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Atom: From
Philosophical ldea to
Scientific Theory
The
When you crush a lump of sugar, you can see that it is made
up of many smaller sugar particles. You may grind these
particles into a very fine powder, but each tiny piece is still
sugar. Now suppose you mix the sugar powder into water. The
tiny particles seem to disappear. Yet if you were to taste the
solution, you'd know that the sugar is still there.
W
law of conservation o{ mass
law ol definite proportions
law of multiple p.opodions
Observations like these led people to wonder about the
nature of matter. Can matter be divided into piecbs forever or
is it made of miniature pieces that cannot be divided at all?
The particle theory of matter was supported as early as
400 B.C. by certain Greek thinkers, such as Democritus. He
called nature's basic particle an atom, based on the Greek
word meaning "indivisible." On the other hand, Aristotle
did not believe in atoms. He thought that all matter was
continuous. He lived in the generation after Democritus, and
his opinion was accepted for nearly 2000 years.
The opinions of Aristotle and Democritus were not
based on experimental evidence. The discussion remained
a philosophical one until the eighteenth century. Then
scientists began to gather evidence favoring the atomic
theory of matter.
Three basic laws describe how matter behaves in
chemical reactions.
By the late 1700s, chemists agreed that elements cannot be
broken down further by ordinary chemical means. They also
agreed that elements combine to form compounds that have
different properties from the elements that form them. They
did not agree on what makes up elements, or if a compound
always has the same ratio of elements in it.
Sugar seerFs to disappear
when it is mixed with water.
Ql critical
Thinldng
1. Interpret Why are the opinions
of Aristolle and Democritus not
considered scientific theories?
ATOMS: THE EUILDING BLOCKS OF MATTER
69
Law of conservation Mass is neither created nor destroyed during ordinbry chemical
reactions or physical changes.
of mlss
Lew of definite
proportions
Law of multiple
proportions
A compound contains the same elements in exactly the
same
proportions regardless of sample size or source of the compound.
If two or more compounds are composed of the same two elements,
then the ratio of the masses of the second element combined with a
certain mass of the first element is a ratio of small whole numbers'
Toward the end of the eighteenth century scientists made
several discoveries about chemical teaclions. A chemical
reaction is the change of a substance or substances into
one or more new substances. Using improved equipment,
scientists made more exact measurements before and after
reactions than ever before. In the process, they discovered
some basic principles, yhich are summarized in the table'
Law of Conservation of Mass Chemists measured the mass of
substances before and after a reaction. The total mass of the
products was always equal to the total mass of the reactants.
From this evidence, chemists deduced that matter cannot be
duri a reaction. a scientific law known
created or
as the
trr* of conservatiou
Law of Definite Proportions Chemists measured the mass
of two elements before forming a compound with the
elements. They discovered that the compound always
contained the same ratio of the elements' no matter how
the compound was formed. From this evidence, chemists
deduced that all compounds have a fixed composition that
from samole to sam le, a law known as the
does not
law of definite proPortions.
Law of Multiple Proportions Chemists also worked with
multiple compounds made from the same two elements- For
example, carbon and oxygen form carbon monoxide and
carbon dioxide. In carbon monoxide, there is 1.00 g of carbon
for every 1.33 g of oxygen. In carbon dioxide, there is 1.00 g of
carbon for every 2.66 gof oxygen' The ratio of the mass of the
oxygen in the two compounds is 1 to 2' For any two such
made of the same two elements, chemists found a
ihe masses of the variable element via
imole ratio rela
this law of multiple ProPortions.
70
CHAPTER 3
Each of these salt crystals contains
exactly 39.34% sodium and 60.667o
chlorine by mass.
sentence. The
in anY
products
the
of
total mass
to
is
equal
reaction
chemical
2. Complete this
Compounds <ontain atomr in whole-number ratlos.
In 1808, an English schoolteacher named John Dalton
proposed an explanation for the three newly discovered laws
He reasoned that elements were composed of atoms and that
only whole numbers of atoms can combine to form
compounds. His theory is summarized in the table below.
l.
2.
3.
4,
5.
All matter
is composed of extremely small particles called atoms.
Atoms of a given element are identical in size, masg and other
properties. Atoms of different elements differ in these properties.
Atoms cannot be subdivided, created, or destroyed.
Atoms of different elements combine in simple whole-nurnber
ratios to form chemical compounds.
In chemical reactions, atoms are combined, separated, or rearranged.
This theory provides an explanation for the law of conservation of mass during a chemical reaction. According to
Statement 3, atoms cannot be divided, created, or destroyed.
According to Statement 4, atoms form compounds in simple
whole-number ratios. The same number of atoms is present
before and after a compound forms or breaks apart_
'o.o:-
,.:O-O
Carbon.
C
Masg x
O
Massy
Oxygen,
Carbon monoxide, CO
Massx+Massy
r.
Carbon monoxide, CO
Carbon,
Mass x
Massx+Massy
C
In both reactions shown here. the total
mass stays the same during the
reaction because the mass of a carbon
atom and the mass of an oxygen atom
are fixed.
