Solution Manual for Chemistry: The Science in Context, 3rd Edition

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1CHAPTER 1 | Matter, Energy, and the Origins of the Universe1.1.Collect and OrganizeIn Figure P1.1(a) we are shown “molecules” each consisting of one red sphere and one blue sphere and inFigure P1.1(b) we have separate blue spheres and red spheres. In each figure we are to identify whether thesubstance(s) depicted is a solid, liquid, or gas and if the figures show pure elements or compounds.AnalyzeA pure substance (whether element or compound) is composed of all the same type of molecule or atom, not amixture of two kinds. An element is composed of all the same type of atom and a compound is composed oftwo or more types of atoms. Solids have a definite volume and a highly ordered arrangement where the particlesare close together, liquids also have a definite volume but have a disordered arrangement of particles that areclose together, and gases have disordered particles that fill the volume of the container and are far apart fromeach other.Solve(a) Because the particles each consist of one red sphere and one blue sphere, all the particles are the same—thisis a pure compound. The particles fill the container and are disordered, so these particles are in the gas phase.(b) Because Figure P1.1(b) shows a mixture of red and blue spheres, this is depicting a mixture of blue elementatoms and red element atoms. The blue spheres fill the container and are disordered, so these particles are in thegas phase. The red spheres have a definite volume and are slightly disordered, so these particles are in the liquidphase.Think about ItRemember that both elements and compounds may be either pure or present in a mixture.1.2.Collect and OrganizeIn Figure P1.2(a) we are shown “atoms” of only red spheres and in Figure P1.2(b) we have “molecules”consisting of two red spheres or two blue spheres. In each figure we are to identify whether the substance(s)depicted is a solid, liquid, or gas and if the figures show pure elements or compounds.AnalyzeA pure substance (whether element or compound) is composed of all the same type of molecule or atom, not amixture of two kinds. An element is composed of all the same type of atom and a compound is composed oftwo or more types of atoms. Solids have a definite volume and a highly ordered arrangement where the particlesare close together, liquids also have a definite volume but have a disordered arrangement of particles that areclose together, and gases have disordered particles that fill the volume of the container and are far apart fromeach other.Solve(a) Because all the atoms are of the same type, Figure P1.2(a) depicts a pure element. The particles take up adefinite volume and are ordered, so this element is in the solid phase.(b) Because there is a mixture of blue diatomic molecules and red diatomic molecules, Figure P1.2(b) depicts amixture of two elements. Both the blue and red diatomic particles fill the container’s volume and are highlydisordered; the mixture depicted is in the gas phase.Think about ItElements do not need to be present as single atoms. They may be diatomic as in H2or Br2, or even more highlyassociated as in S8or P4.1.3.Collect and OrganizeIn this question we are to consider whether the reactants as depicted undergo a chemical reaction and/or a phasechange.

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2|Chapter 1AnalyzeChemical reactions involve the breaking and making of bonds in which atoms are combined differently in theproducts compared to that of the reactants. In considering a possible phase change, solids have a definitevolume and a highly ordered arrangement where the particles are close together, liquids also have a definitevolume but have a disordered arrangement of particles that are close together, and gases have disorderedparticles that fill the volume of the container and are far apart from each other.SolveIn Figure P1.3 two pure elements (red–red and blue–blue) in the gas phase recombine to form a compound(red–blue) in the solid phase (ordered array of molecules). Therefore,answer b describes the reaction shown.Think about ItA phase change does not necessarily accompany a chemical reaction. We will learn later that the polarity of theproduct will determine whether or not a substance will be in the solid, liquid, or gaseous state at a giventemperature.1.4.Collect and OrganizeIn this question we are to consider whether the reactants as depicted undergo a chemical reaction (eitherrecombination or decomposition) and/or a phase change.AnalyzeChemical reactions involve the breaking and making of bonds in which atoms are combined differently in theproducts compared to that of the reactants. In considering a possible phase change, solids have a definitevolume and a highly ordered arrangement where the particles are close together, liquids also have a definitevolume but have a disordered arrangement of particles that are close together, and gases have disorderedparticles that fill the volume of the container and are far apart from each other.SolveIn Figure P1.4 we see that no recombination of the diatomic molecules occurs. The pure element (red–red)condenses to a slightly disordered phase while the other element (blue–blue) remains in the gas phase.Therefore,answer a describes the reaction pictured.Think about ItCooling of air in this fashion to different temperatures separates the components of air.1.5Collect and OrganizeFrom the space-filling model shown,we are to write the formula for the chemical represented.AnalyzeFrom the Atomic Color Palette shown,on the inside back cover of the textbook, we see that this model containsthree hydrogen atoms bonded to a carbon atom which in turn is bonded to anO–H unit.SolveH3COH or CH4OThink about ItThis model representsmethanol,andthe presence of the O–H unit classifies it as an alcohol. Sometimesmethanol is named “wood alcohol.”1.6.Collect and OrganizeFrom the ball and stick model of acetone shown,we are to write the chemical formula.AnalyzeFrom the Atomic Color Palette shown on the inside back cover of the textbook, we see that this model containstwo CH3units bonded to a C–O unit.

