SECTION 3.3
Counting Atoms
Neon gas only makes up 0.002% of the air you breathe. Yet
there are 5 × ​10​17​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.
All atoms of an element must have the same number
of protons, but not neutrons.
Key Terms
atomic number
isotope
mass number
nuclide
unified atomic mass unit
average atomic mass
mole
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 number
(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 Law.” 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 have two protons, and so on.
The atomic number also identifies an element. If you
want to know which element has atomic number 47, 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.
2
CHAPTER 3
3
Li
Lithium
6.941
[He]2 s1
This periodic table entry shows that
the atomic number of lithium is 3.
READING CHECK
1. How many protons does every
atom of hydrogen have?
2. How many protons does every
atom of lithium have?
Isotopes
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 atoms are known. The most
common type of hydrogen is sometimes called protium.
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 tritium atom is a
hydrogen atom with one electron and a nucleus of one proton
and two neutrons.
Protium, deuterium, and tritium are isotopes of hydrogen.
Isotopes are atoms of the same element that have different
masses. Isotopes of an element have the same number of
protons and electrons but a different number 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
10 stable isotopes, more than any other element.
Mass Number
An isotope is identified by its name, such as protium, or its
atomic number and mass. The mass number of an isotope is
the total number of protons and neutrons that make up its
nucleus. For example, the mass number of protium is one
because there is one particle, a proton, in its nucleus.
TIP
The names for the types of
hydrogen atoms are
derived from the number of
particles in the nucleus. The prefix
proto- means “first,” deutero- means
“second,” and trito- means “third.”
The “o” is dropped before the
ending -ium in the names of the
hydrogen atoms.
1 Proton
Protium
1 Neutron
1 Proton
Deuterium
2 Neutrons
1 Proton
READING CHECK
3.
Tritium
Use the definition of mass number to complete the table.
The three hydrogen isotopes are shown.
Mass Numbers of Hydrogen Isotopes
Atomic number
(number of protons)
Number of neutrons
Mass number
(protons + neutrons)
protium
1
0
1
deuterium
1
1
tritium
1
2
AT O M S : T H E B U I L D I N G B L O C K S O F M AT T E R
3
Identifying Isotopes
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.
• In hyphen notation, the mass number is written with a
hyphen after the name of the element. For example, in
hyphen notation, tritium would be written as hydrogen-3.
• 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 31​ ​H.
Nuclide is a general term for the specific isotope of an
element. 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.
Critical Thinking
4.
Identify A particular isotope of uranium has a nucleus with
92 protons and 143 neutrons. Identify this isotope in two
different ways.
5.
Apply Use the information in the other columns to
complete the table on the five nuclides of hydrogen
and helium.
Isotopes of Hydrogen and Helium
Nuclear
symbol
Number
of protons
Number
of electrons
Number
of neutrons
hydrogen-1 (protium)
​ 11 ​H
1
1
0
hydrogen-2 (deuterium)
​ 21 ​H
1
1
hydrogen-3 (tritium)
​ 31 ​H
1
helium-3
​ 32 ​He
helium-4
​ 42 ​He
Isotope
4
CHAPTER 3
2
2
2
1
SAMPLE PROBLEM
How many protons, electrons, and neutrons are there in an
atom of chlorine-37?
SOLUTION
1 ANALYZE
Determine what information is given and unknown.
Given: name of isotope is chlorine-37
Unknown: number of protons, electrons, and neutrons
2 PLAN
Write equations for the unknowns in terms of what is given.
number of protons = number of electrons = a tomic number
mass number = number of neutrons + number of protons, so
number of neutrons = mass number – number of protons
3 SOLVE
Substitute the known values and calculate.
Because the name of the isotope is chlorine-37, 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 = 17
number of neutrons = 37 – 17 = 20
An atom of chlorine-37 has 17 electrons, 17 protons, and
20 neutrons.
4 CHECK
YOUR
WORK
Determine if the answer makes sense.
he number of protons in a neutral atom equals the number of
T
electrons. The number of protons plus the number of neutrons
equals the mass number because 17 + 20 = 37.
PRACTICE
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 neutrons =
Number of electrons:
–
=
AT O M S : T H E B U I L D I N G B L O C K S O F M AT T E R
5
Atomic mass is a relative measure.
Masses of atoms expressed in grams are very small. For
example, an atom of oxygen-16 has a mass of 2.656 × ​10​–23​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 unified atomic mass unit, or u, is exactly
1/12 the mass of a carbon-12 atom. In other words, one u is the
average mass of a particle in the nucleus of a carbon-12 atom.
The value of u in grams is 1.660 540 × 1​ 0​–24​g.
LOOKING CLOSER
6. Define the two parts of the term
unified atomic mass unit separately
in your own words:
unified atomic mass
The mass of a hydrogen-1 atom is slightly more than one
unified atomic mass unit—1.007 825 u. An oxygen-16 atom has
a precise mass of 15.994 915 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.
unit
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.
