be
3
3 11 g Pb/m
How many Pb atoms would be present in a 0.500 L sample of this air (the
volume of air displaced in the lungs between inhaling and exhaling)?
65. Without doing detailed calculations, determine which of the following samples has the
greatest number of atoms:
(a) a cube of iron with a length of 10.0 cm
( )
3
7 86 g/cmd=
(b) 1.00 kg of hydrogen contained in a 10,000 L -balloon
(c) a mound of sulfur weighing 20.0 kg
(d) a 76 lb sample of liquid mercury
( )
13 5 g/mLd=
66. Without doing detailed calculations, determine which of the following samples occupies the
largest volume:
(a) 25.5 mol of sodium metal
( )
3
0 971 g/cmd=
(b) 0.725 L of liquid bromine
( )
3 12 g/mLd=
(c)
25
1 25 10
atoms of chromium metal
( )
3
9 4 g/cmd=
(d) 2.15 kg of plumber’s solder
( )
3
9 4 g/cmd,=
a lead–tin alloy with a 2:1 atom
ratio of lead to tin
Integrative and Advanced Exercises
67. A solution was prepared by dissolving 2.50 g potassium chlorate (a substance used in
fireworks and flares) in 100.0 mL of water at 40 °C. When the solution was cooled to 20 °C,
its volume was still found to be 100.0 mL, but some of the potassium chlorate had
crystallized (deposited from the solution as a solid). At 40 °C, the density of water is
0 9922 g/mL,
and at 20 °C, the potassium chlorate solution had a density of
1 0085 g/mL
(a) Estimate, to two significant figures, the mass of potassium chlorate that
crystallized.
(b) Why can’t the answer in (a) be given more -precisely?
68. William Prout (1815) proposed that all other atoms are built up of hydrogen atoms,
suggesting that all elements should have integral atomic masses based on an atomic mass of
one for hydrogen. This hypothesis appeared discredited by the discovery of atomic masses,
such as 24.3 u for magnesium and 35.5 u for chlorine. In terms of modern knowledge,
explain why Prout’s hypothesis is actually quite reasonable.
69. Fluorine has a single atomic species,
19 F
Determine the atomic mass of
19 F
by summing the
masses of its protons, neutrons, and electrons, and compare your results with the value listed
on the inside front cover. Explain why the agreement is poor.
70. Use
13
1 10 cm
−
as the approximate diameter of the spherical nucleus of the hydrogen-1
atom, together with data from Table 2.1, to estimate the density of matter in a proton.
71. Use fundamental definitions and statements from Chapters 1 and 2 to establish the fact that
72. In each case, identify the element in question.
(a) The mass number of an atom is 234, and the atom has 60.0% more neutrons than
protons.
(b) An ion with a
2+
charge has 10.0% more protons than electrons.
(c) An ion with a mass number of 110 and a
2+
charge has 25.0% more neutrons
2+
74. Determine the only possible isotope (E) for which the following conditions are met:
• The mass number of E is 2.50 times its atomic number.
• The atomic number of E is equal to the mass number of another isotope (Y). In
turn, isotope Y has a neutron number that is 1.33 times the atomic number of Y and
75. Suppose we redefined the atomic mass scale by arbitrarily assigning to the naturally
occurring mixture of chlorine isotopes an atomic mass of 35.00000 u.
(a) What would be the atomic masses of helium, sodium, and iodine on this new
atomic mass scale?
(b) Why do these three elements have nearly integral (whole-number) atomic masses
based on carbon-12, but not based on naturally occurring chlorine?
76. The two naturally occurring isotopes of nitrogen have masses of 14.0031 and 15.0001 u,
respectively. Use the conventional atomic mass of nitrogen to estimate the percentage of
15 N
atoms in naturally occurring nitrogen.
