 5) 9 5 Textbook Website MHHE Website 1.8 FIGURE 1.11 balance. HANDLING NUMBERS 21 A single-pan SIGNIFICANT FIGURES Except when all the numbers involved are integers (for example, in counting the number of students in a class), it is often impossible to obtain the exact value of the quantity under investigation. For this reason, it is important to indicate the margin of error in a measurement clearly by indicating the number of significant figures, which are the meaningful digits in a measured or calculated quantity. When significant figures are used, the last digit is understood to be uncertain. For example, we might measure the volume of a given amount of liquid using a graduated cylinder with a scale that gives an uncertainty of 1 mL in the measurement. If the volume is found to be 6 mL, then the actual volume is in the range of 5 mL to 7 mL. We represent the volume of the liquid as (6 1) mL. In this case, there is only one significant figure (the digit 6) that is uncertain by either plus or minus 1 mL. For greater accuracy, we might use a graduated cylinder that has finer divisions, so that the volume we measure is now uncertain by only 0.1 mL. If the volume of the liquid is now found to be 6.0 mL, we may express the quantity as (6.0 0.1) mL, and the actual value is somewhere between 5.9 mL and 6.1 mL. We can further improve the measuring device and obtain more significant figures, but in every case, the last digit is always uncertain; the amount of this uncertainty depends on the particular measuring device we use. Figure 1.11 shows a modern balance. Balances such as this one are available in many general chemistry laboratories; they readily measure the mass of objects to four decimal places. Therefore the measured mass typically will have four significant figures (for example, 0.8642 g) or more (for example, 3.9745 g). Keeping track of the number of significant figures in a measurement such as mass ensures that calculations involving the data will reflect the precision of the measurement. Guidelines for Using Significant Figures We must always be careful in scientific work to write the proper number of significant figures. In general, it is fairly easy to determine how many significant figures a number has by following these rules: Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 22 CHEMISTRY: THE STUDY OF CHANGE Any digit that is not zero is significant. Thus 845 cm has three significant figures, 1.234 kg has four significant figures, and so on. Zeros between nonzero digits are significant. Thus 606 m contains three significant figures, 40,501 kg contains five significant figures, and so on. Zeros to the left of the first nonzero digit are not significant. Their purpose is to indicate the placement of the decimal point. For example, 0.08 L contains one significant figure, 0.0000349 g contains three significant figures, and so on. If a number is greater than 1, then all the zeros written to the right of the decimal point count as significant figures. Thus 2.0 mg has two significant figures, 40.062 mL has five significant figures, and 3.040 dm has four significant figures. If a number is less than 1, then only the zeros that are at the end of the number and the zeros that are between nonzero digits are significant. This means that 0.090 kg has two significant figures, 0.3005 L has four significant figures, 0.00420 min has three significant figures, and so on. For numbers that do not contain decimal points, the trailing zeros (that is, zeros after the last nonzero digit) may or may not be significant. Thus 400 cm may have one significant figure (the digit 4), two significant figures (40), or three significant figures (400). We cannot know which is correct without more information. By using scientific notation, however, we avoid this ambiguity. In this particular case, we can express the number 400 as 4 102 for one significant figure, 4.0 102 for two significant figures, or 4.00 102 for three significant figures. • • • • • The following example shows the determination of significant figures. EXAMPLE 1.4 Determine the number of significant figures in the following measurements: (a) 478 cm, (b) 6.01 g, (c) 0.825 m, (d) 0.043 kg, (e) 1.310 1022 atoms, (f) 7000 mL. (a) Three, (b) Three, (c) Three, (d) Two, (e) Four, (f) This is an ambiguous case. The number of significant figures may be four (7.000 103), three (7.00 103), two (7.0 103), or one (7 103). Answer Similar problems: 1.33, 1.34. PRACTICE EXERCISE Determine the number of significant figures in each of the following measurements: (a) 24 mL, (b) 3001 g, (c) 0.0320 m3, (d) 6.4 104 molecules, (e) 560 kg. A second set of rules specifies how to handle significant figures in calculations. • In addition and subtraction, the number of significant figures to the right of the decimal point in the final sum or difference is determined by the smallest number of significant figures to the right of the decimal point in any of the original numbers. Consider these examples: 89.332 01.100 m88 one significant figure after the decimal point 90.432 m88 round off to 90.4 2.097 0.12 0m88 two significant figures after the decimal point 1.977 m88 round off to 1.98 Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 1.8 HANDLING NUMBERS 23 The rounding-off procedure is as follows. To round off a number at a certain point we simply drop the digits that follow if the first of them is less than 5. Thus 8.724 rounds off to 8.72 if we want only two figures after the decimal point. If the first digit following the point of rounding off is equal to or greater than 5, we add 