Observations in Science
1.6 Material Selection and Bicycle Frames
level visualization again shows how the chemical reaction rearranges atoms at the par- ticulate level, it is worth remembering that this process is carried out on a massive scale: the U.S. aluminum industry produces about 2.6 million metric tons of alumi- num per year.
The visualization techniques introduced in this section will help us to develop a particulate level understanding of many concepts we encounter throughout the text.
At this point, let’s take some time to look at one application where the properties of aluminum metal make it a popular material choice for engineering a consumer product—a bicycle.
INSIGHT INTO
Of course, the engineer has more than the choice of material available in mak- ing a design for a bicycle frame. The size and connectivity of the tubing can also be adjusted, for example. Aluminum frames generally feature tubing with a much larger diameter than that in steel or titanium frames. These larger diameter tubes give the frame itself a much stiffer feel—so much so that many cyclists fi nd aluminum frames too stiff to give a comfortable ride. Many modern frames also use tubing that is not round but rather is oval to withstand specifi c types of stress commonly encountered in cycling. Some very expensive frames for competitive cycling are made from more exotic materials. New aluminum alloys containing trace amounts of scandium, for example, can achieve lower frame weights without the large tubing diameters that cause the jarring ride for which aluminum is usually known. The extremely aero- dynamic bikes preferred for high-speed time trial racing are most often made from carbon fiber composites that are molded easily into exotic shapes that reduce air resistance.
Chemistry and chemists have played an essential role in helping engineers develop and exploit these new materials. And the intersection between chemistry and engi- neering illustrated in this chapter for bicycles and soda cans is also apparent in many other familiar products. Throughout this text we’ll look at places where the chemistry we learn has an impact on engineering designs. At this point, we know enough to say that if a lightweight bicycle frame is your desire, you may want to take advantage of aluminum and its low mass density. In Chapter 2, we take the next step and look at atoms and molecules in more detail and simultaneously introduce polymers—another important class of engineering materials.
FO C U S O N P RO B L E M S O LV I N G
Engineering students often wonder whether their college chemistry courses will prove useful later in their careers. Through the opening and closing “Insight” sections of the chapters of this book, we’ll make connections between the content of the chemistry course and places where that content is relevant in engineering applications. But this type of connection isn’t the only place where things learned in chemistry courses help future engineers.
Engineers solve problems. And the exposure to various problem solving tech- niques in courses like this will help you to develop and diversify your skills. We will emphasize this connection after each chapter with a special section like this one. In these “Focus on Problem Solving” sections, we will look at chemistry problems related to the chapter just presented. The difference will be that the “ correct” answer will not be a number but rather the identifi cation of an appropriate strategy for approaching the problem.
Question Describe how you would determine which has a greater mass, a sphere of iron shot with a radius of 4.00 mm or a cube of nickel with an edge length of 4.00 mm. Which formulas are needed, and what other information would have to be looked up?
Strategy Like many real world problems, this question does not have enough information given to provide an answer. To devise a strategy, we have to think about what it takes to compare two materials—in this case iron and nickel. Moreover, we are asked to compare masses of the two materials, so that provides a clue. The dimen- sional information given, along with formulas that are familiar or can be looked up, provides information about volume. Mass and volume were related in this chapter by density, and density values for common materials can be found easily.
Solution To answer this problem, fi rst we need to look up the densities of both iron and nickel. Then, we need to use the data provided to determine the volume of each
sample. For a cube, we can calculate the volume by taking the given measure for the side (s) and cubing it (s 3). The volume of a sphere is given by (4/3)pr 3. Multiplying the density by volume provides the mass, so with the data we looked up for density and the calculated volumes we could answer the question.
S U M M A RY
Chemistry is the science of matter, and since all engineering designs involve matter, the links between chemistry and engi- neering are many. We began to explore the role of materials in engineering by considering aluminum. By applying some very simple chemical concepts, we can begin to understand the trans- formation of aluminum from a precious metal to a common and inexpensive material.
One common trait of an experienced chemist is the abil- ity to consider a given situation from a number of perspectives.
Both the physical and chemical properties of substances can be considered at the macroscopic or microscopic (particulate) level depending on the nature of the question or problem being con- sidered. In addition, chemists often use symbolic representations to describe what is happening in chemical systems. Becoming comfortable with these different perspectives can give students an edge in understanding many chemistry problems.
Chemistry is an empirical science. It relies on experimental observations to develop an understanding of matter. The path from observation toward an understanding of the universe typi- cally involves several steps, relying on inductive or deductive rea- soning, or both. By applying reasoning skills to our observations, we construct models for understanding chemical phenomena.
