Download Atomic Masses

Atomic Mass and The Mole
Unit: The Mole and Atomic Mass
Topic: AMU’s & Atomic Mass
Objectives: Day 1 of 3
• To learn how we define 1 amu (atomic
mass unit)
• To learn how we derive atomic mass from
amu (atomic mass unit)
• To learn how atomic mass is calculated
using the average natural abundance of
isotopes
Quickwrite
Answer one of the questions below 1-2
sentences:
• 1 light year (the distance light travels in a year) is equal to
9.5 trillion kilometers!!!!!!!!!! Why do you think we
measure distances to nearby stars in light years
and not kilometers?????
• Consider the reaction below, In order to make
one molecule of CO2 (g), each carbon atom needs
how many molecules of oxygen gas????
C(s) +
O2 (g)  CO2 (g)
Atomic Mass
• The balanced Chemical
equation for the reaction of solid
carbon and gaseous oxygen to
form gaseous carbon dioxide is
as follows:
• Now suppose you have a small
pile of carbon, and you want to
know how many oxygen
molecules are required to
C(s) + O2 (g)  CO2 (g)
convert all this carbon into
1 Atom reacts with 1 Molecule to yield 1 Molecule
carbon dioxide
• The balanced equation tells us
that one oxygen molecule (O2)
is required for each carbon
atom (C)
Atomic Mass
• To determine the number of oxygen
molecules required, we must know how
many carbon atoms are present in the pile
C(s) + O2 (g)  CO2 (g)
of carbon
1 Atom reacts with 1 Molecule to yield 1 Molecule
• But individual atoms are to small to see
• We can easily count things like jelly beans
and pennies, but atoms are far too small to
be counted
Atomic Mass
• The mass of one proton in a carbon atom is
1.66 x 10-24 grams
• You can’t exactly put a carbon proton on a scale
and weigh it
• To simplify things, and to avoid using very small
complex numbers like 1.66 x 10-24 grams,
scientists have defined a unit of mass called the
atomic mass unit or amu for short
• 1 AMU = 1.66 x 10-24 grams or 1/12 the mass of
a carbon atom
Atomic Mass
• The mass of one carbon
proton is equal to 1 AMU or
1.66 x 10-24 grams
• Neutrons and protons weigh
the same and electrons
virtually have no mass or
weight
• So how many protons and
neutrons does carbon have?
• That’s right, 12, so carbon
has 12 atomic mass units
• Or, we say carbon has an
average atomic mass of
12.01 AMU
What is Atomic Mass Unit (amu)?
1/12
• A unit of mass equal to _____the
mass of a carbon atom
• 1 amu = 1/12 the mass of a
______
carbon atom or 1.66 x 10-24
grams
simplify the mass
• It is a way to _______
of a proton or ________
neutron
Answer Bank
average
1/12
simplify
Carbon
abundance
neutron
Atomic Mass
• A hydrogen atom is composed
of one proton or 1 amu
• Remember, neutrons and
protons weigh the same and
electrons virtually have no
mass or weight
• A helium has 2 protons and 2
neutrons
• What is the average atomic
mass for Helium?
• That’s right, 4!
What is the average atomic mass
for some common elements?
Element
Hydrogen
Average
Atomic Mass
1.008
Helium
4.00
Carbon
12.01
Nitrogen
14.01
Oxygen
16.00
Aluminum
26.98
Sodium
22.99
Atomic Mass
• The average atomic mass for carbon is 12.01
amu
• Where does the 0.01 come from?
• 0.01 is the percent abundance in nature of
the carbon isotopes
• For example, if we weighed 12 grams of
carbon, 0.01 percent is the amount of
Carbon 14 and carbon 13 isotopes that exist
in nature
Atomic Mass
• Atomic Mass is the weighted average
mass of the atoms in a naturally occurring
element
• It is based on AMU’s and the natural
abundance of an elements isotopes
What is atomic mass?
average mass of
• The weighted _______
the atoms in a naturally
occurring element
• It is based on AMU’s and the
natural _________
abundance of an
elements isotopes
Answer Bank
average
1/12
simplify
Carbon
abundance
neutron
Atomic Mass
• Now that we know the average mass of a carbon
atom, we can count carbon atoms by weighing
samples of natural carbon
• For example, let’s say you want to count out 100
carbon atoms
• Because 12.01 amu is the average atomic mass,
Mass of 100 natural carbon atoms = 100 atoms
12.01 amu
1 carbon atom
= 1,201 amu
Atomic Mass
• Now let’s assume that when we weigh
the pile of natural carbon mentioned
earlier, the result is 3.00 x 1020 amu
• How many carbon atoms are present?