77. The masses of the naturally occurring mercury isotopes are
196 Hg,
195.9658 u;
198 Hg,
1 9 7 . 9 6 6 8 u ;
199 Hg,
1 9 8 . 9 6 8 3 u ;
200 Hg,
1 9 9 . 9 6 8 3 u ;
201 Hg,
200.9703 u;
78. Germanium has three major naturally occurring isotopes:
70 Ge
(69.92425 u, 20.85%),
72 Ge
(71.92208 u, 27.54%),
74 Ge
(73.92118 u, 36.29%). There are also two minor isotopes:
73 Ge
(72.92346 u) and
76 Ge
(75.92140 u). Calculate the percent isotopic abundances of the two
79. From the densities of the lines in the mass spectrum of krypton gas, the following observations
were made:
• Somewhat more than 50% of the atoms were krypton-84.
• The numbers of krypton-82 and krypton-83 atoms were essentially equal.
• The number of krypton-86 atoms was 1.50 times as great as the number of krypton-82
atoms.
• The number of krypton-80 atoms was 19.6% of the number of krypton-82 atoms.
• The number of krypton-78 atoms was 3.0% of the number of krypton-82 atoms.
The masses of the isotopes are
80. The two naturally occurring isotopes of chlorine are
35 Cl
(34.9689 u, 75.77%) and
37 Cl
(36.9658 u, 24.23%). The two naturally occurring isotopes of bromine are
79 Br
(78.9183 u,
50.69%) and
81 Br
(80.9163 u, 49.31%). Chlorine and bromine combine to form bromine
monochloride, BrCl. Sketch a mass spectrum for BrCl with the relative number of molecules
81. How many atoms are present in a 1.50 m length of 20-gauge copper wire? A 20-gauge wire has
a dia-meter of 0.03196 in., and the density of copper is
3
8 92 g/cm
82. Monel metal is a corrosion-resistant copper–nickel alloy used in the electronics industry. A
particular alloy with a density of
3
8 80 g/cm
and containing 0.022% Si by mass is used to
make a rectangular plate 15.0 cm long, 12.5 cm wide, 3.00 mm thick, and has a 2.50 cm
diameter hole drilled through its center. How many silicon-30 atoms are found in this plate?
The mass of a silicon-30 atom is 29.97376 u, and the percent isotopic abundance of silicon-30
is 3.10%.
83. Deuterium,
2H
(2.0140 u), is sometimes used to replace the principal hydrogen isotope
1H
in
chemical studies. The percent isotopic abundance of deuterium is 0.015%. If it can be done
with 100% efficiency, what mass of hydrogen gas would have to be processed to obtain a
sample containing
21 2
2 50 10 H
atoms?
84. An alloy that melts at about the boiling point of water has Bi, Pb, and Sn atoms in the ratio
10:6:5, respectively. What mass of alloy contains a total of one mole of atoms?
85. A particular silver solder (used in the electronics industry to join electrical components) is to
have the atom ratio of
5 00 Ag/4 00 Cu/1 00 Zn
What masses of the three metals must be
melted together to prepare 1.00 kg of the solder?
86. A low-melting Sn–Pb–Cd alloy called eutectic alloy is analyzed. The mole ratio of tin to
lead is 2.73:1.00, and the mass ratio of lead to cadmium is 1.78:1.00. What is the mass
percent composition of this alloy?
87. In an experiment, 125 cm3 of zinc and 125 cm3 of iodine are mixed together and the iodine is
completely converted to 164 cm3 of zinc iodide. What volume of zinc remains unreacted? The
densities of zinc, iodine, and zinc iodide are 7.13 g/cm3, 4.93 g/cm3, and 4.74 g/cm3,
respectively.
88. Atoms are spherical and so when silver atoms pack together to form silver metal, they cannot
fill all the available space. In a sample of silver metal, approximately 26.0% of the sample is
empty space. Given that the density of silver metal is 10.5 g/cm3, what is the radius of a
silver atom? Express your answer in picometers.
Feature Problems
89. The data Lavoisier obtained in the experiment described on page 35 are as follows:
Before heating: glass vessel tin air++
13 onces 2 gros 2 50 grains,,=
After heating: glass vessel tin calx remaining air++
13 onces 2 gros 5 62 grains,,=
How closely did Lavoisier’s results conform to the law of conservation of mass?
