Download Section 2.9 Molar Mass: Counting Atoms by Weighing Them

Chapter 2
Atoms and Elements
Chapter 2
Atoms and Elements
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
Imaging and Moving Individual Molecules
Early Ideas about the building blocks of Matter
Modern Atomic theory and the Laws that led to it
The Discovery of the Electron
The Structure of the Atom
Subatomic Particles: Protons, Neutrons and Electrons
in Atoms
Finding Patterns: The Periodic Law and the Periodic
Table
Atomic Mass: The Average Mass of an Element’s
Atoms
Molar Mass: Counting Atoms by Weighing Them
2
Section 2.1
Imaging and Moving Individual Atoms
Atomos - indivisible
• An atom of carbon is the smallest unit that we
can divide graphite into and still call it carbon.
• Is an atom of carbon truly indivisible?
3
Section 2.3
Modern Atomic Theory and the Laws that Led to It
Three Laws
• Modern Atomic Theory
–
All matter is composed of atoms
• Offers an explanation for observations and laws
• The Three Most Influential
–
–
–
The Law of Conservation of Mass
The Law of Definite Proportions
The Law of Multiple Proportions
4
Section 2.3
Modern Atomic Theory and the Laws that Led to It
The Law of Conservation of Mass
• In a chemical reaction, matter is neither
created nor destroyed
– This is a Law because it describes what happens not
why (theory or model)
• The particles of matter rearrange during a
chemical reaction
• The amount of matter is conserved because the
particles themselves are not changed
• This was Lavoisier (Chapter 1)
5
Section 2.3
Modern Atomic Theory and the Laws that Led to It
Conceptual Connection
• When a log burns up in a fire the mass of the
ash is much less than the mass of the log. What
happened the the extra mass?
6
Section 2.3
Modern Atomic Theory and the Laws that Led to It
Solution
• When a log burns up in a fire the mass of the
ash is much less than the mass of the log. What
happened the the extra mass?
• The extra mass is released into the air as carbon
dioxide (CO2) and water (H2O)
7
Section 2.3
Modern Atomic Theory and the Laws that Led to It
The Law of Definite Proportions
• Joseph Proust
• Studied the composition of compounds vs
mixtures and noticed that:
• Elements in a compound always present in
fixed (definite) proportions
• Elements in a mixture can be present in any
proportions
8
Section 2.3
Modern Atomic Theory and the Laws that Led to It
The Law of Definite Proportions
• For example he found that
copper (II) carbonate CuCO3 is
always 5.3 parts copper to 4
parts oxygen to 1 part carbon.
http://www.timna.co.il/92847/Basic-Copper-Carbonate
9
Section 2.3
Modern Atomic Theory and the Laws that Led to It
Think – Pair - Share
• If copper (II) carbonate CuCO3
is always 5.3 parts copper to 4
parts oxygen to 1 part carbon.
• Why doesn’t this match the
formula?
• Why isn’t the formula Cu5.3CO4?
http://www.timna.co.il/92847/Basic-Copper-Carbonate
10
Section 2.3
Modern Atomic Theory and the Laws that Led to It
The Law of Definite Proportions
• All samples of a given compound, regardless
of their source or how they were prepared,
have the same proportion of their constituent
elements.
• Basically what he is saying is that water is
always H2O never H3O or HO2.
• This seems obvious to us – but back in the early
days of chemistry they were just figuring this
stuff out.
11
Section 2.3
Modern Atomic Theory and the Laws that Led to It
The Law of Multiple Proportions
• Law of definite proportions got another scientist
(John Dalton) thinking.
• Dalton reasoned when atoms combined into
compounds they would combine as whole units
12
Section 2.3
Modern Atomic Theory and the Laws that Led to It
The Law of Multiple Proportions
• If A reacts with B to from more than one kind of
compound then you will get combinations like
this
• AB, AB2, AB3, A2B, A3B etc
• But remember they still don’t know formulas – all
they can measure is masses of elements in
compounds
13
Section 2.3
Modern Atomic Theory and the Laws that Led to It
The Law of Multiple Proportions
• Lets say we have 1 g of carbon that we react with
oxygen
• We end up with two different compounds
– One contains 2.67 g of oxygen
– One contains 1.33 g of oxygen
14
Section 2.3
Modern Atomic Theory and the Laws that Led to It
The Law of Multiple Proportions
• Does not seem that helpful until you take the ratio
of the oxygen 2.67/1.33 = 2
– One compound has twice as much oxygen as the other
– Of course we know now that the two compounds are
CO2 and CO.
15
Section 2.3
Modern Atomic Theory and the Laws that Led to It
The Law of Multiple Proportions
• When two elements (call them A and B) form
two different compounds, the masses of
element B that combine with 1 g of element A
can be expressed as a ratio of whole
numbers.
