Chemistry

Raymond Chang, Jason Overby

Chapter 1

Measurement and the Properties of Matter - all with Video Answers

Educators

Chapter Questions

Problem 1

Explain what is meant by the scientific method.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 2

What is the difference between qualitative data and quantitative data?

Nicole Smina

Numerade Educator

Problem 3

Classify the following as qualitative or quantitative statements, giving your reasons. (a)
The sun is approximately 93 million miles from Earth. (b) Leonardo da Vinci was a better
painter than Michelangelo. (c) Ice is less dense than water. (d) Butter tastes better than
margarine. (e) A stitch in time saves nine.

Ted Gray

Numerade Educator

Problem 4

Classify each of the following statements as a hypothesis, a law, or a theory. (a)
Beethoven’s contribution to music would have been much greater if he had married. (b) An
autumn leaf gravitates toward the ground because there is an attractive force between the
leaf and Earth. (c) All matter is composed of very small particles called atoms

David Collins

Numerade Educator

Problem 5

Name the SI base units that are important in chemistry. Give the SI units for expressing
the following: (a) length, (b) volume, (c) mass, (d) time, (e) energy, (f ) temperature.

Daniel Lai

Numerade Educator

Problem 6

Write the numbers represented by the following
prefixes: (a) mega-, (b) kilo-, (c) deci-, (d) centi-,
(e) milli-, (f ) micro-, (g) nano-, (h) pico-.

Himanshu Garg

Numerade Educator

Problem 7

What units do chemists normally use for density
of liquids and solids? For gas density? Explain the differences.

Daniel Lai

Numerade Educator

Problem 8

Describe the three temperature scales used in the laboratory and in everyday life: the
Fahrenheit scale, the Celsius scale, and the Kelvin scale.

David Collins

Numerade Educator

Problem 9

Bromine is a reddish-brown liquid. Calculate its density (in g/mL) if 586 g of the
substance occupies 188 mL.

Daniel Lai

Numerade Educator

Problem 10

The density of methanol, a colorless organic liquid used as solvent, is 0.7918 g/mL.
Calculate the mass of 89.9 mL of the liquid.

David Collins

Numerade Educator

Problem 11

Convert the following temperatures to degrees
Celsius or Fahrenheit: (a) 95°F, the temperature on a hot summer day; (b) 12°F, the
temperature on a cold winter day; (c) a 102°F fever; (d) a furnace operating at 1852°F; (e)
−273.15°C (theoretically the lowest attainable temperature).

Daniel Lai

Numerade Educator

Problem 12

(a) Normally the human body can endure a temperature of 105°F for only short periods
of time without permanent damage to the brain and other vital organs. What is this
temperature in degrees Celsius? (b) Ethylene glycol is a liquid organic compound that is
used as an antifreeze in car radiators. It freezes at −11.5°C. Calculate its freezing
temperature in degrees Fahrenheit. (c) The temperature on the surface of the sun is about
6300°C. What is this temperature in degrees Fahrenheit? (d) The ignition temperature of
paper is 451°F. What is the temperature in degrees Celsius?

David Collins

Numerade Educator

Problem 13

Convert the following temperatures to kelvin:
(a) 113°C, the melting point of sulfur, (b) 37°C, the normal body temperature, (c) 357°C, the boiling point of mercury.

Daniel Lai

Numerade Educator

Problem 14

Convert the following temperatures to degrees
Celsius: (a) 77 K, the boiling point of liquid nitrogen, (b) 4.2 K, the boiling point of liquid
helium,
(c) 601 K, the melting point of lead.

David Collins

Numerade Educator

Problem 15

.What is the advantage of using scientific notation over decimal notation?

Daniel Lai

Numerade Educator

Problem 16

Define significant figure. Discuss the importance of using the proper number of
significant figures in measurements and calculations.

David Collins

Numerade Educator

Problem 17

Express the following numbers in scientific notation: (a) 0.000000027, (b) 356, (c)
47,764, (d) 0.096.

Daniel Lai

Numerade Educator

Problem 18

Express the following numbers as decimals: (a) $1.52 \times 10^{-2}$, (b) $7.78 \times 10^{-8}$.
.

David Collins

Numerade Educator

Problem 19

Express the answers to the following calculations in scientific notation:
(a) $145.75+\left(2.3 \times 10^{-1}\right)$
(b) $79,500 \div\left(2.5 \times 10^2\right)$
(c) $\left(7.0 \times 10^{-3}\right)-\left(8.0 \times 10^{-4}\right)$
(d) $\left(1.0 \times 10^4\right) \times\left(9.9 \times 10^6\right)$

Daniel Lai

Numerade Educator

Problem 20

Express the answers to the following calculations in scientific notation:
(a) $0.0095+\left(8.5 \times 10^{-3}\right)$
(b) $653 \div\left(5.75 \times 10^{-8}\right)$
(c) $850,000-\left(9.0 \times 10^5\right)$
(d) $\left(3.6 \times 10^{-4}\right) \times\left(3.6 \times 10^6\right)$

David Collins

Numerade Educator

Problem 21

What is the number of significant figures in each of the following measurements?
(a) 4867 mi
(b) 56 mL
(c) 60,104 tons
(d) 2900 g
(e) $40.2 \mathrm{~g} / \mathrm{cm}^3$
(f) 0.0000003 cm
(g) 0.7 min
(h) $4.6 \times 10^{19}$ atoms

Daniel Lai

Numerade Educator

Problem 22

How many significant figures are there in each of the following? (a) 0.006 L , (b) 0.0605 dm , (c) 60.5 mg , (d) $605.5 \mathrm{~cm}^2$, (e) $960 \times 10^{-3} \mathrm{~g}$, (f) 6 kg , (g) 60 m .

