CHAPTER 1
Chemistry and Measurement
■ SOLUTIONS TO EXERCISES
Note on significant figures: If the final answer to a solution needs to be rounded off, it is given first with
one nonsignificant figure, and the last significant figure is underlined. The final answer is then rounded to
the correct number of significant figures. In multistep problems, intermediate answers are given with at
least one nonsignificant figure; however, only the final answer has been rounded off.
1.1. From the law of conservation of mass,
Mass of wood + mass of air = mass of ash + mass of gases
Substituting, you obtain
1.85 grams + 9.45 grams = 0.28 grams + mass of gases
or,
Mass of gases = (1.85 + 9.45 − 0.28) grams = 11.02 grams
Thus, the mass of gases in the vessel at the end of the experiment is 11.02 grams.
1.2. Physical properties: soft, silvery-colored metal; melts at 64°C.
Chemical properties: reacts vigorously with water, with oxygen, and with chlorine.
1.3. a. The factor 9.1 has the fewest significant figures, so the answer should be reported to two
significant figures.
5.61 7.891
= 4.86 = 4.9
9.1
b. The number with the least number of decimal places is 8.91. Therefore, round the answer to
two decimal places.
8.91 − 6.435 = 2.475 = 2.48
c. The number with the least number of decimal places is 6.81. Therefore, round the answer to
two decimal places.
6.81 − 6.730 = 0.080 = 0.08
d. You first do the subtraction within parentheses. In this step, the number with the least
number of decimal places is 6.81, so the result of the subtraction has two decimal places.
The least significant figure for this step is underlined.
38.91 (6.81 − 6.730) = 38.91 0.080
Next, perform the multiplication. In this step, the factor 0.080 has the fewest significant
figures, so round the answer to one significant figure.
38.91 0.080 = 3.11 = 3
1
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
, 2 Chapter 1: Chemistry and Measurement
1.4. a. 1.84 x 10−9 m = 1.84 nm
b. 5.67 x 10−12 s = 5.67 ps
c. 7.85 x 10−3 g = 7.85 mg
d. 9.7 x 103 m = 9.7 km
e. 0.000732 s = 0.732 ms, or 732 µs
f. 0.000000000154 m = 0.154 nm, or 154 pm
1.5. a. Substituting, we find that
5C 5C
tC = (tF − 32°F) = (102.5°F − 32°F) = 39.167°C
9F 9F
= 39.2°C
b. Substituting, we find that
1K 1K
TK = tc + 273.15 K = 78C + 273.15 K = 195.15 K
1C 1C
= 195 K
1.6. Recall that density equals mass divided by volume. You substitute 159 g for the mass and 20.2
g/cm3 for the volume.
m 159 g
d= = = 7.871 g/cm3 = 7.87 g/cm3
V 20.2 cm3
The density of the metal equals that of iron.
1.7. Rearrange the formula defining the density to obtain the volume.
m
V=
d
Substitute 30.3 g for the mass and 0.789 g/cm3 for the density.
30.3 g
V= = 38.40 cm3 = 38.4 cm3
0.789 g/cm3
1.8. Since one pm = 10−12 m, and the prefix milli- means 10−3, you can write
1012 m 1 mm
121 pm 3 = 1.21 10−7 mm
1 pm 10 m
3 3
1010 m 1 dm
1.9. 67.6 Å3 1 = 6.76 10 dm
−26 3
1Å 10 m
1.10. From the definitions, you obtain the following conversion factors:
36 in 2.54 cm 10-2 m
1= 1= 1=
1 yd 1 in 1 cm
The conversion factor for yards to meters is as follows:
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
, Chapter 1: Chemistry and Measurement 3
36 in 2.54 cm 10-2 m
1.000 yd x x x = 0.9144 m (exact)
1 yd 1 in 1 cm
Finally,
0.9144 m
3.54 yd x = 3.237 m = 3.24 m
1 yd
■ ANSWERS TO CONCEPT CHECKS
1.1. Box A contains a collection of identical units; therefore, it must represent an element. Box B
contains a compound because a compound is the chemical combination of two or more elements
(two elements in this case). Box C contains a mixture because it is made up of two different
substances.