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Matter, Energy, and the Origins of the Universe|3SolveH3C(CO)CH3or C3H6OThink about ItAcetone is classified as a ketone and is a useful solvent. It is the main component in nail-polish remover.1.7.Collect and OrganizeThis question considersifandhowmatter and energy are related. In particular, we consider whether the sun isall mass or all energy.AnalyzeEinstein showed that matter and energy are interconvertible throughE=mc2.SolveThe sun is an example where matter is being changed into energy through nuclear fusion reactions. Therefore,both students are correct.Think about ItThrough Einstein’s equation we see that a little bit of mass contains a great deal of energy locked into the nucleiof the atoms.1.8.Collect and OrganizeIn this question, we consider how elements and compounds compare.AnalyzeCompounds can be made from the elements and have different types of atoms in them. Elements are composedof atoms all of the same kind.SolveCompounds are different from elements in that they are made up of two or more elements, these elements canbe separated from each other (but elements cannot be separated further), and compounds have differentchemical and physical properties from the elements that compose them. Elements are also rarely found innature. Compounds are similar to elements in that they are composed of atoms, have definite physical andchemical properties, and can be isolated in pure form.Think about ItBy combining the different elements with each other, we can arrive at many, many compounds which are usedas fuels, medicines, plastics, etc.1.9.Collect and OrganizeFor this question we are to list some chemical and physical properties of gold.AnalyzeA chemical property is seen when a substance undergoes a chemical reaction thereby becoming a differentsubstance. A physical property can be seen without any transformation of one substance into another.SolveOne chemical property of gold is its resistance to corrosion (oxidation). Gold’s physical properties include itsdensity, color, melting temperature, and electrical and thermal conductivity.Think about ItAnother metal that does not corrode (or rust) is platinum. Platinum and gold, along with palladium, are oftencalled “noble metals.”

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4|Chapter 11.10.Collect and OrganizeFor this question we are to compare the physical properties of gold and silver.AnalyzePhysical properties include color, metallic luster, malleability, ductility, melting point, boiling point, density,electrical conductivity, and thermal conductivity.SolveBoth gold and silver have metallic luster, are malleable, and conduct electricity. However, gold and silver havedifferent densities, different melting temperatures, and different colors.Think about ItThe yellow color of pure gold compared to most metals, which are silvery, is due to relativistic effects in theatom.1.11.Collect and OrganizeThis question asks us to use differences in physical or chemical properties to separate a mixture of substances.Using filtration, we are to propose a method to separate salt from sand in a mixture.AnalyzeThe difference between sand and salt is salt’s solubility in water versus sand’s insolubility in water.SolveBy adding water to the salt–sand mixture, the salt will dissolve. Passing the sand–solution mixture through afilter will leave the sand on the filter. The salt can be recovered by evaporating the water from the solution thatpassed through the filter.Think about ItThe filtration method works very well for a mixture of two substances, one of which is soluble and the other ofwhich is insoluble in a solvent, anditis used often to separate and purify a desired product in a chemicalreaction.1.12.Collect and OrganizeWe are to describe how we can use distillation to remove the salt from seawater.AnalyzeDistillation involves the boiling of an impure liquid until the vaporization of the pure liquid occurs. The pureliquid, now a pure compound, is isolated by cooling the vapor through a condenser.SolveWhen seawater is boiled, only the water enters the vapor phase, leaving the salts and other impurities behind.Condensing the vaporized water gives pure water.Think about ItBy distilling seawater, we can render the undrinkable seawater safe to drink.1.13.Collect and OrganizeFor the four processes named, we are to determine which involve a chemical change.AnalyzeChemical changes involve transforming one substance into another to give that substance different physicaland chemical properties.

