Transcript Chapter 3

Bellwork 10/21
What does 1 mole of Eagle football equal?
What kind of conversions use Avogadro’s number?
How many moles of selenium are in 5.20 x 10-62 atoms
of selenium?
How many atoms of molybdenum are in 6.35 moles of
molybdenum?
Word Wall
Mole (mol)
Avogadro’s number
Chapter 3
Part II
where things get fun around here!
Is it practical to measure each grain of sand?
How else might you measure or quantify the
sand?
Let’s try it…
Paper clips…the triple beam balance…
And YOU!
Please make groups of 3 or 4.
You need a handout and a sample of paperclips.
You’ll have to share the balances.
Sand isn’t the only thing too small to count…
Atoms are too!
Learning Targets:
Review dimensional analysis to convert units.
Describe how Avogadro’s number is related to a
mole of any substance.
Calculate the mass of a mole of any substance.
We live in a quantitative world.
Quantities that answer “how much” or “how
many”. Like the grade you got on your last test… or
how many times you heard your favorite song…
Chemistry is a quantitative science. Chemists need
to know how many milligrams of elements or
compounds combine to make fertilizer or paint…
Pharmacists measure chemicals in medicine…
How do you measure matter?
Songs on your playlist?
Touchdowns?
What about gasoline?
Bananas or potatoes?
Cough medicine?
Soda?
Some units always indicate a specific
number of items.
A pair always means…
A dozen always means…
A baker’s dozen means…
But think about apples.
Apples can be measured different ways…
At a fruit stand… usually by count, right? (5 for $4)
At Kroger… usually by weight/mass. ($1.95 a kg)
At an orchard… by volume. ($12.00 a bushel)
Each of these measurements can be equated to a
dozen apples.
By count: 1 dozen apples = 12 apples
By mass: 1 dozen apples = 2.0 kg apples
By volume: 1 dozen apples = 0.20 bushel apples
The mole…
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The mole is a measuring unit.
In chemistry, we do calculations using a
measuring unit called a mole.
The mole is an SI unit (remember this one?!) that
measures the amount of a substance. Just like a
dozen… or a bushel… or a pair.
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The mole can be related to the number of
particles (a count), the mass, and the volume of
an element or a compound just as a dozen was
related to these three units for apples.
Let’s try some conversions with apples.
1. What is the mass of 90 average sized apples?
Use the conversion factor :
1 dozen apples = 2.0 kg apples
Number of apples  dozens  mass of apples
Analyze, Calculate… Evaluate
Does the result make sense?
Because a dozen apples has a mass of 2.0 kg and
90 apples is less than 10 dozen apples, the mass
should be less than 20 kg of apples.
(10 doz x 2.0 kg/doz)
Try the practice problems in your notes.
Atoms are very, very, very small.
Because they’re so darn small, it just isn’t
practical to count them. Like our paper clips!
But different… in many ways. Not like the paper clips much at all, actually…
However! We can do something similar to
counting paper clips… We can use a term that
represents a specified number of particles.
Voila! We need The Mole…
The Mole (mol): A unit to count numbers of particles
Dozen = 12
Pair = 2
Ream of paper
Baker’s dozen
Gross
Fortnight
Googol
Byte
The Mole (mol): A unit to count numbers of particles
Dozen = 12
Pair = 2
Baker’s dozen
Gross
Donkey power
Fortnight
Googol
Mole = 6.0221367 x 1023
The mole is a counting unit…
The mole is the SI unit for amount of substance.
It’s abbreviation is mol.
Just as a dozen eggs represents 12 eggs, a mole
(mol) of a substance represents 6.022 x 10 23
particles of that substance.
This is Avogadro’s number .
It is an experimentally determined number
(based on Carbon-12, again!).
It’s called Avogadro’s number in honor of
Amedeo Avogadro di Quarengna (1776-1856).
A mole (mol) of a substance represents
6.022 x 10 23 particles of that substance.
• A mole of carbon atoms is 6.022 x1023 carbon
atoms.
• A mole of chemistry teachers is 6.022 x1023
chemistry teachers.
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1 mole of M&Ms…
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It's a lot easier to write the word
'mole' than to write 6.022x1023
anytime you want to refer to a large
number of things!
• Basically, that's why this particular unit was
invented.
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Just how big is that?!