1.2. a. For a person who weighs less than 100 pounds, two significant figures are typically used,
although one significant figure is possible (for example, 60 pounds). For a person who
weighs 100 pounds or more, three significant figures are typically used to report the weight
(given to the whole pound), although people often round to the nearest unit of 10, which
may result in reporting the weight with two significant figures (for example, 170 pounds).
b. Assuming a weight of 165 pounds, rounded to two significant figures this would be
reported as 1.7 x 102 pounds.
c. For example, 165 lb weighed on a scale that can measure in 100-lb increments would be
200 lb. Using the conversion factor 1 lb = 0.4536 kg, 165 lb is equivalent to 74.8 kg. Thus,
on a scale that can measure in 50-kg increments, 165 lb would be 50 kg.
1.3. a. If your leg is approximately 32 inches long, this would be equivalent to 0.81 m, 8.1 dm, or
81 cm.
b. One story is approximately 10 feet, so three stories is 30 feet. This would be equivalent to
approximately 9 m.
c. Normal body temperature is 98.6°F, or 37.0°C. Thus, if your body temperature were 39°C
(102°F), you would feel as if you had a moderate fever.
d. Room temperature is approximately 72°F, or 22°C. Thus, if you were sitting in a room at
23°C (73°F), you would be comfortable in a short-sleeve shirt.
1.4. Gold is a very unreactive substance, so comparing physical properties is probably your best
option. However, color is a physical property you cannot rely on in this case to get your answer.
One experiment you could perform is to determine the densities of the metal and the chunk of
gold. You could measure the mass of the nugget on a balance and the volume of the nugget by
water displacement. Using this information, you could calculate the density of the nugget. Repeat
the experiment and calculations for the sample of gold. If the nugget is gold, the two densities
should be equal and be 19.3 g/cm3.
Also, you could determine the melting points of the metal and the chunk of pure gold. The two
melting points should be the same (1338 K) if the metal is gold.
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
, 4 Chapter 1: Chemistry and Measurement
■ ANSWERS TO SELF-ASSESSMENT AND REVIEW QUESTIONS
1.1. One area of technology that chemistry has changed is the characteristics of materials. The liquid-
crystal displays (LCDs) in devices such as watches, cell phones, computer monitors, and
televisions are materials made of molecules designed by chemists. Electronics and
communications have been transformed by the development of optical fibers to replace copper
wires. In biology, chemistry has changed the way scientists view life. Biochemists have found
that all forms of life share many of the same molecules and molecular processes.
1.2. An experiment is an observation of natural phenomena carried out in a controlled manner so that
the results can be duplicated and rational conclusions obtained. A theory is a tested explanation of
basic natural phenomena. They are related in that a theory is based on the results of many
experiments and is fruitful in suggesting other, new experiments. Also, an experiment can
disprove a theory but can never prove it absolutely. A hypothesis is a tentative explanation of
some regularity of nature.
1.3. Rosenberg conducted controlled experiments and noted a basic relationship that could be stated
as a hypothesis—that is, that certain platinum compounds inhibit cell division. This led him to do
new experiments on the anticancer activity of these compounds.
1.4. Matter is the general term for the material things around us. It is whatever occupies space and can
be perceived by our senses. Mass is the quantity of matter in a material. The difference between
mass and weight is that mass remains the same wherever it is measured, but weight is
proportional to the mass of the object divided by the square of the distance between the center of
mass of the object and that of the earth.
1.5. The law of conservation of mass states that the total mass remains constant during a chemical
change (chemical reaction). To demonstrate this law, place a sample of wood in a sealed vessel
with air, and weigh it. Heat the vessel to burn the wood, and weigh the vessel after the
experiment. The weight before the experiment and that after it should be the same.
1.6. Mercury metal, which is a liquid, reacts with oxygen gas to form solid mercury(II) oxide. The
color changes from that of metallic mercury (silvery) to a color that varies from red to yellow
depending on the particle size of the oxide.
1.7. Gases are easily compressible and fluid. Liquids are relatively incompressible and fluid. Solids
are relatively incompressible and rigid.
1.8. An example of a substance is the element sodium. Among its physical properties: It is a solid, and
it melts at 98°C. Among its chemical properties: It reacts vigorously with water, and it burns in
chlorine gas to form sodium chloride.
1.9. An example of an element: sodium; of a compound: sodium chloride, or table salt; of a
heterogeneous mixture: salt and sugar; of a homogeneous mixture: sodium chloride dissolved in
water to form a solution.
1.10. A glass of bubbling carbonated beverage with ice cubes contains three phases: gas, liquid, and
solid.
1.11. A compound may be decomposed by chemical reactions into elements. An element cannot be
decomposed by any chemical reaction. Thus, a compound cannot also be an element in any case.
