Chapter Questions
a. There are 365 days per year, 24 hours per day, 12 months per year, and 60 minutes per hour. Use these data to determine how many minutes are in a month.b. Now use the following data to calculate the number of minutes in a month: 24 hours per day, 60 minutes per hour, 7 days per week, and 4 weeks per month.c. Why are these answers different? Which (if any) is more correct? Why?
You go to a convenience store to buy candy and find the owner to be rather odd. He allows you to buy pieces in multiples of four, and to buy four, you need $\$ 0.23 .$ He only allows you to do this by using 3 pennies and 2 dimes. You have a bunch of pennies and dimes, and instead of counting them, you decide to weigh them. You have $636.3 \mathrm{~g}$ of pennies, and each penny weighs $3.03 \mathrm{~g}$. Each dime weighs $2.29 \mathrm{~g}$. Each piece of candy weighs $10.23 \mathrm{~g}$.a. How many pennies do you have?b. How many dimes do you need to buy as much candy as possible?c. How much should all these dimes weigh?d. How many pieces of candy could you buy? (number of dimes from part b)e. How much would this candy weigh?f. How many pieces of candy could you buy with twice as many dimes?
When a marble is dropped into a beaker of water, it sinks to the bottom. Which of the following is the best explanation?a. The surface area of the marble is not large enough to be held up by the surface tension of the water.b. The mass of the marble is greater than that of the water.c. The marble weighs more than an equivalent volume of the water.d. The force from dropping the marble breaks the surface tension of the water.e. The marble has greater mass and volume than the water. Justify your choice, and for choices you did not pick, explain what is wrong about them.
You have two beakers, one filled to the $100-\mathrm{mL}$ mark with sugar (the sugar has a mass of $180.0 \mathrm{~g}$ ) and the other filled to the $100-\mathrm{mL}$ mark with water (the water has a mass of $100.0 \mathrm{~g}$ ). You pour all the sugar and all the water together in a bigger beaker and stir until the sugar is completely dissolved.a. Which of the following is true about the mass of the solution? Explain.i. It is much greater than $280.0 \mathrm{~g}$.ii. It is somewhat greater than $280.0 \mathrm{~g}$.iii. It is exactly $280.0 \mathrm{~g}$.iv. It is somewhat less than $280.0 \mathrm{~g}$.v. It is much less than $280.0 \mathrm{~g}$.b. Which of the following is true about the volume of the solution? Explain.i. It is much greater than $200.0 \mathrm{~mL}$.ii. It is somewhat greater than $200.0 \mathrm{~mL}$.iii. It is exactly $200.0 \mathrm{~mL}$.iv. It is somewhat less than $200.0 \mathrm{~mL}$.v. It is much less than $200.0 \mathrm{~mL}$.
You may have noticed that when water boils, you can see bubbles that rise to the surface of the water.a. What is inside these bubbles?i. airii. hydrogen and oxygen gasiii. oxygen gas iv. water vaporv. carbon dioxide gasb. Is the boiling of water a chemical or physical change? Explain.
If you place a glass rod over a burning candle, the glass appears to turn black. What is happening to each of the following (physical change, chemical change, both, or neither) as the candle burns? Explain each answer.a. the waxb. the wickc. the glass rod
Which characteristics of a solid, a liquid, and a gas are exhibited by each of the following substances? How would you classify each substance?a. a bowl of puddingb. a bucketful of sand
You have water in each graduated cylinder shown:You then add both samples to a beaker. How would you write the number describing the total volume? What limits the precision of this number?
Paracelsus, a sixteenth-century alchemist and healer, adopted as his slogan: "The patients are your textbook, the sickbed is your study." Is this view consistent with using the scientific method?
What is wrong with the following statement? "The results of the experiment do not agree with the theory. Something must be wrong with the experiment."
Why is it incorrect to say that the results of a measurement were accurate but not precise?
What data would you need to estimate the money you would spend on gasoline to drive your car from New York to Chicago? Provide estimates of values and a sample calculation.
Sketch two pieces of glassware: one that can measure volume to the thousandths place and one that can measure volume only to the ones place.
You have a $1.0-\mathrm{cm}^{3}$ sample of lead and a $1.0-\mathrm{cm}^{3}$ sample of glass. You drop each in separate beakers of water. How do the volumes of water displaced by each sample compare? Explain.
Sketch a magnified view (showing atoms/molecules) of each of the following and explain:a. a heterogeneous mixture of two different compoundsb. a homogeneous mixture of an element and a compound
You are driving $65 \mathrm{mi} / \mathrm{h}$ and take your eyes off the road for "just a second." What distance (in feet) do you travel in this time?
Consider the addition of $15.4$ to 28 . What would a mathematician say the answer is? What would a scientist say? Justify the scientist's answer, not merely citing the rule, but explaining it.
Consider multiplying $26.2$ by $16.43 .$ What would a mathematician say the answer is? What would a scientist say? Justify the scientist's answer, not merely citing the rule, but explaining it.
The difference between a law and a theory is the difference between what and why. Explain.
The scientific method is a dynamic process. What does this mean?
Explain the fundamental steps of the scientific method.
What is the difference between random error and systematic error?
A measurement is a quantitative observation involving both a number and a unit. What is a qualitative observation? What are the SI units for mass, length, and volume? What is the assumed uncertainty in a number (unless stated otherwise)? The uncertainty of a measurement depends on the precision of the measuring device. Explain.