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Matter, Energy, and the Origins of the Universe|5Solve(a) Distillation purifies a substance—not a chemical change.(b) Combustion transforms the fuel (such as wood) into carbon dioxide and water—a chemical change.(c) Filtration separates substances from each other—not a chemical change.(d) Condensation changes a vapor into a liquid—not a chemical change.Think about ItDistillation, filtration, and condensation all involve physical changes, not chemical changes.1.14.Collect and OrganizeWe are to determine whether gasohol (mixture of gasoline and ethanol) is a heterogeneous or a homogeneousmixture.AnalyzeIn a homogeneous mixture the components are evenly distributed throughout the mixture,giving a uniformappearance to the eye. A heterogeneous mixture contains distinct, observable, individual components.SolveBecause the ethanol is dissolved in the gasoline, we do not see regions of ethanol distinct from regions ofgasoline. Gasohol, therefore, is homogeneous.Think about ItMost cars on the road today can run well on a 10% ethanol to 90% gasoline fuel mixture. There is widespreadinterest in using ethanol as a fuel, despite its expense, because of lower CO and NOxemissions and as a meansto replace reliance on petroleum, a fossil fuel.1.15.Collect and OrganizeFor the foods listed, we are to determine which are heterogeneous.AnalyzeA heterogeneous mixture has visible regions of different compositions.SolveThere are clear regions of differing composition in a Snickers bar (b) and in an uncooked hamburger (d), butnot in solid butter (a) or in grape juice (c).Think about ItWhen butter is melted, you notice that there are milk solids and clear regions that are definitely discernible.Therefore, homogeneous solid butter becomes heterogeneous when heated.1.16.Collect and OrganizeFor the foods listed, we are to determine which are homogeneous.AnalyzeHomogeneous mixtures have the same composition throughout.SolveFreshly brewed coffee and vinegar (a, b) are homogeneous mixtures. A slice of white bread and a slice of ham(c, d) are heterogeneous mixtures.Think about ItA slice of white bread is considered to be heterogeneous because its crust is different from the interior bread,and the bread contains gas bubbles that are clearly seen as tiny holes in the bread.

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6|Chapter 11.17.Collect and OrganizeFor the foods listed, we are to determine which are heterogeneous.AnalyzeA heterogeneous mixture has visible regions of different compositions.SolveThere are clear regions of differing composition in orange juice (with pulp) (d), but not in apple juice, cookingoil, solid butter, or tomato juice (a–c, e).Think about ItWhen butter is melted, you notice that there are milk solids and clear regions that are definitely discernible.Therefore, homogeneous solid butter becomes heterogeneous when heated.1.18.Collect and OrganizeFor the substances listed, we are to determine which are homogeneous.AnalyzeHomogeneous mixtures have the same composition throughout.SolveA wedding ring, sweat, and compressed air in a scuba tank (a, b, e) are homogeneous. Nile River water andhuman blood (c, d) are heterogeneous.Think about ItA gold wedding ring is made up of an alloy (a solid solution of one metal dissolved in another) of gold withanother metal such as palladium or copper to give the soft gold metal strength and make it less expensive than100% gold.1.19.Collect and OrganizeWe are asked in this question to name three properties to distinguish between table sugar, water, and oxygen.AnalyzeWe can distinguish between substances using either physical properties (color, melting point, density, etc.) orchemical properties (chemical reactions, corrosion, flammability, etc.).SolveWe can distinguish between table sugar, water, and oxygen by examining their physical states (sugar is a solid,water is a liquid, and oxygen is a gas) and by their densities, melting points, and boiling points.Think about ItThese three substances are also very different at the atomic level. Oxygen is a pure element made up ofdiatomic molecules, water is a liquid compound made up of discrete molecules of hydrogen and oxygen (H2O),and table sugar is a solid compound made up of carbon, hydrogen, and oxygen atoms.1.20.Collect and OrganizeWe are asked in this question to name three properties to distinguish between table salt, sand, and copper.AnalyzeWe can distinguish between substances using either physical properties (color, melting point, density, etc.) orchemical properties (chemical reactions, corrosion, flammability, etc.).SolveWe can distinguish between table salt, sand, and copper by examining their color (salt is composed of smallcubic white crystals, sand is irregularly shaped and many-colored, and copper is reddish). Salt will dissolve in