1 to the preceding digit. Thus 8.727 rounds off to 8.73, and 0.425 rounds off to 0.43. • In multiplication and division, the number of significant figures in the final product or quotient is determined by the original number that has the smallest number of significant figures. The following examples illustrate this rule: • 4.5039 12.61092 m88 round off to 13 6.85 112.04 2.8 0.0611388789 m88 round off to 0.0611 Keep in mind that exact numbers obtained from definitions or by counting numbers of objects can be considered to have an infinite number of significant figures. If an object has a mass of 0.2786 g, then the mass of eight such objects is 0.2786 g 8 2.229 g We do not round off this product to one significant figure, because the number 8 is 8.00000 . . . , by definition. Similarly, to take the average of the two measured lengths 6.64 cm and 6.68 cm, we write 6.64 cm 6.68 cm 2 6.66 cm because the number 2 is 2.00000 . . . , by definition. The following example shows how significant figures are handled in arithmetic operations. EXAMPLE 1.5 Carry out the following arithmetic operations: (a) 11,254.1 g 0.1983 g, (b) 66.59 L 3.113 L, (c) 8.16 m 5.1355, (d) 0.0154 kg 88.3 mL, (e) 2.64 103 cm 3.27 102 cm. Register to View Answer 11,254.1 g 0.1983 g 11,254.2983 g m88 round off to 11,254.3 g (b) 66.59 L 3.113 L 63.477 L m88 round off to 63.48 L (c) 8.16 m (d) Similar problems: 1.35, 1.36. Back Forward Main Menu 5.1355 0.0154 kg 88.3 mL 41.90568 m m88 round off to 41.9 m 0.000174405436 kg/mL m88 round off to 0.000174 kg/mL or 1.74 10 4 kg/mL (e) First we change 3.27 102 cm to 0.327 103 cm and then carry out the addition (2.64 cm 0.327 cm) 103. Following the procedure in (a), we find the answer is 2.97 103 cm. TOC Study Guide TOC Textbook Website MHHE Website 24 CHEMISTRY: THE STUDY OF CHANGE PRACTICE EXERCISE Carry out the following arithmetic operations and round off the answers to the appropriate number of significant figures: (a) 26.5862 L 0.17 L, (b) 9.1 g 4.682 g, (c) 7.1 104 dm 2.2654 102, (d) 6.54 g 86.5542 mL, (e) (7.55 104 m) (8.62 103 m). The above rounding-off procedure applies to one-step calculations. In chain calculations, that is, calculations involving more than one step, we use a modified procedure. Consider the following two-step calculation: First step: A B C Second step: C D E Let us suppose that A 3.66, B 8.45, and D 2.11. Depending on whether we round off C to three or four significant figures, we obtain a different number for E: Method 1 Method 2 3.66 8.45 30.9 3.66 30.9 2.11 65.2 30.93 8.45 2.11 30.93 65.3 However, if we had carried out the calculation as 3.66 8.45 2.11 on a calculator without rounding off the intermediate result, we would have obtained 65.3 as the answer for E. In general, we will show the correct number of significant figures in each step of the calculation. However, in some worked examples, only the final answer is rounded off to the correct number of significant figures. The answers for all intermediate calculations will be carried to one extra figure. Accuracy and Precision In discussing measurements and significant figures it is useful to distinguish between accuracy and precision. Accuracy tells us how close a measurement is to the true value of the quantity that was measured. To a scientist there is a distinction between accuracy and precision. Precision refers to how closely two or more measurements of the same quantity agree with one another (Figure 1.12). The difference between accuracy and precision is a subtle but important one. Suppose, for example, that three students are asked to determine the mass of a piece of copper wire. The results of two successive weighings by each student are STUDENT A STUDENT C 1.964 g 1.978 g Average value STUDENT B 1.972 g 1.968 g 2.000 g 2.002 g 1.971 g 1.970 g 2.001 g The true mass of the wire is 2.000 g. Therefore, Student B’s results are more precise than those of Student A (1.972 g and 1.968 g deviate less from 1.970 g than 1.964 g and 1.978 g from 1.971 g), but neither set of results is very accurate. Student C’s results are not only the most precise, but also the most accurate, since the average value is closest to the true value. Highly accurate measurements are usually precise too. On the other hand, highly precise measurements do not necessarily guarantee accurate results. For example, an improperly calibrated meter stick or a faulty balance may give precise readings that are in error. Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 1.9 FIGURE 1.12 The distribution of darts on a dart board shows the difference between precise and accurate. (a) Good accuracy and good precision. (b) Poor accuracy and good precision. (c) Poor accuracy and poor precision. THE FACTOR-LABEL METHOD OF SOLVING PROBLEMS 10 10 30 30 30 60 60 60 100 100 100 (a) 1.9 10 (b) 25 (c) THE FACTOR-LABEL METHOD OF SOLVING PROBLEMS Careful measurements and the proper use of significant figures, along with correct calculations, will yield accurate numerical results. But to be meaningful, the answers also must be expressed in the desired units. The procedure we will use to convert between units in solving chemistry problems is called the factor-label method, or dimensional analysis. A simple technique requiring little memorization, the factor-label method is based on the relationship between different units that express the same physical quantity. We know, for example, that the unit “dollar ’’ for money is different from the unit “penny.’’ However, we say that 1 dollar is equivalent to 100 pennies because they both represent the same amount of money. This equivalence allows us to write 1 dollar 100 pennies Because 1 dollar is equal to 100 pennies, it follows that their ratio has a value of 1; that is, 1 dollar 100 pennies 1 This ratio can be read as 1 dollar per 100 pennies. The fraction is called a unit factor (equal to 1) because the numerator and denominator describe the same amount of money. We can also write the ratio as 100 pennies per dollar: 100 pennies 1 dollar 1 This fraction is also a unit factor. We see that the reciprocal of any unit factor is also a unit factor. The usefulness of unit factors is that they allow us to carry out conversions between different units that measure the same quantity. Suppose that we want to convert 2.46 dollars into pennies. This problem may be expressed as ? pennies 2.46 dollars Since this is a dollar-to-penny conversion, we choose the unit factor that has the unit “dollar ’’ in the denominator (to cancel the “dollars’’ in 2.46 dollars) and write 2.46 dollars Back Forward Main Menu TOC 100 pennies 1 dollar Study Guide TOC 246 pennies Textbook Website MHHE Website 26 CHEMISTRY: THE STUDY OF CHANGE Note that the unit factor 100 pennies/1 dollar contains exact numbers, so it does not affect the number of significant figures in the final answer. Next let us consider the conversion of 57.8 meters to centimeters. This problem may be expressed as ? cm 57.8 m By definition, 1 cm 1 2 10 m Since we are converting “m’’ to “cm,’’ we choose the unit factor that has meters in the denominator, 1 cm 10 2 m 1 1 and write the conversion as ? cm 57.8 m 1 cm 10 2 m 1 5780 cm 5.78 103 cm Note that scientific notation is used to indicate that the answer has three significant figures. The unit factor 1 cm/1 10 2 m contains exact numbers; therefore, it does not affect the number of significant figures. In the factor-label method the units are carried through the entire sequence of calculations. Therefore, if the equation is set up correctly, then all the units will cancel except the desired one. If this is not the case, then an error must have been made somewhere, and it can usually be spotted by reviewing the solution. The following examples illustrate the use of the factor-label method. EXAMPLE 1.6 A hydrogen molecule. The distance between two hydrogen atoms in a hydrogen molecule is 74 pm. Convert this distance to meters. Answer The problem is ?m 74 pm By definition, 1 pm 1 10 12 m The unit factor is 10 12 m 1 pm 1 1 Therefore we write ?m Similar problem: 1.37(a). 74 pm 1 10 12 m 1 pm 7.4 10 11 m PRACTICE EXERCISE Convert 197 pm, the radius of a calcium (Ca) atom, to centimeters. Back Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 1.9 THE FACTOR-LABEL METHOD OF SOLVING PROBLEMS 27 EXAMPLE 1.7 Conversion factors for some of the English system units commonly used in the United States for nonscientific measurements (for example, pounds and inches) are provided inside the back cover of this book. A person’s average daily intake of glucose (a form of sugar) is 0.0833 pound (lb). What is this mass in milligrams (mg)? (1 lb 453.6 g) Answer The problem can be expressed as ? mg 0.0833 lb so the unit factor is 453.6 g 1 lb 1 and 1 mg 1 10 3 g so we must also include the unit factor 1 mg 10 3 g 1 1 Thus ? mg Similar problem: 1.43. 0.0833 lb 453.6 g 1 lb 1 1 mg 10 3 g 104 mg 3.78 PRACTICE EXERCISE A roll of aluminum foil has a mass of 1.07 kg. What is its mass in pounds? Note that unit factors may be squared or cubed, because 12 such factors is illustrated in Examples 1.8 and 1.9. 13 1. The use of EXAMPLE 1.8 An average adult has 5.2 liters of blood. What is the volume of blood in m3? Since 1 L lem can be stated as Answer 1000 cm3, 5.2 L is equivalent to 5.2 ? m3 103 cm3. The prob- 103 cm3 5.2 By definition 1m 100 cm The unit factor is 1m 100 cm 1 It follows that 1m 100 cm 3 13 1 Therefore we write ? m3 Back Forward Main Menu TOC 5.2 103 cm3 Study Guide TOC 1m 100 cm 3 5.2 10 3 m3 Textbook Website MHHE Website 28 CHEMISTRY: THE STUDY OF CHANGE Chemistry in Action Chemistry in Action Chemistry in Action Chemistry in Action Chemistry in Action Chemistry in Action Chemistry Chemistry in Action Chemistry in Action Chemistry in Action Chemistry in Action Chemistry in Action Chemistry Back Primordial Helium and The Big Bang Theory Where did we come from? How did the universe begin? Humans have asked these questions for as long as we have been able to think. The search for answers provides an example of the scientific method. In the 1940s the Russian-American physicist George Gamow hypothesized that our universe burst into being billions of years ago in a gigantic explosion, or Big Bang. In its earliest moments, the universe occupied a tiny volume and was unimaginably hot. This blistering fireball of radiation mixed with microscopic particles of matter gradually cooled enough for atoms to form. Under the influence of gravity, these atoms clumped together to make billions of galaxies including our own Milky Way Galaxy. Gamow’s idea is interesting and highly provocative. It has been tested experimentally in a number of ways. First, measurements showed that the universe is expanding; that is, galaxies are all moving away from one another at high speeds. This fact is consistent with the universe’s explosive birth. By imagining the expansion running backwards, like a movie in reverse, astronomers have deduced that the universe was born about 15 billion years ago. The second observation that supports Gamow’s hypothesis is the detection of cosmic background radiation. Over billions of years, the searingly hot universe has cooled down to a mere 3 K (or 