To determine the volume of a cube, a student measured one of the dimensions of the cube several times. If the true dimension of the cube is $10.62 \mathrm{~cm}$, give an example of four sets of measurements that would illustrate the following.a. imprecise and inaccurate datab. precise but inaccurate datac. precise and accurate data Give a possible explanation as to why data can be imprecise or inaccurate. What is wrong with saying a set of measurements is imprecise but accurate?
What are significant figures? Show how to indicate the number one thousand to 1 significant figure, 2 significant figures, 3 significant figures, and 4 significant figures. Why is the answer, to the correct number of significant figures, not $1.0$ for the following calculation?$$\frac{1.5-1.0}{0.50}=$$
What is the volume per unit mass equal to? What unit conversion would the volume per unit mass be useful for?
When the temperature in degrees Fahrenheit $\left(T_{\mathrm{F}}\right)$ is plotted versus the temperature in degrees Celsius $\left(T_{\mathrm{C}}\right)$, a straight-line plot results. A straight-line plot also results when $T_{\mathrm{C}}$ is plotted versus $T_{\mathrm{K}}$ (the temperature in kelvins). Reference Appendix $\mathrm{A} 1.3$ and determine the slope and $y$ -intercept of each of these two plots.
Give four examples illustrating each of the following terms.a. homogeneous mixtured. elementb. heterogeneous mixturee. physical changec. compoundf. chemical change
Which of the following are exact numbers?a. There are $100 \mathrm{~cm}$ in $1 \mathrm{~m}$.b. One meter equals $1.094$ yards.c. We can use the equation${ }^{\circ} \mathrm{F}=\frac{9 \circ}{2} \mathrm{C}+32$to convert from Celsius to Fahrenheit temperature. Are the numbers $\frac{9}{3}$ and 32 exact or inexact?d. $\pi=3.1415927$.
Indicate the number of significant figures in each of the following:a. This book contains more than 1000 pages.b. A mile is about $5300 \mathrm{ft}$.c. A liter is equivalent to $1.059$ qt.d. The population of the United States is approaching $3.0 \times 10^{2}$ million.e. A kilogram is $1000 \mathrm{~g}$.f. The Boeing 747 cruises at around $600 \mathrm{mi} / \mathrm{h}$.
How many significant figures are there in each of the following values?a. $6.07 \times 10^{-15}$e. $463.8052$b. $0.003840$f. 300c. $17.00$g. 301d. $8 \times 10^{8}$h. 300 .
How many significant figures are in each of the following?a. 100e. $0.0048$b. $1.0 \times 10^{2}$f. $0.00480$c. $1.00 \times 10^{3}$g. $4.80 \times 10^{-3}$d. 100 .h. $4.800 \times 10^{-3}$
Round off each of the following numbers to the indicated number of significant digits and write the answer in standard scientific notation.a. $0.00034159$ to three digitsb. $103.351 \times 10^{2}$ to four digitsc. $17.9915$ to five digitsd. $3.365 \times 10^{5}$ to three digits
Use exponential notation to express the number 385,500 toa. one significant figure.b. two significant figures.c. three significant figures.d. five significant figures.
Evaluate each of the following and write the answer to the appropriate number of significant figures.a. $212.2+26.7+402.09$b. $1.0028+0.221+0.10337$c. $52.331+26.01-0.9981$d. $2.01 \times 10^{2}+3.014 \times 10^{3}$e. $7.255-6.8350$
Perform the following mathematical operations, and express each result to the correct number of significant figures.a. $\frac{0.102 \times 0.0821 \times 273}{1.01}$b. $0.14 \times 6.022 \times 10^{23}$c. $4.0 \times 10^{4} \times 5.021 \times 10^{-3} \times 7.34993 \times 10^{2}$d. $\frac{2.00 \times 10^{6}}{3.00 \times 10^{-7}}$
Perform the following mathematical operations and express the result to the correct number of significant figures.a. $\frac{2.526}{3.1}+\frac{0.470}{0.623}+\frac{80.705}{0.4326}$b. $(6.404 \times 2.91) /(18.7-17.1)$c. $6.071 \times 10^{-5}-8.2 \times 10^{-6}-0.521 \times 10^{-4}$d. $\left(3.8 \times 10^{-12}+4.0 \times 10^{-13}\right) /\left(4 \times 10^{12}+6.3 \times 10^{13}\right)$e. $\frac{9.5+4.1+2.8+3.175}{4}$(Assume that this operation is taking the average of four numbers. Thus 4 in the denominator is exact.)f. $\frac{8.925-8.905}{8.925} \times 100$(This type of calculation is done many times in calculating a percentage error. Assume that this example is such a calculation; thus 100 can be considered to be an exact number.)