David Collins

Numerade Educator

Problem 23

Carry out the following operations as if they were calculations of experimental results, and express each answer in the correct units with the correct number of significant figures.
(a) $5.6792 \mathrm{~m}+0.6 \mathrm{~m}+4.33 \mathrm{~m}$
(b) $3.70 \mathrm{~g}-2.9133 \mathrm{~g}$
(c) $4.51 \mathrm{~cm} \times 3.6666 \mathrm{~cm}$
(d) $\left(3 \times 10^4 \mathrm{~g}+6.827 \mathrm{~g}\right)\left(0.043 \mathrm{~cm}^3-0.021 \mathrm{~cm}^3\right)$

Oluwapelumi Kolawole

Oluwapelumi Kolawole

Numerade Educator

Problem 24

Carry out the following operations as if they were calculations of experimental results, and express each answer in the correct units with the correct number of significant figures.
(a) $7.310 \mathrm{~km} \div 5.70 \mathrm{~km}$
(b) $\left(3.26 \times 10^{-3} \mathrm{mg}\right)-\left(7.88 \times 10^{-5} \mathrm{mg}\right)$
(c) $\left(4.02 \times 10^6 \mathrm{dm}\right)+\left(7.74 \times 10^7 \mathrm{dm}\right)$
(d) $(7.8 \mathrm{~m}-0.34 \mathrm{~m})(1.15 \mathrm{~s}+0.82 \mathrm{~s})$

David Collins

Numerade Educator

Problem 25

Three students (A, B, and C) are asked to determine the volume of a sample of ethanol. Each student measures the volume three times with a graduated cylinder. The results in milliliters are: $\mathrm{A}(87.1,88.2,87.6) ; \mathrm{B}(86.9,87.1,87.2) ; \mathrm{C}(87.6,87.8,87.9)$. The true volume is 87.0 mL . Comment on the precision and the accuracy of each student's results.

Himanshu Garg

Numerade Educator

Problem 26

Three apprentice tailors (X, Y, and Z) are assigned the task of measuring the $\overline{\text { Page } 34}$ seam of a pair of trousers. Each one makes three measurements. The results in inches are X $(31.5,31.6,31.4) ; \mathrm{Y}(32.8,32.3,32.7) ; \mathrm{Z}(31.9,32.2,32.1)$. The true length is 32.0 in .
Comment on the precision and the accuracy of each tailor's measurements.

David Collins

Numerade Educator

Problem 27

Carry out the following conversions: (a) 22.6 m to decimeters, (b) 25.4 mg to kilograms, (c) 556 mL to liters, (d) $10.6 \mathrm{~kg} / \mathrm{m}^3$ to $\mathrm{g} / \mathrm{cm}^3$.

Daniel Lai

Numerade Educator

Problem 28

Carry out the following conversions: (a) 242 lb to milligrams, (b) $68.3 \mathrm{~cm}^3$ to cubic meters, (c) $7.2 \mathrm{~m}^3$ to liters, (d) $28.3 \mu \mathrm{~g}$ to pounds.

Himanshu Garg

Numerade Educator

Problem 29

The average speed of helium at $25^{\circ} \mathrm{C}$ is $1255 \mathrm{~m} / \mathrm{s}$. Convert this speed to miles per hour (mph).

Daniel Lai

Numerade Educator

Problem 30

How many seconds are there in a solar year ( 365.24 days)?

Himanshu Garg

Numerade Educator

Problem 31

How many minutes does it take light from the sun to reach Earth? (The distance from the sun to Earth is 93 million mi ; the speed of light $=3.00 \times 10^8 \mathrm{~m} / \mathrm{s}$.)

Himanshu Garg

Numerade Educator

Problem 32

A jogger runs a mile in 8.92 min . Calculate the speed in (a) $\mathrm{in} / \mathrm{s}$, (b) $\mathrm{m} / \mathrm{min}$, (c) $\mathrm{km} / \mathrm{h}$. (1 $\mathrm{mi}=1609 \mathrm{~m} ; 1 \mathrm{in}=2.54 \mathrm{~cm}$.)

David Collins

Numerade Educator

Problem 33

A $6.0-\mathrm{ft}$ person weighs 168 lb . Express this person's height in meters and weight in kilograms. ( $1 \mathrm{lb}=453.6 \mathrm{~g} ; 1 \mathrm{~m}=3.28 \mathrm{ft}$.)

