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CHEMISTRY: The Molecular Nature of Matter and Change 2016

Martin S. Silberberg, Patricia G. Amateis

Chapter 1

Keys to the Study of Chemistry

Educators


Problem 1

Scenes A–D represent atomic-scale views of different samples of substances:
(a) Under one set of conditions, the substances in A and B mix, and the result is depicted in C. Does this represent a chemical or a physical change?
(b) Under a second set of conditions, the same substances mix, and the result is depicted in D. Does this represent a chemical or a physical change?
(c) Under a third set of conditions, the sample depicted in C changes to that in D. Does this represent a chemical or a physical change?
(d) After the change in part (c) has occurred, does the sample have different chemical properties? Physical properties?

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Problem 2

Describe solids, liquids, and gases in terms of how they fill a container. Use your descriptions to identify the physical state (at room temperature) of the following: (a) helium in a toy balloon; (b) mercury in a thermometer; (c) soup in a bowl.

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Problem 3

Use your descriptions from Problem 1.2 to identify the physical state (at room temperature) of the following: (a) the air in your room; (b) tablets in a bottle of vitamins; (c) sugar in a packet.

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Problem 4

Define physical property and chemical property. Identify each type of property in the following statements:
(a) Yellow-green chlorine gas attacks silvery sodium metal to form white crystals of sodium chloride (table salt).
(b) A magnet separates a mixture of black iron shavings and white sand.

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Problem 5

Define physical change and chemical change. State which type of change occurs in each of the following statements:
(a) Passing an electric current through molten magnesium chloride yields molten magnesium and gaseous chlorine.
(b) The iron in discarded automobiles slowly forms reddish brown, crumbly rust.

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Problem 6

Which of the following is a chemical change? Explain your reasoning: (a) boiling canned soup; (b) toasting a slice of bread; (c) chopping a log; (d) burning a log.

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Problem 7

Which of the following changes can be reversed by changing the temperature: (a) dew condensing on a leaf; (b) an egg turning hard when it is boiled; (c) ice cream melting; (d) a spoonful of batter cooking on a hot griddle?

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Problem 8

For each pair, which has higher potential energy?
(a) The fuel in your car or the gaseous products in its exhaust
(b) Wood in a fire or the ashes after the wood burns

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Problem 9

For each pair, which has higher kinetic energy?
(a) A sled resting at the top of a hill or a sled sliding down the hill
(b) Water above a dam or water falling over the dam

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Problem 10

The alchemical, medical, and technological traditions were precursors to chemistry. State a contribution that each made to the development of the science of chemistry.

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Problem 11

How did the phlogiston theory explain combustion?

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Problem 12

One important observation that supporters of the phlogiston theory had trouble explaining was that the calx of a metal weighs more than the metal itself. Why was that observation important? How did the phlogistonists respond?

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Problem 13

Lavoisier developed a new theory of combustion that overturned the phlogiston theory. What measurements were central to his theory, and what key discovery did he make?

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Problem 14

How are the key elements of scientific thinking used in the following scenario? While making toast, you notice it fails to pop out of the toaster. Thinking the spring mechanism is stuck, you notice that the bread is unchanged. Assuming you forgot to plug in the toaster, you check and find it is plugged in. When you take the toaster into the dining room and plug it into a different outlet, you find the toaster works. Returning to the kitchen, you turn on the switch for the overhead light and nothing happens.

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Problem 15

Why is a quantitative observation more useful than a nonquantitative one? Which of the following is (are) quantitative? (a) The Sun rises in the east. (b) A person weighs one-sixth as much on the Moon as on Earth. (c) Ice floats on water. (d) A hand pump cannot draw water from a well more than 34 ft deep.

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Problem 16

Describe the essential features of a well-designed experiment.

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Problem 17

Describe the essential features of a scientific model.

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Problem 18

Explain the difference between mass and weight. Why is your weight on the Moon one-sixth that on Earth?

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Problem 19

When you convert feet to inches, how do you decide which part of the conversion factor should be in the numerator and which in the denominator?

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Problem 20

For each of the following cases, state whether the density of the object increases, decreases, or remains the same:
(a) A sample of chlorine gas is compressed.
(b) A lead weight is carried up a high mountain.
(c) A sample of water is frozen.
(d) An iron bar is cooled.
(e) A diamond is submerged in water.