Perform the following mathematical operations, and express the result to the correct number of significant figures.a. $6.022 \times 10^{23} \times 1.05 \times 10^{2}$b. $\frac{6.6262 \times 10^{-34} \times 2.998 \times 10^{8}}{2.54 \times 10^{-9}}$c. $1.285 \times 10^{-2}+1.24 \times 10^{-3}+1.879 \times 10^{-1}$d. $\frac{(1.00866-1.00728)}{6.02205 \times 10^{2.3}}$e. $\frac{9.875 \times 10^{2}-9.795 \times 10^{2}}{9.875 \times 10^{2}} \times 100(100$ is exact)f. $\frac{9.42 \times 10^{2}+8.234 \times 10^{2}+1.625 \times 10^{3}}{3}(3$ is exact)
Perform each of the following conversions.a. $8.43 \mathrm{~cm}$ to millimetersb. $2.41 \times 10^{2} \mathrm{~cm}$ to metersc. $294.5 \mathrm{~nm}$ to centimetersd. $1.445 \times 10^{4} \mathrm{~m}$ to kilometerse. $235.3 \mathrm{~m}$ to millimetersf. $903.3 \mathrm{~nm}$ to micrometers
a. How many kilograms are in one teragram?b. How many nanometers are in $6.50 \times 10^{2}$ terameters?c. How many kilograms are in 25 femtograms?d. How many liters are in $8.0$ cubic decimeters?e. How many microliters are in one milliliter?f. How many picograms are in one microgram?
Perform the following unit conversions.a. Congratulations! You and your spouse are the proud parents of a new baby, born while you are studying in a country that uses the metric system. The nurse has informed you that the baby weighs $3.91 \mathrm{~kg}$ and measures $51.4 \mathrm{~cm}$. Convert your baby's weight to pounds and ounces and her length to inches (rounded to the nearest quarter inch).b. The circumference of the earth is $25,000 \mathrm{mi}$ at the equator. What is the circumference in kilometers? in meters?c. A rectangular solid measures $1.0 \mathrm{~m}$ by $5.6 \mathrm{~cm}$ by $2.1 \mathrm{dm} .$ Express its volume in cubic meters, liters, cubic inches, and cubic feet.
Perform the following unit conversions.a. 908 oz to kilogramsb. $12.8 \mathrm{~L}$ to gallonsc. $125 \mathrm{~mL}$ to quartsd. $2.89$ gal to milliliterse. $4.48 \mathrm{lb}$ to gramsf. $550 \mathrm{~mL}$ to quarts
Use the following exact conversion factors to perform the stated calculations:$$\begin{aligned}5 \frac{1}{2} \text { yards } &=1 \text { rod } \\40 \text { rods } &=1 \text { furlong } \\8 \text { furlongs } &=1 \mathrm{mile}\end{aligned}$$a. The Kentucky Derby race is $1.25$ miles. How long is the race in rods, furlongs, meters, and kilometers?b. A marathon race is 26 miles, 385 yards. What is this distance in rods, furlongs, meters, and kilometers?
Although the preferred SI unit of area is the square meter, land is often measured in the metric system in hectares (ha). One hectare is equal to $10,000 \mathrm{~m}^{2}$. In the English system, land is often measured in acres ( 1 acre $=160$ rod $^{2}$ ). Use the exact conversions and those given in Exercise 43 to calculate the following.a. $1 \mathrm{ha}=$$\mathrm{km}^{2}$b. The area of a $5.5$ -acre plot of land in hectares, square meters, and square kilometers.c. A lot with dimensions $120 \mathrm{ft}$ by $75 \mathrm{ft}$ is to be sold for $\$ 6500$. What is the price per acre? What is the price per hectare?
Precious metals and gems are measured in troy weights in the English system:$\begin{aligned} 24 \text { grains } &=1 \text { pennyweight (exact) } \\ 20 \text { pennyweight } &=1 \text { troy ounce (exact) } \\ 12 \text { troy ounces } &=1 \text { troy pound (exact) } \\ 1 \text { grain } &=0.0648 \text { gram } \\ 1 \text { carat } &=0.200 \mathrm{gram} \end{aligned}$a. The most common English unit of mass is the pound avoirdupois. What is one troy pound in kilograms and in pounds?b. What is the mass of a troy ounce of gold in grams and in carats?c. The density of gold is $19.3 \mathrm{~g} / \mathrm{cm}^{3} .$ What is the volume of a troy pound of gold?
Apothecaries (druggists) use the following set of measures in the English system:$$\begin{aligned}20 \text { grains ap } &=1 \text { scruple (exact) } \\3 \text { scruples } &=1 \text { dram ap (exact) } \\8 \text { dram ap } &=1 \text { oz ap (exact) } \\1 \text { dram ap } &=3.888 \mathrm{~g}\end{aligned}$$a. Is an apothecary grain the same as a troy grain? (See Exercise $45 .$ )b. 1 oz ap $=$ oz troy.c. An aspirin tablet contains $5.00 \times 10^{2} \mathrm{mg}$ of active ingredient. What mass in grains ap of active ingredient does it contain? What mass in scruples?d. What is the mass of 1 scruple in grams?
Science fiction often uses nautical analogies to describe space travel. If the starship U.S.S. Enterprise is traveling at warp factor $1.71$, what is its speed in knots and in miles per hour? (Warp $1.71=5.00$ times the speed of light; speed of light $=$ $3.00 \times 10^{\mathrm{s}} \mathrm{m} / \mathrm{s} ; 1 \mathrm{knot}=2000 \mathrm{yd} / \mathrm{h}$, exactly. $)$
The world record for the hundred meter dash is $9.74 \mathrm{~s}$. What is the corresponding average speed in units of $\mathrm{m} / \mathrm{s}, \mathrm{km} / \mathrm{h}, \mathrm{ft} / \mathrm{s}$, and $\mathrm{mi} / \mathrm{h}$ ? At this speed, how long would it take to run $1.00 \times 10^{2}$ yards?