Oxygen, O
Mass y
Which statement in Dalton's atomic theory implies that an
atom of gold is exactly the same as any other atom of gold?
ATOMS: THE BUtLDtNG BLOCKS OF MATTER
'71
o.o=o
(a)
Carbon,
C
Oxygen,
O
Carbon monoxide, CO
orygen,
o
orygen,
o
carbon dioxide, co2
(a) CO is always cornposed of one
C atom and one O atom. (b) CO2
rnolecules are always composed of
one C atom and two O atoms The
same number of CO, molecules
contain twice as many O atom$
'o.o.O=o
carbon,
c
Dalton's theory also provides an explanation for the law of
definite proportions and the law of multiple proportions. .
Statement 4 implies that a compound is always formed using
atoms in the same whole-number ratio. Because an atom has a
fixed masE it also follows that using twice as many atoms of an
element will result in a cornpound containing twice the mass of
that element. For example, carbon dioxide molecules always
contain two oxygen atoms for every atom of carbon. Carbon
monoxide always contains one oxygen atom for every atom of
carbon. So carbon dioxide will always have twice as many
oxygen atoms as carbon monoxide for every atom of carbon.
Atohs can be ruHMded lnto rmallet Partklet.
Dalton turned Democritus's idea abottt atoms into a scientific
theory that could be tested by experiment. But not all aspects
of Dalton s atomic theory have proven to be correct. For
example, today we know that atoms are divisible into even
smaller particles. And, as you will see in Section 3 of this
chapter, a given element can have atoms with different masses
However, atomic theory has not been discarded. Instead,
has been modified to explain the new observations The
following important concepts remain unchanged.
it
. A[ matter is composed of atoms.
. Atoms of any one element differ in properties from atorns
of another element.
Ol ctiti*t rhinking
4. Infer When scientists discovered that atoms are composed
of smaller particles, why didn't they reject atomic theory?
i:r72:
CHAPTER 3
@
VOCABULARY
l.
What chemical laws can be explained by Dalton s atomic theory?
REVIEW
2. List the five main points of Dalton's atomic theory.
1.
2.
3.
1.
5.
Critical Thinking
3. AIlAtfAilG lllFORtAIlOll Three compounds containing potassium and
orygen are compared. Analysis shows that for each 1..00 g of q the
compounds have 1.22 9,2.44 g, and 4.89 g of K, respectively. Show how
these data support the law of multiple proportions,
ATOMS: THE EUILDING BLOCKS OF
MAffER
ffi
Elgor
The Structure
the Atom
of
The atomic theory proposed by John Dalton stated that atoms
are indivisible. This idea was proven incorrect by the end of
the nineteenth century. It became clear that atoms are actually
cornposed of several basic types of particles. The number and
arrangement of these particles determine the properties of
the atom.
nuclear lorces
The atom is now defined as the smallest particle of
anelementthut.e@
@ons.
Each .egion .ontuins
different types of particles, called sabato mic particles.
Tlte nucleus is a very small region located at the center of
the atom. The nucleus includes at least one positively
charged particle called a proton and usually one or more
neutral particles called neutrons.
Surrounding the nucleus is a much larger region that
contains negatively charged particles called electrons.
Atoms contaln posltlve and negatlve partlcles.
The electron was the first subatomic particle to be discovered.
In the late 1800s, many experiments were performed in
which electric current was passed through various gases. A
gas with the same pressure as the air at Earth's surface is a
poor conductor of electricity. For that reason, the scientists
made sure to keep the gases in their experiments at very
low pressures.
For their experiments, scientists made glass tubes called
cathode-ray tubes, and filled them with low-pressure gas. Metal
disks were placed on either side of the tube. One disk, the
cathode, was given a positive charge. The other disk, the
anode, was given a negative charge.
t4
CHAPTER 3
1. Draw a model showing the two
regions of an atorn in the space
below. I-abel the riucleus and the
electron region.
Cathode Rays and Electront
Scientists discovered that the surface of a
cathode-ray tube glowed when electric current
was passed through the tube. They hypothesized
that the glow was caused by a stream of particles,
called a cathode ray, that traveled from the cathode
to the anode. They also found that cathode rays
could be deflected by a magnet or away from a
negatively charged object. This led to the
hypothesis that the particles in a cathode ray are
negatively charged.
Voltage 50urce
Gas
at low pressure
\
"-
-,-*_rq:}---
-.
Cathode
(metal disk)
(a)
Experiments carried out by English physicist
Joseph John Thomson in 1897 supported this
hypothesis. He was able to calculate the ratio of
the charge of the particles to the mass of the
particles in a cathode ray. He found that this ratio
was the same. no matter what metals were used in
the cathode and anode. thglatig a!!e rl!eye!!_tLheThomson concluded that all cathode rays are
composed of identical negatively charged particles
called electrons. The atoms in the cathode-ray
experiments above were releasing electrons. This was
evidence that atoms are divisible and that electrons
are present in different types of atoms.