270 C)! At this temperature, most energy is in the microwave region. Because the Big Bang would have occurred simultaneously throughout the tiny volume of the forming universe, the radiation it generated should have filled the entire universe. Thus the radiation should be the same in any direction that we observe. Indeed, the microwave signals recorded by astronomers are independent of direction. The third piece of evidence supporting Gamow’s hypothesis is the discovery of primordial helium. Scientists believe that helium and hydrogen (the lightest elements) were the first elements formed in the early stages of cosmic evolution. (The heavier elements, like carbon, nitrogen, and oxygen, are thought to have originated later via nuclear reactions involving hydrogen and helium in the center of stars.) If so, a dif- Forward Main Menu TOC fuse gas of hydrogen and helium would have spread through the early universe before much of the galaxies formed. In 1995 astronomers analyzed ultraviolet light from a distant quasar (a strong source of light and radio signals that is thought to be an exploding galaxy at the edge of the universe) and found that some of the light was absorbed by helium atoms on the way to Earth. Since this particular quasar is more than 10 billion light years away (a light year is the distance traveled by light in a year), the light reaching Earth reveals events that took place 10 billion years ago. Why wasn’t the more abundant hydrogen detected? A hydrogen atom has only one electron, which is stripped by the light from a quasar in a process known as ionization. Ionized hydrogen atoms cannot absorb any of the quasar’s light. A helium atom, on the other hand, has two electrons. Radiation may strip a helium atom of one electron, but not always both. Singly ionized helium atoms can still absorb light and are therefore detectable. Proponents of Gamow’s explanation rejoiced at the detection of helium in the far reaches of the universe. In recognition of all the supporting evidence, scientists now refer to Gamow’s hypothesis as the Big Bang theory. Photo showing some distant galaxy, including the position of a quasar. Study Guide TOC Textbook Website MHHE Website SUMMARY OF KEY EQUATIONS 29 Notice that in cubing the quantity [1 m/(100 cm)] we cube both the numbers and the units. Comment Similar problem: 1.48(d). PRACTICE EXERCISE 108 dm3. What is the volume in m3? The volume of a room is 1.08 EXAMPLE 1.9 The density of silver is 10.5 g/cm3. Convert the density to units of kg/m3. The problem can be stated as Answer ? kg/m3 A silver coin. 10.5 g/cm3 We need two unit factors — one to convert g to kg and the other to convert cm3 to m3. We know that 1 kg 1000 g so 1 kg 1000 g Second, since 1 cm 1 10 2 1 cm 1 10 2 m 1 m, the following unit factors can be generated: 1 and 1 cm 1 10 2 m 3 1 Finally we can calculate the density in the desired units as follows: ? kg/m3 10.5 g 1 cm3 1 kg 1000 g 1 1 cm 10 2 m 3 10,500 kg/m3 1.05 Similar problem: 1.49. Comment 104 kg/m3 The units kg/m3 give inconveniently large values for density. PRACTICE EXERCISE The density of the lightest metal, lithium (Li), is 5.34 density to g/cm3. SUMMARY OF KEY EQUATIONS m V •d (1.1) Equation for density • ?C Main Menu 32 F) 9F 5C ( C) • ?K Forward (F • ?F Back (C TOC 102 kg/m3. Convert the 5C 9F (1.2) Converting F to C 32 F (1.3) Converting C to F 273.15 C) 1K 1C (1.4) Study Guide TOC Converting C to K Textbook Website MHHE Website 30 CHEMISTRY: THE STUDY OF CHANGE SUMMARY OF FACTS AND CONCEPTS 1. The study of chemistry involves three basic steps: observation, representation, and interpretation. Observation refers to measurements in the macroscopic world; representation involves the use of shorthand notation symbols and equations for communication; interpretations are based on atoms and molecules, which belong to the microscopic world. 2. The scientific method is a systematic approach to research that begins with the gathering of information through observation and measurements. In the process, hypotheses, laws, and theories are devised and tested. 3. Chemists study matter and the changes it undergoes. The substances that make up matter have unique physical properties that can be observed without changing their identity and unique chemical properties that, when they are demonstrated, do change the identity of the substances. Mixtures, whether homogeneous or heterogeneous, can be separated into pure components by physical means. 4. The simplest substances in chemistry are elements. Compounds are formed by the chemical combination of atoms of different elements in fixed proportions. 5. All substances, in principle, can exist in three states: solid, liquid, and gas. The interconversion between these states can be effected by changing the temperature. 6. SI units are used to express physical quantities in all sciences, including chemistry. 7. Numbers expressed in scientific notation have the form N 10n, where N is between 1 and 10, and n is a positive or negative integer. Scientific notation helps us handle very large and very small quantities. KEY WORDS Accuracy, p. 24 Chemical property, p. 13 Chemistry, p. 4 Compound, p. 11 Density, p. 14 Element, p. 11 Extensive property, p. 14 Heterogeneous mixture, p. 10 Homogeneous mixture, p. 10 Hypothesis, p. 9 Intensive property, p. 14 International System of Units (SI), p. 15 Kelvin, p. 17 Law, p. 9 Liter, p. 16 Macroscopic property, p. 14 Mass, p. 14 Matter, p. 10 Microscopic property, p. 14 Mixture, p. 10 Physical property, p. 13 Precision, p. 24 Qualitative, p. 8 Quantitative, p. 8 Scientific method, p. 8 Significant figures, p. 21 Substance, p. 10 Theory, p. 9 Volume, p. 14 Weight, p. 15 QUESTIONS AND PROBLEMS THE SCIENTIFIC METHOD Review Questions 1.1 Explain what is meant by the scientific method. 