Would a car traveling at a constant speed of $65 \mathrm{~km} / \mathrm{h}$ violate a40. mi/h speed limit?
You pass a road sign saying "New York $112 \mathrm{~km}$." If you drive at a constant speed of $65 \mathrm{mi} / \mathrm{h}$, how long should it take you to reach New York? If your car gets 28 miles to the gallon, how many liters of gasoline are necessary to travel $112 \mathrm{~km}$ ?
You are in Paris, and you want to buy some peaches for lunch. The sign in the fruit stand indicates that peaches cost $2.45$ euros per kilogram. Given that 1 euro is equivalent to approximately $\$ 1.46$, calculate what a pound of peaches will cost in dollars.
Carbon monoxide (CO) detectors sound an alarm when peak levels of carbon monoxide reach 100 parts per million (ppm). This level roughly corresponds to a composition of air that contains $400,000 \mu \mathrm{g}$ carbon monoxide per cubic meter of air $\left(400,000 \mu \mathrm{g} / \mathrm{m}^{3}\right)$. Assuming the dimensions of a room are $18 \mathrm{ft} \times$ $12 \mathrm{ft} \times 8 \mathrm{ft}$, estimate the mass of carbon monoxide in the room that would register $100 \mathrm{ppm}$ on a carbon monoxide detector.
Convert the following Fahrenheit temperatures to the Celsius and Kelvin scales.a. $-459^{\circ} \mathrm{F}$, an extremely low temperatureb. $-40 .{ }^{\circ} \mathrm{F}$, the answer to a trivia questionc. $68^{\circ} \mathrm{F}$, room temperatured. $7 \times 10^{7}{ }^{\circ} \mathrm{F}$, temperature required to initiate fusion reactions in the sun
A thermometer gives a reading of $96.1^{\circ} \mathrm{F} \pm 0.2^{\circ} \mathrm{F}$. What is the temperature in ${ }^{\circ} \mathrm{C}$ ? What is the uncertainty?
Convert the following Celsius temperatures to Kelvin and to Fahrenheit degrees.a. the temperature of someone with a fever, $39.2^{\circ} \mathrm{C}$b. a cold wintery day, $-25^{\circ} \mathrm{C}$c. the lowest possible temperature, $-273^{\circ} \mathrm{C}$d. the melting-point temperature of sodium chloride, $801^{\circ} \mathrm{C}$
Convert the following Kelvin temperatures to Celsius and Fahrenheit degrees.a. the temperature that registers the same value on both the Fahrenheit and Celsius scales, $233 \mathrm{~K}$b. the boiling point of helium, $4 \mathrm{~K}$c. the temperature at which many chemical quantities are determined, $298 \mathrm{~K}$d. the melting point of tungsten, $3680 \mathrm{~K}$
At what temperature is the temperature in degrees Fahrenheit equal to twice the temperature in degrees Celsius?
The average daytime temperatures on earth and Jupiter are $72^{\circ} \mathrm{F}$ and $313 \mathrm{~K}$, respectively. Calculate the difference in temperature, in ${ }^{\circ} \mathrm{C}$, between these two planets.
A material will float on the surface of a liquid if the material has a density less than that of the liquid. Given that the density of water is approximately $1.0 \mathrm{~g} / \mathrm{mL}$, will a block of material having a volume of $1.2 \times 10^{4} \mathrm{in}^{3}$ and weighing $350 \mathrm{lb}$ float or sink when placed in a reservoir of water?
For a material to float on the surface of water, the material must have a density less than that of water $(1.0 \mathrm{~g} / \mathrm{mL})$ and must not react with the water or dissolve in it. A spherical ball has a radius of $0.50 \mathrm{~cm}$ and weighs $2.0 \mathrm{~g}$. Will this ball float or sink when placed in water? (Note: Volume of a sphere $=\frac{4}{3} \pi r^{3}$.)
A star is estimated to have a mass of $2 \times 10^{36} \mathrm{~kg}$. Assuming it to be a sphere of average radius $7.0 \times 10^{5} \mathrm{~km}$, calculate the average density of the star in units of grams per cubic centimeter.
A rectangular block has dimensions $2.9 \mathrm{~cm} \times 3.5 \mathrm{~cm} \times 10.0 \mathrm{~cm}$. The mass of the block is $615.0 \mathrm{~g}$. What are the volume and density of the block?
Diamonds are measured in carats, and 1 carat $=0.200 \mathrm{~g}$. The density of diamond is $3.51 \mathrm{~g} / \mathrm{cm}^{3}$.a. What is the volume of a $5.0$ -carat diamond?b. What is the mass in carats of a diamond measuring $2.8 \mathrm{~mL}$ ?
Ethanol and benzene dissolve in each other. When $100 . \mathrm{mL}$ of ethanol is dissolved in $1.00 \mathrm{~L}$ of benzene, what is the mass of the mixture? (See Table $1.5$.)
A sample containing $33.42 \mathrm{~g}$ of metal pellets is poured into a graduated cylinder initially containing $12.7 \mathrm{~mL}$ of water, causing the water level in the cylinder to rise to $21.6 \mathrm{~mL}$. Calculate the density of the metal.