To get a sense of how large Avogadro’s number
is, consider the following: If every person living
on Earth (6.8 billion people) worked to count the
atoms in one mole of an element, and if each
person counted continuously at a rate of one
atom per second, it would take about 3 million
years for all the atoms to be counted.
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Total Recall:
How do we put powers of 10 in our calculator in
Chemistry class?
Conversions with
Avogadro’s Number
We use Avogadro’s number to find the number of
atoms of an element or compound in moles
Or
To find the amount of an element or compound
in moles from the number of atoms.
Moles  atoms or atoms  moles
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Example-1 with an element:
How many moles of magnesium are in 1.25 x
1023 atoms of magnesium?
Atoms  moles
1 mol Mg = 6.022 x 1023 atoms of Mg
Let’s work some in small groups
Textbook pg. 82
Check the sample problem then work #1 – 3.
We’ll check them in large group.
Example with a compound:
To determine how many atoms are in a mole of a
compound, we have to look at the chemical formula of
the compound.
Each molecule of CO2 has 3 atoms.
A mole of CO2 has 3 times Avogadro’s number of CO2
molecules.
A molecule of CO has _____ atoms and _____ times
Avogadro’s number of CO molecules.
Let’s practice counting atoms…
How many atoms are there in each compound:
1 molecule of NO2
1 molecule of O3
1 molecule C8H8O4
1 molecule of C12H22O11 =
And just for fun… how many oxygen atoms are
in each compound?
To find the number of atoms in a compound,
you must determine the number of atoms that
comprise the compound and multiply that
number by Avogadro’s number.
Example 2:
How many atoms are in 2.12 mol of propane
(C3H8)?
Moles  molecules  atoms
Now let’s practice in small group.
There are practice problems in your notes.
Work them in small groups and we’ll check them
in large group.
What about going the other way?
Example 3:
How many moles are there in 4.65 x 1024
molecules of NO2?
MOL  atoms  mol
Show me!
Micro World
atoms and
molecules
Macro World
grams
The mole (mol) is the amount of a substance
that contains as many particles as there are
atoms in exactly 12.00 grams of 12C
1 mol = 6.022 x 1023
Avogadro’s number (NA)
shoes
Molar mass is the mass of 1 mole of
in grams
eggs
cats
• The answer is that moles give us a
consistent method to convert between
atoms/molecules and grams. It's simply a
convenient unit to use when performing
calculations.
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Molar mass
1 mole 12C atoms = 6.022 x 1023 atoms = 12.00 g
1 12C atom = 12.00 amu
For any element
atomic mass (amu) = molar mass (grams)
One Mole of:
S
C
Hg
Cu
Fe
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The molar mass of He is 4.00 g/mol.
To find how many g of He there are in 2 moles of He,
multiply by the molar mass.
2 .00 mol He x 4.00 g He = 8.00 g He
1 mol He
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• The abbreviation for mole is mol.
• Molar mass is the weight of one mole of a
chemical compound.
• Molar mass is usually written in units
g/mol.
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Chapter 3
Section 3 Counting Atoms
Sample Problem B
•What is the mass in grams of 3.50 mol
of the element copper, Cu?
Chapter 3
Section 3 Counting Atoms
Relating Mass to Numbers of
Atoms, continued
•Sample Problem B Solution, continued
•The molar mass of copper from the
periodic table is rounded to 63.55
g/mol.
Chapter 3
Section 3 Counting Atoms
Relating Mass to Numbers of
Atoms, continued
•Sample Problem C
•A chemist produced 11.9 g of
aluminum, Al. How many moles of
aluminum were produced?
Chapter 3
Section 3 Counting Atoms
Relating Mass to Numbers of
Atoms, continued
• Sample Problem C Solution
• Given: 11.9 g Al
• Unknown: amount of Al in moles
grams Al ´
• Solution:
moles Al
= moles Al
grams Al
The molar mass of aluminum from the periodic table is
rounded to 26.98 g/mol.
1 mol Al
11.9 g Al ´
= 0.441 mol Al
26.98 g Al
Chapter 3
Section 3 Counting Atoms
Relating Mass to Numbers of Atoms,
continued
•Sample Problem D
•How many moles of silver, Ag, are in
3.01  1023 atoms of silver?