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Matter, Energy, and the Origins of the Universe|7water while sand and copper will not. Copper conducts electricity while solid table salt and sand do not. Thedensities of these substances will also differ.Think about ItThese three substances are also very different at the atomic level. Table salt is a crystalline ionic compoundcomposed of sodium cations and chloride anions. Sand is a compound most commonly composed of silica, acompound of silicon and oxygen. Copper is a pure element and a metal.1.21.Collect and OrganizeFrom the list of properties of sodium, we are to determine which are physical and which are chemicalproperties.AnalyzePhysical properties are those that can be observed without transforming the substance into another substance.Chemical properties are only observed when one substance reacts with another and therefore is transformedinto another substance.SolveDensity, melting point, thermal and electrical conductivity, and softness (a–d) are all physical properties whiletarnishing and reaction with water (e and f) are both chemical properties.Think about ItBecause the density of sodium is less than that of water, a piece of sodium will float on water as it reacts.1.22.Collect and OrganizeFrom the list of properties of hydrogen gas, we are to determine which are physical and which are chemicalproperties.AnalyzePhysical properties are those that can be observed without transforming the substance into another substance.Chemical properties are only observed when one substance reacts with another and therefore is transformedinto another substance.SolveDensity, boiling point, and electrical conductivity (a, c, and d) are all physical properties while the reaction ofhydrogen with oxygen (b) is a chemical property.Think about ItBecause the density of hydrogen gas is lower than that of any other gas, a lightweight balloon filled withhydrogen will float in air like the more familiar helium balloon.1.23.Collect and OrganizeIn this question we consider whether distillation or filtration would be a suitable method to separate a protein(enzyme) in egg whites, for example, from water in a solution.AnalyzeDistillation vaporizes a liquid in a mixture and then condenses it in pure form. Filtration separates suspendedsolids from a liquid.SolveDistillation will separate the water and the dissolved proteins that have formed a homogeneous solution withthe water. This would have to be accomplished, however, at low temperature, because heating the solution ofthe enzyme might cause a chemical change.Think about ItFiltration is not appropriate because the enzyme in water forms a homogeneous solution.

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8|Chapter 11.24.Collect and OrganizeFor this question we consider how to separate two phases of water: ice and liquid.AnalyzeWe have two physical methods available to separate mixtures: distillation and filtration. Distillation vaporizesa liquid in a mixture and then condenses it in pure form. Filtration separates suspended solids from a liquid.SolveWater could be separated from ice by simply pouring the water off of the heterogeneous mixture—a crudefiltration.Think about ItDistillation will not work for the obvious reason that heating the ice–water mixture for the distillation willresult in melting of the ice.1.25.Collect and OrganizeFor each of the elements listed, we are to determine the state (gas, liquid, or solid) at room temperature andpressure.AnalyzeSome periodic tables indicate which elements are liquids, which are solids, and which are gases under ordinaryconditions.SolveAt ordinary temperatures Fe is a solid, O2is a gas, and Hg is a liquid.Think about ItMercury is unique in that it is a liquid metal. This arises from relativistic effects that cause the mercury atomsto not be as chemically reactive and to be less willing to share their electrons with other mercury atoms,and sothe metallic bond between mercury atoms is weak.1.26.Collect and OrganizeFrom the list of consumer products,we are to decide which are solid at room temperature and pressure.AnalyzeSolids have a definite volume and shape of their own. Liquids have a definite volume but take on the shape ofthe container. Gases have no definite volume but rather fill their container.SolveAt ordinary temperatures sea salt and ready-to-eat Jell-O are solids,but ketchup is not.Think about ItKetchup would be classified as a liquid since it takes on the shape of its container.1.27.Collect and OrganizeWe are to explain if an extensive property can be used to identify a substance.AnalyzeAn extensive property is one that, like mass, length, and volume, is determined by size or amount.SolveExtensive properties will change with the size of the sample and therefore cannot be used to identify asubstance.

