Chapter 1
Matter: Its Properties and Measurement
Exercises
(see also Appendices A-1 and A-5)
The Scientific Method
1. What are the principal reasons that one theory might be adopted over a conflicting one?
2. Can one predict how many experiments are required to verify a natural law? Explain.
3. A common belief among scientists is that there exists an underlying order to nature. Einstein
described this belief in the words “God is subtle, but He is not malicious.” What do you think
Einstein meant by this remark?
4. Describe several ways in which a scientific law differs from a legislative law.
As opposed to scientific laws, legislative laws are voted on by people and thus are subject to the
5. Describe the necessary characteristics of an experiment that is suitable to test a theory.
The experiment should be carefully set up so as to create a controlled situation in which one can
6. Describe the necessary characteristics of a scientific theory.
For a theory to be considered plausible, it must, first and foremost, agree with and/or predict the
Properties and Classification of Matter
7. State whether the following properties of matter are physical or chemical.
(a) An iron nail is attracted to a magnet.
(b) A piece of paper spontaneously ignites when its temperature reaches 451 °F.
(c) A bronze statue develops a green coating (patina) over time.
(d) A block of wood floats on water.
8. State whether the following properties are physical or chemical.
(a) A piece of sliced apple turns brown.
(b) A slab of marble feels cool to the touch.
(c) A sapphire is blue.
(d) A clay pot fired in a kiln becomes hard and covered by a glaze.
9. Indicate whether each sample of matter listed is a substance or a mixture; if it is a mixture,
indicate whether it is homogeneous or heterogeneous.
(a) clean fresh air
(b) a silver-plated spoon
(c) garlic salt
(d) ice
10. Indicate whether each sample of matter listed is a substance or a mixture; if it is a mixture,
indicate whether it is homogeneous or heterogeneous.
(a) a wooden beam
(b) red ink
(c) distilled water
(d) freshly squeezed orange juice
11. Suggest physical changes by which the following mixtures can be separated.
(a) iron filings and wood chips
(b) ground glass and sucrose (cane sugar)
(c) water and olive oil
(d) gold flakes and water
12. What type of change—physical or chemical—is necessary to separate the following?
[Hint: Refer to a listing of the elements.]
(a) sugar from a sand/sugar mixture
(b) iron from iron oxide (rust)
(c) pure water from seawater
(d) water from a slurry of sand in water
Exponential Arithmetic
13. Express each number in exponential notation. (a) 8950.; (b) 10,700.; (c) 0.0240; (d) 0.0047;
14. Express each number in common decimal form. (a)
3
5 12 10 ;
−
(b)
5
8 05 10 ;
−
(c)
4
291 1 10 ;
−
(d)
2
72 1 10−
15. Express each value in exponential form. Where appropriate, include units in your answer.
(a) speed of sound (sea level): 34,000 centimeters per second
(b) equatorial radius of Earth: 6378 kilometers
(c) the distance between the two hydrogen atoms in the hydrogen molecule: 74
trillionths of a meter
(d)
( ) ( )
32
3
2 2 10 4 7 10
5 8 10−
+ =
16. Express each value in exponential form. Where appropriate, include units in your answer.
(a) solar radiation received by Earth: 173 thousand trillion watts
(b) average human cell diameter: 1 ten-millionth of a meter
(c) the distance between the centers of the atoms in silver metal: 142 trillionths of a
meter
(d)
( ) ( )
( )
2
43
2
5 07 10 1 8 10
0 065 3 3 10
−
−
=
+
Significant Figures
17. Indicate whether each of the following is an exact number or a measured quantity subject to
uncertainty.
(a) the number of sheets of paper in a ream of paper
(b) the volume of milk in a liter bottle
(c) the distance between Earth and the sun
(d) the distance between the centers of the two oxygen atoms in the oxygen molecule
18. Indicate whether each of the following is an exact number or a measured quantity subject to
uncertainty.
(a) the number of pages in this text
(b) the number of days in the month of January
(c) the area of a city lot
(d) the distance between the centers of the atoms in a gold medal
19. Express each of the following to four significant -figures. (a) 3984.6; (b) 422.04; (c)
186,000; (d) 33,900; (e)
4
6 321 10 ;
(f)
4
5 0472 10−
20. How many significant figures are shown in each of the following? If this is indeterminate,
explain why. (a) 450; (b) 98.6; (c) 0.0033; (d) 902.10; (e) 0.02173; (f) 7000; (g) 7.02; (h)
67,000,000
21. Perform the following calculations; express each answer in exponential form and with the
appropriate number of significant figures.