Then these models are refi ned and adapted over time. The ideas that we will explore in this text involve many models or theories that have been developed through the scientifi c method.
Many of the observations of nature that are used to develop theories and models need to be quantitative, that is, they must assess what is being observed with some level of numerical detail. The need for numerical observations throughout the development of chemistry (and other sciences) has given rise to systematic ways to communicate this information. A number alone is not suffi cient to impart all the meaning of a measure- ment; experimental observations are expected to include units of measurement. An important skill in the study of both chem- istry and engineering is the ability to manipulate numerical information, including the units attached to that information.
The use of ratios to convert between a measurement in one unit and desired information in another related unit represents a core skill for problem solving in chemistry and engineering.
The method of dimensional analysis, sometimes called the fac- tor-label method, provides one common way to carry out these transformations.
We will build on these fundamental ideas as we proceed in the study of chemistry. The ability to look at problems from several perspectives, extract and manipulate numerical informa- tion, and ultimately gain a broad understanding of the chemical principles that underlie the behavior of the universe will provide an interesting challenge as we survey the connections between chemistry and engineering in this book.
K E Y T E R M S
accuracy (1.3) atoms (1.2)
chemical properties (1.2) combustion (1.2)
conceptual chemistry problems (1.5) deductive reasoning (1.3)
density (1.2)
dimensional analysis (1.5) elastic modulus (1.6) elements (1.2)
factor-label method (1.5) gases (1.2)
inductive reasoning (1.3)
laws (1.3) liquids (1.2)
macroscopic perspective (1.2) malleability (1.2)
mass density (1.2) matter (1.2)
microscopic perspective (1.2) molecules (1.2)
particulate perspective (1.2) parts per billion (ppb) (1.4) parts per million (ppm) (1.4) phases of matter (1.2) physical properties (1.2)
precision (1.3) random error (1.3) scientifi c method (1.1) scientifi c models (1.3) scientifi c notation (1.4) signifi cant fi gures (1.4) solids (1.2)
symbolic perspective (1.2) systematic error (1.3) temperature scales (1.4) units (1.4)
visualization in chemistry (1.5) yield strength (1.6)
P RO B L E M S A N D E X E RC I S E S
■ denotes problems assignable in OWL INSIGHT INTO Aluminum
1.1 Use the web to determine the mass of a steel beverage can from the 1970s and the mass of a modern aluminum can. How much more would a 12-pack of soda weigh in steel cans?
1.2 Which properties of aluminum might concern you if you had to use the aluminum tableware that Napoleon employed to impress his guests?
1.3 Where does the scientific method “start”? What is the fi rst step?
1.4 Use the web to determine the amount of aluminum used in the United States in a single year. What is the primary use for this material?
1.5 Use the web to fi nd current prices offered for aluminum for recycling. Is there variation in the price based on where in the United States the aluminum is returned?
1.6 Use the web to determine the differences in the amounts of aluminum recycled in states where there are deposits on aluminum cans versus states where recycling is voluntary.
What is the most reliable way to estimate this value? What uncertainty is there in the estimate?
The Study of Chemistry
1.7 When we make observations in the laboratory, which per- spective of chemistry are we normally using?
1.8 Which of the following items are matter and which are not? (a) a fl ashlight, (b) sunlight, (c) an echo, (d) air at sea level, and (e) air at the top of Mount Everest.
1.9 Which macroscopic characteristics differentiate solids, liq- uids, and gases? (List as many as possible.)
1.10 How can a liquid be distinguished from a fine pow- der? What type of experiment or observation might be undertaken?
1.11 Some farmers use ammonia, NH3, as a fertilizer. This ammonia is stored in liquid form. Use the particulate perspective to show the transition from liquid ammonia to gaseous ammonia.
1.12 Do the terms element and atom mean the same thing? If not, how do they differ?
1.13 ■ Label each of the following as either a physical process or a chemical process: (a) rusting of an iron bridge, (b) melting of ice, (c) burning of a wooden stick, (d) digestion of a baked potato, (e) dissolving of sugar in water
1.14 Why do physical properties play a role in chemistry if they do not involve any chemical changes?
1.15 Physical properties may change because of a chemical change. For example, the color of an egg white changes from clear to white because of a chemical change when it is cooked. Think of another common situation when a chemical change also leads to a physical change.
1.16 ■ Which part of the following descriptions of a compound or element refers to its physical properties and which to its chemical properties?