Section 3 Counting Atoms
Chapter 3
Relating Mass to Numbers of
Atoms, continued
• Sample Problem D Solution
• Given: 3.01 × 1023 atoms of Ag
• Unknown: amount of Ag in moles
• Solution:
moles Ag
Ag atoms ´
= moles Ag
Avogadro's number of Ag atoms
3.01 ´ 10
23
1 mol Ag
Ag atoms ´
=
23
6.022 ´ 10 Ag atoms
0.500 mol Ag
Chapter 3
Section 3 Counting Atoms
Relating Mass to Numbers of
Atoms, continued
•Sample Problem E
•What is the mass in grams of 1.20  108
atoms of copper, Cu?
Chapter 3
Section 3 Counting Atoms
Relating Mass to Numbers of Atoms, continued
• Sample Problem E Solution
• Given: 1.20 × 108 atoms of Cu
• Unknown: mass of Cu in grams
• Solution:
moles Cu
grams Cu
Cu atoms ´
´
= grams Cu
Avogadro's number of Cu atoms
moles Cu
The molar mass of copper from the periodic table is rounded to 63.55
g/mol.
In chemistry there are many different
concepts of mass…
We need to talk about 3 of them.
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First, atomic mass…
• Isotopes are atoms of the same element (and so
with the same number of p+ and e-) but with
different masses due to having different
numbers of n0. Right?
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• The mass of an atom is incredibly small and it
doesn’t make sense to use units like grams to
measure it…
• It’s easier to measure it in atomic mass units.
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Scientists like a standard…
• Scientists set up a scale of atomic mass, one
atom was arbitrarily chosen as the standard.
Carbon-12
Chemists use this standard to compare units of
atomic mass. It’s a relative scale… relative to C12.
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Atomic mass unit
It is defined as the mass equal to 1/12th the mass
of one C-12 atom.
Or amu…
(our textbook uses just plain “u”)
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Atomic mass is the mass of an atom in atomic
mass units (amu)
By definition: 1 atom 12C “weighs” 12 amu
On this scale
1H
= 1.008 amu
16O
= 16.00 amu
Micro World
atoms and
molecules
Macro World
grams
• The answer is that moles give us a
consistent method to convert between
atoms/molecules and grams. It's simply a
convenient unit to use when performing
calculations.
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The mole (mol) is the amount of a substance that
contains as many particles as there are atoms in exactly 12.00 grams of 12C
1 mol = 6.0221367 x 1023
Avogadro’s number (NA)
eggs
Molar mass is the mass of 1 mole of shoes in grams
cats
• A mole of carbon atoms is 6.02x1023 carbon
atoms.
• A mole of chemistry teachers is 6.02x1023
chemistry teachers.
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1 mole of M&Ms…
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It's a lot easier to write the word
'mole' than to write '6.02x1023’
anytime you want to refer to a large
number of things!
• Basically, that's why this particular unit was
invented.
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• The abbreviation for mole is mol.
• Molar mass is the weight of one mole of a
chemical compound.
• Molar mass is usually written in units
g/mol.
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Molar mass
1 mole 12C atoms = 6.022 x 1023 atoms = 12.00 g
1 12C atom = 12.00 amu
For any element
atomic mass (amu) = molar mass (grams)
One Mole of:
S
C
Hg
Cu
Fe
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The molar mass of He is 4.00 g/mol.
To find how many g of He there are in 2 moles of He,
multiply by the molar mass.
2 .00 mol He x 4.00 g He = 8.00 g He
1 mol He
Conversions with
Avogadro’s Number
• We use Avogadro’s number to find the number
of atoms of an element in moles
• Or
• To find the amount of an element in moles
from the number of atoms.
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Chapter 3
Section 3 Counting Atoms
Sample Problem B
•What is the mass in grams of 3.50 mol
of the element copper, Cu?
Chapter 3
Section 3 Counting Atoms
Relating Mass to Numbers of
Atoms, continued
•Sample Problem B Solution, continued
•The molar mass of copper from the
periodic table is rounded to 63.55
g/mol.
Chapter 3
Section 3 Counting Atoms
Relating Mass to Numbers of
Atoms, continued
•Sample Problem C
•A chemist produced 11.9 g of
aluminum, Al. How many moles of
aluminum were produced?
Chapter 3
Section 3 Counting Atoms
Relating Mass to Numbers of
Atoms, continued
• Sample Problem C Solution
• Given: 11.9 g Al
• Unknown: amount of Al in moles
grams Al ´
• Solution:
moles Al
= moles Al
grams Al
The molar mass of aluminum from the periodic table is
rounded to 26.98 g/mol.