1.2 What is the difference between qualitative data and quantitative data? tion to music would have been much greater if he had married. (b) An autumn leaf gravitates toward the ground because there is an attractive force between the leaf and Earth. (c) All matter is composed of very small particles called atoms. CLASSIFICATION AND PROPERTIES OF MATTER Review Questions Problems 1.3 Classify the following as qualitative or quantitative statements, giving your reasons. (a) The sun is approximately 93 million miles from Earth. (b) Leonardo da Vinci was a better painter than Michelangelo. (c) Ice is less dense than water. (d) Butter tastes better than margarine. (e) A stitch in time saves nine. 1.4 Classify each of the following statements as a hypothesis, a law, or a theory. (a) Beethoven’s contribu- Back Forward Main Menu TOC 1.5 Give an example for each of the following terms: (a) matter, (b) substance, (c) mixture. 1.6 Give an example of a homogeneous mixture and an example of a heterogeneous mixture. 1.7 Using examples, explain the difference between a physical property and a chemical property? 1.8 How does an intensive property differ from an extensive property? Which of the following properties are Study Guide TOC Textbook Website MHHE Website QUESTIONS AND PROBLEMS intensive and which are extensive? (a) length, (b) volume, (c) temperature, (d) mass. 1.9 Give an example of an element and a compound. How do elements and compounds differ? 1.10 What is the number of known elements? Problems 1.11 Do the following statements describe chemical or physical properties? (a) Oxygen gas supports combustion. (b) Fertilizers help to increase agricultural production. (c) Water boils below 100°C on top of a mountain. (d) Lead is denser than aluminum. (e) Sugar tastes sweet. 1.12 Does each of the following describe a physical change or a chemical change? (a) The helium gas inside a balloon tends to leak out after a few hours. (b) A flashlight beam slowly gets dimmer and finally goes out. (c) Frozen orange juice is reconstituted by adding water to it. (d) The growth of plants depends on the sun’s energy in a process called photosynthesis. (e) A spoonful of table salt dissolves in a bowl of soup. 1.13 Give the names of the elements represented by the chemical symbols Li, F, P, Cu, As, Zn, Cl, Pt, Mg, U, Al, Si, Ne. (See Table 1.1 and the inside front cover.) 1.14 Give the chemical symbols for the following elements: (a) potassium, (b) tin, (c) chromium, (d) boron, (e) barium, (f) plutonium, (g) sulfur, (h) argon, (i) mercury. (See Table 1.1 and the inside front cover.) 1.15 Classify each of the following substances as an element or a compound: (a) hydrogen, (b) water, (c) gold, (d) sugar. 1.16 Classify each of the following as an element, a compound, a homogeneous mixture, or a heterogeneous mixture: (a) seawater, (b) helium gas, (c) sodium chloride (table salt), (d) a bottle of soft drink, (e) a milkshake, (f) air, (g) concrete. MEASUREMENT 31 Problems 1.21 Bromine is a reddish-brown liquid. Calculate its density (in g/mL) if 586 g of the substance occupies 188 mL. 1.22 Mercury is the only metal that is a liquid at room temperature. Its density is 13.6 g/mL. How many grams of mercury will occupy a volume of 95.8 mL? 1.23 Convert the following temperatures to degrees Celsius: (a) 95 F, the temperature on a hot summer day; (b) 12 F, the temperature on a cold winter day; (c) a 102 F fever; (d) a furnace operating at 1852 F. 1.24 (a) Normally the human body can endure a temperature of 105 F for only short periods of time without permanent damage to the brain and other vital organs. What is this temperature in degrees Celsius? (b) Ethylene glycol is a liquid organic compound that is used as an antifreeze in car radiators. It freezes at 11.5 C. Calculate its freezing temperature in degrees Fahrenheit. (c) The temperature on the surface of the sun is about 6300 C. What is this temperature in degrees Fahrenheit? 1.25 Convert the following temperatures to Kelvin: (a) 113 C, the melting point of sulfur, (b) 37 C, the normal body temperature, (c) 357 C, the boiling point of mercury. 1.26 Convert the following temperatures to degrees Celsius: (a) 77 K, the boiling point of liquid nitrogen, (b) 4.2 K, the boiling point of liquid helium, (c) 601 K, the melting point of lead. HANDLING NUMBERS Review Questions 1.27 What is the advantage of using scientific notation over decimal notation? 1.28 Define significant figure. Discuss the importance of using the proper number of significant figures in measurements and calculations. Review Questions Back Problems 1.17 Name the SI base units that are important in chemistry. Give the SI units for expressing the following: (a) length, (b) volume, (c) mass, (d) time, (e) energy, (f) 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, the Celsius scale, and the Kelvin scale. 1.29 Express the following numbers in scientific notation: (a) 0.000000027, (b) 356, (c) 47,764, (d) 0.096. 1.30 Express the following numbers as decimals: (a) 1.52 10 2, (b) 7.78 10 8. 