Himanshu Garg

Numerade Educator

Problem 34

The speed limit on parts of the German autobahn was once set at 286 kilometers per hour (km/h).
Calculate the speed limit in miles per hour (mph).

David Collins

Numerade Educator

Problem 35

For a fighter jet to take off from the deck of an aircraft carrier, it must reach a speed of $62 \mathrm{~m} / \mathrm{s}$.
Calculate the speed in miles per hour (mph).

Nicole Basile

Numerade Educator

Problem 36

The "normal" lead content in human blood is about 0.40 part per million (that is, 0.40 g of lead per million grams of blood). A value of 0.80 part per million (ppm) is considered to be dangerous. How many grams of lead are contained in $6.0 \times 10^3 \mathrm{~g}$ of blood (the amount in an average adult) if the lead content is 0.62 ppm ?

Himanshu Garg

Numerade Educator

Problem 37

Carry out the following conversions: (a) 1.42 light-years to miles (a light-year is an astronomical measure of distance-the distance traveled by light in a year, or 365 days; the speed of light is $3.00 \times$
$10^8 \mathrm{~m} / \mathrm{s}$ ), (b) 32.4 yd to centimeters, (c) $3.0 \times$
$10^{10} \mathrm{~cm} / \mathrm{s}$ to $\mathrm{ft} / \mathrm{s}$.

Himanshu Garg

Numerade Educator

Problem 38

Carry out the following conversions: (a) 70 kg , the average weight of a male adult, to pounds; (b) 14 billion years (roughly the age of the universe) to seconds (assume there are 365 days in a year); (c) 7 ft 6 in , the height of the basketball player Yao Ming, to meters; (d) $88.6 \mathrm{~m}^3$ to liters.

David Collins

Numerade Educator

Problem 39

Aluminum is a lightweight metal (density $=2.70 \mathrm{g} / \mathrm{cm}^3$ ) used in aircraft construction, high-voltage transmission lines, beverage cans, and foils. What is its density in $\mathrm{kg} / \mathrm{m}^3$ ?

Himanshu Garg

Numerade Educator

Problem 40

Ammonia gas is used as a refrigerant in large-scale cooling systems. The density of ammonia gas under certain conditions is $0.625 \mathrm{~g} / \mathrm{L}$. Calculate its density in $\mathrm{g} / \mathrm{cm}^3$.

David Collins

Numerade Educator

Problem 41

What is the mass of one mole of ants? (Useful
information: A mole is the unit used for atomic and subatomic particles. It is approximately $6 \times 10^{23}$.
A $1-\mathrm{cm}$-long ant weighs about 3 mg .)

Daniel Lai

Numerade Educator

Problem 42

How much time (in years) does an 80-year-old person spend sleeping during his or her life span?

David Collins

Numerade Educator

Problem 43

Estimate the daily amount of water (in gallons) used indoors by a family of four in the United States.

Ashley Jordon

Numerade Educator

Problem 44

Bowling alleys generally stock bowling balls from 8 to 16 lb , where the mass is given in whole numbers. Given that regulation bowling balls have a diameter of 8.6 in , which (if any) of these bowling balls would you expect to float in water?

David Collins

Numerade Educator

Problem 45

Give an example for each of the following terms: (a) matter, (b) substance, (c) mixture.

Daniel Lai

Numerade Educator

Problem 46

Give an example of a homogeneous mixture and an example of a heterogeneous mixture.

David Collins

Numerade Educator

Problem 47

Give an example of an element and a compound. How do elements and compounds differ?

Daniel Lai

Numerade Educator

Problem 48

What is the number of known elements?

Arron Martel

Numerade Educator

Problem 49

Give the names of the elements represented by the chemical symbols $\mathrm{Li}, \mathrm{F}, \mathrm{P}, \mathrm{Cu}, \mathrm{As}$, $\mathrm{Zn}, \mathrm{Cl}, \mathrm{Pt}, \mathrm{Mg}, \mathrm{U}, \mathrm{Al}, \mathrm{Si}, \mathrm{Ne}$. (See Table 1.4 and the list of The Elements with Their Symbols and Atomic Masses.)

Ted Gray

Numerade Educator

Problem 50

Give the chemical symbols for the following elements: (a) cesium, (b) germanium, (c) gallium, (d) strontium, (e) uranium, (f ) selenium, (g) neon, (h) cadmium. (See Table 1.4 and the list of The Elements with Their Symbols and Atomic Masses.)

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 51

Classify each of the following substances as an element or a compound: (a) hydrogen, (b) water,
(c) gold, (d) sugar.

Daniel Lai

Numerade Educator

Problem 52

Classify each of the following as an element, a compound, a homogeneous mixture, or a heterogeneous mixture: (a) water from a well, (b) argon gas, (c) sucrose, (d) a bottle of red wine, (e) chicken noodle soup, (f) blood flowing in a capillary, (g) ozone.