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Chemistry and Measurement
■ SOLUTIONS TO EXERCISES
Note on significant figures: If the final answer to a solution needs to be rounded off, it is given first with
one nonsignificant figure, and the last significant figure is underlined. The final answer is then rounded to
the correct number of significant figures. In multistep problems, intermediate answers are given with at
least one nonsignificant figure; however, only the final answer has been rounded off.
1.1. From the law of conservation of mass,
Mass of wood + mass of air = mass of ash + mass of gases
Substituting, you obtain
1.85 grams + 9.45 grams = 0.28 grams + mass of gases
or,
Mass of gases = (1.85 + 9.45 − 0.28) grams = 11.02 grams
Thus, the mass of gases in the vessel at the end of the experiment is 11.02 grams.
1.2. Physical properties: soft, silvery-colored metal; melts at 64°C.
Chemical properties: reacts vigorously with water, with oxygen, and with chlorine.
1.3. a. The factor 9.1 has the fewest significant figures, so the answer should be reported to two
significant figures.
5.61 7.891
= 4.86 = 4.9
9.1
b. The number with the least number of decimal places is 8.91. Therefore, round the answer to
two decimal places.
8.91 − 6.435 = 2.475 = 2.48
c. The number with the least number of decimal places is 6.81. Therefore, round the answer to
two decimal places.
6.81 − 6.730 = 0.080 = 0.08
d. You first do the subtraction within parentheses. In this step, the number with the least
number of decimal places is 6.81, so the result of the subtraction has two decimal places.
The least significant figure for this step is underlined.
38.91 (6.81 − 6.730) = 38.91 0.080
Next, perform the multiplication. In this step, the factor 0.080 has the fewest significant
figures, so round the answer to one significant figure.
38.91 0.080 = 3.11 = 3
1
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
, 2 Chapter 1: Chemistry and Measurement
1.4. a. 1.84 x 10−9 m = 1.84 nm
b. 5.67 x 10−12 s = 5.67 ps
c. 7.85 x 10−3 g = 7.85 mg
d. 9.7 x 103 m = 9.7 km
e. 0.000732 s = 0.732 ms, or 732 µs
f. 0.000000000154 m = 0.154 nm, or 154 pm
1.5. a. Substituting, we find that
5C 5C
tC = (tF − 32°F) = (102.5°F − 32°F) = 39.167°C
9F 9F
= 39.2°C
b. Substituting, we find that
1K 1K
TK = tc + 273.15 K = 78C + 273.15 K = 195.15 K
1C 1C
= 195 K
1.6. Recall that density equals mass divided by volume. You substitute 159 g for the mass and 20.2
g/cm3 for the volume.
m 159 g
d= = = 7.871 g/cm3 = 7.87 g/cm3
V 20.2 cm3
The density of the metal equals that of iron.
1.7. Rearrange the formula defining the density to obtain the volume.
m
V=
d
Substitute 30.3 g for the mass and 0.789 g/cm3 for the density.
30.3 g
V= = 38.40 cm3 = 38.4 cm3
0.789 g/cm3
1.8. Since one pm = 10−12 m, and the prefix milli- means 10−3, you can write
1012 m 1 mm
121 pm 3 = 1.21 10−7 mm
1 pm 10 m
3 3
1010 m 1 dm
1.9. 67.6 Å3 1 = 6.76 10 dm
−26 3
1Å 10 m
1.10. From the definitions, you obtain the following conversion factors:
36 in 2.54 cm 10-2 m
1= 1= 1=
1 yd 1 in 1 cm
The conversion factor for yards to meters is as follows:
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
, Chapter 1: Chemistry and Measurement 3
36 in 2.54 cm 10-2 m
1.000 yd x x x = 0.9144 m (exact)
1 yd 1 in 1 cm
Finally,
0.9144 m
3.54 yd x = 3.237 m = 3.24 m
1 yd
■ ANSWERS TO CONCEPT CHECKS
1.1. Box A contains a collection of identical units; therefore, it must represent an element. Box B
contains a compound because a compound is the chemical combination of two or more elements
(two elements in this case). Box C contains a mixture because it is made up of two different
substances.