16
Section 2.3
Modern Atomic Theory and the Laws that Led to It
Example
• The following data were collected for several
compounds of nitrogen and oxygen. How do
these data illustrate the law of multiple
proportions?
Mass of Nitrogen That
Combines with 1 g of
Oxygen
Compound A
1.750 g
Compound B
0.8750 g
Compound C
0.4375 g
17
Section 2.3
Modern Atomic Theory and the Laws that Led to It
Example
•
For the law of multiple proportions to hold, the ratios of the masses
of nitrogen combining with 1 gram of oxygen in each pair of
compounds should be small whole numbers.
Mass of Nitrogen That
Combines with 1 g of
Oxygen
Compound A
1.750 g
Compound B
0.8750 g
Compound C
0.4375 g
A/B = 1.750/0.8750 = 2/1
B/C = 0.8750/0.4375 = 2/1
A/C = 1.750/0.4375 = 4/1
18
Section 2.3
Modern Atomic Theory and the Laws that Led to It
Definite vs Multiple Proportions
• The Law of definite proportion states that in
two or more samples of the same compound the
ratio of one element to the other is always the
same. Carbon dioxide always CO2 and carbon
monoxide always CO
• The Law of multiple proportion states that
carbon and oxygen can combine in more than
one way (CO and CO2).
19
Section 2.3
Modern Atomic Theory and the Laws that Led to It
John Dalton and the Atomic Theory
• We have been talking about Laws
– Descriptions of “What Happens”
• John Dalton brought together the best thinking
and ideas of lots of other scientists and
published a theory (or model)
– Attempt to explain “Why”
20
Section 2.3
Modern Atomic Theory and the Laws that Led to It
Dalton’s Atomic Theory
1.
2.
3.
4.
Each element is made up of tiny indestructible particles
called atoms.
All atoms of a given element have the same mass and other
properties that distinguish them from atoms of other
elements
Atoms combine in simple whole number ratios to form
compounds.
Atoms of one element cannot change into atoms of another
element. In a chemical reaction, atoms only change the way
that they are bound together with other atoms.
21
Section 2.4
The Discovery of the Electron
Scientists can’t leave well enough alone
•
•
•
•
So now we have the Atomic Theory
All matter is composed of atoms
Atoms are indivisible
So, of course, scientists immediately went about
trying to figure out what atoms were made of
22
Section 2.4
The Discovery of the Electron
Cathode Rays
• Electricity is the hot new tool in science
• JJ Thomson
• Ran a current of electricity between two
electrodes at either end of a partially evacuated
tube (cathode tube)
• Noticed a beam of particles travelling from the
cathode (negative electrode) to the anode
(positive electrode)
• He named them “cathode rays”
23
Section 2.4
The Discovery of the Electron
Cathode Rays
Fig 2.3
24
Section 2.4
The Discovery of the Electron
Cathode Rays
• Stream of charged particles emitted
from a electrically charged metal
plate
– Travel in a straight line
– Independent of material used for
cathode
– Repelled by negative pole of applied
electrical field
25
Section 2.4
The Discovery of the Electron
Cathode Rays
• Thomson calculated the charge-to-mass ratio
e
8 C
=  1.76 x 10
m
g
26
Section 2.4
The Discovery of the Electron
The Electron
• Thomson had discovered the electron
• Negatively charged, low mass particle within all
atoms.
• So it turns out the atom is not indivisible after all
27
Section 2.4
The Discovery of the Electron
The Electron
• Atom is not indivisible
• This opened up the field of “subatomic structure”
• Also asked new questions
– What are the characteristics of this new “subatomic”
particle?
– What is the structure of the atom itself?
• Lets look at how they tried to figure these out
28
Section 2.4
The Discovery of the Electron
Millikan’s Oil Droplet Experiment and the Charge of Electrons
• How did he figure out the charge of an electron
with oil drops?
• Pretty clever actually
• Used electricity
• Also used the new tool
– Radioactivity
29
Section 2.4
The Discovery of the Electron
Millikan’s Oil Droplet Experiment and the Charge of Electrons
• Fine mist of oil
droplets
• Fall thru tiny pinhole
• “Charge them up” with
electrons using
Ionizing Radiation*
• Look at drops through
a microscope
* Radioactivity
30
Section 2.4
The Discovery of the Electron
Millikan’s Oil Droplet Experiment and the Charge of Electrons
• Suspend the fall of
the droplets by
adjusting the voltage
across two plates.
31
Section 2.4
The Discovery of the Electron
Millikan’s Oil Droplet Experiment and the Charge of Electrons
• Charge on an oil drop
is always a whole
number multiple of
1.60217646 × 10 – 19
coulombs
• This is the charge on a
single electron
32
Section 2.4
The Discovery of the Electron
Millikan’s Oil Droplet Experiment and the Charge of Electrons
• Determined the magnitude of the charge on a
single electron.
• Why does this matter?
• 2 reasons
– 1. Now that we are dividing atoms up into subatomic
particles it is helpful and informative to know the
characteristics of these particles.