Atomic Masses and Abundances of Several Naturally Occurring Isotopes
Isotope
Hydrogen-1
Hydrogen-2
Mass number
1
2
Percentage natural
abundance
99.9885
0.0115
Unified atomic mass
unit (u)
1.007 825
2.014 102
Average atomic mass
of element (u)
1.007 94
Carbon-12
Carbon-13
12
13
98.93
1.07
12 (by definition)
13.003 355
12.0107
Oxygen-16
Oxygen-17
Oxygen-18
16
17
18
99.757
0.038
0.205
15.994 915
16.999 132
17 .999 160
15.9994
Copper-63
Copper-65
63
65
69.15
30.85
62.929 601
64.927 794
63.546
Cesium-133
133
132.905 447
132.905
6
CHAPTER 3
100
Average atomic mass is a weighted value.
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 average atomic mass is
the weighted average of the atomic masses of the isotopes
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.
READING CHECK
7. Define the two parts of the term
average atomic mass separately in
your own words:
average
Calculating 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, 69.15% of the copper atoms in a sample
are copper-63 atoms. This isotope has an atomic mass of
62.93 u. The remaining 30.85% 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% × 62.93 u = 43.52 u of copper-63
TIP
In this book, an element’s
atomic mass is usually
rounded to two decimal places
before it is used in a calculation.
30.85% × 64.93 u = 20.03 u of copper-65
43.52 u + 20.03 u = 63.55 u
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.
Critical Thinking
8.
Reasoning Why is the average atomic mass usually
a decimal number and not a whole number like the
mass number?
AT O M S : T H E B U I L D I N G B L O C K S O F M AT T E R
7
A relative mass scale makes counting atoms possible.
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 mole is the amount of a
substance that contains as many particles as there are atoms in
exactly 12 g of carbon-12. The mole is a counting unit, just like
a dozen. If you buy two dozen ears of corn at a 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.
Avogadro’s Number
Chemists have determined that 12 g of carbon-12 contains
6.022 141 79 × 1​ 0​23​atoms. This means that one mole of any
substance contains 6.022 141 79 × ​10​23​atoms. This number is
called Avogadro’s number after Amedeo Avogadro.
A nineteenth-century Italian scientist, Avogadro helped
explain the relationship between mass and numbers of atoms.
For most calculations, the number given above is rounded
to four significant figures. So, Avogadro’s number is the
number of particles in exactly one mole of a pure substance,
and is given by 6.022 × ​10​23​. To get a sense of how large this
number is, 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.
READING CHECK
9.
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?
8
CHAPTER 3
A penny contains about 1/20 mol of
copper atoms, or 2.964 × 1​022
​ ​atoms.
A sample of 20 copper pennies is a
little less than one mole of copper.
(a)
(b)
(c)
About one molar mass of (a) carbon (graphite), (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 molar mass of that substance. Molar mass is usually
written in units of g/mol. The molar mass 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.
Gram/Mole 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.
molar mass
= of element ×
1 mol
Mass of element
in grams
1 mol
× molar mass =
of element
Amount
of element
in moles
=
×
READING CHECK
11. The periodic table gives the
average atomic mass of mercury as
200.59 u. What is the mass of one
mole of mercury?
1 mol
6.022 × 1023 atoms
6.022 × 1023 atoms =
1 mol
×
Number of atoms
of element
The diagram shows the relationship among mass, moles, and number of atoms.
AT O M S : T H E B U I L D I N G B L O C K S O F M AT T E R
9
SAMPLE PROBLEM
A chemist produced 11.9 g of aluminum, Al. How many
moles of aluminum were produced?
SOLUTION
1 ANALYZE
Determine what information is given and unknown.
Given: 11.9 g Al
Unknown: amount of Al in moles
2 PLAN
Determine the equation and conversion factor needed.
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.
gram Al =
grams Al × ________
​ moles Al ​
grams Al
= moles Al
3 SOLVE
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.
11.9 g Al =
11.9 g Al × _________
​  mol Al  ​
26.98 g Al
= 0.441 mol Al
4 CHECK
YOUR
WORK
Determine if the answer makes sense.
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.
PRACTICE
B. What
is the mass in grams of 2.25 mol of iron, Fe?
Molar mass of iron:
2.25 mol Fe = 2.25 mol Fe ×
=
10
CHAPTER 3
g Fe
SAMPLE PROBLEM
How many moles of silver, Ag, are in 3.01 × 1​023
​ ​atoms
of silver?
SOLUTION
1 ANALYZE
Determine what information is given and unknown.