• We know that carbon has an average
atomic mass of 12.01 amu, so we can
compute the carbon atoms using the
following conversion factor
1 carbon atom
• 1 carbon atom = 12.01 amu or
12.01 amu
3.00 x 1020 amu
1 carbon atom
12.01 amu
= 2.50 x 1019
carbon atoms
Practice:
• Calculate the mass or weight in amu of a
sample of aluminum that contains 75
atoms
75 aluminum atoms
26.98 amu
= 2,024 amu
1 aluminum atom
Practice:
• How many aluminum atoms are present in
a sample of aluminum that has a mass of
2,024 amu?
2,024 amu
1 aluminum atom
= 75 atoms
26.98 amu
Summarize:
 Why do scientist’s use AMU’s and light years???
 What is the mass, in AMU of one nitrogen
atom???
 1 amu = 1/12 the mass of a _____ nucleus or
_________ grams
 ______ _____ is the weighted average mass of
the atoms in a naturally occurring element
 It is based on AMU’s and the natural ______ of
elemental isotopes
Unit: The Mole and Atomic Mass
Topic: The Mole
Objectives: Day 2 of 3
• To understand the quantity of a mole
• To understand the huge quantity of
Avogadro’s number
• To understand the mole mass relationship
Quickwrite
Answer one of the questions below 1-2
sentences:
• Your pencil uses graphite (pure carbon) to write
with; how many atoms do you think are in 12
grams of graphite or carbon????????
• How many items make up a dozen????? How
many items make up a half dozen???? How
many items are in two dozen??
The Mole
• In the previous section we used atomic
mass units for mass, but these are
extremely small units
• In a laboratory, the gram is the preferred
and more convenient unit for mass
• Remember our sample of carbon?
• It weighs 12.01 gram
• But how many atoms are in a sample of
carbon that weighs 12.01 grams?
The Mole
•
•
•
•
Lets look at the periodic table
What is the atomic mass of carbon?
That’s right, 12.01
A sample of carbon with a mass of
12.01 has 6.022 x1023 atoms!
• The number of atoms present in
12.01 grams of carbon is called the
mole
6.022 x1023
Average
Atomic
Mass in
grams
1.008
6.022 x1023
4.00
6.022 x1023
12.01
6.022 x1023
14.01
6.022 x1023
16.00
Aluminum 6.022 x1023
26.98
6.022 x1023
22.99
How many
atoms
does
How
many
Element
How
many
1.008
grams
ofis,
How
many
atoms
does
The
point
atoms
does
hydrogen
contain?
atoms
does
14.01
grams
of
a
sample
4.00 grams of
12.01
grams
of
nitrogen
contain?
Of
any
element
helium contain?
Hydrogen
carbon
contain?
that weighs
A number of Helium
23
6.022
x10
grams
equal
Carbon
To
the
average
23
6.022 x10
atomic mass of Nitrogen
23
6.022
x10
that element
contains
Oxygen
23
6.022x10
x10
23 atoms!
6.022
Sodium
Number of
Atoms
Present
What is a Mole?
• The amount
_____ of a substance
6.022 x 1023
that contains __________
particles of a substance
• It is also the number equal
to the amount of carbon
atoms in 12.01
_____ grams of
carbon
Answer Bank
12.01
Atoms
24
Amount
6.022 x 1023(2)
The Mole
• As it turns out, one mole of anything contains 6.022
x1023 units of that substance
• Just as a dozen eggs is 12 eggs, a mole of eggs is
6.022 x1023 eggs
• The mole is an incredibly large number to imagine 602,000,000,000,000,000,000,000!!!!!!!!!!!!!!!!!
• We use scientific notation to simply this number
• We call this unbelievably large number Avogadro’s
number
The Mole
• If I have a dozen eggs how many eggs do
I have?
• If I have 2 dozen eggs, how many eggs do
I have?