(
1 livre 16 onces;=
1 once 8 gros;=
1 gros 72 grains=
In modern terms,
1 livre 30 59 g=
)
The sensitivity of Lavoisier’s balance can be as little as 0.01 grain, which seems to be the limit
90. Some of Millikan’s oil–drop data are shown below. The measured quantities were not actual
charges on oil drops but were proportional to these charges. Show that these data are consistent
with the idea of a fundamental electronic charge.
Observatio
n
Measured
Quantity
Observation
Measure
d
Quantity
1
19.66
8
53.91
2
24.60
9
59.12
3
29.62
10
63.68
4
34.47
11
68.65
5
39.38
12
78.34
6
44.42
13
83.22
7
49.41
w
91. Before 1961, the standard for atomic masses was the isotope
16 O,
to which physicists
assigned a value of exactly 16. At the same time, chemists assigned a value of exactly 16 to
the naturally occurring mixture of the isotopes
16 17
O O,,
and
18 O
Would you expect atomic
masses listed in a 60-year-old text to be the same, generally higher, or generally lower than in
this text? Explain.
92. German chemist Fritz Haber proposed paying off the reparations imposed against Germany
after World War I by extracting gold from seawater. Given that
(1) the amount of the reparations was $28.8 billion dollars, (2) the value of gold at the time was
about $21.25 per troy ounce
( )
1 troy ounce 31 103 g ,=
and (3) gold occurs in seawater to the
extent of
17
4 67 10 atoms
per ton of seawater
( )
1 ton 2000 lb ,=
how many cubic
kilometers of seawater would have had to be processed to obtain the required amount of
gold? Assume that the density of seawater is
3
1 03 g/cm
(Haber’s scheme proved to be
commercially infeasible, and the reparations were never fully paid.)
93. Mass spectrometry is one of the most versatile and powerful tools in chemical analysis because
of its capacity to discriminate between atoms of different masses. When a sample containing a
mixture of –isotopes is introduced into a mass spectrometer, the ratio of the peaks observed
reflects the ratio of the percent isotopic abundances. This ratio provides an internal standard from
which the amount of a certain
isotope present in a sample can be determined. This is accomplished by deliberately introducing
a known quantity of a particular isotope into the sample to be analyzed. A comparison of the new
isotope ratio to the first ratio allows the determination of the amount of the isotope present in the
original sample.
An analysis was done on a rock sample to determine its rubidium content. The rubidium
content of a portion of rock weighing 0.350 g was extracted, and to the extracted sample was
added an additional
29 45 g
of
87 Rb
The mass spectrum of this spiked sample showed a
87 Rb
peak that was 1.12 times as high as the peak for
85 Rb
Assuming that the two isotopes
react identically, what is the Rb content of the rock (expressed in parts per million by mass)?
T h e i s o t o p i c a b u n d a n c e s a n d i s o t o p i c m a s s e s a r e s h o w n i n t h e t a b l e .
Self-Assessment Exercises
94. In your own words, define or explain these terms or symbols: (a)
E
A
Z
; (b)
particle; (c)
isotope; (d)
16 O
; (e) molar mass.
95. Briefly describe
(a) the law of conservation of mass
(b) Rutherford’s nuclear atom
(c) weighted-average atomic mass
(d) a mass spectrum
96. Explain the important distinctions between each pair of terms:
(a) cathode rays and X-rays
(b) protons and neutrons
(c) nuclear charge and ionic charge
(d) periods and groups of the periodic table
(e) metal and nonmetal
(f) the Avogadro constant and the mole
97. A certain element contains one atom of mass 10.013 u for every four atoms of mass 11.009 u.
Compute the atomic weight of the element.
98. When 10.0 g zinc and 8.0 g sulfur are allowed to react, all the zinc is consumed, 14.9 g zinc
sulfide is produced, and the mass of unreacted sulfur remaining is
(a) 2.0 g
(b) 3.1 g
(c) 4.9 g
(d) impossible to predict from this information alone
99. One oxide of rubidium has 0.187 g O per gram of Rb. A possible O:Rb mass ratio for a
second oxide of rubidium is (a) 16:85.5; (b) 8:42.7; (c) 1:2.674; (d) any of these.