Given: 3.01 × 1​023
​ ​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 moles, 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 × _____________________________
​
Avogadro’s number of Ag atoms
= moles Ag
3 SOLVE
Substitute the known values and calculate.
mol Ag
3.10 × 1​023
​ ​Ag atoms= 3.01 × 1​023
​ ​Ag atoms × ____________________
​
6.022 × 1​023
​ ​Ag atoms
= 0.500 mol Ag
4 CHECK
YOUR
WORK
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.
PRACTICE
C. How
many atoms of aluminum, Al, are in 2.75 mol
of aluminum?
Molar mass of aluminum:
2.75 mol Al =
2.75 mol Al ×
=
atoms Al
AT O M S : T H E B U I L D I N G B L O C K S O F M AT T E R
11
SAMPLE PROBLEM
What is the mass in grams of 1.20 × 1​08​ ​atoms of copper, Cu?
SOLUTION
1 ANALYZE
Determine what information is given and unknown.
Given: 1.20 g × 1​08​ ​atoms of Cu
Unknown: mass of Cu in grams
2 PLAN
Determine the equation and conversion factors needed.
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 mass, multiply by the molar mass.
moles
Cu
​
Cu atoms = Cu atoms × _____________________________
​
Avogadro’s number of Cu atoms
grams Cu
​
× _________
​
moles Cu
= grams Cu
3 SOLVE
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 g Cu
1 mol
Cu   ​×​ __________
​
​
1.20 × 1​08​ ​Cu atoms × ___________________
23
mol Cu
6.22 × 1​0​ ​Cu atoms
= 1.27 × 1​0–14​g Cu
4 CHECK
YOUR
WORK
Determine if the answer makes sense.
The units cancel correctly to give the answer in grams. The order of
magnitude of the answer is also reasonable because 1​08​ ​divided by
​ ​.
1​024
​ ​and then multiplied by 1​02​ ​is 1​0–14
PRACTICE
D. How
many atoms of sulfur, S, are in 4.00 g of sulfur?
Molar mass of sulfur:
4.00 g S = 4.00 g S ×
=
12
CHAPTER 3
×
S atoms
SECTION 3.3 REVIEW
VOCABULARY
1. Define the term molar mass.
REVIEW
2. Complete the table at the right.
Isotope
3. Write the nuclear symbol and hyphen
notation for each of the following isotopes.
sodium-23
a.mass number of 28, atomic number of 14
calcium-40
b.26 protons and 30 neutrons Number of
protons
Number of
electrons
Number of
neutrons
​ 64
​Cu
29
​ 108
​Ag
47
4. To two decimal places, what is the relative atomic mass and the molar mass
of the element potassium, K?
5. Determine the mass in grams of the following:
a.
2.00 mol N
b.
3.01 × ​10​23​atoms Cl
b.
1.50 × ​10​23​atoms F
6. Determine the amount in moles of the following:
a.
12.15 g mol Mg Critical Thinking
7. ANALYZING DATA Beaker A contains 2.06 mol of copper, and Beaker B
contains 222 g of silver.
a. Which beaker contains the larger mass?
b. Which beaker has the larger number of atoms?
AT O M S : T H E B U I L D I N G B L O C K S O F M AT T E R
13
Math Tutor
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 quantity, you can multiply the quantity by a conversion factor.
With SI 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 in milliliters to liters. You
can use the relationship 1 L = 1000 mL. From this relationship, you can
derive the conversion factors shown at the right.
_______
​ 1000 mL
​ and _______
​  1 L  ​
1L
Problem-Solving TIPS
• 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 definitions, so significant figures do not
apply to these factors. The number of significant figures in a converted measurement
depends on the certainty of the measurement you start with.
SAMPLE
A sample of aluminum has a mass of 0.087 g. What is the sample’s
mass in milligrams?
Based on SI prefixes, you know that 1 g = 1000 mg. The possible
conversion factors are
1g
1000 mg
​ and ​ ________ ​
​ ________
1g
1000 mg
The first conversion factor cancels grams, leaving milligrams.
1000 mg
​= 87 g
0.087 g = 0.087 g × ​ ________
1g
A sample of a mineral has 4.08 × 1​0-5
​ ​mol of vanadium per kilogram
of mass. How many micromoles of vanadium per kilogram does the
mineral contain?
1 μmol = 1 × 1​0-6
​ ​mol. The possible conversion factors are
1 μmol
mol
____________
​
​and ____________
​
​ 1 × 1​0​ ​
-6
1 μmol
1 × 1​0-6
​ ​mol
The second conversion factor cancels moles, leaving micromoles.
1 μmol
​ ​mol × ____________
​
​= 40.8 μmol
4.08 × 1​0​-5​mol = 4.08 × 1​0-5
1 × 1​0-6
​ ​mol
Practice Problems: Chapter Review practice problems 8–10
and 13–14
14
CHAPTER 3
1000 mL