(a) A simple cathode-ray tube. (b) A magnet above
a cathode-ray tube deflect! the beam downward.
showing that the particles in the beam must have a
negative charge.
Charge and MaJs of the Electron
Thomson's experiments also revealed that the eiectron has
a very large charge-to-mass ratio. In 1909, the American
physicist Robert A. Millikan was able to measure the
charge of the electron. Scientists used this information to
determine the mass of an electron. They found that an
electron has about one two-thousandth the mass of the
smallest known atom.
Thomson proposed a plum pudding model to explain the
properties of the atom known at the time. Because atoms
are electrically neutral, he proposed that the electrons were
balanced by a "pudding" of positive charge. The electrons
were embedded within this positively-charged material. The
region of positive charge was also thought to contain most of
the mass of the atom, since the electron has so little mass.
$
conxecr
Today. cxperiments have determined that the electron has a mass
of9.1o9 x 1o-rrkg.This is 1/1837
the mass of the smallest type of
hydrogen atom.
2. Sketch the plum pudding model
proposed by Thomson. t-abel the
electrons and the region of
positive charge.
ATOMS: THE EUILDING ELOCKS OF MATTER
75
More detail of the structure of atoms was discovered by New
Zealander Emest Rutherford and his associates Hans Geiger
and Ernest Marsden. They bombarded a piece of gold foil
with fast-moving alpha particles, which are positively charged
particles with four times the mass of a hydrogen atom. They
expected the beam to pass through the foil with a very slight
deflection because the mass and charge were evenly
distributed in the gold foil. They were surprised when about
1 in 8000 particles deflected backwards toward the source.
(a) Geiger and Marsden bombarded a
thin piece of gold foil with a beam of
alpha particles. (b) Some of the
particles were deflected back toward
their source.
Rutherford hypothesized that small, densely
packed bundles of matter with a positive charge must
have caused the backwards deflections. The bundles
had to be small because so few of the particles
bounced backwards. Rutherford used the term
nucleus to describe each bundle of matter.
Rutherford had discovered that the
volume of the nucleus was very small
compared to the total volume of an
atom. The source of the positive
charge of an atom had been
discovered. Rutherford's student,
Niels Bohr, later discovered the
location of the electrons in an atom.
3. What is the nucleus of an atom?
76
CHAPTER 3
e..-
or
Posti.re
I
l
nanictes
I
Most particles passed through the
gold foil undisturbed. A small number
were deflectcd by the nucleus.
A nucleus contains protons and neutrons.
With one exception, all atomic nuclei are made of two kinds of
particle$ protons and neutrons. A proton has a positive charge
equal in magnitude to the negative charge of an electron.
Atoms are electrically neutral because they contain equal
numbers of protons and electrons. A neutron has no charge,
and, like an atom, is electrically neutral.
Many words derived from
l-atin that end with -&t
form plurals by changing the
ending to -i. ThuE the plural of
nucleus is nuclei arl.d the plural of
radius rs radii.
The one atomic nucleus that lacks a neutron is that of the
simplest hydrogen atom. Its nucleus is a single proton with
a single electron moving around it.A proton has a mass of
I.673 x 1027 kg, which is 1836 times greater than the mass of
an electron. Therefore, a proton has nearly all of the mass in
the simplest hydrogen atom. The mass of a neutron is
1.675 x lTti kg, which is slightly larger than the mass of
a proton.
The nuclei of atoms of different elements differ in the
number of protons they possess. Therefore, the number of
protons determines an atom's identity. For every proton
an atom has in its nucleus, the same number of electrons
surrounds the nucleus. Physicists have discovered other
subatomic particleq but they have little effect on the chemical
properties of matter. The properties of electrons, protons, and
neutrons, are summarized in the table below.
4. What quantity determines the identity of an atom?
Relative
Symbols
electric
charge
Electron
"-, _\"
-1
0.000 5486
9.109
x
10-31
Proton
p*,lH
+1
t.007 276
1.673
x
Io-27
1.008 665
1.675
x \0-27
Particle
Neutron
Mass
Relative
number
mass (u*)
"",lon
*1 u (unified atomic mass unit)
=
1.660 540
x
Actual mass (kg)
10-27 kg
ATOMS: THE EUILDtNG BLOCKS OF MATTER
77
Forces ln the Nucleus
Generally, particles that have the same electric charge repel
one another. Therefore, you might expect a nucleus with more
than one proton in it to be unstable. However, a force exists
between two protons that overcomes the electric force trying
to push them apart. This force only acts when two protons are
very close to one another.
A similar force acts when two neutrons are very close
together, or when a neutron and a proton are very close
together. Together, these short-range proton-proton,
neutron-neutron, and proton-neutron forces are called nuderr
forces. These forces allow atoms with up to 83 positivelycharged protons in the same nucleus to be stable.
The radll of atoms are exprersed ln plcometers.