The density of pure silver is $10.5 \mathrm{~g} / \mathrm{cm}^{3}$ at $20^{\circ} \mathrm{C}$. If $5.25 \mathrm{~g}$ of pure silver pellets is added to a graduated cylinder containing $11.2 \mathrm{~mL}$ of water, to what volume level will the water in the cylinder rise?
In each of the following pairs, which has the greater mass? (See Table 1.5.)a. $1.0 \mathrm{~kg}$ of feathers or $1.0 \mathrm{~kg}$ of leadb. $1.0 \mathrm{~mL}$ of mercury or $1.0 \mathrm{~mL}$ of waterc. $19.3 \mathrm{~mL}$ of water or $1.00 \mathrm{~mL}$ of goldd. $75 \mathrm{~mL}$ of copper or $1.0 \mathrm{~L}$ of benzene
a. Calculate the mass of ethanol in $1.50$ qt of ethanol. (See Table $1.5 .$ )b. Calculate the mass of mercury in $3.5 \mathrm{in}^{3}$ of mercury. (See Table $1.5 .$ )
In each of the following pairs, which has the greater volume?a. $1.0 \mathrm{~kg}$ of feathers or $1.0 \mathrm{~kg}$ of leadb. $100 \mathrm{~g}$ of gold or $100 \mathrm{~g}$ of waterc. $1.0 \mathrm{~L}$ of copper or $1.0 \mathrm{~L}$ of mercury
Using Table $1.5$, calculate the volume of $25.0 \mathrm{~g}$ of each of the following substances at 1 atm.a. hydrogen gasb. waterc. ironChapter 5 discusses the properties of gases. One property unique to gases is that they contain mostly empty space. Explain using the results of your calculations.
The density of osmium (the densest metal) is $22.57 \mathrm{~g} / \mathrm{cm}^{3} .$ If a $1.00-\mathrm{kg}$ rectangular block of osmium has two dimensions of $4.00 \mathrm{~cm} \times 4.00 \mathrm{~cm}$, calculate the third dimension of the block.
A copper wire (density $=8.96 \mathrm{~g} / \mathrm{cm}^{3}$ ) has a diameter of $0.25 \mathrm{~mm}$. If a sample of this copper wire has a mass of $22 \mathrm{~g}$, how long is the wire?
Match each description below with the following microscopic pictures. More than one picture may fit each description. A picture may be used more than once or not used at all.a. a gaseous compoundb. a mixture of two gaseous elementsc. a solid elementd. a mixture of a gaseous element and a gaseo
Define the following terms: solid, liquid, gas, pure substance, element, compound, homogeneous mixture, heterogeneous mixture, solution, chemical change, physical change.
What is the difference between homogeneous and heterogeneous matter? Classify each of the following as homogeneous or heterogeneous.a. a doorb. the air you breathec. a cup of coffee (black)d. the water you drinke. salsaf. your lab partner
Classify the following mixtures as homogeneous or as heterogeneous.a. potting soild. window glassb. white winee. granitec. your sock drawer
Classify each of the following as a mixture or a pure substance.a. waterf. uraniumb. bloodg. winec. the oceansh. leatherd. ironi. table salte. brass Of the pure substances, which are elements and which are compounds?
Suppose a teaspoon of magnesium filings and a teaspoon of powdered sulfur are placed together in a metal beaker. Would this constitute a mixture or a pure substance? Suppose the magnesium filings and sulfur are heated so they react with each other, forming magnesium sulfide. Would this still be a "mixture"? Why or why not?
If a piece of hard white blackboard chalk is heated strongly in a flame, the mass of the piece of chalk will decrease, and eventually the chalk will crumble into a fine white dust. Does this change suggest that the chalk is composed of an element or a compound?
During a very cold winter, the temperature may remain below freezing for extended periods. However, fallen snow can still disappear, even though it cannot melt. This is possible because a solid can vaporize directly, without passing through the liquid state. Is this process (sublimation) a physical or a chemical change?
Classify the following as physical or chemical changes.a. Moth balls gradually vaporize in a closet.b. Hydrofluoric acid attacks glass, and is used to etch calibration marks on glass laboratory utensils.c. A French chef making a sauce with brandy is able to burn off the alcohol from the brandy, leaving just the brandy flavoring.d. Chemistry majors sometimes get holes in the cotton jeans they wear to lab because of acid spills.
The properties of a mixture are typically averages of the properties of its components. The properties of a compound may differ dramatically from the properties of the elements that combine to produce the compound. For each process described below, state whether the material being discussed is most likely a mixture or a compound, and state whether the process is a chemical change or a physical change.a. An orange liquid is distilled, resulting in the collection of a yellow liquid and a red solid.b. A colorless, crystalline solid is decomposed, yielding a pale yellow-green gas and a soft, shiny metal.c. A cup of tea becomes sweeter as sugar is added to it.
For a pharmacist dispensing pills or capsules, it is often easier to weigh the medication to be dispensed than to count the individual pills. If a single antibiotic capsule weighs $0.65 \mathrm{~g}$, and a pharmacist weighs out $15.6 \mathrm{~g}$ of capsules, how many capsules have been dispensed?
Lipitor, a pharmaceutical drug that has been shown to lower "bad" cholesterol levels while raising "good" cholesterol levels in patients taking the drug, had over $\$ 11$ billion in sales in 2006 . Assuming one $2.5$ -g pill contains $4.0 \%$ of the active ingredient by mass, what mass in $\mathrm{kg}$ of active ingredient is present in one bottle of 100 . pills?