David Collins

Numerade Educator

Problem 53

Identify each of the diagrams shown here as gas, liquid, or solid.
a.FIGURE CANT COPY
b.FIGURE CANT COPY
c.FIGURE CANT COPY

Aadit Sharma

Numerade Educator

Problem 54

Explain how the distances between particles typically change with different states of matter.

Syon Schlecht

Numerade Educator

Problem 55

Using examples, explain the difference between a physical property and a chemical property.

Daniel Lai

Numerade Educator

Problem 56

How does an intensive property differ from an extensive property? Which of the following properties are intensive and which are extensive? (a) length,
(b) volume, (c) temperature, (d) mass.

Ronald Prasad

Numerade Educator

Problem 57

Do the following statements describe chemical or physical properties? (a) Oxygen gas supports combustion. (b) Fertilizers help to increase agricultural production. (c) Water boils below $100^{\circ} \mathrm{C}$ on top of a mountain. (d) Lead is more dense than aluminum. (e) Uranium is a radioactive element.

Ted Gray

Numerade Educator

Problem 58

Does each of the following describe a physical change or a chemical change? (a) The helium gas inside a balloon tends to leak out after a few hours. (b) A flashlight beam slowly gets dimmer and finally goes out. (c) Frozen orange juice is reconstituted by adding water to it. (d) The growth of plants depends on the sun's energy in a process called photosynthesis. (e) A spoonful of table salt dissolves in a bowl of soup.

David Collins

Numerade Educator

Problem 59

Give one qualitative and one quantitative statement about each of the following: (a) water, (b) carbon, (c) iron, (d) hydrogen gas, (e) sucrose (cane sugar), (f ) table salt (sodium chloride), (g) mercury, (h) gold, (i) air.

Dr. Satish Ingale

Dr. Satish Ingale

Numerade Educator

Problem 60

Which of the following statements describe physical properties and which describe chemical properties? (a) Iron has a tendency to rust. (b) Rainwater in industrialized regions tends to be acidic. (c) Hemoglobin molecules have a red color. (d) When a glass of water is left out in the sun, the water gradually disappears. (e) Carbon dioxide in air is converted to more complex molecules by plants during photosynthesis.

Himanshu Garg

Numerade Educator

Problem 61

In 2008, about 95.0 billion pounds of sulfuric acid were produced in the United States. Convert this quantity to tons.

Daniel Lai

Numerade Educator

Problem 62

In determining the density of a rectangular metal bar, a student made the following measurements: length, 8.53 cm ; width, 2.4 cm ; height, 1.0 cm ; mass, 52.7064 g . Calculate the density of the metal to the correct number of significant figures.

Himanshu Garg

Numerade Educator

Problem 63

Calculate the mass of each of the following: (a) a sphere of gold with a radius of 10.0 cm [the volume of a sphere with a radius $r$ is $V=(4 / 3) \pi r^3$; the density of gold $=19.3 \mathrm{~g} / \mathrm{cm}^3$ ],
(b) a cube of platinum of edge length 0.040 mm (the density of platinum $=21.4 \mathrm{~g} / \mathrm{cm}^3$ ), (c) 50.0 mL of ethanol (the density of ethanol $=0.798 \mathrm{~g} / \mathrm{mL}$ ).

Daniel Lai

Numerade Educator

Problem 64

A cylindrical glass bottle 21.5 cm in length is filled with cooking oil of density 0.953 $\mathrm{g} / \mathrm{mL}$. If the mass of the oil needed to fill the bottle is 1360 g , calculate the inner diameter of the bottle.

David Collins

Numerade Educator

Problem 65

The following procedure was used to determine the volume of a flask. The flask was weighed dry and then filled with water. If the masses of the empty flask and filled flask were 56.12 g and 87.39 g , respectively, and the density of water is $0.9976 \mathrm{~g} / \mathrm{cm}^3$, calculate the volume of the flask in $\mathrm{cm}^3$.

Crystal Wang

Numerade Educator

Problem 66

The speed of sound in air at room temperature is about $343 \mathrm{~m} / \mathrm{s}$. Calculate this speed in miles per hour. ( $1 \mathrm{mi}=1609 \mathrm{~m}$.)

Himanshu Garg

Numerade Educator

Problem 67

A piece of silver ( Ag ) metal weighing 194.3 g is placed in a graduated cylinder containing 242.0 mL of water. The volume of water now reads 260.5 mL . From these data calculate the density of silver.

Daniel Lai

Numerade Educator

Problem 68

The experiment described in Problem 1.65 is a crude but convenient way to determine the density of some solids. Describe a similar experiment that would enable you to measure the density of ice. Specifically, what would be the requirements for the liquid used in your experiment?

David Collins

Numerade Educator

Problem 69

A lead sphere of diameter 48.6 cm has a mass of $6.852 \times 10^5 \mathrm{~g}$. Calculate the density of lead.

Nicole Krahulik

Nicole Krahulik

Numerade Educator

Problem 70

Lithium is the least dense metal known (density: $0.53 \mathrm{~g} / \mathrm{cm}^3$ ). What is the volume occupied by $1.20 \times 10^3 \mathrm{~g}$ of lithium?