Because the nucleus is so small. the size of an atom is
determined by the size of the region in which electrons are
present. This region is sometimes thought of as an electron
cloud a cloud of negative charge. The radius of an atom is
the distance from the center of the nucleus to the outer edge
-
of the electron cloud.
Because atomic radii are so small, they are expressed in a
unit that is mote convenient for the sizes of atoms. This unit is
called the picometer. Anorher unit, called lhe unified atomic
mass unit, or u, is used to express the mass of atoms.
1
pm
1
u
-
= 10-lo cm
1.660 540 x 10-27 kg
-
10-12
m
To get an idea of how small a picometer is, consider that
1 cm is the same fractional part of 1000 km (about 600 mi) as
100 pm is of 1 cm. Atomic radii range from 40 pm to 270 pm
across. Atomic nuclei have a much smaller radius, about
0.001 pm. Atomic nuclei are also incredibly dense, with a
density of about 2 x 10la g/cm3.
0l ctiti*t Thinldng
s. Calculate Verify the value for the density of an
atomic nucleus given above for a spherical atom
with a mass of 1 u. Recall that the volume of a
sphere is given bY
78
CHAPTER 3
, :4{rt.
Q6 conr.ficr
In physics, there are four known
fundamental forces that describe
how matter interacts, These forces
are the eleclromagnetic force, the
gravitational force, the strong
nuclear force. and the weak
nuclear force.
@
VOCABULARY
t. Define each of the following:
a. atom
b. neutron
nEvlEw
2. Describe one conclusion made by each scientist that led to the development
of the current atomic theory.
a. Thomson
b. Millikan
c. Rutherford
3. Compare the three subatomic particles in terms of location in the atom,
masq and relative charge.
tL Why is the cathode-ray tube shown earlier in this section connected to a
vacuum pump?
Critical Thinking
5. EVAIUATII{G lDEAlS Nuclear forces are said to hold protons and neutrons
together. What is it about the composition of the nucleus that requires the
concept of nuclear forces?
ATOMS: THE BUILDING SLOCKS OF
MAffER
S
-:!.sF.*L.*qs.i€i*{!F*t
:.i:
:ls:::i.:
ailra
00, OA Or
-:": .-. .:
Counting Atoms
Neon gas only makes up 0.002olo of the air you breathe. Yet
there are 5 x 1017 atoms of neon in each breath you take. In
most experiments, atoms are too small and numerous to
track individually. Instead, chemists make calculations that
take into account the properties of large groups of atoms.
@
atomic number
isotope
mass number
nuclide
unified atomic mass unil
average atomic mass
mole
All atoms of an element must have the same number
of protonr, but not neutronJ.
Avogadro's number
molar mass
All atoms are composed of the
same basic particles. Yet all
atoms are not the same. Atoms of different elements have
different numbers of protons. Atoms of the same element
all have the same number of protons. The atomic nmber
(Z) of an element is the number of protons of each atom of
that element.
Turn to the large periodic table in Section 2 of the chapter
"The Periodic l-aw." The periodic table square for lithium is
also shown at the right. An element's atomic number is
indicated above its symbol. Notice that the elements are
placed in order in the periodic table according to the atomic
number. At the top left is hydrogen, H, with an atomic
number of 1. Next in order is helium, He, with an atomic
number of 2. The next row of the periodic table includes the
elements with the atomic numbers 3, 4, 5, and so on.
The atomic numbers give the number of protons in an
element. So all atoms of hydrogen have one proton, all
atoms of helium h4ve two protons, and so on.
The atomic number also identifies an element. If you '
want to know which element has atomic number 4f, you can
look at the periodic table for the box with a"47" at the top.
Silver, Ag, is the correct element. You then know that all
silver atoms have 47 protons. Since atoms are electrically
neutral, you also know that all silver atoms must also have
47 electrons.
80
CHAPTER 3
3
Li
Lithium
6"941
lHel2
sl
This periodic table entry shows that
the atomic number of lithium is 3.
1. How many protons does every
atom of hydrogen have?
2. How many protons
atom of lithium have?
does every
Iiotopes
The simplest atoms are those of hydrogen. All hydrogen
atoms have only one proton. However, like many naturally
occurring elements, hydrogen atoms can have different
numbers of neutrons.
Three types of hydrogen atorns are known. The most
common type of hydrogen is sometimes calle d protiwn.
It accounts for 99.9885% of the hydrogen atoms found on
Earth. A protium atom has one electron and a nucleus with
one proton. Another form of hydrogen is called deuterium.
A deuterium atom has one electron and a nucleus with two
particles: a neutron and a proton. Finally,, a tritivm atom is a
hydrogen atom with one electron and a nucleus of one proton
and two neutrons
The names for the types of
hydrogen atoms are
derived from the number of
particles in the nucleus. The. prefix
proro- means "first," deutero- means
"second," and trito- means "third."