• If I have a mole of eggs, how many eggs
do I have?
• If I have a 2 mole of eggs, how many eggs
do I have? (2) x (6.022 x 1023)
What is Avogadro’s Number?
atoms in 1 mole Answer Bank
• The amount of _____
12.01
of a substance which is
Atoms
24
________
6.022
x 1023
Amount
• Just as two dozen is (2) x (12), 6.022 x 1023(2)
or ____eggs,
a mole of atoms
24
is equal to (2) x (6.022 x 1023 )
atoms
The Mole
• Consider the following sample of hydrogen
atoms below (symbolized by red dots) which
contains one mole (6.022 x 1023) of hydrogen
atoms
• Now consider another sample in which the
number of hydrogen atoms is unknown
Sample A = 1.008 grams
Sample B = 0.500 grams
The Mole
• We know sample A has 6.022 x1023
hydrogen atoms
• But how many atoms are in sample B?
• We know the mass is 0.500 grams
Sample A = 1.008 grams
Sample B = 0.500 grams
The Mole
• Let’s consider what we know
• We know that 1 mol of hydrogen atoms has a
mass of 1.008 grams
• Sample B has a mass of 0.500 grams which is
exactly half the mass of a mole of hydrogen
atoms
Sample A = 1.008 grams
Sample B = 0.500 grams
The Mole
• Let’s consider what we know
• We know that 1 mol of hydrogen atoms has a
mass of 1.008 grams
• Sample B has a mass of 0.500 grams which is
exactly half the mass of a mole of hydrogen
atoms
Sample A = 1.008 grams
Sample B = 0.500 grams
The Mole
• Let’s do the math!
0.500 grams of hydrogen
We know we
have 0.500 grams
of hydrogen
Our conversion factor is:
1mol hydrogen
1.008 grams
1 mol hydrogen
1.008 grams of hydrogen
Sample A = 1.008 grams
= 0.496 mol
of hydrogen
in sample B
Sample B = 0.500 grams
Our conversion factor is:
23
6.022
x10
The Mole
1 mol
• Now that we have moles, we can compute the
number of atoms by using our conversion factor
0.496 mol of hydrogen
6.022 x1023 hydrogen atoms
= 2.99 x1023
We solved for moles
In the last example
1 mol of hydrogen
hydrogen atoms
in sample B
Sample A = 1.008 grams
Sample B = 0.500 grams
Contains 6.022 x1023 Atoms
Contains ???? Atoms
Practice:
• Your chicken laid 562 eggs. How many dozen
eggs do you have?
562 eggs
1 dozen
= 46 dozen
12 eggs
Practice:
• How many moles are in a 42 gram sample of
aluminum?
grams
42 grams Al
moles
1 mol aluminum
26.98 grams Al
= 1.56 mol
of Aluminum
Practice:
• How many atoms are in 1.56 mol of aluminum?
moles
1.56 mol Al
number of atoms
6.022 x1023 Al atoms
1 mol Al
= 9.39 x1023
Aluminum Atoms
Practice:
• Calculate the mass of 1.56 mol of Aluminum:
moles
1.56 mol Al
grams
26.98 grams Al
1 mol Al
= 42 grams
Aluminum
Practice:
• How many atoms are in a 18 gram
sample of carbon?
grams
moles
18 grams C 1 mol C
12.01 grams C
number of atoms
6.022 x1023 C atoms
1 mol C
= 9.07 x1023
Carbon Atoms
Summarize:
• If I have a _____of something I have_______
particles
• Avogadro number is ___________
• A mole of carbon atoms weighs(mass)
______grams and contains ______ atoms
• 2 moles of carbons atoms weighs _____ grams
• Review: An ______ is atom with a different
amount of neutron than protons
Unit: The Mole and Atomic Mass
Topic: Molar Mass/Molecular Weight
Objectives: Day 3 of 3
• To learn how to calculate Molar Mass
• To learn how to convert between moles and
grams
• To learn how to calculate % composition
Quickwrite
Answer one of the questions below 1-2
sentences:
• Let’s say you want to find the weight of your dog,
which is too big to stand on your bathroom
scale; how could you find his weight???
• Together, you and your dog weigh 100
kilograms, you know that you weigh 75
kilograms, what percent by weight does your
dog weigh????