(a) Calcium carbonate is a white solid with a density of 2.71 g/cm3. It reacts readily with an acid to produce gaseous carbon dioxide.
(b) Gray powdered zinc metal reacts with purple iodine to give a white compound.
1.17 Use a molecular level description to explain why gases are less dense than liquids or solids.
1.18 All molecules attract each other to some extent, and the attraction decreases as the distance between particles in- creases. Based on this idea, which state of matter would you expect has the strongest interactions between particles:
solids, liquids, or gases?
Observations and Models
1.19 We used the example of attendance at a football game to emphasize the nature of observations. Describe another example where deciding how to count subjects of interest could affect the observation.
1.20 Complete the following statement: Data that have a large random error but otherwise fall in a narrow range are (a) accurate, (b) precise, or (c) neither.
1.21 Complete the following statement: Data that have a large systematic error can still be (a) accurate, (b) precise, or (c) neither.
1.22 Two golfers are practicing shots around a putting green.
Each golfer takes 20 shots. Golfer 1 has 7 shots within 1 meter of the hole, and the other 13 shots are scattered around the green. Golfer 2 has 17 shots that go into a small sand trap near the green and 3 just on the green near the trap. Which golfer is more precise? Which is more accurate?
1.23 Use your own words to explain the difference between deductive and inductive reasoning.
1.24 Suppose that you are waiting at a corner for a bus. Three different routes pass this particular corner. You see buses pass by from the two routes that you are not interested in taking. When you say to yourself, “My bus must be next,”
what type of reasoning (deductive or inductive) are you using? Explain your answer.
1.25 When a scientist looks at an experiment and then predicts the results of other related experiments, which type of rea- soning is she using? Explain your answer.
1.26 What is the difference between a hypothesis and a question?
1.27 Should the words theory and model be used interchangeably in the context of science? Defend your answer using infor- mation found in a web search.
1.28 What is a law of nature? Are all scientifi c laws examples of laws of nature?
Numbers and Measurements
1.29 Describe a miscommunication that can arise because units are not included as part of the information.
1.30 What is the difference between a qualitative and a quanti- tative measurement?
1.31 Identify which of the following units are base units in the SI system: grams, meters, joules, liters, amperes.
1.32 What is a “derived” unit?
1.33 Rank the following prefi xes in order of increasing size of the number they represent: centi-, giga-, nano-, and kilo-.
1.34 The largest computers now include disk storage space measured in petabytes. How many bytes are in a petabyte?
(Recall that in computer terminology, the prefix is only
“close” to the value it designates in the metric system.) 1.35 Historically, some unit differences reflected the belief
that the quantity measured was different when it was later revealed to be a single entity. Use the web to look up the origins of the energy units erg and calorie, and describe how they represent an example of this type of historical development.
1.36 Use the web to determine how the Btu was initially estab- lished. For the engineering applications where this unit is still used today, why is it a sensible unit?
1.37 How many micrograms are equal to one gram?
1.38 Convert the value 0.120 ppb into ppm.
1.39 How was the Fahrenheit temperature scale calibrated?
Describe how this calibration process refl ects the measure- ment errors that were evident when the temperature scale was devised.
1.40 ■ Superconductors are materials that have no resistance to the fl ow of electricity, and they hold great promise in many engineering applications. But to date superconductivity has only been observed under cryogenic conditions. The highest temperature at which superconductivity has been observed is 138 K. Convert this temperature to both °C and °F.
1.41 Express each of the following temperatures in kelvins:
(a) −10.°C, (b) 0.00°C, (c) 280.°C, (d) 1.4 × 103°C 1.42 ■ Express (a) 275°C in K, (b) 25.55 K in °C, (c) −47.0°C
in °F, and (d) 100.0°F in K
1.43 Express each of the following numbers in scientifi c notation:
(a) 62.13, (b) 0.000414, (c) 0.0000051, (d) 871,000,000, (e) 9100
1.44 ■ How many signifi cant fi gures are there in each of the fol- lowing? (a) 0.136 m, (b) 0.0001050 g, (c) 2.700 × 10−3 nm, (d) 6 × 10−4 L, (e) 56003 cm3
1.45 ■ How many signifi cant fi gures are present in these mea- sured quantities? (a) 1374 kg, (b) 0.00348 s, (c) 5.619 mm, (d) 2.475 × 10−3 cm, (e) 33.1 mL
1.46 ■ Perform these calculations and express the result with the proper number of signifi cant fi gures.