Himanshu Garg

Numerade Educator

Problem 71

The medicinal thermometer commonly used in homes can be read $\pm 0.1^{\circ} \mathrm{F}$, whereas those in the doctor's office may be accurate to $\pm 0.1^{\circ} \mathrm{C}$. In degrees Celsius, express the percent error expected from each of these thermometers in measuring a person's body temperature of $38.9^{\circ} \mathrm{C}$.

Daniel Lai

Numerade Educator

Problem 72

Vanillin (used to flavor vanilla ice cream and other foods) is the substance whose aroma the human nose detects in the smallest amount. The threshold limit is $2.0 \times 10^{-11} \mathrm{~g}$ per liter of air. If the current price of 50 g of vanillin is $$\$ 112$$, determine the cost to supply enough vanillin so that the aroma could be detected in a large aircraft hangar with a volume of 5.0 $\times 10^7 \mathrm{ft}^3$.

Himanshu Garg

Numerade Educator

Problem 73

At what temperature does the numerical reading on a Celsius thermometer equal that on a Fahrenheit thermometer?

Daniel Lai

Numerade Educator

Problem 74

Suppose that a new temperature scale has been devised on which the melting point of ethanol $\left(-117.3^{\circ} \mathrm{C}\right)$ and the boiling point of ethanol $\left(78.3^{\circ} \mathrm{C}\right)$ are taken as $0^{\circ} \mathrm{S}$ and $100^{\circ} \mathrm{S}$, respectively, where S is the symbol for the new temperature scale. Derive an equation relating a reading on this scale to a reading on the Celsius scale. What would this thermometer read at $25^{\circ} \mathrm{C}$ ?

Himanshu Garg

Numerade Educator

Problem 75

A resting adult requires about 240 mL of pure oxygen/min and breathes about 12 times every minute. If inhaled air contains $20 \%$ oxygen by volume and exhaled air $16 \%$, what is the volume of air per breath? (Assume that the volume of inhaled air is equal to that of exhaled air.)

Daniel Lai

Numerade Educator

Problem 76

(a) Referring to Problem 1.75, calculate the total volume (in liters) of air an adult breathes in a day. (b) In a city with heavy traffic, the air contains $2.1 \times 10^{-6} \mathrm{~L}$ of carbon monoxide (a poisonous gas) per liter. Calculate the average daily intake of carbon monoxide in liters by a person.

Ronald Prasad

Numerade Educator

Problem 77

Three different $25.0-\mathrm{g}$ samples of solid pellets are added to 20.0 mL of water in three different measuring cylinders. The results are shown here. Given the densities of the three metals used, identify the cylinder that contains each sample of solid pellets:
A $\left(2.9 \mathrm{~g} / \mathrm{cm}^3\right), \mathrm{B}\left(8.3 \mathrm{~g} / \mathrm{cm}^3\right)$, and C $\left(3.3 \mathrm{~g} / \mathrm{cm}^3\right)$.
a.FIGURE CANT COPY
b.FIGURE CANT COPY
c.FIGURE CANT COPY

Katherine Pohly

Katherine Pohly

Numerade Educator

Problem 78

The circumference of an NBA-approved basketball is 29.6 in. Given that the radius of Earth is about 6400 km , how many basketballs would it take to circle around the equator with the basketballs touching one another? Round off your answer to an integer with three significant figures.

David Collins

Numerade Educator

Problem 79

A student is given a crucible and asked to prove whether it is made of pure platinum. She first weighs the crucible in air and then weighs it suspended in water (density $=0.9986$ $\mathrm{g} / \mathrm{mL})$. The readings are 860.2 g and 820.2 g , respectively. Based on these measurements and given that the density of platinum is $21.45 \mathrm{~g} / \mathrm{cm}^3$, what should her conclusion be?
(Hint: An object suspended in a fluid is buoyed up by the mass of the fluid displaced by the object. Neglect the buoyance of air.)

Crystal Wang

Numerade Educator

Problem 80

The surface area and average depth of the Pacific Ocean are $1.8 \times 10^8 \mathrm{~km}^2$ and $3.9 \times 10^3$ m , respectively. Calculate the volume of water in the ocean in liters.

David Collins

Numerade Educator

Problem 81

The unit "troy ounce" is often used for precious metals such as gold ( Au ) and platinum (Pt). (1 troy ounce $=31.103 \mathrm{~g}$.) (a) A gold coin weighs 2.41 troy ounces. Calculate its mass in grams. (b) Is a troy ounce heavier or lighter than an ounce? $(1 \mathrm{lb}=16 \mathrm{oz}$;

$$
1 \mathrm{lb}=453.6 \mathrm{~g} .)
$$

Daniel Lai

Numerade Educator

Problem 82

Osmium (Os) is the densest element known (density $=22.57 \mathrm{~g} / \mathrm{cm}^3$ ). Calculate the mass in pounds and in kilograms of an Os sphere 15 cm in diameter (about the size of a grapefruit). [The volume of a sphere of radius $r$ is $(4 / 3) \pi r^3$.]