– 2. We can use the charge of the electron to
determine its mass.
33
Section 2.4
The Discovery of the Electron
Millikan’s Oil Droplet Experiment and the Charge of Electrons
• Using the charge of an electron to determine the
mass.
• Well we already have the charge/mass ratio.
– Thomson figured this out with the Cathode rays
• So if we figure out the charge then we can
calculate the mass of a subatomic particle.
34

Section 2.4
The Discovery of the Electron
Millikan’s Oil Droplet Experiment and the Charge of Electrons
• Since he knew the ratio of charge to mass he
was able use the charge of an electron to
determine its mass.
mass
Charge x
charge
1.60x10
 19
= mass
g
Cx
= 9.10 x 10
8
1.76 x 10 C
 28
g
• Mass of the electron is 9.10 x 10 – 28 g

35
Section 2.5
The Structure of the Atom
Models of the Structure of the Atom
• JJ Thomson reasoned that if atoms contain
negative particles then they must also contain
positive charge of some type that balances out
negative charge because most atoms are
neutral.
• The question he wanted to answer was how are
these positive and negative charges arranged.
What is the internal structure of the atom?
36
Section 2.5
The Structure of the Atom
JJ Thomson (Plum Pudding Model)
•
Reasoned that the atom
might be thought of as a
uniform “pudding” of
positive charge with
enough negative
electrons scattered
within to counterbalance
that positive charge.
37
Section 2.5
The Structure of the Atom
Ernest Rutherford (1911)
•
•
•
•
Graduate student of J.J. Thompson
Father of nuclear physics
Wanted to test the plum pudding model of
atomic structure
New “big thing” in science
is radioactivity
38
Section 2.5
The Structure of the Atom
Gold Foil Experiment
•
Ernest Rutherford
– Shoot large, positive particles (a particles)
•
Product of radioactive decay
– At a thin gold foil
– Observe how particles are deflected
39
Section 2.5
The Structure of the Atom
Fig 2.6
Source = Piece of uranium
Fig. 4-5, p. 84
40
Section 2.5
The Structure of the Atom
Gold Foil Experiment
•
•
If Plum pudding model correct most a particles
would fly right through barely deflected
Not what they saw
−
−
•
Most particles went right through
A few bounced off at weird angles – like they were
hitting something
“Almost as if you had fired a 15 inch shell at a
piece of tissue paper and it came back and hit
you”
41
Section 2.5
The Structure of the Atom
Gold Foil Experiment
•
•
How to explain these results
Rutherford reasoned that most of the mass of
the atom must be concentrated in a relatively
small area
42
Section 2.5
The Structure of the Atom
Fig. 4-6, p. 84
43
Section 2.5
The Structure of the Atom
Nuclear Theory of the Atom
1. Most of the atom’s mass and all of its positive
charge are contained in a small core called the
nucleus.
2. Most of the volume of the atom is empty space,
throughout which tiny, negatively charged
particles are dispersed.
3. There are as many negatively charged particles
outside the nucleus as there are positively
charged particles (named protons) within the
nucleus, so the atom is electrically neutral.
44
Section 2.5
The Structure of the Atom
Discovery of the Neutron
•
•
•
•
OK so we have a model of the atom.
But we still have some problems
Hydrogen atom has 1 proton and Helium atom
has 2 yet Helium weighs 4 times as much as
Hydrogen
Rutherford and his student (Chadwick) went to
work on this one
45
Section 2.5
The Structure of the Atom
Discovery of the Neutron
•
•
•
•
•
Turns out most nuclei also contain a neutral
particle called the neutron.
A neutron is similar in mass to a proton but has
no charge.
Hydrogen has no neutrons and Helium has 2
Hydrogen – 1 proton 0 neutrons
Helium – 2 protons 2 neutrons
46
Section 2.6
Subatomic Particles: Protons, Neutrons and Electrons in Atoms
Subatomic Particles
• The atom contains:
• Protons – found in the nucleus; positive charge
equal in magnitude to the electron’s negative
charge.
• Neutrons – found in the nucleus; no charge;
virtually same mass as a proton.
• Electrons – found outside the nucleus;
negatively charged.
47
Section 2.6
Subatomic Particles: Protons, Neutrons and Electrons in Atoms
Nuclear Atom Viewed in Cross Section
• The nucleus is:
• Extremely Small
compared with the overall
size of the atom.
− Pea at the center of Qwest
field
• Extremely dense;
accounts for almost all of
the atom’s mass.
48
Section 2.6
Subatomic Particles: Protons, Neutrons and Electrons in Atoms
Section 2.6
Subatomic Particles: Protons, Neutrons and Electrons in Atoms
•
The atom contains:
What do you need to know from this table
Relative charges +1, 0, –1
Relative masses protons and neutrons appx 1amu and electrons appx 1/2000 amu
50
Section 2.6
Subatomic Particles: Protons, Neutrons and Electrons in Atoms
Elements: Defined by Their Number of Protons
• If all atoms are composed of the same
subatomic particles then how can atoms can be
different from each other.