(a) (4.850 g − 2.34 g)/1.3 mL (b) V = pr 3, where r = 4.112 cm (c) (4.66 × 10−3) × 4.666 (d) 0.003400/65.2
1.47 ■ Calculate the following to the correct number of sig- nificant figures. Assume that all these numbers are measurements.
(a) x = 17.2 + 65.18 − 2.4 (b) x =13.0217/17.10
(c) x = (0.0061020)(2.0092)(1200.00)
(d) x = 0.0034 + √‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾ (0.0034)2 + 4(1.000)(6.3 × 10−4 )
————————————————
(2)(1.000)
1.48 ■ In an attempt to determine the velocity of a person on a bicycle, an observer uses a stopwatch and fi nds the length of time it takes to cover 25 “squares” on a sidewalk. The bicycle takes 4.82 seconds to travel this far. A measurement of one of the squares shows that it is 1.13 m long. What velocity, in m/s, should the observer report?
1.49 A student fi nds that the mass of an object is 4.131 g and its volume is 7.1 mL. What density should be reported in g/mL?
1.50 Measurements indicate that 23.6% of the residents of a city with a population of 531,314 are college graduates.
Considering signifi cant fi gures, how many college gradu- ates are estimated to reside in this city?
1.51 A student weighs 10 quarters and finds that their total mass is 56.63 grams. What should she report as the aver- age mass of a quarter based on her data?
1.52 ■ A rock is placed on a balance and its mass is determined as 12.1 g. When the rock is then placed in a graduated cyl- inder that originally contains 11.3 mL of water, the new volume is roughly 17 mL. How should the density of the rock be reported?
Problem Solving in Chemistry and Engineering
1.53 A package of eight apples has a mass of 1.00 kg. What is the average mass of one apple in grams?
1.54 If a 1.00-kg bag containing eight apples costs $1.48, how much does one apple cost? What mass of apples costs $1.00?
1.55 A person measures 173 cm in height. What is this height in meters? feet and inches?
1.56 The distance between two atoms in a molecule is 148 pm.
What is this distance in meters?
1.57 Carry out the following unit conversions: (a) 3.47 × 10−6 g to μg, (b) 2.73 × 10−4 L to mL, (c) 725 ns to s, (d) 1.3 m to km
1.58 ■ Carry out each of the following conversions: (a) 25.5 m to km, (b) 36.3 km to m, (c) 487 kg to g, (d) 1.32 L to mL, (e) 55.9 dL to L, (f ) 6251 L to cm3
1.59 ■ Convert 22.3 mL to (a) liters, (b) cubic inches, and (c) quarts.
1.60 ■ If a vehicle is traveling 92 m/s, what is its velocity in miles per hour? (0.62 miles = 1.00 km)
1.61 ■ A load of asphalt weights 254 lbs. and occupies a volume of 220.0 L. What is the density of this asphalt in g/L?
1.62 ■ One square mile contains exactly 640 acres. How many square meters are in one acre?
1.63 ■ A sample of crude oil has a density of 0.87 g/mL. What volume in liters does a 3.6-kg sample of this oil occupy?
1.64 Mercury has a density of 13.6 g/mL. What is the mass of 4.72 L of mercury?
1.65 ■ The area of the 48 contiguous states is 3.02 × 106 mi2. Assume that these states are completely fl at (no mountains and no valleys). What volume of water, in liters, would cover these states with a rainfall of two inches?
1.66 ■ The dimensions of aluminum foil in a box for sale in su- permarkets are 66 2/3 yards by 12 inches. The mass of the foil is 0.83 kg. If its density is 2.70 g/cm3, then what is the thickness of the foil in inches?
1.67 ■ Titanium is used in airplane bodies because it is strong and light. It has a density of 4.55 g/cm3. If a cylinder of titanium is 7.75 cm long and has a mass of 153.2 g, calcu- late the diameter of the cylinder. (V = pr 2h, where V is the volume of the cylinder, r is its radius, and h is the height.) 1.68 ■ Wire is often sold in pound spools according to the wire
gauge number. That number refers to the diameter of the wire. How many meters are in a 10-lb spool of 12-gauge alu- minum wire? A 12-gauge wire has a diameter of 0.0808 in.
and aluminum has a density of 2.70 g/cm3. (V = pr 2l ) 1.69 ■ An industrial engineer is designing a process to manufac-
ture bullets. The mass of each bullet must be within 0.25%
of 150 grains. What range of bullet masses, in mg, will meet this tolerance? 1 gr = 64.79891 mg.