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Problem 21

Explain the difference between heat and temperature. Does 1 $\mathrm{L}$ of water at $65^{\circ} \mathrm{F}$ have more, less, or the same quantity of energy as 1 $\mathrm{L}$ of water at $65^{\circ} \mathrm{C} ?$

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Problem 22

A one-step conversion is sufficient to convert a temperature in the Celsius scale to the Kelvin scale, but not to the Fahrenheit scale. Explain.

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Problem 23

Describe the difference between intensive and extensive properties. Which of the following properties are intensive: (a) mass; (b) density; (c) volume; (d) melting point?

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Problem 24

Write the conversion factor(s) for
(a) $\mathrm{in}^{2}\mathrm{tom}^{2} \quad$ (b) $\mathrm{km}^{2}$ to $\mathrm{cm}^{2}$
(c) $\mathrm{mi/h}$ to $\mathrm{m} / \mathrm{s} \quad$ (d) $\mathrm{Ib} / \mathrm{ft}^{3}$ to $\mathrm{g} / \mathrm{cm}^{3}$

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Problem 25

Write the conversion factor(s) for
(a) $\mathrm{cm} / \mathrm{min}$ to $\mathrm{in} / \mathrm{s} \quad$ (b) $\mathrm{m}^{3}$ to $\mathrm{in}^{3}$
(c) $\mathrm{m} / \mathrm{s}^{2}$ to $\mathrm{km} / \mathrm{h}^{2} \quad$ (d) $\mathrm{gal} / \mathrm{h}$ to $\mathrm{L} / \mathrm{min}$

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Problem 26

The average radius of a molecule of lysozyme, an enzyme in tears, is 1430 pm. What is its radius in nanometers (nm)?

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Problem 27

1.27 The radius of a barium atom is $2.22 \times 10^{-10} \mathrm{m} .$ What is its radius in angstroms ( A)?

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Problem 28

What is the length in inches (in) of a 100.-m soccer field?

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Problem 29

The center on your school’s basketball team is 6 ft 10 in tall. How tall is the player in millimeters (mm)?

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Problem 30

A small hole in the wing of a space shuttle requires a $20.7-\mathrm{cm}^{2}$ patch. (a) What is the patch's area in square kilometers $\left(\mathrm{km}^{2}\right) ?(\mathrm{b})$ If the patching material costs $\mathrm{NASA} \$ 3.25 / \mathrm{in}^{2}$ , what is the cost of the patch?

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Problem 31

The area of a telescope lens is 7903 $\mathrm{mm}^{2}$ . (a) What is the area in square feet $\left(\mathrm{ft}^{2}\right) ?(\mathrm{b})$ If it takes a technician 45 $\mathrm{s}$ to polish $135 \mathrm{mm}^{2},$ how long does it take her to polish the entire lens?

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Problem 32

Express your body weight in kilograms (kg).

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Problem 33

There are $2.60 \times 10^{15}$ short tons of oxygen in the atmosphere $(1 \text { short ton }=2000 \text { lb). How many metric tons of oxygen are }$ present $(1 \text { metric ton }=1000 \mathrm{kg}) ?$

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Problem 34

The average density of Earth is 5.52 $\mathrm{g} / \mathrm{cm}^{3} .$ What is its density in (a) $\mathrm{kg} / \mathrm{m}^{3} ;(\mathrm{b}) \mathrm{Ib} / \mathrm{ft}^{3} ?$

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Problem 35

The speed of light in a vacuum is $2.998 \times 10^{8} \mathrm{m} / \mathrm{s}$ . What is its speed in ( a ) $\mathrm{km} / \mathrm{h} ;(\mathrm{b})$ milmin?