1.31 Express the answers to the following calculations in scientific 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 in scientific notation: (a) 0.0095 (8.5 10 3) Forward Main Menu TOC Study Guide TOC Textbook Website MHHE Website 32 1.33 1.34 1.35 1.36 CHEMISTRY: THE STUDY OF CHANGE (b) 653 (5.75 10 8) (c) 850,000 (9.0 105) (d) (3.6 10 4) (3.6 106) What is the number of significant figures in each of the following measurements? (a) 4867 mi (b) 56 mL (c) 60,104 ton (d) 2900 g (e) 40.2 g/cm3 (f) 0.0000003 cm (g) 0.7 min (h) 4.6 1019 atoms How many significant figures are there in each of the following? (a) 0.006 L, (b) 0.0605 dm, (c) 60.5 mg, (d) 605.5 cm2, (e) 960 10 3 g, (f) 6 kg, (g) 60 m. Carry out the following operations as if they were calculations of experimental results, and express each answer in the correct units with the correct number of significant figures: (a) 5.6792 m 0.6 m 4.33 m (b) 3.70 g 2.9133 g (c) 4.51 cm 3.6666 cm Carry out the following operations as if they were calculations of experimental results, and express each answer in the correct units with the correct number of significant 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 METHOD Problems 1.37 Carry out the following conversions: (a) 22.6 m to decimeters, (b) 25.4 mg to kilograms. 1.38 Carry out the following conversions: (a) 242 lb to milligrams, (b) 68.3 cm3 to cubic meters. 1.39 The price of gold on November 3, 1995, was $384 per ounce. How much did 1.00 g of gold cost that day? (1 ounce 28.4 g.) 1.40 How many seconds are there in a solar year (365.24 days)? 1.41 How many minutes does it take light from the sun to reach Earth? (The distance from the sun to Earth is 93 million mi; the speed of light 3.00 108 m/s.) 1.42 A slow jogger runs a mile in 13 min. Calculate the speed in (a) in/s, (b) m/min, (c) km/h. (1 mi 1609 m; 1 in 2.54 cm.) 1.43 A 6.0-ft person weighs 168 lb. Express this person’s height in meters and weight in kilograms. (1 lb 453.6 g; 1 m 3.28 ft.) Back Forward Main Menu TOC 1.44 The current speed limit in some states in the U.S. is 55 miles per hour. What is the speed limit in kilometers per hour? (1 mi 1609 m.) 1.45 For a fighter jet to take off from the deck of an aircraft carrier, it must reach a speed of 62 m/s. Calculate the speed in mph. 1.46 The “normal’’ lead content in human blood is about 0.40 part per million (that is, 0.40 g of lead per million grams of blood). A value of 0.80 part per million (ppm) is considered to be dangerous. How many grams of lead are contained in 6.0 103 g of blood (the amount in an average adult) if the lead content is 0.62 ppm? 1.47 Carry out the following conversions: (a) 1.42 lightyears to miles (a light-year is an astronomical measure of distance — the distance traveled by light in a year, or 365 days; the speed of light is 3.00 108 m/s), (b) 32.4 yd to centimeters, (c) 3.0 1010 cm/s to ft/s. 1.48 Carry out the following conversions: (a) 47.4 F to degrees Celsius, (b) 273.15 C (the lowest attainable temperature) to degrees Fahrenheit, (c) 71.2 cm3 to m3, (d) 7.2 m3 to liters. 1.49 Aluminum is a lightweight metal (density 2.70 g/cm3) used in aircraft construction, high-voltage transmission lines, beverage cans, and foils. What is its density in kg/m3? 1.50 The density of ammonia gas under certain conditions is 0.625 g/L. Calculate its density in g/cm3. ADDITIONAL PROBLEMS 1.51 Give one qualitative and one quantitative statement about each of the following: (a) water, (b) carbon, (c) iron, (d) hydrogen gas, (e) sucrose (cane sugar), (f) table salt (sodium chloride), (g) mercury, (h) gold, (i) air. 1.52 Which of the following statements describe physical properties and which describe chemical properties? (a) Iron has a tendency to rust. (b) Rainwater in industrialized regions tends to be acidic. (c) Hemoglobin molecules have a red color. (d) When a glass of water is left out in the sun, the water gradually disappears. (e) Carbon dioxide in air is converted to more complex molecules by plants during photosynthesis. 1.53 In 1995, 95.4 billion pounds of sulfuric acid were produced in the United States. Convert this quantity to tons. 1.54 In determining the density of a rectangular metal bar, a student made the following measurements: length, 8.53 cm; width, 2.4 cm; height, 1.0 cm; mass, 52.7064 g. Calculate the density of the metal to the correct number of significant figures. 1.55 Calculate the mass of each of the following: (a) a sphere of gold with a radius of 10.0 cm [the volume Study Guide TOC Textbook Website MHHE Website QUESTIONS AND PROBLEMS 1.56 1.57 1.58 1.59 1.60 1.61 1.62 1.63 1.64 1.65 1.66 Back of a sphere with a radius r is V (4/3) r3; the density of gold 19.3 g/cm3], (b) a cube of platinum of edge length 0.040 mm (the density of platinum 21.4 g/cm3), (c) 50.0 mL of ethanol (the density of ethanol 0.798 g/mL). A cylindrical glass tube 12.7 cm in length is filled with mercury. The mass of mercury needed to fill the tube is 105.5 g. Calculate the inner diameter of the tube. (The density of mercury 13.6 g/mL.) The following procedure was used to determine the volume of a flask. The flask was weighed dry and then filled with water. If the masses of the empty flask and filled flask were 56.12 g and 87.39 g, respectively, and the density of water is 0.9976 g/cm3, calculate the volume of the flask in cm3. The speed of sound in air at room temperature is about 343 m/s. Calculate this speed in miles per hour (mph). (1 mi 1609 m.) A piece of silver (Ag) metal weighing 194.3 g is placed in a graduated cylinder containing 242.0 mL of water. The volume of water now reads 260.5 mL. From these data calculate the density of silver. The experiment described in Problem 1.59 is a crude but convenient way to determine the density of some solids. Describe a similar experiment that would allow you to measure the density of ice. Specifically, what would be the requirements for the liquid used in your