• What makes a carbon atom a carbon atom as
distinct from a sodium atom or a copper atom?
• The number of particles
• More specifically, the number of protons.
51
Section 2.6
Subatomic Particles: Protons, Neutrons and Electrons in Atoms
Elements: Defined by Their Number of Protons
• The number of protons in an atom is called the
atomic number
– Carbon has 6 protons – atomic number = 6
– Sodium has 11 protons – atomic number = 11
– Copper has 29 protons – atomic number = 29
• Identity of an element arises from number of
protons.
52
Section 2.6
Subatomic Particles: Protons, Neutrons and Electrons in Atoms
Elements: Defined by Their Number of Protons
• So far 116 elements have been discovered or
synthesized
53
Section 2.6
Subatomic Particles: Protons, Neutrons and Electrons in Atoms
Elements: Defined by Their Number of Protons
• Each element has
– Unique atomic number
– Unique chemical symbol
• Some of these are based on the English names
– H for Hydrogen He for Helium
• Others are based on the Latin names
– Na for sodium (from the Latin natrium) – atomic
number 11
– Sn for tin (from the Latin stannum) – atomic number
50
54
Section 2.6
Subatomic Particles: Protons, Neutrons and Electrons in Atoms
Isotopes: When the Number of Neutrons Varies
• Turns out all atoms are not exactly the same
• Isotopes are atoms with the same number of
protons but different numbers of neutrons
55
Section 2.6
Subatomic Particles: Protons, Neutrons and Electrons in Atoms
Isotopes: When the Number of Neutrons Varies
•
•
•
•
•
•
•
2 isotopes of sodium.
Both have 11 protons
One has 12 neutrons
Other has 13
Show almost identical chemical properties
In nature most elements contain mixtures of
isotopes.
Where do isotopes come from? How are they
formed?
56
57
Section 2.6
Subatomic Particles: Protons, Neutrons and Electrons in Atoms
Isotopic Notation
A
Z
•
•
•
•
X
14
6
C
To specify isotopes we use symbolic notation
X = the symbol of the element
Z = the atomic number (# of protons)
A = the mass number (# of protons and
neutrons)
58
Section 2.6
Subatomic Particles: Protons, Neutrons and Electrons in Atoms
Isotopes – An Example
14
6
•
•
•
C
C = the symbol for
carbon
6 = the atomic number
(6 protons)
14 = the mass number
(6 protons and 8
neutrons)
12
6
C
• C = the symbol for
carbon
• 6 = the atomic number
(6 protons)
• 12 = the mass number
(6 protons and 6
neutrons)
59
Section 2.6
Subatomic Particles: Protons, Neutrons and Electrons in Atoms
Concept Check
Write the symbolic notation for these two
isotopes of sodium.
60
Section 2.6
Subatomic Particles: Protons, Neutrons and Electrons in Atoms
Solution
Write the symbolic notation for these two
isotopes of sodium.
23
11 Na
24
11 Na
61
Section 2.6
Subatomic Particles: Protons, Neutrons and Electrons in Atoms
Learning Check
A certain isotope X contains 54 electrons and 78
neutrons.
• What is the mass number of this isotope?
62
Section 2.6
Subatomic Particles: Protons, Neutrons and Electrons in Atoms
Solution
A certain isotope X contains 54 electrons and 78
neutrons.
• What is the mass number of this isotope?