A children's pain relief elixir contains $80 . \mathrm{mg}$ acetaminophen per $0.50$ teaspoon. The dosage recommended for a child who weighs between 24 and $35 \mathrm{lb}$ is $1.5$ teaspoons. What is the range of acetaminophen dosages, expressed in mg acetaminophen/kg body weight, for children who weigh between 24 and $35 \mathrm{lb}$ ?
This year, like many past years, you begin to feel very sleepy after eating a large helping of Thanksgiving turkey. Some people attribute this sleepiness to presence of the amino acid tryptophan in turkey. Tryptophan can be used by the body to produce serotonin, which can calm the brain's activity and help to bring on sleep.a. What mass in grams of tryptophan is in a $0.25-\mathrm{lb}$ serving of turkey (assume tryptophan accounts for $1.0 \%$ of the turkey mass)?b. What mass in grams of tryptophan is in $0.25$ quart of milk (assume tryptophan accounts for $2.0 \%$ of milk by mass and that the density of milk is $1.04 \mathrm{~kg} / \mathrm{L}$ )?
In recent years, there has been a large push for an increase in the use of renewable resources to produce the energy we need to power our vehicles. One of the newer fuels that has become more widely available is a mixture of $85 \%$ ethanol and $15 \%$ gasoline, E85. Despite being more environmentally friendly, one of the potential drawbacks of E85 fuel is that it produces less energy than conventional gasoline. Assume a car gets $28.0 \mathrm{mi} / \mathrm{gal}$ using gasoline at $\$ 3.50 / \mathrm{gal}$ and $22.5 \mathrm{mi} / \mathrm{gal}$ using $\mathrm{E} 85$ at $\$ 2.85 / \mathrm{gal}$. How much will it cost to drive 500 . miles using each fuel?
The active ingredient of aspirin tablets is acetylsalicylic acid, which has a density of $1.4 \mathrm{~g} / \mathrm{cm}^{3} .$ In a lab class, a student used paper chromatography to isolate another common ingredient of headache remedies. The isolated sample had a mass of $0.384 \mathrm{~g}$ and a volume of $0.32 \mathrm{~cm}^{3}$. Given the data in the following table, what was the other ingredient in the headache remedy?$$\begin{array}{l}\text { Density Values for Potential } \\\text { Headache Remedies } \\\begin{array}{lc}\text { Compound } & \text { Density }\left(\mathrm{g} / \mathrm{cm}^{3}\right) \\\hline \text { White table sugar } & 0.70 \\\text { Caffeine } & 1.2 \\\text { Acetylsalicylic acid } & 1.4 \\\text { Sodium chloride } & 2.2 \\\hline\end{array}\end{array}$$
Mercury poisoning is a debilitating disease that is often fatal. In the human body, mercury reacts with essential enzymes leading to irreversible inactivity of these enzymes. If the amount of mercury in a polluted lake is $0.4 \mathrm{\mug} \mathrm{Hg} / \mathrm{mL}$, what is the total mass in kilograms of mercury in the lake? (The lake has a surface area of $100 \mathrm{mi}^{2}$ and an average depth of $20 \mathrm{ft}$.)
Consider the following organic substances (substances based on carbon). Which are pure substances and which are mixtures?a. milkb. honeyc. benzened. an ear of corne. anhydrous ammonia (for fertilization)
Which of the following are chemical changes? Which are physical changes?a. the cutting of foodb. interaction of food with saliva and digestive enzymesc. proteins being broken down into amino acidsd. complex sugars being broken down into simple sugarse. making maple syrup by heating maple sap to remove water through evaporationf. DNA unwinding
In Shakespeare's Richard III, the First Murderer says:"Take that, and that! [Stabs Clarence] If that is not enough, I'll drown you in a malmsey butt within'"Given that 1 butt $=126$ gal, in how many liters of malmsey (a foul brew similar to mead) was the unfortunate Clarence about to be drowned?
The contents of one $40 .$ lb bag of topsoil will cover 10. square feet of ground to a depth of $1.0$ inch. What number of bags are needed to cover a plot that measures 200 . by $300 . \mathrm{m}$ to a depth of $4.0 \mathrm{~cm}$ ?
In the opening scenes of the movie Raiders of the Lost Ark. Indiana Jones tries to remove a gold idol from a booby-trapped pedestal. He replaces the idol with a bag of sand of approximately equal volume. (Density of gold $=19.32 \mathrm{~g} / \mathrm{cm}^{3} ;$ density of sand $\approx 2 \mathrm{~g} / \mathrm{cm}^{3}$.)a. Did he have a reasonable chance of not activating the masssensitive booby trap?b. In a later scene he and an unscrupulous guide play catch with the idol. Assume that the volume of the idol is about $1.0 \mathrm{~L}$. If it were solid gold, what mass would the idol have? Is playing catch with it plausible?
A parsec is an astronomical unit of distance where 1 parsec $=$ $3.26$ light years ( 1 light year equals the distance traveled by light in one year). If the speed of light is $186,000 \mathrm{mi} / \mathrm{s}$, calculate the distance in meters of an object that travels $9.6$ parsecs.
Mars is roughly 60 million $\mathrm{km}$ from earth. How long does it take for a radio signal originating from earth to reach Mars? Radio signals travel at the speed of light, $186,000 \mathrm{mi} / \mathrm{s}$.