The "o" is dropped before the
ending -ilm in the names of the
hydrogen atoms
Protium, deuterium, and tritium are isotopes of hydrogen.
b{ol6 are atoms of the same element that have different
masses. ls
protons and electrons but a different nrrrnfsr of neutrons All
isotopes of an atom are electrically neutral. A sample of an
element usually consists of a mixture of its isotopes. Tin has
1.0 stable isotopeg more than any other element.
Mass Number
An isotope is identified by its name, such
as
Protium
protium, or its
of an isotope is
atomic number and mass The &Ifd!tr
the total number of protons and neutrons
nucleus For example, the mass number of protium is one
because there is one particle, a proton, in its nucleus.
thil i[6ii-lti
Deuterium
2 Neutrons
Tritium
3. Use the definition of mass number to complete the table.
: The three hydrogen isotopes are shown.
Atomic number
(number of protons)
Number of neutrons
Mass number
(protons + neutrons)
protium
1
0
I
deuterium
l1
tritium
12
ATOM|: THE gUtLDtNG
BLOCKS OF
MATTER
:8t*
_s+:s:_
ldentifylng lsotopes
That the isotopes of hydrogen have their own names is
unusual. An isotope is usually identified by specifying its mass
number. There are two methods for specifying isotopes.
o ln hyphen notation,lhe
written with a
hyphen after the name of the element. For example, in
hyphen notation, tritium would be written as hydrogen-3.
c A nuclear symbol is used to show the composition of an
isotope's nucleus. A number to the upper left of the element
symbol indicates the mass number (protons + neutrons). A
number to the lower left of the element symbol indicates
the atomic number (number of protons). For example, the
nuclear symbol for tritium is lH.
Nuclide is a general term for the specific isotope of an
glggel,t For example, you could say that deuterium is a
hydrogen nuclide. You could also say that hydrogen has three
different nuclides. The composition of the three isotopes, or
nuclides, of hydrogen and the two isotopes of helium are given
in the table below.
0l
mass number is
criticat Thinking
a. Identify A particular isotope of uranium has a nucleus with
92 protons and 143 neutrons. Identify this isotope in two
different ways.
s. Apply Use the information in the other columns to
complete the table on the five nuclides of hydrogen
and helium.
lsotope
82
Nuclear
symbol
hydrogen-1 (protium)
lH
hydrogen-2 (deuterium)
fH
hydrogen-3 (tritium)
lH
helium-3
Itt.
helium-4
1H.
CHAPTER 3
Number Number
of protons of electrons
Number
of neutrons
How many protons, electrons, and neutrons are there in an
atom of chlorine-37?
soluTrolr
1
ANAIYZE
Determine what information k given and unknown.
Given: name of isotope is chlorine-37
Unknown: number of protong electrons, and neutrons
2
PTAN
Write equations for the unknowns in terms of what is given.
number of protons = number of electrons
mass number
:
50LVE
atomic number
number of neutrons + number of protons, so
number of neutrons
3
:
:
mass number
-
number of protons
Substitute the known values and calculate.
Because the name of the isotope is chlorine-31 its mass number
is 37 The element chlorine is element 17 on the periodic table, so
its atomic number is 17
number of protons = number of electrons
number of neutrons
-
37
An atom of chlorine-37 has
-
17
17
-
=
17
20
electrong 17 protons, and
20 neutrons.
4
CHECK
YOUR
WORK
Determine if the answer makes sense.
The number of protons in a neutral atom equals the number of
electrons. The number of protons plus the number of neutrons
equals the mass number because 17 + 20 : 37.
A.
How many protons, electrons, and neutrons make up an atom
of bromine-80?
Mass number of bromine-80:
Atomic number of bromine:
Number of protons:
Number of electrons:
Number of neutrons =
ATOMS: THE EU|LD|NG BLOCKS OF
MATTER 83
Atoml< mars lc a relatlve measure.
Masses of atorhs expressed in grams are very small. For
example, an atom of oxygen-16 has amass of 2.656 x 10-2J g.
It is usually more convenient to talk about the relative mass of
an atom. The relative atomic mass of an atom is the mass of
the atom as compared to the mass of a defined standard.
Scientists use a standard measurement for comparing
atomic mass. One rrnified atomic mass unit, or u, is exactly
l/12 the mass-of a carbon-12 atom. In other words. one u is the
nucleus of a carbon-12 atom.
The value of u in grams is 1.660 540 x 10-2a g.
@e
[Q] .oo*,Nc
cLosER
6. Deline the two parts ofthe term
untfied stomic mass unit separately
in your own words:
unified atomic mass
The mass of a hydrogen-l atom is slightly more than one
unified atomic mass unit-1.007 825 u. An oxygen-16 atom has
a precise mass of 15.994 91,5 u. Additional atomic masses for
the isotopes of certain elements are given in the table below.
Isotopes of an element do not differ significantly in their
chemical behavior from the other isotopes of the element. So
the three isotopes of oxygen all have the same chemical
properties despite varying in mass.