100. An attempt was made to determine the atomic mass of element X. If X forms a
compound with oxygen that contains 46.7% X by mass and has the formula XO, what is the
atomic mass of X?
101. Cathode rays
(a) may be positively or negatively charged
(b) are a form of electromagnetic radiation similar to visible light
(c) have properties identical to
particles
(d) have masses that depend on the cathode that emits them
102. The scattering of
particles by thin metal foils established that
(a) the mass of an atom is concentrated in a positively charged nucleus
(b) electrons are fundamental particles of all matter
(c) all electrons carry the same charge
103. Which of the following have the same charge and approximately the same mass?
(a) an electron and a proton; (b) a proton and a
neutron; (c) a hydrogen atom and a proton; (d) a neutron and a hydrogen atom; (e) an
electron and an
ion
104. Which of the following is not a fundamental particle? (a) proton; (b) neutron; (c) beta
particle; (d) alpha particle; (e) all are fundamental particles
105. Which of the following scientists did not contribute to determining the structure of the
atom?
(a) Thomson; (b) Rutherford; (c) Millikan;
106. A subatomic particle that has about the same mass as the hydrogen atom and a negative
107. What is the correct symbol for the species that contains 18 neutrons, 17 protons, and 16
electrons?
108. The properties of magnesium will most resemble those of which of the following? (a)
cesium; (b) sodium;
(c) aluminum; (d) calcium; (e) manganese.
109. Which group in the main group of elements contains (a) no metals or metalloids? (b) only
one metal or metalloid? (c) only one nonmetal? (d) only nonmetals?
110. The two species that have the same number of electrons as
32 S
are (a)
32 Cl
; (b)
34S+
; (c)
111. To four significant figures, all of the following masses are possible for an individual
titanium atom except one. The exception is (a) 45.95 u; (b) 46.95 u; (c) 47.87 u; (d) 47.95 u;
(e) 48.95 u; (f) 49.94 u.
112. The mass of the isotope
84
36 Xe
is 83.9115 u. If the atomic mass scale were redefined so that
84
36 Xe 84 u,=
exactly, the mass of the
12
6C
isotope would be (a) 11.9115 u; (b) 11.9874 u;
( c ) 1 2 u e x a c t l y ; ( d ) 1 2 . 0 1 2 7 u ; ( e ) 1 2 . 0 8 8 5 u .
113. A 5.585-kg sample of iron (Fe) contains
(a) 10.0 mol Fe
(b) twice as many atoms as does 600.6 g C
(c) 10 times as many atoms as does 52.00 g Cr
(d)
24
6 022 10
atoms
114. A 91.84 g sample of Ti contains (a) 4.175 mol of Ti; (b) 6.022 3 1023 Ti atoms; (c) 1.155
3 1024 protons;
115. There are three common iron–oxygen compounds. The one with the greatest proportion of
iron has one Fe atom for every O atom and the formula FeO. A second compound has 2.327 g
Fe per 1.000 g O, and the third has 2.618 g Fe per 1.000 g O. What are the formulas of these
other two iron–oxygen compounds?
116. The four naturally occurring isotopes of strontium have the atomic masses 83.9134 u;
85.9093 u; 86.9089 u; and 87.9056 u. The percent isotopic abundance of the lightest isotope is
0.56% and of the heaviest, 82.58%. Estimate the percent isotopic abundances of the other two.
Why is this result only a rough approximation?
117. Gold is present in seawater to the extent of
0 15 mg/ton
Assume the density of the
seawater is
1 03 g/mL
and determine how many Au atoms could conceivably be extracted
f r o m 0 . 2 5 0 L o f s e a w a t e r
( )
3
1 ton 2 000 10 lb; 1 kg 2 205 lb= =
118. Appendix E describes a useful study aid known as concept mapping. Using the method
presented in Appendix E, construct a concept map illustrating the different concepts in