1 mol Al
11.9 g Al ´
= 0.441 mol Al
26.98 g Al
Chapter 3
Section 3 Counting Atoms
Relating Mass to Numbers of Atoms,
continued
•Sample Problem D
•How many moles of silver, Ag, are in
3.01  1023 atoms of silver?
Types of radioactivity
uranium compound
84
Types of radioactivity
The Bohr Model of the Atom
Niels Bohr
(1922 Nobel Prize in Physics)
Thus one mole of ethyl alcohol, C2H6O, weighs 46.069 g. One mole of water
weighs 18.015 g. If we mix 46.069 g of ethyl alcohol with 18.015 g of water, we can
be assured that the mixture contains 1 molecule of ethyl alcohol per molecule of
water. Further, we will know that there are 2 atoms of C and 8 atoms of H per
each 2 atoms of O. Thus the mole allows us to weigh convenient amounts of
material containing known numbers of atoms; i.e., it allows us to count atoms.
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• http://www.youtube.com/watch?v=WjjmzMYV1s
• Molar eclipse of the heart
• http://www.youtube.com/watch?v=oIkC7SRq
XP0
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In chemistry there are many different
concepts of mass…
We need to talk about 3 of them.
93
First, atomic mass…
• Isotopes are atoms of the same element (and so
with the same number of p+ and e-) but with
different masses due to having different
numbers of n0. Right?
94
• The mass of an atom is incredibly small and it
doesn’t make sense to use units like grams to
measure it…
• It’s easier to measure it in atomic mass units.
95
Scientists like a standard…
• Scientists set up a scale of atomic mass, one
atom was arbitrarily chosen as the standard.
Carbon-12
Chemists use this standard to compare units of
atomic mass. It’s a relative scale… relative to C12.
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Atomic mass unit
It is defined as the mass equal to 1/12th the mass
of one C-12 atom.
Or amu…
(our textbook uses just plain “u”)
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Atomic mass is the mass of an atom in atomic
mass units (amu)
By definition: 1 atom 12C “weighs” 12 amu
On this scale
1H
= 1.008 amu
16O
= 16.00 amu
Compare that to
average atomic mass
• The average atomic mass of an element is the
weighted average of the masses of its isotopes
on this scale…
• Just like how your grades are weighted.
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Average atomic mass
This is the number you see on the periodic table.
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Average atomic mass
We have to consider that most elements occur
naturally as a mixture of isotopes.
Scientists determine the average mass of a
sample of an element’s isotopes by determining
the percentages of each of the isotopes and then
giving the proper weight to each value. (Just like
your grades!)
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The Mole (mol): A unit to count numbers of particles
Dozen = 12
Pair = 2
Ream of paper
Baker’s dozen
Gross
Fortnight
Googol
Byte
The Mole (mol): A unit to count numbers of particles
Dozen = 12
Pair = 2
Baker’s dozen
Gross
Donkey power
Fortnight
Googol
Mole = 6.0221367 x 1023
• Elements rarely occur as only one isotope.
• They exist as mixtures of different isotopes of
various masses.
• This way, the less common isotopes are
accounted for.
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Don’t confuse mass number with average
atomic mass.
Mass number is the mass of one particular
atom.
Average atomic mass is the average mass of a
group of atoms of the same element that takes
into consideration all the isotopes.
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• The average atomic mass of an element
depends of both the mass and relative
abundance of each of the element’s isotopes.
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The average atomic mass is the weighted
average of all of the naturally occurring
isotopes of the element.
Percent
Isotope Abundance
12C
98.90%
13C
1.10%
Isotopic
Mass, amu
12.00000
13.00335
How do we find
atomic mass (average atomic mass)?
The average atomic mass of an element
depends of both the mass and relative
abundance of each of the element’s isotopes.
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Copper consists of 69.15% copper-63, which has an atomic mass of 62.929 601
amu, and 30.85% copper-65, which has an atomic mass of 64.927 794 amu.
Calculate the average atomic mass for Cu.
Calculating average atomic mass
Step 1: multiply the atomic mass of each isotope
by its relative abundance.
Step 2: add the results.
0.6915 x 62.929 amu + 0.3085 x 64.927 794 amu
= 63.55 amu**
*Our textbook is going to round to 2 decimal places.