The table below shows some isotopes that can be found in
nature. The natural abundance, or relative amount of each
isotope in a sample of an element, is also given in the table.
Artificial isotopes can only be created in the laboratory. They
have a natural abundance of zero.
lsotope
Hydrogen-1
Hydrogen.2
Mass number
1
2
Percentage natural
abundance
99.9885
0.0115
Unified atomic mass
unit (u)
1.007 825
2.01.4 tO2
' 12
(by definition)
Average atomic mass
of element {u)
t.007 94
Carbon-12
Carbon-13
12
13
98.93
7.07
13.003 355
Oxygen-16
Oxygen-17
Oxygen-18
76
17
18
99.75'l
0.038
0.205
t5.994 915
t6.999 132
17.999 160
15.9994
Copper-63
Copper-65
63
69.15
65
30.85
62.929 601
64.927 794
63.546
1.32.905 447
132.905
Cesium-133
84
CHAPTER 3
133
r00
12.01.07
Aveageatomk mrrl k erdghtedrrrftrc.
Chemists have found that a sample of an element will contain
the same percentage of each isotope no matter where on
Earth the sample is obtained. This percentage is taken into
account when calculating the average atomic mass that is
reported on the periodic table.The 1qq13ar3odcrl is
the wei
of the atomic masses of the
of an element found in nature. The table on the bottom of the
previous page also includes the average atomic mass for each
element in the table.
7. Define the two parts of the term
average atomic mass separately
in
your own words:
average
Calculatlng Average Atomic Mass
The average atomic mass of an element is a weighted average.
It depends on both the mass of each isotope and the natural
abundance of each isotope of the element.
atomic mass
For example,69.150lo of the copper atoms in a sample
are copper-63 atoms. This isotope has an atomic mass of
62.93 u.The remaining 30.85o/o of the sample is copper-65,
which has an atomic mass of 64.93 u. The weighted average is
the sum of the proportions of the mass that are taken up by
each type of atom.
69.15"/"
x
62.93 u
- 43.52 u of copper-63
30.85"/o x 64.93 u 20.03 u of copper-65
43.52u + 20.03 u - 63.55 u
In this book, an element's
atomic mass is usually
rounded to two decimal places
before it is used in a calculation.
The value is reasonable because the average atomic mass is
closer to the atomic mass of copper-63 than the mass of
copper-65, because copper-63 takes up the largest proportion
of a natural sample of copper. The value also matches
the average atomic mass in the periodic table to four
significant figures.
S
Ctiti."t Thinking
8. Reasoning Why is the average atomic mass usually
a decimal number and not a whole number like the
mass number?
ATOMS: fHE EUILD\NG BLOiKS OF
MATTER 85
.
A rrlatlve mars rcalc malcs countlng atomt poslble.
The unified atomic mass unit allows scientists to compare the
mass of an atom to the mass of a standard atom. The average
atomic mass gives scientists a value for the average mass of an
atom in a sample. Another quantity that scientists also need to
determine is the number of atoms in a sample.
The Mole
The mole is the SI unit for the amount of a substance. The
abbreviation for a mole is mol.A nolc is the amount of a
substance that contains as many particl$ii ttrEre aFatoms in
farm stand,
you are purchasing 2 times 12,or 24 ears of corn. Similarly, a
chemist might desire 1 mol of carbon or 2.567 mol of calcium.
a dozen.
If you buy two dozen ears of corn at
a
Avogadro's Number
Chemists have determined that 12 g of carbon-12 contains
6.022 l4L 79 x 1.G3 atoms This means that one rnole of any
atoms. This number is
substance contains 6.022 I4I79 x
called Avogadro's number after Amedeo Avogadro.
A nineteenth-century Italian scientist, Avogadro helped
explain the relationship between mass and numbers of atoms.
lF
For most calculations, the number given above is rounded
to four significant figures. So, Aslrm nnbs is the
substance,
one mole of a
number of
and is given by 6.022 x 1#r. To get a sense of how large this
number iE consider this: If every one of the 7 billion people
on Earth counted one atom per second, it would take the
7 billion people about 7 million years to count all of the atoms
in one mole.
g. What is the SI unit for the number of particles in a sample?
10. How many particles does the SI unit for the number of
particles represent?
CHAPTE R 3
A penny contains about 120 mol of
copper atoms, or 2.964 x 10P atoms
A sample of 20 copper pennies is a
little less than one mole of copper.
About one molar mass of (a) carbon (graphit€), (b) iron (nails), and (c) copper
(wire) is shown on each balance.
Molar Mass
The number of particles in one mole of a substance is given by
Avogadro's number. The mass of one mole of a substance is
called the molr m
v
written in units of g/molJhe rnolar rn-ass of an element in
g/mol is equivalent to the atomic mass of the element as given
on the periodic table in u. For example, the molar mass of
carbon is 12.01 g/mol, the molar mass of iron is 55.84 g/mol,
and the molar mass of copper is 63.55 g/mol.