132
63
Section 2.6
Subatomic Particles: Protons, Neutrons and Electrons in Atoms
Ions: Losing and Gaining Electrons
• In a neutral atoms the number of protons is
equal to the number of electrons
– Negative charge = positive charge
64
Section 2.6
Subatomic Particles: Protons, Neutrons and Electrons in Atoms
Concept Check
• How many protons and electrons in a neutral
atom of
• Lithium (Li)
• Bromine (Br)
65
Section 2.6
Subatomic Particles: Protons, Neutrons and Electrons in Atoms
Solution
• How many protons and electrons in a neutral
atom of
• Lithium (Li)
3 protons and 3 electrons
• Bromine (Br)
35 protons and 35 electrons
66
Section 2.6
Subatomic Particles: Protons, Neutrons and Electrons in Atoms
Ions: Losing and Gaining Electrons
• During chemical changes atoms can gain or lose
electrons to become ions (charged atom)
• Metals tend to lose electrons to become
positively charged cations
– Li  Li+ + 1 e –
• Nonmetals tend to gain electrons to become
negatively charged anions
– Br + 1 e –  Br –
67
Section 2.6
Subatomic Particles: Protons, Neutrons and Electrons in Atoms
Concept Check
• How many protons and electrons in the lithium
and bromine ions
• Lithium cation (Li+)
• Bromine anion (Br –)
68
Section 2.6
Subatomic Particles: Protons, Neutrons and Electrons in Atoms
Solution
• How many protons and electrons in the lithium
and bromine ions
• Lithium cation (Li+)
3 protons and 2 electrons
• Bromine anion (Br –) 35 protons and 36 electrons
69
Section 2.7
Finding Patterns: The Periodic Law and the Periodic Table
The Periodic Table
70
Section 2.7
Finding Patterns: The Periodic Law and the Periodic Table
Mendeleev
• Elements were discovered and purified one at
a time
• Late 1800s scientists started to group
chemicals together that all behaved the same
way
• 1872, Dmitri Mendeleev arranged the 60 know
elements into groups with similar properties
and arranged them in order of increasing
atomic mass
71
Section 2.7
Finding Patterns: The Periodic Law and the Periodic Table
Periodic Table from Mendeleev’s 1869 paper
http://www.aip.org/history/curie/periodic.htm
72
Section 2.7
Finding Patterns: The Periodic Law and the Periodic Table
Superimpose on Modern Periodic Table
http://www.msnucleus.org/membership/html/jh/physical/periodictable/lesson5/periodic5b.html
73
Section 2.7
Finding Patterns: The Periodic Law and the Periodic Table
Predictive Power of Mendeleev’s Table
• There are bunch of gaps in Mendeleev’s first
version of the periodic table
• This is because lots of elements had not been
discovered or characterized yet.
• His table was revolutionary and ingenious
because it actually predicted the properties of
elements that had not been discovered yet!
74
Section 2.7
Finding Patterns: The Periodic Law and the Periodic Table
The Periodic Law
• When the elements are arranged in order of
increasing mass, certain sets of properties recur
periodically
Fig. 2.10
75
Section 2.7
Finding Patterns: The Periodic Law and the Periodic Table
Periodic Law and Quantum Mechanical Theory
• The Periodic Law was something that was
observed
– Properties of elements repeat in a periodic way
– It is a law because it describes what happens but
does not attempt to explain why
• About 50 years later the theory of Quantum
Mechanics was presented that explains why the
periodic behavior exists. (Ch 7 and 8)
76
Section 2.7
Finding Patterns: The Periodic Law and the Periodic Table
Periodic Table
Representative Elements
1A – 8A
Transition Elements
1B – 8B
Second numbering system
1 – 18
We will use the 1 – 8 A and B
You are responsible for the names and symbols of the elements
Listed (in pink) on the elements PDFs in the handouts module.
77
Section 2.7
Finding Patterns: The Periodic Law and the Periodic Table
Groups and Periods
On the periodic table,
• elements are arranged according to similar
properties
• groups contain elements with similar
properties in vertical columns
• periods are horizontal rows of elements
78
Section 2.7
Finding Patterns: The Periodic Law and the Periodic Table
Groups and Periods
79
Section 2.7
Finding Patterns: The Periodic Law and the Periodic Table
Classification of Groups
80
Section 2.7
Finding Patterns: The Periodic Law and the Periodic Table
Groups with Specific Names
• Alkali Metals (1A)
* Braniac
– Very reactive metals, explode in water, very soft
• Alkaline Earth Metals (2A)
– Less reactive than alkali metals, less soft, found in
higher concentrations in rocks and soil
• Halogens (7A)
– Reactive nonmetals, most are gases at room
temperature
• Noble Gases (8A)
– Non reactive gases
81
Section 2.7
Finding Patterns: The Periodic Law and the Periodic Table
Metals, Nonmetals, and Metalloids
• The heavy zigzag line separates metals and
nonmetals.
• Metals are located to the left.
• Nonmetals are located to the right. *
• Metalloids are located along the heavy zigzag
line between the metals and nonmetals.
− Aluminum and Polonium are exceptions
• * notice there is one lonely nonmetal on the left
side of the table
82
Section 2.7
Finding Patterns: The Periodic Law and the Periodic Table
Metals, Nonmetals, and Metalloids
83
Section 2.7
Finding Patterns: The Periodic Law and the Periodic Table
Properties of Metals, Nonmetals, and Metalloids
Metals (most elements)
• Are shiny and ductile (can be pulled into wires) and malleable (can
be hammered into sheets)
• Are good conductors of heat and electricity
• Most are solid at room temperature. Which isn’t?
Nonmetals
• Are dull, brittle, and poor conductors
• Are good insulators
• Solids, liquids or gases and room temperature
Metalloids
• Are better conductors than nonmetals, but not as good as metals
• Are used as semiconductors and insulators
84
Section 2.7
Finding Patterns: The Periodic Law and the Periodic Table
7 Elements Exist as Diatomic Molecules in their Elemental Forms
85
Section 2.7
Finding Patterns: The Periodic Law and the Periodic Table
Allotropes
•
•
Different forms of a given element.
Example: Solid carbon occurs in three forms.