experiment? A lead sphere has a mass of 1.20 104 g, and its volume is 1.05 103 cm3. Calculate the density of lead. Lithium is the least dense metal known (density: 0.53 g/cm3). What is the volume occupied by 1.20 103 g of lithium? The medicinal thermometer commonly used in homes can be read 0.1 F, while those in the doctor ’s office may be accurate to 0.1 C. In degrees Celsius, express the percent error expected from each of these thermometers in measuring a person’s body temperature of 38.9 C. Vanillin (used to flavor vanilla ice cream and other foods) is the substance whose aroma the human nose detects in the smallest amount. The threshold limit is 2.0 10 11 g per liter of air. If the current price of 50 g of vanillin is $112, determine the cost to supply enough vanillin so that the aroma could be detected in a large aircraft hangar with a volume of 5.0 107 ft3. At what temperature does the numerical reading on a Celsius thermometer equal that on a Fahrenheit thermometer? Suppose that a new temperature scale has been devised on which the melting point of ethanol ( 117.3 C) and the boiling point of ethanol (78.3 C) are taken as 0 S Forward Main Menu TOC 1.67 1.68 1.69 1.70 1.71 1.72 1.73 1.74 33 and 100 S, respectively, where S is the symbol for the new temperature scale. Derive an equation relating a reading on this scale to a reading on the Celsius scale. What would this thermometer read at 25 C? A resting adult requires about 240 mL of pure oxygen/min and breathes about 12 times every minute. If inhaled air contains 20 percent oxygen by volume and exhaled air 16 percent, what is the volume of air per breath? (Assume that the volume of inhaled air is equal to that of exhaled air.) (a) Referring to Problem 1.67, calculate the total volume (in liters) of air an adult breathes in a day. (b) In a city with heavy traffic, the air contains 2.1 10 6 L of carbon monoxide (a poisonous gas) per liter. Calculate the average daily intake of carbon monoxide in liters by a person. The total volume of seawater is 1.5 1021 L. Assume that seawater contains 3.1 percent sodium chloride by mass and that its density is 1.03 g/mL. Calculate the total mass of sodium chloride in kilograms and in tons. (1 ton 2000 lb; 1 lb 453.6 g) Magnesium (Mg) is a valuable metal used in alloys, in batteries, and in the manufacture of chemicals. It is obtained mostly from seawater, which contains about 1.3 g of Mg for every kilogram of seawater. Referring to Problem 1.69, calculate the volume of seawater (in liters) needed to extract 8.0 104 tons of Mg, which is roughly the annual production in the United States. A student is given a crucible and asked to prove whether it is made of pure platinum. She first weighs the crucible in air and then weighs it suspended in water (density 0.9986 g/mL). The readings are 860.2 g and 820.2 g, respectively. Based on these measurements and given that the density of platinum is 21.45 g/cm3, what should her conclusion be? (Hint: An object suspended in a fluid is buoyed up by the mass of the fluid displaced by the object. Neglect the buoyance of air.) The surface area and average depth of the Pacific Ocean are 1.8 108 km2 and 3.9 103 m, respectively. Calculate the volume of water in the ocean in liters. The unit “troy ounce’’ is often used for precious metals such as gold (Au) and platinum (Pt). (1 troy ounce 31.103 g) (a) A gold coin weighs 2.41 troy ounces. Calculate its mass in grams. (b) Is a troy ounce heavier or lighter than an ounce. (1 lb 16 oz; 1 lb 453.6 g) Osmium (Os) is the densest element known (density 22.57 g/cm3). Calculate the mass in pounds and in kilograms of an Os sphere 15 cm in diameter (about the size of a grapefruit). See Problem 1.55 for volume of a sphere. Study Guide TOC Textbook Website MHHE Website 34 CHEMISTRY: THE STUDY OF CHANGE 1.75 Percent error is often expressed as the absolute value of the difference between the true value and the experimental value, divided by the true value: percent error true value experimental value true value 100% 1.85 The vertical lines indicate absolute value. Calculate the percent error for the following measurements: (a) The density of alcohol (ethanol) is found to be 0.802 g/mL. (True value: 0.798 g/mL.) (b) The mass of gold in an earring is analyzed to be 0.837 g. (True value: 0.864 g.) 1.76 The natural abundances of elements in the human body, expressed as percent by mass, are: oxygen (O), 65%; carbon (C), 18%; hydrogen (H), 10%; nitrogen (N), 3%; calcium (Ca), 1.6%; phosphorus (P), 1.2%; all other elements, 1.2%. Calculate the mass in grams of each element in the body of a 62-kg person. 1.77 The men’s world record for running a mile outdoors (as of 1997) is 3 minutes 44.39 seconds. At this rate, how long would it take to run a 1500-m race? (1 mi 1609 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 can be obtained from 5.11 103 kg of the ore? 1.80 It has been estimated that 8.0 104 tons of gold (Au) have been mined. Assume gold costs $350 per ounce. What is the total worth of this quantity of gold? 1.81 A 1.0-mL volume of seawater contains about 4.0 10 12 g of gold. The total volume of ocean water is 1.5 1021 L. Calculate the total amount of gold (in grams) that is present in seawater, and the worth of the gold in dollars (see Problem 1.80). With so much gold out there, why hasn’t someone become rich by mining gold from the ocean? 1.82 Measurements show that 1.0 g of iron (Fe) contains 1.1 1022 Fe atoms. How many Fe atoms are in 4.9 g of Fe, which is the total amount of iron in the body of an average adult? 