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Problem 36

The volume of a certain bacterial cell is 2.56$\mu \mathrm{m}^{3}$. (a) What is its volume in cubic millimeters (mm3)? (b) What is the volume of $10^{5}$ cells in liters $(\mathrm{L}) ?$

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Problem 37

(a) How many cubic meters of milk are in 1 qt $(946.4 \mathrm{mL})$ ? (b) How many liters of milk are in 835 gal $(1 \mathrm{gal}=4 \mathrm{qt}) ?$

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Problem 38

An empty vial weighs 55.32 g. (a) If the vial weighs 185.56 g when filled with liquid mercury $\left(d=13.53 \mathrm{g} / \mathrm{cm}^{3}\right),$ what is its volume? (b) How much would the vial weigh if it were filled with water $\left(d=0.997 \mathrm{g} / \mathrm{cm}^{3} \text { at } 25^{\circ} \mathrm{C}\right) ?$

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Problem 39

An empty Erlenmeyer flask weighs 241.3 g. When filled with water $\left(d=1.00 \mathrm{g} / \mathrm{cm}^{3}\right),$ the flask and its contents weigh 489.1 $\mathrm{g} .$ (a) What is the flask's volume? (b) How much does the flask weigh when filled with chloroform $\left(d=1.48 \mathrm{g} / \mathrm{cm}^{3}\right) ?$

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Problem 40

A small cube of aluminum measures 15.6 $\mathrm{mm}$ on a side and weighs 10.25 $\mathrm{g}$ . What is the density of aluminum in $\mathrm{g} / \mathrm{cm}^{3} ?$

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Problem 41

A steel ball-bearing with a circumference of 32.5 $\mathrm{mm}$ weighs 4.20 $\mathrm{g} .$ What is the density of the steel in $\mathrm{g} / \mathrm{cm}^{3}(\mathrm{V} \text { of a sphere }=$ $\frac{4}{3} \pi r^{3} ;$ circumference of a circle $=2 \pi r ) ?$

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Problem 42

Perform the following conversions:
(a) $68^{\circ} \mathrm{F}$ (a pleasant spring day) to ' $^{\circ} \mathrm{C}$ and $\mathrm{K}$
(b) $-164^{\circ} \mathrm{C}$ (the boiling point of methane, the main component of natural gas) to $\mathrm{K}$ and $^{\circ} \mathrm{F}$
(c) 0 $\mathrm{K}$ (absolute zero, theoretically the coldest possible temperature) to $^{\circ} \mathrm{C}$ and $^{\circ} \mathrm{F}$

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Problem 43

Perform the following conversions:
(a) $106^{\circ} \mathrm{F}$ (the body temperature of many birds) to $\mathrm{K}$ and $^{\circ} \mathrm{C}$
(b) $3410^{\circ} \mathrm{C}$ (the melting point of tungsten, the highest for any metallic element) to $\mathrm{K}$ and $^{\circ} \mathrm{F}$
(c) $6.1 \times 10^{3} \mathrm{K}$ (the surface temperature of the Sun) to $^{\circ} \mathrm{F}$ and $^{\circ} \mathrm{C}$

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Problem 44

A 25.0 -g sample of each of three unknown metals is added to 25.0 $\mathrm{mL}$ of water in graduated cylinders $\mathrm{A}, \mathrm{B},$ and $\mathrm{C},$ and the final volumes are depicted in the circles below. Given their densities, identify the metal in each cylinder: zinc $(7.14 \mathrm{g} / \mathrm{mL}),$ iron $(7.87 \mathrm{g} / \mathrm{mL}),$ or nickel $(8.91 \mathrm{g} / \mathrm{mL}) .$

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Problem 45

The distance between two adjacent peaks on a wave is called the wavelength.
(a) The wavelength of a beam of ultraviolet light is 247 nanometers $(\mathrm{nm}) .$ What is its wavelength in meters?
(b) The wavelength of a beam of red light is 6760 $\mathrm{pm} .$ What is its wavelength in angstroms $(\mathrm{A}) ?$

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Problem 46

Each of the beakers depicted below contains two liquids that do not dissolve in each other. Three of the liquids are designated A, B, and C, and water is designated W.
(a) Which of the liquids is (are) more dense than water and which less dense?
(b) If the densities of $\mathrm{W}, \mathrm{C},$ and $\mathrm{A}$ are $1.0 \mathrm{g} / \mathrm{mL}, 0.88 \mathrm{g} / \mathrm{mL}$ , and 1.4 $\mathrm{g} / \mathrm{mL}$ , respectively, which of the following densities is possible for liquid $\mathrm{B} : 0.79 \mathrm{g} / \mathrm{mL}, 0.86 \mathrm{g} / \mathrm{mL}, 0.94 \mathrm{g} / \mathrm{mL}$ , or 1.2 $\mathrm{g} / \mathrm{mL} ?$