• Diamond
• Graphite
• Buckminsterfullerene
86
Section 2.7
Finding Patterns: The Periodic Law and the Periodic Table
Ions and The Periodic Table
• Metals tend to lose electrons in chemical
reaction
– Li  Li+ + 1 e –
Lithium cation
• Nonmetals tend to gain electrons in chemical
reactions
– Br + 1 e –  Br –
Bromine anion
• In both of these examples only one electron is
gained or lost but this is not always the case,
sometimes 2 or even 3
87
Section 2.7
Finding Patterns: The Periodic Law and the Periodic Table
How to Predict the Charges of Ions
• Groups 1, 2 and 3 lose 1, 2 and 3
– Metals lose electrons
• Groups 5 – 7 gain 8 minus (group number)
– Nonmetals gain electrons
88
Section 2.7
Finding Patterns: The Periodic Law and the Periodic Table
Learning Check
Predict the charges of ions formed by the
following:
A. Sr
B. Se
C. Cs
89
Section 2.7
Finding Patterns: The Periodic Law and the Periodic Table
Solution
Predict the charges of ions formed by the
following:
A. Sr 2+
Sr is in group 2 – loses 2 electrons
B. Se 2 –
Se is in group 6 – gains 2 electrons
C. Cs +
Cs is in group 1 – loses 1 electron
90
Section 2.8
Atomic Mass: The Average Mass of an Elements Atoms
Atomic Mass
•
Dalton thought that all atoms of the same
element had exactly the same mass
–
–
•
•
Not strictly true
Isotopes have slightly different masses
We can calculate an average mass of the
atoms of an element
This is called the Atomic Mass
–
Average mass of the isotopes of an element
weighted according to their abundance.
91
Section 2.8
Atomic Mass: The Average Mass of an Elements Atoms
Atomic Mass for Carbon
•
•
•
•
When we look at the periodic table, the atomic
mass for carbon is not 12. It is 12.01.
That is because carbon naturally exists as a
mixture of isotopes.
The mass of carbon is an average of the
masses of the different isotopes.
12C, 13C and 14C
–
–
All have 6 protons – that is what makes them carbon
Have 6, 7 and 8 neutrons – that is what makes them
isotopes
92
Section 2.8
Atomic Mass: The Average Mass of an Elements Atoms
Atomic Mass for Carbon
•
98.89% of 12C and 1.11% of 13C
–
(14C is negligible)
•
98.89% of 12 amu + 1.11% of 13.0034 amu =
•
(0.9889)(12 amu) + (0.0111)(13.0034 amu) =
•
12.01 amu
93
Section 2.8
Atomic Mass: The Average Mass of an Elements Atoms
Learning Check
An element consists of 62.60% of an isotope
with mass 186.956 amu and 37.40% of an
isotope with mass 184.953 amu.
• Calculate the average atomic mass and
identify the element.
94
Section 2.8
Atomic Mass: The Average Mass of an Elements Atoms
Solution
An element consists of 62.60% of an isotope
with mass 186.956 amu and 37.40% of an
isotope with mass 184.953 amu.
• Calculate the average atomic mass and
identify the element.
• (0.6260)(186.956 amu) + (0.3740)(184.953
amu) =
186.2 amu Rhenium (Re)
95
Section 2.8
Atomic Mass: The Average Mass of an Elements Atoms
Atomic Mass Unit
•
•
•
It doesn’t make sense to refer to the mass of
an atom in grams – atoms are really small
So chemists defined the Atomic Mass Unit
Originally corresponded the the mass of 1H
–
•
•
Makes sense – smallest atom
Then for a while is was 1/16 the atomic weight
of a single atom of oxygen
Both of these roughly corresponded to a
nucleon (particle that makes up the nucleus)
–
Either a proton of neutron
96
Section 2.8
Atomic Mass: The Average Mass of an Elements Atoms
Atomic Mass Unit
•
•
•
•
Current definition of an atomic mass unit
One atom of 12C is assigned the mass of
exactly 12 atomic mass units
So 1 amu = 1/12 the mass of an atom of 12C
Masses of all other atoms are assigned relative
to this standard.
97
Section 2.8
Atomic Mass: The Average Mass of an Elements Atoms
Average Atomic Mass for Carbon
•
•
Even though natural carbon does not
contain a single atom with mass 12.01, for
stoichiometric purposes, we can consider
carbon to be composed of only one type of
atom with an average mass of 12.01 amu.
This enables us to count atoms of natural
carbon by weighing a sample of carbon.
98
Section 2.8
Atomic Mass: The Average Mass of an Elements Atoms
Mass Spectrometry
•
•
•
So 1 amu = 1/12 the mass of an atom of 12C
Masses of all other atoms are assigned relative
to this standard.
Most accurate method to determine atomic
mass is mass spectrometry.