A column of liquid is found to expand linearly on heating $5.25$ $\mathrm{cm}$ for a $10.0^{\circ} \mathrm{F}$ rise in temperature. If the initial temperature of the liquid is $98.6^{\circ} \mathrm{F}$, what will the final temperature be in ${ }^{\circ} \mathrm{C}$ if the liquid has expanded by $18.5 \mathrm{~cm}$ ?
A $25.00-\mathrm{g}$ sample of a solid is placed in a graduated cylinder and then the cylinder is filled to the $50.0-\mathrm{mL}$ mark with benzene. The mass of benzene and solid together is $58.80 \mathrm{~g}$. Assuming that the solid is insoluble in benzene and that the density of benzene is $0.880 \mathrm{~g} / \mathrm{cm}^{3}$, calculate the density of the solid.
For each of the following, decide which block is more dense:the orange block, the blue block, or it cannot be determined. Explain your answers.
According to the Official Rules of Baseball, a baseball must have a circumference not more than $9.25$ in or less than $9.00$ in and a mass not more than $5.250 \mathrm{z}$ or less than $5.00 \mathrm{oz}$. What range of densities can a baseball be expected to have? Express this range as a single number with an accompanying uncertainty limit.
The density of an irregularly shaped object was determined as follows. The mass of the object was found to be $28.90 \mathrm{~g} \pm 0.03 \mathrm{~g}$. A graduated cylinder was partially filled with water. The reading of the level of the water was $6.4 \mathrm{~cm}^{3} \pm 0.1 \mathrm{~cm}^{3}$. The object was dropped in the cylinder, and the level of the water rose to $9.8 \mathrm{~cm}^{3} \pm 0.1 \mathrm{~cm}^{3}$. What is the density of the object with appropriate error limits? (See Appendix 1.5.)
The chemist in Example $1.14$ did some further experiments. She found that the pipet used to measure the volume of the cleaner is accurate to $\pm 0.03 \mathrm{~cm}^{3}$. The mass measurement is accurate to $\pm 0.002 \mathrm{~g} .$ Are these measurements sufficiently precise for the chemist to distinguish between isopropyl alcohol and ethanol?
A rule of thumb in designing experiments is to avoid using a result that is the small difference between two large measured quantities. In terms of uncertainties in measurement, why is this good advice?
Draw a picture showing the markings (graduations) on glassware that would allow you to make each of the following volume measurements of water and explain your answers (the numbers given are as precise as possible).a. $128.7 \mathrm{~mL}$b. $18 \mathrm{~mL}$c. $23.45 \mathrm{~mL}$If you made the measurements of three samples of water and then poured all of the water together in one container, what total volume of water should you report? Support your answer.
Many times errors are expressed in terms of percentage. The percent error is the absolute value of the difference of the true value and the experimental value, divided by the true value, and multiplied by 100 .Percent error $=\frac{\mid \text { true value }-\text { experimental value } \mid}{\text { true value }} \times 100$Calculate the percent error for the following measurements.a. The density of an aluminum block determined in an experiment was $2.64 \mathrm{~g} / \mathrm{cm}^{3}$. (True value $2.70 \mathrm{~g} / \mathrm{cm}^{3}$.)b. The experimental determination of iron in iron ore was $16.48 \%$. (True value $16.12 \% .)$c. A balance measured the mass of a $1.000-\mathrm{g}$ standard as $0.9981 \mathrm{~g}$
A person weighed 15 pennies on a balance and recorded the following masses:$$\begin{array}{|lll|}\hline 3.112 \mathrm{~g} & 3.109 \mathrm{~g} & 3.059 \mathrm{~g} \\2.467 \mathrm{~g} & 3.079 \mathrm{~g} & 2.518 \mathrm{~g} \\3.129 \mathrm{~g} & 2.545 \mathrm{~g} & 3.050 \mathrm{~g} \\3.053 \mathrm{~g} & 3.054 \mathrm{~g} & 3.072 \mathrm{~g} \\3.081 \mathrm{~g} & 3.131 \mathrm{~g} & 3.064 \mathrm{~g} \\\hline\end{array}$$Curious about the results, he looked at the dates on each penny. Two of the light pennies were minted in 1983 and one in 1982 . The dates on the 12 heavier pennies ranged from 1970 to $1982 .$ Two of the 12 heavier pennies were minted in 1982 .a. Do you think the Bureau of the Mint changed the way it made pennies? Explain.b. The person calculated the average mass of the 12 heavy pennies. He expressed this average as $3.0828 \mathrm{~g} \pm 0.0482 \mathrm{~g} .$ What is wrong with the numbers in this result, and how should the value be expressed?