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Problem 47

A cylindrical tube 9.5 $\mathrm{cm}$ high and 0.85 $\mathrm{cm}$ in diameter is used to collect blood samples. How many cubic decimeters (dm $^{3} )$ of blood can it hold (V of a cylinder $=\pi r^{2} h ) ?$

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Problem 48

Copper can be drawn into thin wires. How many meters of 34 -gauge wire (diameter $=6.304 \times 10^{-3}$ in ) can be produced from the copper in 5.01 lb of covellite, an ore of copper that is 66$\%$ copper by mass? (Hint: Treat the wire as a cylinder: $V$ of cylinder $=$ $\pi r^{2} h ; d$ of copper $=8.95 \mathrm{g} / \mathrm{cm}^{3} . )$

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Problem 49

What is an exact number? How are exact numbers treated differently from other numbers in a calculation?

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Problem 50

Which procedure(s) decrease(s) the random error of a measurement: (1) taking the average of more measurements; (2) calibrating the instrument; (3) taking fewer measurements? Explain.

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Problem 51

A newspaper reported that the attendance at Slippery Rock’s home football game was 16,532. (a) How many significant figures does this number contain? (b) Was the actual number of people counted? (c) After Slippery Rock’s next home game, the newspaper reported an attendance of 15,000. If you assume that this number contains two significant figures, how many people could actually have been at the game?

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Problem 52

Underline the significant zeros in the following numbers:
(a) $0.41 \quad$ (b) $0.041 \quad$ (c) $0.0410 \quad$ (d) $4.0100 \times 10^{4}$

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Problem 53

Underline the significant zeros in the following numbers:
(a) $5.08 \quad$ (b) $508 \quad$ (c) $5.080 \times 10^{3} \quad$ (d) $0.05080$

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Problem 54

Round off each number to the indicated number of significant figures (sf): (a) 0.0003554 (to 2 sf); (b) 35.8348 (to 4 sf); (c) 22.4555 (to 3 sf).

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Problem 55

Round off each number to the indicated number of significant figures (sf): (a) 231.554 (to 4 sf); (b) 0.00845 (to 2 sf); (c) 144,000 (to 2 sf).

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Problem 56

Round off each number in the following calculation to one fewer significant figure, and find the answer:
$$\frac{19 \times 155 \times 8.3}{3.2 \times 2.9 \times 4.7}$$

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Problem 57

Round off each number in the following calculation to one fewer significant figure, and find the answer:
$$\frac{10.8 \times 6.18 \times 2.381}{24.3 \times 1.8 \times 19.5}$$

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Problem 58

Carry out the following calculations, making sure that your answer has the correct number of significant figures:
(a) $\frac{2.795 \mathrm{m} \times 3.10 \mathrm{m}}{6.48 \mathrm{m}}$
(b) $V=\frac{4}{3} \pi r^{3},$ where $r=17.282 \mathrm{mm}$
(c) $1.110 \mathrm{cm}+17.3 \mathrm{cm}+108.2 \mathrm{cm}+316 \mathrm{cm}$

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Problem 59

Carry out the following calculations, making sure that your answer has the correct number of significant figures:
(a) $\frac{2.420 \mathrm{g}+15.6 \mathrm{g}}{4.8 \mathrm{g}} \quad$ (b) $\frac{7.87 \mathrm{mL}}{16.1 \mathrm{mL}-8.44 \mathrm{mL}}$
(c) $V=\pi r^{2} h,$ where $r=6.23 \mathrm{cm}$ and $h=4.630 \mathrm{cm}$

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Problem 60

Write the following numbers in scientific notation:
(a) $131,000.0 \quad$ (b) $0.00047 \quad$ (c) $210,006 \quad$ (d) $2160.5$

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Problem 61

Write the following numbers in scientific notation:
(a) $282.0 \quad$ (b) $0.0380 \quad$ (c) $4270.8 \quad$ (d) $58,200.9$

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Problem 62

Write the following numbers in standard notation. Use a terminal decimal point when needed.
(a) $5.55 \times 10^{3} \quad$ (b) $1.0070 \times 10^{4}$ (c) $8.85 \times 10^{-7}$ (d) $3.004 \times 10^{-3}$

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Problem 63

Write the following numbers in standard notation. Use a terminal decimal point when needed.
(a) $6.500 \times 10^{3} \quad$ (b) $3.46 \times 10^{-5}$ (c) $7.5 \times 10^{2}$ (d) $1.8856 \times 10^{2}$