Himanshu Garg

Numerade Educator

Problem 83

Percent error is often expressed as the absolute value of the difference between the true value and the experimental value, divided by the true value:

$$
\text { percent error }=\frac{\mid \text { true value }- \text { experimental value } \mid}{\mid \text { true value } \mid} \times 100 \%
$$

The vertical lines indicate absolute value. Calculate the percent error for the following measurements: (a) The density of alcohol (ethanol) is found to be $0.802 \mathrm{~g} / \mathrm{mL}$. (True value: $0.798 \mathrm{~g} / \mathrm{mL}$.) (b) The mass of gold in an earring is analyzed to be 0.837 g . (True value: 0.864 g .)

Daniel Lai

Numerade Educator

Problem 84

The natural abundances of elements in the human body, expressed as percent by mass, are: oxygen $(\mathrm{O}), 65$ percent; carbon $(\mathrm{C}), 18$ percent; hydrogen $(\mathrm{H})$,
10 percent; nitrogen $(\mathrm{N}), 3$ percent; calcium $(\mathrm{Ca}), 1.6$ percent; phosphorus $(\mathrm{P}), 1.2$ percent; all other elements, 1.2 percent. Calculate the mass in grams of each element in the body of a $62-\mathrm{kg}$ person.

David Collins

Numerade Educator

Problem 85

The men's world record for running a mile outdoors (as of 1999) is 3 min 43.13 s . At this rate, how long would it take to run a $1500-\mathrm{m}$ race? $(1 \mathrm{mi}=1609 \mathrm{~m})$

Daniel Lai

Numerade Educator

Problem 86

Venus, the second closest planet to the sun, has a surface temperature of $7.3 \times 10^2 \mathrm{~K}$. Convert this temperature to ${ }^{\circ} \mathrm{C}$ and ${ }^{\circ} \mathrm{F}$.

David Collins

Numerade Educator

Problem 87

Chalcopyrite, the principal ore of copper $(\mathrm{Cu})$, contains $34.63 \% \mathrm{Cu}$ by mass. How many grams of Cu can be obtained from $5.11 \times 10^3 \mathrm{~kg}$ of the ore?

Himanshu Garg

Numerade Educator

Problem 88

It has been estimated that $8.0 \times 10^4$ tons of gold $(\mathrm{Au})$ have been mined. Assume gold costs $$\$ 948$$ per ounce. What is the total worth of this quantity of gold?

David Collins

Numerade Educator

Problem 89

A $1.0-\mathrm{mL}$ volume of seawater contains about $4.0 \times 10^{-12} \mathrm{~g}$ of gold. The total volume of ocean water is $1.5 \times 10^{21} \mathrm{~L}$. Calculate the total amount of gold (in grams) that is present in seawater, and the worth of the gold in dollars (see Problem 1.88). With so much gold out there, why hasn't someone become rich by mining gold from the ocean?

Daniel Lai

Numerade Educator

Problem 90

Measurements show that 1.0 g of iron $(\mathrm{Fe})$ contains $1.1 \times 10^{22} \mathrm{Fe}$ atoms. How many Fe atoms are in 4.9 g of Fe , which is the total amount of iron in the body of an average adult?

David Collins

Numerade Educator

Problem 91

The thin outer layer of Earth, called the crust, contains only $0.50 \%$ of Earth's total mass and yet is the source of almost all the elements (the atmosphere provides elements such as oxygen, nitrogen, and a few other gases). Silicon (Si) is the second most abundant element in Earth's crust ( $27.2 \%$ by mass). Calculate the mass of silicon in kilograms in Earth's crust. (The mass of Earth is $5.9 \times 10^{21}$ tons. 1 ton $=2000 \mathrm{lb} ; 1 \mathrm{lb}=453.6 \mathrm{~g}$.)

Jean Gephart

Numerade Educator

Problem 92

The radius of a copper $(\mathrm{Cu})$ atom is roughly $1.3 \times 10^{-10} \mathrm{~m}$. How many times can Page 37 you divide evenly a piece of $10-\mathrm{cm}$ copper wire until it is reduced to two separate copper atoms? (Assume there are appropriate tools for this procedure and that copper atoms are lined up in a straight line, in contact with each other. Round off your answer to an integer.)

David Collins

Numerade Educator

Problem 93

One gallon of gasoline in an automobile's engine produces on the average 9.5 kg of carbon dioxide, which is a greenhouse gas, that is, it promotes the warming of Earth's atmosphere. Calculate the annual production of carbon dioxide in kilograms if there are 250 million cars in the United States and each car covers a distance of 5000 mi at a consumption rate of 20 miles per gallon.

Daniel Lai

Numerade Educator

Problem 94

A sheet of aluminum (Al) foil has a total area of $1.000 \mathrm{ft}^2$ and a mass of 3.636 g . What is the thickness of the foil in millimeters? (Density of $\mathrm{Al}=2.699 \mathrm{~g} / \mathrm{cm}^3$.)