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Matter, Energy, and the Origins of the Universe|9Think about ItWe could, for example, have the same mass of feathers and lead, but their mass alone will not tell us whichmass measurement belongs to which—the feathers or the lead.1.28.Collect and OrganizeOf the properties listed, we are to choose which are intensive properties.AnalyzeAn intensive property is not dependent on the size or amount of the sample.SolveOf the properties on the list, freezing point and temperature are intensive properties. Heat content depends onsample size.Think about ItIntensive properties are related to chemical interactions between atoms and molecules in the substance.1.29.Collect and OrganizeIn this question we think about the information needed to formulate a hypothesis.AnalyzeA hypothesis is a tentative explanation for an observation.SolveTo form a hypothesis we need at least one observation, experiment, or idea (from examining nature).Think about ItA hypothesis that is tested and shown to be valid can become a theory.1.30.Collect and Organize/ AnalyzeIn this question we consider how a hypothesis becomes a theory.SolveA theory is formed from a hypothesis when the hypothesis has been extensively tested by many observationsand experiments. A theory is the best (current) possible explanation that is extensively supported byexperimentation.Think about ItA theory, further tested over time, may be elevated further to become a scientific law.1.31.Collect and OrganizeWe are to consider whether we can disprove a hypothesis.AnalyzeA hypothesis is a tentative explanation for an observation.SolveIt is possible to disprove a scientific hypothesis. In fact, many experiments are designed to do just that as thebest test of the hypothesis’s validity.Think about ItIt is even possible to disprove a theory (albeit harder to do so) or cause a theory to be modified when newevidence, a new experimental technique, or new data from a new instrument give observations that are counterto the explanation stated by the theory.

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10|Chapter 11.32.Collect and OrganizeIn this question we consider why the atomic theory is universally accepted.AnalyzeAtomic theory states that all matter is composed of atoms. This theory is accepted despite the fact thatscientists have not seen atoms directly.SolveThe atomic theory is universally accepted because of the sheer volume of evidence from various experimentsand observations that support the hypothesis that matter is composed of atoms.Think about ItIn the 1980s, the techniques of scanning tunneling microscopy and atomic force microscopy were developed togive us indirect “pictures” of atoms and molecules.1.33.Collect and OrganizeWe are to definetheoryas used in conversation.AnalyzeTheoryin everyday conversation has a different meaning than it does in science.SolveTheoryin normal conversation is someone’s idea or opinion or speculation that can easily be changed and maynot have much evidence or many arguments to support it.Think about ItAtheoryin science is a generally accepted and highly tested explanation of observed facts.1.34.Collect and OrganizeWe consider in this question whether a theory can be proven.AnalyzeTheoryin science is the best (current) possible explanation that is extensively supported by experimentationand observations.SolveTheoryis nearly equivalent to fact in science, without being the absolute truth. A theory is hard to proveabsolutely, but has many, many supporting experiments whose observations strongly support the theory.Think about ItOne experiment that is counter to the explanation for a phenomenon explained by the theory could disprove atheory, so theories may be toppled and replaced with new explanations and theories.1.35.Collect and OrganizeWe are to compare SI units to English units.AnalyzeSI units are based on a decimal system to describe basic units of mass, length, temperature, energy, etc.English units vary.SolveSI units, which were based on the original metric system, can be easily converted into a larger or smaller unitby multiplying or dividing by multiples of 10. English units are more complicated to manipulate. For example,to convert miles to feet you have to know that there are 5280 feet in 1 mile and to convert gallons to quarts youhave to know that 4 quarts are in 1 gallon.