99
Section 2.8
Atomic Mass: The Average Mass of an Elements Atoms
Mass Spectrometry
1)
2)
3)
4)
Vaporize sample
Ionize sample – create positive ions
Electric field accelerates particles
Ions are deflected in magnetic field
100
Section 2.8
Atomic Mass: The Average Mass of an Elements Atoms
Mass Spectrometry
• How does deflection of
ions help us determine
atomic mass?
– Large ions deflected the least and
small ions deflected the most
– Amount of defection is an
indication of relative size
– To get a measure of absolute size
the samples are always compared
to a standard that is mixed into
the sample
http://www.rug.nl/research/isotope-research/projects/radiocarbon/radiocarbonams?lang=en
101
Section 2.8
Atomic Mass: The Average Mass of an Elements Atoms
Mass Spectrometry
•
•
Mass
Mass
When 12C and 13C are analyzed 13C is
deflected slightly less (more massive)
The degree of deflection of ions if translated
into a ratio of masses
13
C
= 1.0836129 so :
12
C
Mass of
C = 1.083612912 amu  = 13.003355 amu
13
102
Section 2.8
Atomic Mass: The Average Mass of an Elements Atoms
Mass Spectrometry
How does deflection of ions help us
determine the abundance of two
isotopes?
1.
Fig 2.17
The position of each peak indicates the
atomic mass
The intensity of the peak indicates the
relative abundance of the two isotopes
2.
•
Each peak is a percentage of the total intensity
100%
Abundance of Ag 107 =
x 100% = 51.84%
100% + 92.90%
92.90%
Abundance of Ag 109 =
x 100% = 48.16%
100% + 92.90%
103
Section 2.9
Molar Mass: Counting Atoms by Weighing Them
Counting by Weighing
•
•
When we count by weighing we use the
average mass of an individual object in a
sample
The average mass of the object allows us to
behave as though they were all identical.
104
Section 2.9
Molar Mass: Counting Atoms by Weighing Them
Average Mass of an Atom
• The Atomic Mass is expressed in amu – atomic
mass units
– Atomic mass of carbon is 12.01 amu
– Atomic mass of helium is 4.003 amu
– Atomic mass of sodium is 22.99 amu
105
Section 2.9
Molar Mass: Counting Atoms by Weighing Them
The Mole: A Chemist’s Dozen
• Samples of matter contain enormous numbers
of atoms
• So just like we needed a special unit for the
mass of an atom (amu), we need a unit for a
collection of atoms
106
Section 2.9
Molar Mass: Counting Atoms by Weighing Them
The Mole: A Chemist’s Dozen
• Can’t use a dozen or a hundred
• The unit we use is the Mole
• The number of carbon atoms in exactly 12
grams of 12C
• This number was determined to be 6.022 x 1023
C atoms (Again from mass spectrometry)
• Avogadro’s number
– After the first scientist who estimated it
107
Section 2.9
Molar Mass: Counting Atoms by Weighing Them
The Mole: A Chemist’s Dozen
•
A mole is both a Number of particles and a Mass
•
•
•
•
Mole is a Number of particles
A mole is a unit just like a dozen
1 dozen = 12 of something
1 mole = 6.022 x 1023 particles
•
•
•
Mole is also a Mass
A dozen eggs has a mass ~ a pound or so
Mass of a mole in grams = to atomic weight in amu *
* See the Proof called “The Mole” on the website
108
Section 2.9
Molar Mass: Counting Atoms by Weighing Them
The Mole: A Chemist’s Dozen
•
This means that a mole of any element has a mass in grams
that is equal to its atomic weight in amu.
•
Carbon
12.01 amu/atom
12.01 g/mole
6.022 x 1023 C atoms
•
Helium
4.003 amu/atom
4.003 g/mole
6.022 x 1023 C atoms
•
Sodium
22.99 amu/atom
22.99 g/mole
6.022 x 1023 C atoms
109
Section 2.9
Molar Mass: Counting Atoms by Weighing Them
Problem Solving
• So out of all these numbers and equations there are
only two things you need to remember in order to
solve problems
• 6.022 x 1023 particles/mole
Avogadro’s number
• Grams/mole = amu/atom
From periodic table
110
Section 2.9
Molar Mass: Counting Atoms by Weighing Them
One-Mole Quantities
111
Section 2.9
Molar Mass: Counting Atoms by Weighing Them
Converting between number of Moles and Number of Atoms
• How many atoms in 2.50 moles of carbon?
6.022 x 10 23 atoms C
2.50 moles C x
= 1.51 x 10 24 atoms C
mole C
• How many moles in 5.25 x 1025 atoms of
Helium?
5.25 x 10
25
1 mole He
atoms He x
87.2 moles He
23
6.022 x 10 atoms He
112
Section 2.9
Molar Mass: Counting Atoms by Weighing Them
Learning Check
• How many atoms in 7.50 moles of argon?
• How many moles in 7.35 x 1026 atoms of
sodium?