David Collins

Numerade Educator

Problem 95

Comment on whether each of the following is a homogeneous mixture or a heterogeneous mixture: (a) air in a closed bottle, (b) air over New York City.

Himanshu Garg

Numerade Educator

Problem 96

Chlorine is used to disinfect swimming pools. The accepted concentration for this purpose is 1 ppm chlorine, or 1 g of chlorine per million grams of water. Calculate the volume of a chlorine solution (in milliliters) a homeowner should add to her swimming pool if the solution contains $6.0 \%$ chlorine by mass and there are $2.0 \times 10^4$ gallons of water in the pool. ( 1 gallon $=3.79 \mathrm{~L}$; density of liquids $=1.0 \mathrm{~g} / \mathrm{mL}$.)

Himanshu Garg

Numerade Educator

Problem 97

An aluminum cylinder is 10.0 cm in length and has a radius of 0.25 cm . If the mass of a single Al atom is $4.48 \times 10^{-23} \mathrm{~g}$, calculate the number of Al atoms present in the cylinder. The density of aluminum is $2.70 \mathrm{~g} / \mathrm{cm}^3$.

Daniel Lai

Numerade Educator

Problem 98

A pycnometer is a device for measuring the density of liquids. It is a glass flask with a close-fitting ground glass stopper having a capillary hole through it. (a) The volume of the pycnometer is determined by using distilled water at $20^{\circ} \mathrm{C}$ with a known density of $0.99820 \mathrm{~g} / \mathrm{mL}$. First, the water is filled to the rim. With the stopper in place, the fine hole allows the excess liquid to escape. The pycnometer is then carefully dried with filter paper. Given that the masses of the empty pycnometer and the same one filled with water are 32.0764 g and 43.1195 g , respectively, calculate the volume of the pycnometer. (b) If the mass of the pycnometer filled with ethanol at $20^{\circ} \mathrm{C}$ is 40.8051 g , calculate the density of ethanol. (c) Pycnometers can also be used to measure the density of solids. First, small zinc granules weighing 22.8476 g are placed in the pycnometer, which is then filled with water. If the combined mass of the pycnometer plus the zinc granules and water is 62.7728 g , what is the density of zinc?

David Collins

Numerade Educator

Problem 99

In 1849 a gold prospector in California collected a bag of gold nuggets plus sand. Given that the density of gold and sand are $19.3 \mathrm{~g} / \mathrm{cm}^3$ and $2.95 \mathrm{~g} / \mathrm{cm}^3$, respectively, and that the density of the mixture is $4.17 \mathrm{~g} / \mathrm{cm}^3$, calculate the percent by mass of gold in the mixture.

Cheryl Glor

Numerade Educator

Problem 100

The average time it takes for a molecule to diffuse a distance of $x \mathrm{~cm}$ is given by

$$
t=\frac{x^2}{2 D}
$$

where $t$ is the time in seconds and $D$ is the diffusion coefficient. Given that the diffusion coefficient of glucose is $5.7 \times 10^{-7} \mathrm{~cm}^2 / \mathrm{s}$, calculate the time it would take for a glucose molecule to diffuse $10 \mu \mathrm{~m}$, which is roughly the size of a cell.

Himanshu Garg

Numerade Educator

Problem 101

A human brain weighs about 1 kg and contains about $10^{11}$ cells. Assuming that each cell is completely filled with water (density $=1 \mathrm{~g} / \mathrm{mL}$ ), calculate the length of one side of such a cell if it were a cube. If the cells are spread out in a thin layer that is a single cell thick, what is the surface area in square meters?

Himanshu Garg

Numerade Educator

Problem 102

(a) Carbon monoxide (CO) is a poisonous gas because it binds very strongly to the oxygen carrier hemoglobin in blood. A concentration of $8.00 \times$ $10^2 \mathrm{ppm}$ by volume of carbon monoxide is considered lethal to humans. Calculate the volume in liters occupied by carbon monoxide in a room that measures 17.6 m long, 8.80 m wide, and 2.64 m high at this concentration. (b) Prolonged exposure to mercury ( Hg ) vapor can cause neurological disorders and respiratory problems. For safe air quality control, the concentration of mercury vapor must be under $0.050 \mathrm{mg} / \mathrm{m}^3$. Convert this number to $\mathrm{g} / \mathrm{L}$.
(c) The general test for type II diabetes is that the blood sugar (glucose) level should be below 120 mg per deciliter ( $\mathrm{mg} / \mathrm{dL}$ ). Convert this number to micrograms per milliliter $(\mu \mathrm{g} / \mathrm{mL})$.

David Collins

Numerade Educator

Problem 103

A bank teller is asked to assemble "one-dollar" sets of coins for his clients. Each set is made of three quarters, one nickel, and two dimes. The masses of the coins are: quarter: 5.645 g ; nickel: 4.967 g ; dime: 2.316 g . What is the maximum number of sets that can be assembled from 33.871 kg of quarters, 10.432 kg of nickels, and 7.990 kg of dimes? What is the total mass (in g ) of the assembled sets of coins?