(a)
0 406 0 0023 =
(b)
0 1357 16 80 0 096 =
(c)
0 458 0 12 0 037 + − =
(d)
32 18 0 055 1 652 + − =
22. Perform the following calculations; express each number and the answer in exponential form
and with the appropriate number of significant figures.
(a)
320 24 9
0 080
=
(b)
432 7 6 5 0 002300
62 0 103
=
(c)
32 44 4 9 0 304
82 94
+ − =
(d)
8 002 0 3040
13 4 0 066 1 02
+ =
− +
23. Perform the following calculations and retain the appropriate number of significant figures in each
result.
(a)
( ) ( )
35
38 4 10 6 36 10
−
=
(b)
( ) ( )
( )
24
2
3
1 45 10 8 76 10
9 2 10
−
−
=
(c)
24 6 18 35 2 98 + − =
(d)
( ) ( ) ( )
3 2 4
1 646 10 2 18 10 1 36 10 − +
( )
2
5 17 10−
=
(e)
( )
( )
( )
( )
2
4 4 5
7 29 10 7 29 10 4 1 00 2 7 10
2 1 00
− − −
− + +
[Hint: The significant figure rule for the extraction of a root is the same as for
multiplication.]
24. Express the result of each of the following calculations in exponential form and with the
appropriate number of significant figures.
(a)
( ) ( ) ( )
4 2 3
4 65 10 2 95 10 6 663 10 8 2
−−
=
(b)
( ) ( )
( )
43
3
4
1912 0 0077 10 3 12 10
4 18 10
−
−
=
(c)
( )
3
3 46 10 0 087 15 26 1 0023 =
(d)
( )
2
2
3
4 505 10 1 080 1545 9
0 03203 10
−
=
(e)
( ) ( )
( )
( )
( )
2
4 4 5
3 61 10 3 61 10 4 1 00 1 9 10
2 1 00
− − −
− + +
25. An American press release describing the 1986 nonstop, round-the-world trip by the ultra-
lightweight aircraft Voyager included the following data:
flight distance: 25,012 mi
flight time: 9 days, 3 minutes, 44 seconds
fuel capacity: nearly 9000 lb
fuel remaining at end of flight: 14 gal
To the maximum number of significant figures permitted, calculate
(a) the average speed of the aircraft in kilometers per hour
(b) the fuel consumption in kilometers per kilogram of fuel (assume a density of
0 70 g/mL
for the fuel)
26. Use the concept of significant figures to criticize the way in which the following
information was presented. “The estimated proved reserve of natural gas as of January 1,
1982, was 2,911,346 trillion cubic feet.”
Units of Measurement
27. Perform the following conversions.
(a)
0 127 L mL=
(b)
15 8 mL L=
(c)
3
981 cm L=
(d)
33
2 65 m cm=
28. Perform the following conversions.
(a)
2 35 kg g=
(b)
792 g kg=
(c)
3869 mm cm=
(d)
0 043 cm mm=
29. Perform the following conversions from non-SI to SI units. (Use information from the inside
back cover, as needed.)
(a)
68 4 in cm=
(b)
94 ft m=
(c)
1 42 lb g=
(d)
248 lb kg=
(e)
3
1 85 gal dm=
(f)
3 72 qt mL=
30. Determine the number of the following:
(a) square meters
( )
2
m
in 1 square kilometer
( )
2
km
(b) cubic centimeters
( )
3
cm
in 1 cubic meter
( )
3
m
(c) square meters
( )
2
m
in 1 square mile
( )
2
mi
(1 mi 5280 ft)=
31. Which is the greater mass,
3245 g
or 0.00515 mg? Explain.
32. Which is the greater mass, 3257 mg or 0.000475 kg? Explain.
33. The non-SI unit, the hand (used by equestrians), is 4 inches. What is the height, in meters, of
34. The unit furlong is used in horse racing. The units chain and link are used in surveying.
There are exactly 8 furlongs in 1 mi, 10 chains in 1 furlong, and 100 links in 1 chain. To
three significant figures, what is the length of 1 link in centimeters?