On October 21,1982, the Bureau of the Mint changed the composition of pennies (see Exercise 106$)$. Instead of an alloy of $95 \%$ $\mathrm{Cu}$ and $5 \%$ Zn by mass, a core of $99.2 \% \mathrm{Zn}$ and $0.8 \%$ Cu with a thin shell of copper was adopted. The overall composition of the new penny was $97.6 \% \mathrm{Zn}$ and $2.4 \%$ Cu by mass. Does this account for the difference in mass among the pennies in Exercise 106 ? Assume the volume of the individual metals that make up each penny can be added together to give the overall volume of the penny, and assume each penny is the same size. (Density of $\mathrm{Cu}=8.96 \mathrm{~g} / \mathrm{cm}^{3} ;$ density of $\mathrm{Zn}=7.14 \mathrm{~g} / \mathrm{cm}^{3} .$ )
Ethylene glycol is the main component in automobile antifreeze. To monitor the temperature of an auto cooling system, you intend to use a meter that reads from 0 to 100 . You devise a new temperature scale based on the approximate melting and boiling points of a typical antifreeze solution $\left(-45^{\circ} \mathrm{C}\right.$ and $\left.115^{\circ} \mathrm{C}\right)$. You wish these points to correspond to $0^{\circ} \mathrm{A}$ and $100^{\circ} \mathrm{A}$, respectively.a. Derive an expression for converting between ${ }^{\circ} \mathrm{A}$ and ${ }^{\circ} \mathrm{C}$.b. Derive an expression for converting between ${ }^{\circ} \mathrm{F}$ and ${ }^{\circ} \mathrm{A}$.c. At what temperature would your thermometer and a Celsius thermometer give the same numerical reading?d. Your thermometer reads $86^{\circ} \mathrm{A} .$ What is the temperature in ${ }^{\circ} \mathrm{C}$ and in ${ }^{\circ} \mathrm{F}$ ?e. What is a temperature of $45^{\circ} \mathrm{C}$ in ${ }^{\circ} \mathrm{A}$ ?
Sterling silver is a solid solution of silver and copper. If a piece of a sterling silver necklace has a mass of $105.0 \mathrm{~g}$ and a volume of $10.12 \mathrm{~mL}$, calculate the mass percent of copper in the piece of necklace. Assume that the volume of silver present plus the volume of copper present equals the total volume. Refer to Table $1.5$.Mass percent of copper $=\frac{\text { mass of copper }}{\text { total mass }} \times 100$
Use molecular-level (microscopic) drawings for each of the following.a. Show the differences between a gaseous mixture that is a homogeneous mixture of two different compounds, and a gaseous mixture that is a homogeneous mixture of a compound and an element.b. Show the differences among a gaseous element, a liquid element, and a solid element.
Confronted with the box shown in the diagram, you wish to discover something about its internal workings. You have no tools and cannot open the box. You pull on rope $\mathrm{B}$, and it moves rather freely. When you pull on rope A, rope C appears to be pulled slightly into the box. When you pull on rope $\mathrm{C}$, rope $\mathrm{A}$ almost disappears into the box.*a. Based on these observations, construct a model for the interior mechanism of the box.b. What further experiments could you do to refine your model?
An experiment was performed in which an empty $100-\mathrm{mL}$ graduated cylinder was weighed. It was weighed once again after it had been filled to the $10.0-\mathrm{mL}$ mark with dry sand. A $10-\mathrm{mL}$ pipet was used to transfer $10.00 \mathrm{~mL}$ of methanol to the cylinder. The sand-methanol mixture was stirred until bubbles no longer emerged from the mixture and the sand looked uniformly wet. The cylinder was then weighed again. Use the data obtained from this experiment (and displayed at the end of this problem) to find the density of the dry sand, the density of methanol, and the density of sand particles. Does the bubbling that occurs when the methanol is added to the dry sand indicate that the sand and methanol are reacting?Mass of cylinder plus wet sand $\quad 45.2613 \mathrm{~g}$ Mass of cylinder plus dry sand $\quad 37.3488 \mathrm{~g}$ Mass of empty cylinder $22.8317 \mathrm{~g}$Volume of dry sand $10.0 \mathrm{~mL}$Volume of sand plus methanol $\quad 17.6 \mathrm{~mL}$ Volume of methanol $\quad 10.00 \mathrm{~mL}$
The U.S. trade deficit at the beginning of 2005 was $\$ 475,000,000$. If the wealthiest $1.00$ percent of the U.S. population $(297,000,000)$ contributed an equal amount of money to bring the trade deficit to $\$ 0$, how many dollars would each person contribute? If one of these people were to pay his or her share in nickels only, how many nickels are needed? Another person living abroad at the time decides to pay in pounds sterling (f). How many pounds sterling does this person contribute (assume a conversion rate of $1 \mathrm{f}=\$ 1.869) ?$
The density of osmium is reported by one source to be $22610 \mathrm{~kg} /$ $\mathrm{m}^{3}$. What is this density in $\mathrm{g} / \mathrm{cm}^{3}$ ? What is the mass of a block of osmium measuring $10.0 \mathrm{~cm} \times 8.0 \mathrm{~cm} \times 9.0 \mathrm{~cm} ?$
At the Amundsen-Scott South Pole base station in Antarctica, when the temperature is $-100.0^{\circ} \mathrm{F}$, researchers who live there can join the " 300 Club" by stepping into a sauna heated to $200.0^{\circ} \mathrm{F}$ then quickly running outside and around the pole that marks the South Pole. What are these temperatures in ${ }^{\circ} \mathrm{C}$ ? What are these temperatures in $\mathrm{K}$ ? If you measured the temperatures only in ${ }^{\circ} \mathrm{C}$ and $\mathrm{K}$, can you become a member of the " 300 Club"(that is, is there a 300--degree difference between the temperature extremes when measured in ${ }^{\circ} \mathrm{C}$ and $\mathrm{K}$ )?