GramlMole Conversions
Chemists use molar mass as a conversion factor in chemical
calculations. For example, to find the mass of 2 mol of a
substance, you would multiply 2 mol by the molar mass of the
substance (in grams per mole) to obtain a value in grams.
Conversions with Avogadro's Number
The diagram below can be used to convert between the mass
of a sample, the moles in a sample, and the number of atoms
in a sample.The conversion between moles and number of
atoms is performed using Avogadro's number. The following
sample problems explain how to convert between all three of
these quantities.
11. The periodic table gives the
average atomic mass of mercury as
200.59 u. What is the mass ol one
mole of mercury?
rlF-+-aI
-rti
Mass
of cbmGnt
in glams
The diagram shows the relationship among mass, moleq and number of atoms.
ATOMS: THE EUtLDING BLOCKS OF MATTER
87
A chemist produceil 11..9 g of aluminnm' Al. How many
moles of aluirinun were produced?
soL[moil
'
AiIALYZE
Determine what information is given and unknown.
Given:
11.9 g
Al
Unknown: amount of Al in moles
2
Determine the equation and conversion factor needed.
PIAN
To convert from mass to number of moles, divide by the molar
mass. This is the same as using the reciprocal of molar mass as a
conversion factor, as shown below.
gramAl: gramsAl
" ff-rluu#
= moles Al
3
SOwE
Substitute the known values and calculate.
The molar mass of aluminum from the periodic table, rounded to
four significant figures, is 26.98 g/mol.
11.egAr
-tt.sext"#fu
-
4
0.2141
molAl
CHECK
Determine if the answer makes sense.
YOUR
The answer and the original value have three significant figures.
The answer is reasonable because 11.9 g is a little less than half
of 26.98 g.
WORK
B.
What is the mass in grams of 2.2$ mol of iron, Fe?
Molar mass of iron:
2.25 molFe
-
1.25 mol Fe
x
gFe
88
CHAPTE R 3
How many moles of silver, Ag, are in 3.01 x 104 atoms
of silver?
soruTtol{
1
ANATYZE
Determine what information is given and unknown.
Given: 3.01
x
1023
atoms Ag
Unknown: amount of Ag in moles
2
PLAN
Determine the equation and. conversion factor needed,
To convert from number of atoms to number of moleg divide by
Avogadro's number. This is the same as using the reciprocal of
Avogadro's number as a conversion factor, as shown below.
moles Ag
Ag atoms = Ag atoms x
Avogadro's number of Ag atoms
3
SOwE
moles
Ag
Substitute the known values and calculate.
3.10
x
1023Ag atoms
:3.01 x
4
CHECK
YOUR
WORK
1023{g-ato-ms
0.500 mol
x
molAg
6.022xIG3
x
Ag
$*arfr
Determine if the answer makes sense.
The answer and the original value have three significant figures.
The units cancel correctly and the number of atoms is half of
Avogadro's number.
c.
How many atoms of aluminum, Al, are in 2.i5 mol
of aluminum?
Molar mass of aluminum:
2.75
molAl
-
2.75
molAl x
atoms
Al
ATOMS: THE BUILDING BLOCKS OF
MATTER 89
What is the mass in grams of 1.20 x 1d atoms of copper, Cu?
sonmox
1
AT{AiYZE
Determine what information is given and unknown.
Given: 1.20 g
x
108 atoms
of Cu
.Unknown: mass of Cu in grams
2
Determine the equation and conversion factors needed.
PIAN
As shown in the diagram earlier in this section, converting from
number of atoms to mass is a two-step process. To convert from
number of atoms to moles, divide by Avogadro's number. To
convert from moles to masg multiply by the molar mass.
Cu atoms = Cu atoms x
:
3
SOLVE
grams Cu
Substitute the known values and calculate.
The molar mass of copper from the periodic table, rounded to four
significant figures, is 63.55 g/mol.
63.55 s Cu
1.20
x
108
9u-atoff x
6.022
x
lG3
- I.n x 10-14 g Cu
4
9u*to6s
g;,olfi)
CHECK
Determine if the answer makes sense.
YOI'R
The units cancel correctly to give the answer in gtams. The order of
magnitude of the answer is also reasonable because 108 divided by
1024 and then multiplied by 102 is 10-14.
WORK
D.
How many atoms of sulfur,
S,
are in 4.00 g of sulfur?
Molar mass of sulfur:
4.00gS-4.00gSx
x
S atoms
, 90
^
CHAPTER 3
VOCABULARY
1. Define the term molar mass.
REVIEW
2. Complete the table at the right.
3. Write the nuclear symbol and hyphen
notation for each of the following isotopes
a. mass number of 28, atomic number of 14
b. 26 protons and 30 neutrons
sodium-23
calcium-40
!3cu
toTns
tL To two decimal placeq what is the relative atomic mass
and the molar mass
of the element potassium, K?