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Problem 64

Convert the following into correct scientific notation:
(a) $802.5 \times 10^{2} \quad$ (b) $1009.8 \times 10^{-6} \quad$ (c) $0.077 \times 10^{-9}$

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Problem 65

Convert the following into correct scientific notation:
(a) $14.3 \times 10^{1} \quad$ (b) $851 \times 10^{-2} \quad$ (c) $7500 \times 10^{-3}$

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Problem 66

Carry out each calculation, paying special attention to significant figures, rounding, and units (J 5 joule, the SI unit of energy; mol 5 mole, the SI unit for amount of substance):
(a) $\frac{\left(6.626 \times 10^{-34} \mathrm{J} \cdot \mathrm{s}\right)\left(2.9979 \times 10^{8} \mathrm{m} / \mathrm{s}\right)}{489 \times 10^{-9} \mathrm{m}}$
(b) $\frac{\left(6.022 \times 10^{23} \text { molecules/mol) }\left(1.23 \times 10^{2} \mathrm{g}\right)\right.}{46.07 \mathrm{g} / \mathrm{mol}}$
(c) $\left(6.022 \times 10^{23} \text { atoms/mol) }\left(2.18 \times 10^{-18} \mathrm{J} / \text { atom }\right)\left(\frac{1}{2^{2}}-\frac{1}{3^{2}}\right)\right.$,
where the numbers 2 and 3 in the last term are exact

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Problem 67

Carry out each calculation, paying special attention to significant figures, rounding, and units:
(a) $\frac{4.32 \times 10^{7} \mathrm{g}}{\frac{4}{3}(3.1416)\left(1.95 \times 10^{2} \mathrm{cm}\right)^{3}} \quad$ (The term $\frac{4}{3}$ is exact.)
(b) $\frac{\left(1.84 \times 10^{2} \mathrm{g}\right)(44.7 \mathrm{m} / \mathrm{s})^{2}}{2}$ (The term 2 is exact.)
(c) $\frac{\left(1.07 \times 10^{-4} \mathrm{mol} / \mathrm{L}\right)^{2}\left(3.8 \times 10^{-3} \mathrm{mol} / \mathrm{L}\right)}{\left(8.35 \times 10^{-5} \mathrm{mol} / \mathrm{L}\right)\left(1.48 \times 10^{-2} \mathrm{mol} / \mathrm{L}\right)^{3}}$

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Problem 68

Which statements include exact numbers?
(a) Angel Falls is 3212 ft high.
(b) There are 8 known planets in the Solar System.
(c) There are 453.59 g in 1 lb.
(d) There are 1000 mm in 1 m.

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Problem 69

Which of the following include exact numbers?
(a) The speed of light in a vacuum is a physical constant; to six significant figures, it is $2.99792 \times 10^{8} \mathrm{m} / \mathrm{s}$
(b) The density of mercury at $25^{\circ} \mathrm{C}$ is 13.53 $\mathrm{g} / \mathrm{mL}$.
(c) There are 3600 s in 1 h.
(d) In 2012, the United States had 50 states.

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Problem 70

How long is the metal strip shown below? Be sure to answer with the correct number of significant figures.

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Problem 71

These organic solvents are used to clean compact discs:
$$\begin{array}{ll}{\text { Solvent }} & {\text { Density }(\mathrm{g} / \mathrm{mL}) \text { at } 20^{\circ} \mathrm{C}} \\ \hline {\text { Chloroform }} & \quad\quad\quad {1.492} \\ {\text { Diethyl ether }} & \quad\quad\quad {0.714} \\ {\text { Ethanol }} & \quad\quad\quad {0.789} \\ {\text { Isopropanol }} & \quad\quad\quad {0.785} \\ {\text { Toluene }} & \quad\quad\quad {0.867}\end{array}$$
(a) If a 15.00 -mL sample of CD cleaner weighs 11.775 $\mathrm{g}$ at $20^{\circ} \mathrm{C},$ which solvent does the sample most likely contain?
(b) The chemist analyzing the cleaner calibrates her equipment and finds that the pipet is accurate to $\pm 0.02 \mathrm{mL}$ , and the balance is accurate to $\pm 0.003 \mathrm{g} .$ Is this equipment precise enough to distinguish between ethanol and isopropanol?