113
Section 2.9
Molar Mass: Counting Atoms by Weighing Them
Solution
• How many atoms in 7.50 moles of Argon?
6.022 x 1023 atoms Ar
7.50 moles Ar x
= 4.52 x 1024 atoms Ar
mole Ar
• How many moles in 7.35 x 1026 atoms of
sodium?
7.35 x 10
26
1 mole Na
atoms Na x
1220 moles Na
23
6.022 x 10 atoms Na
114
Section 2.9
Molar Mass: Counting Atoms by Weighing Them
Converting between Mass and Amount (Number of Moles)
• What is the mass (in grams) of 0.535 moles of
copper?
63.55 g Cu
0.535 moles Cu x
= 34.0 g Cu
mole Cu
• How many moles are in 1.22 g of potassium?

1 mole K
1.22 g K x
= 0.0312 mole K
39.10 g K
115
Section 2.9
Molar Mass: Counting Atoms by Weighing Them
Learning Check
• What is the mass (in grams) of 2.88 moles of
iron?
• How many moles are in 25 g of calcium?
116
Section 2.9
Molar Mass: Counting Atoms by Weighing Them
Solution
• What is the mass (in grams) of 2.88 moles of
iron?
55.85 g Fe
2.88 moles Fe x
= 161 g Fe
mole Fe
• How many moles are in 25 g of calcium?
1 mole Ca
25 g Ca x
= 0.62 mole Ca
40.08 g Ca
117
Section 2.9
Molar Mass: Counting Atoms by Weighing Them
Converting between Mass and Number of Atoms
• How many gold atoms are in in a solid gold ring
that weighs 25.0 g
1 mole Au
6.022 x 10 23 atoms Au
25.0 g Au x
x
= 7.64 x 10 22 Au atoms
196.97 g Au
1 mole Au

• What is the mass of a sample of 2.5 x 1027
silicon atoms
2.5 x 10 27 Si atoms x
1 mole Si
28.09 g Si
x
= 1.2 x 10 5 g Si
23
6.022 x 10 Si atoms 1 mole Si
118
Section 2.9
Molar Mass: Counting Atoms by Weighing Them
Learning Check
• Determine both the number of moles and the
number of atoms in 25.0 g of calcium.
119
Section 2.9
Molar Mass: Counting Atoms by Weighing Them
Solution
• Determine both the number of moles and the
number of atoms in 25.0 g of calcium.
25.0 g Ca x 1 mol Ca  0.624 mol Ca
40.08 g

23 atoms
6.022
x
10
0.624 mol Ca x
 3.76 x 1023 Ca atoms
mol Ca
120
Section 2.9
Molar Mass: Counting Atoms by Weighing Them
Learning Check
• Determine the number of atoms in 5.50 mg of lead
121
Section 2.9
Molar Mass: Counting Atoms by Weighing Them
Solution
• Determine the number of atoms in 5.50 mg of lead
1x10 6 g 1 mol Pb
6.022x10 23 atoms
5.50 mg x
x
x
= 1.60 x 1016 atoms
mg
207.2 g Pb
mol
122
Section 2.9
Molar Mass: Counting Atoms by Weighing Them
Learning Check
• Determine the number of moles and the mass of
1.00 x 1022 atoms of silicon.
123
Section 2.9
Molar Mass: Counting Atoms by Weighing Them
Solution
• Determine the number of moles and the mass of
1.00 x 1022 atoms of silicon.
22
1.00 x 10
atoms Si x
1 mol
23
6.022 x 10
1.66 x 102 mol Si x

2
 1.66 x 10
mol
atoms
28.09 g
 0.466 g Si
mol Si

124
Section 2.9
Molar Mass: Counting Atoms by Weighing Them
Conceptual Connection
• Without doing any calculations determine which
sample contains the most atoms
• A. 1 g of calcium 40.08 amu
• B. 1 g of nitrogen 14.01amu
• C. 1 g of gold 196.97 amu
125
Section 2.9
Molar Mass: Counting Atoms by Weighing Them
Solution
• Without doing any calculations determine which
sample contains the most atoms
• A. 1 g of calcium 40.08 amu so 40.08 g in a mole
• B. 1 g of nitrogen 14.01amu so 14.01 g in a mole
• C. 1 g of gold 196.97 amu so 196.97 g in a mole
• So the nitrogen sample is ~ 1/14 of a mole and the
calcium is ~ 1/40th and the gold ~ 1/200th.
• The nitrogen has the most atoms.
126
Section 2.9
Molar Mass: Counting Atoms by Weighing Them
Homework and Review
• Links in Chapter 2 Module
• Review Questions 2 – 11, 13-15, 17, 19, 21-28
• Odd numbered problems 29 – 89 (skip 45, 49, 73,
77, 79)
• Finally – do the Sapling HW – try to do this without
your notes to determine what topics you still need
to review.
127