Determine the mass in grams of the following:
a. 2.00
mol
N
b. 3.01
x
1023
atoms Cl
5. Determine the amount in moles of the following:
a. 12.15 g
mol
Mg
b. 1.50
x
1023
atoms F
Critical Thinking
7. Al{AtlrZlilc DATA Beaker
contains 222 g of silver.
A contains 2.06 mol of copper, and Beaker B
a. Which beaker contains the larger mass?
b. Which beaker has the larger number of atoms?
ATOMS: THE BUtLDtNc BLOCKS OF
MATTER 9l
CONVERSION FACTORS
Most calculations in chemistry require that all measurements of the same quantity
(mass, length, volume, temperature, and so on) be expressed in the same unit. To
change the units of a quantrty, you can multiply the quantity by a conversion factor'
With Sl units, such conversions are easy because units of the same quantity are
related by multiples of 10, 100, 1000, or 1 million.
Suppose you want to convert a given amount rn milliliters to liters. You
can use the relationship 1 L= 1000 mL. From this relationship, you
can
1QQQI1 6n6
derive the conversion {actors shown at the right.
@
Problem-SoIaing
Multiply the given amount by the conversion factor that allows the units from which
you are converting to cancel out and the new units to remain'
Most conversion factors are based on exact definitiong so significant figures do not
measurement
apply to these factors. The number of significant figures in a converted
depends on the certainty of the measurement you start with.
A sample of aluminum has a mass of 0.087 g. What
mass in milligrams?
Based on SI prefixes, You know that
convetsion factors are
1
is the sample's
1000 mg. The possible
1
1000 me
ano looomg
--ll-
g
The first conversion factor cancels grams, leaving milligrams'
/x
0.087 g = 0.087
looq 4g
:
sz g
A sample of a mineral has 4.0E x 10-s mol of vanadium per kilogram
the
of masr. How many micromoles of vanadium per kilogram does
mineral contain?
l
: 1 x 10-6 mol. The possible conversion factors are
I x lO-n r.nol ""- I l'tol
pmot "ndI x 10-6 mol
gmol
The second conversion factor cancels moles, leaving micromoles'
-t
4.08
x
10-s
mol:4.08
x 10-s ryAt
##;i
-
40'8pmol
Practice Problems: Chapter Review practice problems 8-10
and 13-14
92
CH
APTE R 3
1L
1000 mL
l.
Explain each law in terms of Dalton
s
atomic theory.
a. the law of conservation of mass
h
the law of definite proportions
c
the law of multiple proportions
Z Accorditrg to the law of conservation of masg if element A
has
al atomic
6xss 6f I rrnifs and element B has an atomic mass of 3 units, what mass
would be expected for each conpound?
.. AB
h
A2B3
3. What is an atom? What two regions make up all atoms?
*
t
S"mmarize Rutherford's model of the atom and explain how he developed
bis model based on the results of his famous gold-fgil experiment.
What are isotopes? How are the isotopes of a particular element alike and
how are they different?
c
Complete the table at the right
concerning the tblee isotopes
of silicon, Si.
t
What is the defnition of a mole?
How many particles are in one mole,
and what is that number called?
silkon-28
silicon-29
silicon.30
ATOMS:
fHE
BUILDING ATOCXS Or
UArrtn
o
8. What is the mass in grams of each of the following?
a, 1.00 mol
Li
b. 1.00
rnol
c. 1.00
molar mass
d. 1.00 molar mass
e. 6.022
x
7G3 atoms C
f. 6.022
x
lP
atoms
Ag
9. How many moles of atoms are there in each of the following?
a, 6.022
x
1023
atoms Ne
b. 3.011
x
1023
atorns
10. How many moles of atoms are there in each of the following?
a. 3.25 x
lt.
ld
g Pb
b. 4.50 x
10-12 g
O
Three isotopes of argon occur in nature: l!er,l!er, and 13Ar. Calculate the
average atomic mass of argon to two decimal places, given the following
relative atomic masses and abundances of each of the isotopes:
argon-36 (35.97 u',O.337"/"). argon 38 (3796 u10.0630/o). and
argon-210 (39.96 u; 99.600%).
Naturally occurring boron is 80.20"/" boron-l1 (atomic mass of 11.01 u) and
19.807o of sqme other isotopic form of boron. What must the atomic mass of
this second isotope be in order to account for the 10.81 u average atomic
mass of boron? (Write the answer to two decimal places)
CHAPTER 3
t3. What
is the mass in grams of each
a. 3.011 x
lF
atoms F
b, 1.50 x 10P atoms Mg
c. 4.50
l'l
x
1012
atoms Cl
oftie following?
d. 8.42 x
1018
atoms
Br
e. 25 atoms W
L
1
atom Au
Determine the number of atoms in each of the following.
a. 5.,() g B
b. 0.250 mol
e. 1.00 x
S
f.
10-10 g
Au
1.50 mol Na
c. 0.0384 mol K
g. 6.755 mol Pb
d. 0.@5 50 g Pt
lu
702 g Si
AfoMs: fHE autroixe qLocKs oF MAT1ER
&