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Average Atomic Mass
Oxygen has three naturally occurring isotopes in
the following proportions:
O-16 99.762 % (15.99491 amu);
O-17 0.038000% (16.99913 amu);
O-18 0.20000% (17.99916 amu).
What is the average atomic mass of oxygen?
Let’s take it to 2 decimal places
1) .99762 x 15.99491 = 15.957
2) .00038 x 16.99914 = .00646
3) .0020000 x 17.999 = .03599
15.99 amu
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Next up…
113
Atoms are very, very small.
For example, 1 atom of H weighs approximately
1.67 x 10-27 kg.
114
The Mole (mol): A unit to count numbers of particles
Dozen = 12
Pair = 2
Ream of paper
Baker’s dozen
Gross
Fortnight
Googol
Byte
The Mole (mol): A unit to count numbers of particles
Dozen = 12
Pair = 2
Baker’s dozen
Gross
Donkey power
Fortnight
Googol
Mole = 6.0221367 x 1023
Micro World
atoms and
molecules
Macro World
grams
• The answer is that moles give us a
consistent method to convert between
atoms/molecules and grams. It's simply a
convenient unit to use when performing
calculations.
118
The mole (mol) is the amount of a substance that
contains as many particles as there are atoms in exactly 12.00 grams of 12C
1 mol = 6.0221367 x 1023
Avogadro’s number (NA)
eggs
Molar mass is the mass of 1 mole of shoes in grams
cats
• A mole of carbon atoms is 6.02x1023 carbon
atoms.
• A mole of chemistry teachers is 6.02x1023
chemistry teachers.
120
1 mole of M&Ms…
121
It's a lot easier to write the word
'mole' than to write '6.02x1023’
anytime you want to refer to a large
number of things!
• Basically, that's why this particular unit was
invented.
122
• The abbreviation for mole is mol.
• Molar mass is the weight of one mole of a
chemical compound.
• Molar mass is usually written in units
g/mol.
123
Molar mass
1 mole 12C atoms = 6.022 x 1023 atoms = 12.00 g
1 12C atom = 12.00 amu
For any element
atomic mass (amu) = molar mass (grams)
One Mole of:
S
C
Hg
Cu
Fe
125
The molar mass of He is 4.00 g/mol.
To find how many g of He there are in 2 moles of He,
multiply by the molar mass.
2 .00 mol He x 4.00 g He = 8.00 g He
1 mol He
Conversions with
Avogadro’s Number
• We use Avogadro’s number to find the number
of atoms of an element in moles
• Or
• To find the amount of an element in moles
from the number of atoms.
127
129
Chapter 3
Section 3 Counting Atoms
Sample Problem B
•What is the mass in grams of 3.50 mol
of the element copper, Cu?
Chapter 3
Section 3 Counting Atoms
Relating Mass to Numbers of
Atoms, continued
•Sample Problem B Solution, continued
•The molar mass of copper from the
periodic table is rounded to 63.55
g/mol.
Chapter 3
Section 3 Counting Atoms
Relating Mass to Numbers of
Atoms, continued
•Sample Problem C
•A chemist produced 11.9 g of
aluminum, Al. How many moles of
aluminum were produced?
Chapter 3
Section 3 Counting Atoms
Relating Mass to Numbers of
Atoms, continued
• Sample Problem C Solution
• Given: 11.9 g Al
• Unknown: amount of Al in moles
grams Al ´
• Solution:
moles Al
= moles Al
grams Al
The molar mass of aluminum from the periodic table is
rounded to 26.98 g/mol.
1 mol Al
11.9 g Al ´
= 0.441 mol Al
26.98 g Al
Chapter 3
Section 3 Counting Atoms
Relating Mass to Numbers of Atoms,
continued
•Sample Problem D
•How many moles of silver, Ag, are in
3.01  1023 atoms of silver?
Types of radioactivity
uranium compound
135
Types of radioactivity
The Bohr Model of the Atom
Niels Bohr
(1922 Nobel Prize in Physics)
Thus one mole of ethyl alcohol, C2H6O, weighs 46.069 g. One mole of water
weighs 18.015 g. If we mix 46.069 g of ethyl alcohol with 18.015 g of water, we can
be assured that the mixture contains 1 molecule of ethyl alcohol per molecule of
water. Further, we will know that there are 2 atoms of C and 8 atoms of H per
each 2 atoms of O. Thus the mole allows us to weigh convenient amounts of
material containing known numbers of atoms; i.e., it allows us to count atoms.
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