Crystal Wang

Numerade Educator

Problem 104

A graduated cylinder is filled to the $40.00-\mathrm{mL}$ mark with a mineral oil. The masses of the cylinder before and after the addition of the mineral oil are 124.966 g and 159.446 g , respectively. In a separate experiment, a metal ball bearing of mass 18.713 g is placed in the cylinder and the cylinder is again filled to the $40.00-\mathrm{mL}$ mark with the mineral oil. The combined mass of the ball bearing and mineral oil is 50.952 g . Calculate the density and radius of the ball bearing. [The volume of a sphere of radius $r$ is $(4 / 3) \pi r^3$.]

David Collins

Numerade Educator

Problem 105

A cobalt bar (density $=8.90 \mathrm{~g} / \mathrm{cm}^3$ ) is shown here. What is the mass of this bar Page 38 to the appropriate number of significant figures?

Cheryl Glor

Numerade Educator

Problem 106

Bronze is an alloy made of copper $(\mathrm{Cu})$ and tin $(\mathrm{Sn})$ used in applications that require low metal-on-metal friction. Calculate the mass of a bronze cylinder of radius 6.44 cm and length 44.37 cm . The composition of the bronze is $79.42 \% \mathrm{Cu}$ and $20.58 \% \mathrm{Sn}$ and the densities of Cu and Sn are $8.94 \mathrm{~g} / \mathrm{cm}^3$ and $7.31 \mathrm{~g} / \mathrm{cm}^3$, respectively. What assumption should you make in this calculation?

David Collins

Numerade Educator

Problem 107

You are given a liquid. Briefly describe steps you would take to show whether it is a pure substance or a homogeneous mixture.

Himanshu Garg

Numerade Educator

Problem 108

A chemist mixes two liquids A and B to form a homogeneous mixture. The densities of the liquids are $2.0514 \mathrm{~g} / \mathrm{mL}$ for A and $2.6678 \mathrm{~g} / \mathrm{mL}$ for B . When she drops a small object into the mixture, she finds that the object becomes suspended in the liquid; that is, it neither sinks nor floats. If the mixture is made of $41.37 \% \mathrm{~A}$ and $58.63 \% \mathrm{~B}$ by volume, what is the density of the metal? Can this procedure be used in general to determine the densities of solids? What assumptions must be made in applying this method?

David Collins

Numerade Educator

Problem 109

Tums is a popular remedy for acid indigestion. A typical Tums tablet contains calcium carbonate plus some inert substances. When ingested, it reacts with the gastric juice (hydrochloric acid) in the stomach to give off carbon dioxide gas. When a $1.328-\mathrm{g}$ tablet reacted with 40.00 mL of hydrochloric acid (density: $1.140 \mathrm{~g} / \mathrm{mL}$ ), carbon dioxide gas was given off and the resulting solution weighed 46.699 g . Calculate the number of liters of carbon dioxide gas released if its density is $1.81 \mathrm{~g} / \mathrm{L}$.

Narayan Hari

Numerade Educator

Problem 110

$\mathrm{~A} 250-\mathrm{mL}$ glass bottle was filled with 242 mL of water at $20^{\circ} \mathrm{C}$ and tightly capped. It was then left outdoors overnight, where the average temperature was $-5^{\circ} \mathrm{C}$. Predict what would happen. The density of water at $20^{\circ} \mathrm{C}$ is $0.998 \mathrm{~g} / \mathrm{cm}^3$ and that of ice at $-5^{\circ} \mathrm{C}$ is 0.916 $\mathrm{g} / \mathrm{cm}^3$.

Himanshu Garg

Numerade Educator

Problem 111

Fusing "nanofibers" with diameters of 100 to 300 nm gives junctures with very small volumes that would potentially allow the study of reactions involving only a few molecules. Estimate the volume in liters of the junction formed between two such fibers with internal diameters of 200 nm . The scale reads $1 \mu \mathrm{~m}$.

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 112

Estimate the annual consumption of gasoline by passenger cars in the United States.

David Collins

Numerade Educator

Problem 113

Estimate the total amount of ocean water in liters.

David Collins

Numerade Educator

Problem 114

Estimate the volume of blood in an adult in liters.

David Collins

Numerade Educator

Problem 115

Estimate the distance (in miles) covered by an NBA player in a professional basketball game.

David Collins

Numerade Educator

Problem 116

In water conservation, chemists spread a thin film of a certain inert material over the surface of water to cut down on the rate of evaporation of water in reservoirs. This technique was pioneered by Benjamin Franklin three centuries ago. Franklin found that 0.10 mL of oil could spread over the surface of water about $40 \mathrm{~m}^2$ in area. Assuming that the oil forms a monolayer, that is, a layer that is only one molecule thick, estimate the length of each oil molecule in nanometers. ( $1 \mathrm{~nm}=1 \times 10^{-9} \mathrm{~m}$.)

Himanshu Garg

Numerade Educator