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Problem 72

A laboratory instructor gives a sample of amino-acid powder to each of four students, I, II, III, and IV, and they weigh the samples. The true value is 8.72 g. Their results for three trials are
I: $8.72 \mathrm{g}, 8.74 \mathrm{g}, 8.70 \mathrm{g} \quad$ II: $8.56 \mathrm{g}, 8.77 \mathrm{g}, 8.83 \mathrm{g}$
III: $8.50 \mathrm{g}, 8.48 \mathrm{g}, 8.51 \mathrm{g} \quad$ IV: $8.41 \mathrm{g}, 8.72 \mathrm{g}, 8.55 \mathrm{g}$
(a) Calculate the average mass from each set of data, and tell which set is the most accurate.
(b) Precision is a measure of the average of the deviations of each piece of data from the average value. Which set of data is the most precise? Is this set also the most accurate?
(c) Which set of data is both the most accurate and the most precise?
(d) Which set of data is both the least accurate and the least precise?

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Problem 73

The following dartboards illustrate the types of errors often seen in measurements. The bull’s-eye represents the actual value, and the darts represent the data.
(a) Which experiments yield the same average result?
(b) Which experiment(s) display(s) high precision?
(c) Which experiment(s) display(s) high accuracy?
(d) Which experiment(s) show(s) a systematic error?

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Problem 74

Two blank potential energy diagrams appear below. Beneath each diagram are objects to place in the diagram. Draw the objects on the dashed lines to indicate higher or lower potential energy and label each case as more or less stable:
$\begin{array}{ll}{\text { (a) Two balls attached to a }} & {\text { (b) Two positive charges near }} \\ {\text { relaxed or a compressed spring }} & {\text { or apart from each other }}\end{array}$

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Problem 75

The scenes below illustrate two different mixtures. When mixture $A$ at 273 $\mathrm{K}$ is heated to 473 $\mathrm{K}$ , mixture $\mathrm{B}$ results.
(a) How many different chemical changes occur?
(b) How many different physical changes occur?

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Problem 76

Bromine is used to prepare the pesticide methyl bromide and flame retardants for plastic electronic housings. It is recovered from seawater, underground brines, and the Dead Sea. The average concentrations of bromine in seawater $(d=1.024 \mathrm{g} / \mathrm{mL})$ and the Dead Sea $(d=1.22 \mathrm{g} / \mathrm{mL})$ are 0.065 $\mathrm{g} / \mathrm{L}$ and 0.50 $\mathrm{g} / \mathrm{L}$ , respectively. What is the mass ratio of bromine in the Dead Sea to that in seawater?

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Problem 77

An Olympic-size pool is 50.0 $\mathrm{m}$ long and 25.0 $\mathrm{m}$ wide. (a) How many gallons of water $(d=1.0 \mathrm{g} / \mathrm{mL})$ are needed to fill the pool to an average depth of 4.8 $\mathrm{ft} ?(\mathrm{b})$ What is the mass (in kg) of water in the pool?

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Problem 78

At room temperature $\left(20^{\circ} \mathrm{C}\right)$ and pressure, the density of air is 1.189 $\mathrm{g} / \mathrm{L}$ . An object will float in air if its density is less than that of air. In a buoyancy experiment with a new plastic, a chemist creates a rigid, thin-walled ball that weighs 0.12 $\mathrm{g}$ and has a volume of 560 $\mathrm{cm}^{3}$ .
(a) Will the ball float if it is evacuated?
(b) Will it float if filled with carbon dioxide $(d=1.830 \mathrm{g} / \mathrm{L})$?
(c) Will it float if filled with hydrogen $(d=0.0899 \mathrm{g} / \mathrm{L})$?
(d) Will it float if filled with oxygen $(d=1.330 \mathrm{g} / \mathrm{L})$?
(e) Will it float if filled with nitrogen $(d=1.165 \mathrm{g} / \mathrm{L})$?
(f) For any case in which the ball will float, how much weight must be added to make it sink?