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Matter, Energy, and the Origins of the Universe|11Think about ItOnce you can visualize a meter, a gram, and a liter, using the SI system is quite convenient.1.36.Collect and Organize/ AnalyzeIn this question we are to suggest two reasons why SI units are not more widely used in the United States.SolveEnglish units instead of SI units are used everywhere in the United States because many of our manufacturingfacilities have been built to make parts in inches or to bottle liquids in gallons. It has also been difficult forpeople used to buying and measuring in the English units to convert their thinking so as to visualize akilometer instead of a mile or a liter instead of a quart.Think about ItThe only widespread everyday use of an SI unit in the United States is the 2 L soda bottle.1.37.Collect and OrganizeThis problem asks for the conversion of the speed of light in meters per second into kilometers per hour. Wehave to convert both distance and time into other units. We have to convert from meters (a short unit ofdistance) to kilometers (a longer unit of distance) and from seconds (a short unit of time) to an hour (a longerunit of time). There are several ways to convert these units; the most direct would be from meters to kilometersand from seconds to minutes to hours. We will need, therefore, the following equivalencies:1000 meters=1 kilometer60 seconds=1 minute60 minutes=1 hourAnalyzeThe conversion of units for this problem can be expressed as ratios. Since we are converting from meters tokilometers the following ratio for unit conversions is appropriate:1 km1000 mTo convert seconds to hours the following conversion ratios are appropriate:1 min1 hrand60 s60 minSolve892.997910m1 km60 s60 min1.079210km/hrs1000 m1 min1 hrThink about ItThe speed of light in kilometers per hour is nearly the same order of magnitude as the speed in meters persecond. This makes sense in that to convert from meters to kilometers we divided by 1000 and to convert fromseconds to hours we multiplied by 3.6103. The two conversions, therefore, nearly offset each other.1.38.Collect and OrganizeTo compute the runner’s speed we have to use the definition: speed = distance/time. In the marathon runner’scase we are given distance in miles and time in hours plus additional minutes. The first calculation of speed,therefore, in miles per hour will not require any unit conversion. That result, however, will be used to computethe runner’s speed in meters per second using conversions for miles to meters and hours to seconds.AnalyzeThe equation to compute speed is given bydistanceSpeed =time

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12|Chapter 1Because the time is given as 3 hours 40 minutes, we will have to convert the 40 minutes into a part of an hourusing the fact that 1 hour = 60 minutes. We can then divide the marathon distance by this time in hours to getthe speed in miles per hour.To convert this speed to meters per second, we can use the following conversions:1 km0.6214 miand1000 m1 km1 min1 hrand60 s60 minSolveFirst, the number of hours for the runner to complete the marathon is1 hr3 hr + 40 min3.67 hr60 min(a)The speed in miles per hour is26.2 mispeed =7.14 mi/hr3.67 hr(b)Converting this speed to meters per second givesmi1 km1000 m1 hr1 min7.143.19 m/shr0.6214 mi1 km60 min60 sThink about ItBoth of these values seem reasonable. A walking pace is about 3 miles per hour, so running could be imaginedto be twice that fast. Also, 3 meters per second easily can be run by a fast runner.1.39.Collect and OrganizeFor this problem we need to convert the distance of the Olympic mile (1500 m) in meters to miles and then tofeet to compare that distance to an actual mile using a ratio and then converting that into a percentage.AnalyzeFor converting the distance we can make use of these conversions:1 km0.6214 mi5280 ft,,and1000 m1 km1 miTo determine the percentage the Olympic mile distance is compared to the actual mile we will useOlympic mile distance in feet% distance =1005280 ftSolve1 km0.6214 mi5280 ft1500 m4921 ft1000 m1 km1 mi4920 ft% distance =10093.20%5280 ftThink about ItThis calculation shows that the Olympic mile is just a little bit shorter than the actual mile.1.40.Collect and OrganizeTo compare the prices of the soft drinks, we will have to convert to a common unit of volume, either ounces orliters.

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Matter, Energy, and the Origins of the Universe|13AnalyzeWe can use the following conversions to convert ounces to quarts to liters for the soft drink priced at $1.00 for24 oz:1 qt0.9464 Land32 oz1 qtFor the soft drink already priced per half-liter,the price per liter will be double.Solve$1.0032 oz1 qt$1.41/L24 oz1 qt0.9464 L$0.75$1.50/L0.50 LComparing the two prices in common units, it is better to buy the soft drink in the 24 oz bottles, not the half-liter bottles.Think about ItThis problem can also be solved by converting the half-liter volume to ounces. In that case, the price per ouncein the 24 oz bottle would be 4.2¢ while the price per ounce in the half-liter bottle would be 4.4¢. Theconclusion is the same in either case.1.41.Collect and OrganizeA light-year is the distance light travels in 1 year. To determine the distance of 4.3 light-years in kilometers,we will first have to convert 4.3 years into seconds, then use the speed of light to determine the distance thelight travels over that amount of time.AnalyzeThe length of time of 4.3 years in seconds can be found using the conversions1 yr1 d1 hr1 min,,,365.25 d24 hr60 min60 sThe distance of 4.3 light-years in meters can be found from the speed of light:distance of 4.3 light-years = speed of light (in m/s)4.3 yr (in seconds)This can be converted into kilometers using1 km1000 mSolve8365.25 d24 hr60 min60 s4.3 yr1.3610s1 yr1 d1 hr1 min88132.997910m1 kmDistance of Proxima Centauri = (1.3610s)4.110kms1000 mThink about ItThis is a very large distance since light travels so fast. The light-year, being such a large distance, is an idealunit for expressing astronomical distances.1.42.Collect and OrganizeTo solve this problem, we need to know the volume of water in liters that are to be removed from theswimming pool. Using that volume and the rate at which the water can be siphoned, we can find the time itwill take to remove the water.AnalyzeThe volume of water to be removed in cubic meters can be found fromLength of pool (in m)width of pool (in m)depth of water to be removed (in m)