1.83 The thin outer layer of Earth, called the crust, contains only 0.50% of Earth’s total mass and yet is the source of almost all the elements (the atmosphere provides elements such as oxygen, nitrogen, and a few other gases). Silicon (Si) is the second most abundant element in Earth’s crust (27.2% by mass). Calculate the mass of silicon in kilograms in Earth’s crust. (The mass of Earth is 5.9 1021 tons. 1 ton 2000 lb; 1 lb 453.6 g.) 1.84 The diameter of a copper (Cu) atom is roughly 1.3 10 12 m. How many times can you divide evenly a Back Forward Main Menu TOC 1.86 1.87 1.88 1.89 1.90 piece of 10-cm copper wire until it is reduced to two separate copper atoms? (Assume there are appropriate tools for this procedure and that copper atoms are lined up in a straight line, in contact with each other.) Round off your answer to an integer.) One gallon of gasoline in an automobile’s engine produces on the average 9.5 kg of carbon dioxide, which is a greenhouse gas, that is, it promotes the warming of Earth’s atmosphere. Calculate the annual production of carbon dioxide in kilograms if there are 40 million cars in the United States and each car covers a distance of 5000 miles at a consumption rate of 20 miles per gallon. A sheet of aluminum (Al) foil has a total area of 1.000 ft2 and a mass of 3.636 g. What is the thickness of the foil in millimeters? (Density of Al 2.699 g/cm3.) Comment on whether each of the following is a homogeneous mixture or a heterogeneous mixture: (a) air in a closed bottle and (b) air over New York City. It has been proposed that dinosaurs and many other organisms became extinct 65 million years ago because Earth was struck by a large asteroid. The idea is that dust from the impact was lofted into the upper atmosphere all around the globe, where it lingered for at least several months and blocked the sunlight from reaching Earth’s surface. In the dark and cold conditions that temporarily resulted, many forms of life became extinct. Available evidence suggests that about 20% of the asteroid’s mass turned to dust and spread uniformly over Earth after eventually settling out of the upper atmosphere. This dust amounted to about 0.02 g/cm2 of Earth’s surface. The asteroid very likely had a density of about 2 g/cm3. Calculate the mass (in kilograms and tons) of the asteroid and its radius in meters, assuming that it was a sphere. (The area of Earth is 5.1 1014 m2; 1 lb 453.6 g.) (Source: Consider a Spherical Cow — A Course in Environmental Problem Solving by J. Harte, University Science Books, Mill Valley, CA, 1988. Used with permission.) The world’s total petroleum reserve is estimated at 2.0 1022 J (Joule is the unit of energy where 1 J 1 kg 22 m /s ). At the present rate of consumption, 1.8 1020 J/yr, how long would it take to exhaust the supply? Chlorine is used to disinfect swimming pools. The accepted concentration for this purpose is 1 ppm chlorine, or one gram of chlorine per million grams of water. Calculate the volume of a chlorine solution (in milliliters) a homeowner should add to her swimming pool if the solution contains 6.0% chlorine by mass and there are 2.0 104 gallons of water in the pool. (1 gallon 3.79 L; density of liquids 1.0 g/mL.) Study Guide TOC Textbook Website MHHE Website QUESTIONS AND PROBLEMS 1.91 Fluoridation is the process of adding fluorine compounds to drinking water to help fight tooth decay. A concentration of 1 ppm of fluorine is sufficient for the purpose. (1 ppm means one part per million, or 1 g of fluorine per one million grams of water.) The compound normally chosen for fluoridation is sodium fluoride, which is also added to some toothpastes. Calculate the quantity of sodium fluoride in kilograms needed per year for a city of 50,000 people if the daily consumption of water per person is 150 gallons. What percent of the sodium fluoride is “wasted’’ if each person uses only 6.0 L of water a day for drinking and cooking? (Sodium fluoride is 45.0% fluorine by mass. 1 gallon 3.79 L; 1 year 365 days; 1 ton 2000 lb; 1 lb 453.6 g; density of water 1.0 g/mL.) 1.92 In water conservation, chemists spread a thin film of certain inert material over the surface of water to cut down the rate of evaporation of water in reservoirs. This technique was pioneered by Benjamin Franklin two centuries ago. Franklin found that 0.10 mL of oil could spread over the surface of about 40 m2 of water. Assuming that the oil forms a monolayer, that is, Back Forward Main Menu TOC 35 a layer that is only one molecule thick, estimate the length of each oil molecule in nanometers. (1 nm 1 10 9 m.) 1.93 Pheromones are compounds secreted by females of many insect species to attract mates. Typically, 1.0 10 8 g of a pheromone is sufficient to reach all targeted males within a radius of 0.50 mi. Calculate the density of the pheromone (in grams per liter) in a cylindrical air space having a radius of 0.50 mi and a height of 40 ft. 1.94 A gas company in Massachusetts charges $1.30 for 15.0 ft3 of natural gas. (a) Convert this rate to dollars per liter of gas. (b) It takes 0.304 ft3 of gas to boil a liter of water, starting at room temperature (25 C), how much would it cost to boil a 2.1-liter kettle of water? Answers to Practice Exercises: 1.1 96.5 g. 1.2 341 g. 1.3 (a) 621.5 F, (b) 78.3 C, (c) 196 C. 1.4 (a) Two, (b) four, (c) three, (d) two, (e) three or two. 1.5 (a) 26.76 L, (b) 4.4 g, (c) 1.6 107 dm, (d) 0.0756 g/mL, (e) 6.69 104 m. 1.6 1.97 10 8 cm. 1.7 2.36 lb. 1.8 1.08 105 m3. 1.9 0.534 g/cm3. Study Guide TOC Textbook Website MHHE Website ... View Full Document

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