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Problem 79

Asbestos is a fibrous silicate mineral with remarkably high tensile strength. But it is no longer used because airborne asbestos particles can cause lung cancer. Grunerite, a type of asbestos, has a tensile strength of $3.5 \times 10^{2} \mathrm{kg} / \mathrm{mm}^{2}$ (thus, a strand of grunerite with a $1-\mathrm{mm}^{2}$ cross-sectional area can hold up to $3.5 \times 10^{2} \mathrm{kg}$ . The tensile strengths of aluminum and Steel No. 5137 are $2.5 \times 10^{4}$ and $5.0 \times 10^{4}$ lb/in', respectively. Calculate the cross-sectional areas (in $\mathrm{mm}^{2} )$ of wires of aluminum and of Steel No. 5137 that have the same tensile strength as a fiber of grunerite with a cross-sectional area of 1.0$\mu \mathrm{m}^{2}$

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Problem 80

Earth's oceans have an average depth of $3800 \mathrm{m},$ a total surface area of $3.63 \times 10^{8} \mathrm{km}^{2},$ and an average concentration of dissolved gold of $5.8 \times 10^{-9} \mathrm{g} / \mathrm{L}$ (a) How many grams of gold are in the oceans? (b) How many cubic meters of gold are in the oceans? (c) Assuming the price of gold is $\$ 1595 /$ troy oz, what is the value of gold in the oceans $\left(1 \text { troy oz }=31.1 \mathrm{g} ; d \text { of gold }=19.3 \mathrm{g} / \mathrm{cm}^{3}\right) ?$

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Problem 81

Brass is an alloy of copper and zinc. Varying the mass percentages of the two metals produces brasses with different properties. A brass called yellow zinc has high ductility and strength and is $34-37 \%$ zinc by mass. (a) Find the mass range (in g) of copper in 185 g of yellow zinc. (b) What is the mass range (in g) of zinc in a sample of yellow zinc that contains 46.5 $\mathrm{g}$ of copper?

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Problem 82

Liquid nitrogen is obtained from liquefied air and is used industrially to prepare frozen foods. It boils at 77.36 $\mathrm{K}$ . (a) What is this temperature in $^{\circ} \mathrm{C} ?$ (b) What is this temperature in $^{\circ} \mathrm{F} ?$ (c) At the boiling point, the density of the liquid is 809 $\mathrm{g} / \mathrm{L}$ and that of the gas is 4.566 $\mathrm{g} / \mathrm{L}$ . How many liters of liquid nitrogen are produced when 895.0 $\mathrm{L}$ of nitrogen gas is liquefied at 77.36 $\mathrm{K}$ ?

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Problem 83

A jogger runs at an average speed of 5.9 mi/h. (a) How fast is she running in $\mathrm{m} / \mathrm{s} ?$ (b) How many kilometers does she run in 98 $\min ?(\mathrm{c})$ If she starts a run at $11 : 15 \mathrm{am},$ what time is it after she covers $4.75 \times 10^{4} \mathrm{ft}$ ?

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Problem 84

Scenes A and B depict changes in matter at the atomic scale:
(a) Which show(s) a physical change?
(b) Which show(s) a chemical change?
(c) Which result(s) in different physical properties?
(d) Which result(s) in different chemical properties?
(e) Which result(s) in a change in state?

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Problem 85

If a temperature scale were based on the freezing point $\left(5.5^{\circ} \mathrm{C}\right)$ and boiling point $\left(80.1^{\circ} \mathrm{C}\right)$ of benzene and the temperature difference between these points was divided into 50 units (called $^{\circ} \mathrm{X} ),$ what would be the freezing and boiling points of water in $^{\circ} \mathrm{X} ?$ (See Figure $1.11, \mathrm{p} .25 . )$

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Problem 86

Earth's surface area is $5.10 \times 10^{8} \mathrm{km}^{2} ; \mathrm{its}$ crust has a mean thickness of 35 $\mathrm{km}$ and a mean density of 2.8$/ \mathrm{cm}^{3} .$ The two most abundant elements in the crust are oxygen $\left(4.55 \times 10^{5} \mathrm{g} / \mathrm{t}, \text { where t }\right.$ stands for "metric ton"; $1 \mathrm{t}=1000 \mathrm{kg}$ ) and silicon $\left(2.72 \times 10^{5} \mathrm{g} / \mathrm{t}\right)$, and the two rarest nonradioactive elements are ruthenium and rhodium, each with an abundance of $1 \times 10^{-4} \mathrm{g} / \mathrm{t}$ . What is the total mass of each of these elements in Earth's crust?

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