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14|Chapter 1This volume will have to be converted to liters through the conversion331 L110mThe time it would take to siphon the water is determined by the rate at which the siphon pump operatesvolume of water to be siphoned in litersTime to siphon the water = rate at which the water can be siphoned in liters per secondSolveThe volume of the water to be siphoned out of the pool is (using 6 in = 0.50 ft)31 m50.0 m25.0 m3.0 cm37.5 m100 cmConverting this into gallons34331 L37.5 m3.7510L110mThe amount of time it would take to siphon this water is43.7510LTime to siphon the water =7210 s5.2 L/s1 min7210 s120 min or 2.0 h60 sThink about ItThis may be a surprisingly long time to siphon only 3 cm of water from the pool, but the total volume to besiphoned is quite large due to the size of the pool.1.43.Collect and OrganizeTo find the Calories burned by the wheelchair marathoner in a race,we can first find the number of hours therace will be for the marathoner at the pace of 13.1 miles per hour. The Calories burned can then be calculatedfrom that value and the rate at which the marathoner burns Calories.AnalyzeThe time it takes for the marathoner to complete the race will be given bydistance of the marathonTime to complete the marathon =pace of the marathonerThe Calories burned will be computed byCalories burnedCalories burned =length of the marathon racehourSolve26.2 miTime to complete the marathon =2.00 hr13.1 mi/hr665 CalCalories burned =2.00 hr = 1330 CalhrThink about ItThis problem could be solved without touching a calculator! Because it takes the marathoner 2.00 hr tocomplete the race, the Calories she burns is simply twice the number of Calories she burns in one hour.1.44.Collect and OrganizeTo find how much gas is needed,we need only to convert the miles traveled (389 mi) into the gallons thatwould be used by using the known value of the gas mileage for the SUV (18 mi/gal).

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Matter, Energy, and the Origins of the Universe|15AnalyzeThe number of gallons used in the trip can be computed by1 gallonNumber of gallons used = number of miles travelednumber of milesSolve1 galNumber of gallons used = 389 mi22 gal18 miThink about ItThis is a reasonable value. As a quick estimate you can round the trip to 400 miles and the gas mileage to20 miles per gallon. A quick mental computation gives this to be about 20 gallons. The above answer is,therefore, in the correct range.1.45.Collect and OrganizeThis problem asks for a simple conversion of length: from meters to miles.AnalyzeThe conversions that we need include meters to kilometers and kilometers to miles.1 km0.6214 mi,1000 m1 kmSolve31 km0.6214 mi4.010m2.5 mi1000 m1 kmThink about ItThe answer is reasonable because 4000 meters would be a little over 2 miles when estimated. It is surprising,though, for a natural piece of silk to be that long.1.46.Collect and OrganizeThis problem involves the conversion of one volume unit into another. We have to convert from cubic inchesinto liters via the cubic centimeter and cubic liter. We have to be careful to “cube” the units of length in theconversions to getthevolume.AnalyzeThe conversions needed are31 in1 m1 m,,2.54 cm100 cm1000 LSolve33332.54 cm1 m1000 L292 in4.79 L1 in100 cm1 mCompared to the 2005 Thunderbird with a 3.9 L engine, the 1955 Thunderbird had a bigger engine.Think about ItThis might be a difficult conversion to visualize but the value of 4.79 L is reasonable because the volume of anengine is on the liter scale, not a tenth or tens of liters.1.47.Collect and OrganizeWe can solve this by converting the time it takes the runner to complete the race into seconds, then convertingthe distance of the race from kilometers into meters. The runner’s speed is the ratio of distance (meters) to time(seconds).

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