35. A sprinter runs the 100 yd dash in 9.3 s. At this same rate,
(a) how long would it take the sprinter to run 100.0 m?
(b) what is the sprinter’s speed in meters per second?
(c) how long would it take the sprinter to run a distance of 1.45 km?
36. A non-SI unit of mass used in pharmaceutical work is the grain (gr)
( )
15 gr 1 0 g=
An
aspirin tablet –contains 5.0 gr of aspirin. A 161 lb arthritic individual takes two aspirin
tablets per day.
(a) What is the quantity of aspirin in two tablets, expressed in milligrams?
(b) What is the dosage rate of aspirin, expressed in milligrams of aspirin per kilogram
of body mass?
(c) At the given rate of consumption of aspirin tablets, how many days would it take
to consume 1.0 kg of aspirin?
37. In SI units, land area is measured in hectares
( )
2
1 hectare 1 hm=
The commonly used unit for
land area in the United States is the acre. How many acres correspond to 1 hectare?
2
(1 mi 640 acres,1 mi 5280 ft, 1 ft 12 in)= = =
38. In an engineering reference book, you find that the density of iron is
3
0 284 lb/in
What is
t h e d e n s i t y i n
3
g/cm ?
39. In a user’s manual accompanying an American-made automobile, a typical gauge pressure
for optimal performance of automobile tires is
2
32 lb/in
What is this pressure in grams per
square centimeter and kilograms per square meter?
40. The volume of a red blood cell is about
12 3
90 0 10 cm
−
Assuming that red blood cells are
spherical, what is the diameter of a red blood cell in millimeters? T
Temperature Scales
41. We want to mark off a thermometer in both Celsius and Fahrenheit temperatures. On the
Celsius scale, the lowest temperature mark is at
10 C,−
and the highest temperature mark is
at 50 °C. What are the equivalent Fahrenheit temperatures?
42. The highest and lowest temperatures on record for San Bernardino, California, are 118 °F and
17 °F, respectively. What are these temperatures on the Celsius scale?
43. The absolute zero of temperature is
273 15 C−
Should it be possible to achieve a
temperature of
465 F?−
Explain.
44. A family/consumer science class is given an assignment in candy-making that requires a
sugar mixture to be brought to a “soft–ball” stage (234–240 °F). A student borrows a
thermometer having a range from
10 C−
to 110 °C from the chemistry laboratory to do
this assignment. Will this thermometer serve the purpose? Explain.
45. You decide to establish a new temperature scale on which the melting point of mercury
( )
38 9 C−
is 0 °M, and the boiling point of mercury (356.9 °C) is 100 °M. What would
be (a) the boiling point of water in °M; and (b) the temperature of absolute zero in °M?
46. You decide to establish a new temperature scale on which the melting point of ammonia
( )
77 75 C−
is 0 °A and the boiling point of ammonia
( )
33 35 C−
is 100 °A. What would be
(a) the boiling point of water in °A; and (b) the temperature of absolute zero in °A?
Density
47. A 2.18 L sample of butyric acid, a substance present in rancid butter, has a mass of 2088 g.
What is the -density of butyric acid in grams per milliliter?
48. A 15.2 L sample of chloroform at 20 °C has a mass of 22.54 kg. What is the density of
chloroform at 20 °C, in grams per milliliter?
49. To determine the density of acetone, a 55.0 gal drum is weighed twice. The drum weighs
75.0 lb when empty and 437.5 lb when filled with acetone. What is the density of acetone
expressed in grams per milliliter?
50. To determine the volume of an irregularly shaped glass vessel, the vessel is weighed empty
(121.3 g) and when filled with carbon tetrachloride (283.2 g). What is the volume capacity of
the vessel, in milliliters, given that the density of carbon tetrachloride is
1 59 g/mL?
51. A solution consisting of 8.50% acetone and 91.5% water by mass has a density of
0 9867 g/mL
What mass of acetone, in kilograms, is present in 7.50 L of the solution?
52. A solution contains 10.05% sucrose (cane sugar) by mass. What mass of the solution, in
grams, is needed for an application that requires 1.00 kg of sucrose?