1.70 ■ An engineer is working with archaeologists to create a re- alistic Roman village in a museum. The plan for a balance in a marketplace calls for 100 granite stones, each weighing 10 denarium. (The denarium was a Roman unit of mass:
1 denarium = 3.396 g.) The manufacturing process for mak- ing the stones will remove 20% of the material. If the granite to be used has a density of 2.75 g/cm3, what is the minimum volume of granite that the engineer should order?
1.71 Draw a molecular scale picture to show how a crystal dif- fers from a liquid.
1.72 Draw a molecular scale picture that distinguishes between alumina and silica. Is your picture structurally accurate or schematic?
1.73 ■ On average, Earth’s crust contains about 8.1% aluminum by mass. If a standard 12-ounce soft drink can contains ap- proximately 15.0 g of aluminum, how many cans could be made from one ton of the Earth’s crust?
1.74 ■ As computer processor speeds increase, it is necessary for engineers to increase the number of circuit elements packed into a given area. Individual circuit elements are often connected using very small copper “wires” deposited directly onto the surface of the chip. In some current gen- eration processors, these copper interconnects are about 65 nm wide. What mass of copper would be in a 1-mm length of such an interconnect, assuming a square cross section? The density of copper is 8.96 g/cm3.
INSIGHT INTO Material Selection and Bicycle Frames 1.75 Suppose that a new material has been devised with an elas-
tic modulus of 22.0 × 106 psi for a bicycle frame. Is this bike frame likely to be more or less stiff than an aluminum frame?
1.76 Rank aluminum, steel, and titanium in order of increasing stiffness.
1.77 Compare the strengths of aluminum, steel, and titanium.
If high strength were needed for a particular design, would aluminum be a good choice?
1.78 Aluminum is not as strong as steel. What other factor should be considered when comparing the desirability of aluminum versus steel if strength is important for a design?
1.79 Use the web to research the differences in the design of steel-framed bicycles versus aluminum-framed bicycles.
Write a short paragraph that details the similarities and differences you discover.
1.80 Use the web to research the elastic modulus and yield strength of carbon fi ber composites. How do these materi- als compare to aluminum, steel, and titanium?
1.81 Use the web to research the relative cost of aluminum, steel, and titanium frames for bicycles. Speculate about how much of the relative cost is due to the costs of the materials themselves.
FOCUS ON PROBLEM SOLVING EXERCISES 1.82 A student was given two metal cubes that looked similar.
One was 1.05 cm on an edge and had a mass of 14.32 grams;
the other was 2.66 cm on a side and had a mass of 215.3 grams. How can the student determine if these two cubes of metal are the same material using only the data given?
1.83 Battery acid has a density of 1.285 g/mL and contains 38.0% sulfuric acid by mass. Describe how you would de- termine the mass of pure sulfuric acid in a car battery, not- ing which item(s) you would have to measure or look up.
1.84 Unfermented grape juice used to make wine is called a
“must.” The sugar content of the must determines whether the wine will be dry or sweet. The sugar content is found by measuring the density of the must. If the density is lower than 1.070 g/mL, then sugar syrup is added until the density reaches 1.075 g/mL. Suppose that you have a sam- ple taken from a must whose mass is 47.28 g and whose volume is 44.60 mL. Describe how you would determine whether or not sugar syrup needs to be added and if so, how would you estimate how much sugar syrup to add?
1.85 A solution of ethanol in water has a volume of 54.2 mL and a mass of 49.6 g. What information would you need to look up and how would you determine the percentage of ethanol in this solution?
1.86 Legend has it that Archimedes, a famous scientist of An- cient Greece, was once commanded by the king to deter- mine if a crown he received was pure gold or a gold−silver alloy. He was not allowed, however, to damage the crown (by slicing off a piece, for example). If you were assigned this same task, what would you need to know about both gold and silver, and how would you make a measurement that would tell you if the crown was pure gold?
1.87 Imagine that you place a cork measuring 1.30 cm × 4.50 cm × 3.00 cm in a pan of water. On top of this cork, you place a small cube of lead measuring 1.15 cm on a side.
Describe how you would determine if the combination of the cork and lead cube will still fl oat in the water. Note any information you would need to look up to answer the question.
1.88 A calibrated flask was filled to the 25.00-mL mark with ethyl alcohol and it was found to have a mass of 19.7325 g.
In a second experiment, 25.0920 g of metal beads were put into the container and the fl ask was again fi lled to the 25.00-mL mark. The total mass of the metal plus the alco- hol was 43.0725 g. Describe how to determine the density of the metal sample.