1.2. a. For a person who weighs less than 100 pounds, two significant figures are typically used,
although one significant figure is possible (for example, 60 pounds). For a person who
weighs 100 pounds or more, three significant figures are typically used to report the weight
(given to the whole pound), although people often round to the nearest unit of 10, which
may result in reporting the weight with two significant figures (for example, 170 pounds).
b. Assuming a weight of 165 pounds, rounded to two significant figures this would be
reported as 1.7 x 102 pounds.
c. For example, 165 lb weighed on a scale that can measure in 100-lb increments would be
200 lb. Using the conversion factor 1 lb = 0.4536 kg, 165 lb is equivalent to 74.8 kg. Thus,
on a scale that can measure in 50-kg increments, 165 lb would be 50 kg.
1.3. a. If your leg is approximately 32 inches long, this would be equivalent to 0.81 m, 8.1 dm, or
81 cm.
b. One story is approximately 10 feet, so three stories is 30 feet. This would be equivalent to
approximately 9 m.
c. Normal body temperature is 98.6°F, or 37.0°C. Thus, if your body temperature were 39°C
(102°F), you would feel as if you had a moderate fever.
d. Room temperature is approximately 72°F, or 22°C. Thus, if you were sitting in a room at
23°C (73°F), you would be comfortable in a short-sleeve shirt.
1.4. Gold is a very unreactive substance, so comparing physical properties is probably your best
option. However, color is a physical property you cannot rely on in this case to get your answer.
One experiment you could perform is to determine the densities of the metal and the chunk of
gold. You could measure the mass of the nugget on a balance and the volume of the nugget by
water displacement. Using this information, you could calculate the density of the nugget. Repeat
the experiment and calculations for the sample of gold. If the nugget is gold, the two densities
should be equal and be 19.3 g/cm3.
Also, you could determine the melting points of the metal and the chunk of pure gold. The two
melting points should be the same (1338 K) if the metal is gold.
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
, 4 Chapter 1: Chemistry and Measurement
■ ANSWERS TO SELF-ASSESSMENT AND REVIEW QUESTIONS
1.1. One area of technology that chemistry has changed is the characteristics of materials. The liquid-
crystal displays (LCDs) in devices such as watches, cell phones, computer monitors, and
televisions are materials made of molecules designed by chemists. Electronics and
communications have been transformed by the development of optical fibers to replace copper
wires. In biology, chemistry has changed the way scientists view life. Biochemists have found
that all forms of life share many of the same molecules and molecular processes.
1.2. An experiment is an observation of natural phenomena carried out in a controlled manner so that
the results can be duplicated and rational conclusions obtained. A theory is a tested explanation of
basic natural phenomena. They are related in that a theory is based on the results of many
experiments and is fruitful in suggesting other, new experiments. Also, an experiment can
disprove a theory but can never prove it absolutely. A hypothesis is a tentative explanation of
some regularity of nature.
1.3. Rosenberg conducted controlled experiments and noted a basic relationship that could be stated
as a hypothesis—that is, that certain platinum compounds inhibit cell division. This led him to do
new experiments on the anticancer activity of these compounds.
1.4. Matter is the general term for the material things around us. It is whatever occupies space and can
be perceived by our senses. Mass is the quantity of matter in a material. The difference between
mass and weight is that mass remains the same wherever it is measured, but weight is
proportional to the mass of the object divided by the square of the distance between the center of
mass of the object and that of the earth.
1.5. The law of conservation of mass states that the total mass remains constant during a chemical
change (chemical reaction). To demonstrate this law, place a sample of wood in a sealed vessel
with air, and weigh it. Heat the vessel to burn the wood, and weigh the vessel after the
experiment. The weight before the experiment and that after it should be the same.
1.6. Mercury metal, which is a liquid, reacts with oxygen gas to form solid mercury(II) oxide. The
color changes from that of metallic mercury (silvery) to a color that varies from red to yellow
depending on the particle size of the oxide.
1.7. Gases are easily compressible and fluid. Liquids are relatively incompressible and fluid. Solids
are relatively incompressible and rigid.
1.8. An example of a substance is the element sodium. Among its physical properties: It is a solid, and
it melts at 98°C. Among its chemical properties: It reacts vigorously with water, and it burns in
chlorine gas to form sodium chloride.
1.9. An example of an element: sodium; of a compound: sodium chloride, or table salt; of a
heterogeneous mixture: salt and sugar; of a homogeneous mixture: sodium chloride dissolved in
water to form a solution.
1.10. A glass of bubbling carbonated beverage with ice cubes contains three phases: gas, liquid, and
solid.
1.11. A compound may be decomposed by chemical reactions into elements. An element cannot be
decomposed by any chemical reaction. Thus, a compound cannot also be an element in any case.
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