53. A fertilizer contains 21% nitrogen by mass. What mass of this fertilizer, in kilograms, is
required for an application requiring 225 g of nitrogen?
54. A vinegar sample is found to have a density of
1 006 g/mL
and to contain 5.4% acetic acid
by mass. How many grams of acetic acid are present in 1.00 L of this vinegar?
55. Calculate the mass of a block of iron
( )
3
7.86 g/cmd=
with dimensions of
52 8 cm 6 74 cm 3 73 cm
56. Calculate the mass of a cylinder of stainless steel
( )
3
7 75 g/cmd=
with a height of 18.35 cm
and a radius of 1.88 cm.
57. The following densities are given at 20 °C: water,
3
0 998 g/cm ;
iron,
3
7 86 g/cm ;
aluminum,
3
2 70 g/cm
Arrange the following items in terms of increasing mass.
(a) a rectangular bar of iron,
81 5 cm 2 1 cm 1 6 cm
(b) a sheet of aluminum foil,
12 12 m 3 62 m 0 003 cm
(c) 4.051 L of water
58. To determine the approximate mass of a small spher-ical shot of copper, the following
experiment is -performed. When 125 pieces of the shot are counted out and added to 8.4 mL
of water in a graduated cylinder, the total volume becomes 8.9 mL. The density of copper is
3
8 92 g/cm
Determine the approximate mass of a single piece of shot, assuming that all of
the pieces are of the same dimensions.
59. The density of aluminum is
3
2 70 g/cm
A square piece of aluminum foil, 22.86 cm on a side
60. The angle iron pictured here is made of steel with a density of
3
7 78 g/cm
What is the mass,
in grams, of this object?
61. In normal blood, there are about
9
5 4 10
red blood cells per milliliter. The volume of a red
blood cell is about
12 3
90 0 10 cm ,
−
and its density is
1 096 g/mL
How many liters of whole
blood would be needed to collect 0.5 kg of red blood cells?
62. A technique once used by geologists to measure the density of a mineral is to mix two dense
liquids in such proportions that the mineral grains just float. When a sample of the mixture in
which the mineral calcite just floats is put in a special density bottle, the weight is 15.4448 g.
When empty, the bottle weighs 12.4631 g, and when filled with water, it weighs 13.5441 g.
What is the density of the calcite sample? (All measurements were carried out at 25 °C, and
the density of water at 25 °C is
0 9970 g/mL
.) “
Percent Composition
63. In a class of 76 students, the results of a particular examination were 7 A’s, 22 B’s, 37 C’s, 8
D’s, 2 F’s. What was the percent distribution of grades, that is, % A’s, % B’s, and so on?
9.2% A, 28.9% B, 48.7% C, 11% D, 3% F
64. A class of 84 students had a final grade distribution of 18% A’s, 25% B’s, 32% C’s, 13%
D’s, 12% F’s. How many students received each grade?
65. A solution of sucrose in water is 28.0% sucrose by mass and has a density of
1 118 g/mL
What mass of sucrose, in grams, is contained in 3.50 L of this solution?
66. A solution containing 12.0% sodium hydroxide by mass in water has a density of
1 131 g/mL
What -volume of this solution, in liters, must be used in an application requiring 2.75 kg of
sodium hydroxide?
Integrative and Advanced Exercises
67. According to the rules on significant figures, the product of the measured quantities 99.9 m and
1.008 m should be expressed to three significant figures—
2
101 m
Yet, in this case, it would
be more appropriate to express the result to four significant figures—
2
100 7 m
Explain why.
68. For a solution containing 6.38% para-dichlorobenzene by mass in benzene, the density of the
solution as a function of temperature (t) in the temperature range 15 to 65 °C is given by the
equation
69. A solution used to chlorinate a home swimming pool contains 7% chlorine by mass. An ideal
chlorine level for the pool is one part per million (1 ppm). (Think of 1 ppm as being 1 g
chlorine per million grams of water.) If you assume densities of
1 10 g/mL
for the chlorine
solution and
1 00 g/mL
for the swimming pool water, what volume of the chlorine solution,
in liters, is required to produce a chlorine level of 1 ppm in an 18,000-gallon swimming
pool?
70. A standard 1.000 kg mass is to be cut from a bar of steel having an equilateral triangular