Molar Mass/Molecular Weight
• A chemical compound such as
methane (CH4) is a collection of
atoms
• Methane contains 1 carbon atom
and 4 hydrogen atoms
• But how do we calculate the mass
of one mol of methane?
• In other words, what is the mass of
6.022 x1023 C methane molecules?
Molar Mass/Molecular Weight
• Because each methane molecule (CH4)
contains one carbon atom and 4
hydrogen atoms, 1 mol (CH4) molecules
consists of 1 mol carbon atoms and 4
mol of hydrogen atoms
• So the mass of 1 mol of (CH4) is equal
to:
Mass of 1 mol of carbon (C) = 1 x 12.01g = 12.01 g
Mass of 4 mol of hydrogen (H) = 4 x 1.008 = 4.032g
_______
Mass of 1 mol of (CH4) = 16.04 g
1 CH4 molecule
10 CH4 molecule
1 C atom
10 C atoms
4 hydrogen atoms
40 hydrogen atoms
1 mol of C atoms
1 mol of CH4 molecules
(6.022 x1023 CH4 molecules)
(6.022 x1023 C atoms)
4 mol of H atoms
4 (6.022 x1023 H atoms)
What is molar mass or
molecular weight?
• It is the mass in grams of one _____
mole
of a substance or compound
• It is found by _______
adding the atomic
________that
make up a compound
masses
Answer Bank
Total
Percent
Element
adding
mole
masses
or molecule
• Ex: methane
Mass of 1 mol of carbon (C) = 1 x 12.01g = 12.01 g
Mass of 4 mol of hydrogen (H) = 4 x 1.008 _______
= 4.032g
Mass of 1 mol of (CH4) = 16.04 g
Practice:
• Calculate the molar mass of sulfur dioxide:
Mass of 1 mol of sulfur (S) = 1 x 32.07 g = 32.07 g
Mass of 2 mol of oxygen (O) = 2 x 16.00 g =_______
32.00 g
Mass of 1 mol of (SO2) = 64.07 g
Practice:
• A sample of calcium carbonate (chalk) contains
4.86 mol. What is the mass in grams of this
sample:
First calculate the molar mass of CaCO3:
Mass of 1 mol of Calcium (Ca)=1 x 40.08 g = 40.08 g
Mass of 1 mol of Carbon (C) =1x 12.01 g = 12.01 g
Mass of 3 mol of Oxygen (O) =3 x 16.00 g = _______
48.00 g
Mass of 1 mol of (CaCO3): = 100.09 g
4.86 mol CaCO3
100.09 grams CaCO3
1 mol CaCO3
= 486 grams CaCO3
Practice:
• A sample of water weighs 20.56 grams. How
many water molecules are in a sample of water
that weighs 20.56 grams?
20.56 gms H2O
1 mol of H2O
18.016 gms H2O
6.022 x1023 H2O molecules
1 mol H2O
=6.87 x 1023
molecules
Percent Composition
• Chemists often need to know a chemical’s
composition in terms of the masses of it’s
elements
• We can obtain this information from the
formula of the compound by comparing
the mass of each element present in 1 mol
of the compound to the total mass of 1 mol
of the compound
Percent Composition
• The mass fraction for each element is
calculated as follows:
Mass
Mass of the element present in 1 mol of compound
for a given =
Mass of 1 mol of compound
element
• For example, lets consider ethanol (C2H6O):
• We calculate the mass of each element present and the molar
mass of ethanol as follows:
Mass of C = 2 mol C
12.01 grams C
=
1 mol C
Mass of H = 6 mol H
1.008 grams H
= 6.048 g H
16.00 grams O
1 mol O
x100 = 13.13% H
46.07 g C2H6O
1 mol H
Mass of O = 1 mol O
24.02 g C x100 = 52.14 % C
46.07 g C2H6O
=
16.00 g O
x 100 = 34.73% O
46.07 g C2H6O
Mass of 1 mol of C2H6O ethanol = 46.07 g = molar mass
• The mass percent of carbon in ethanol can
be computed by comparing the mass of
carbon in 1 mol of ethanol with the total
mass of 1 mol of ethanol and multiplying
the result by 100%
Mass % of C = Mass of C in 1 mol C2H6O = 24.02 g x 100% = 52.14%
Mass of 1 mol C2H6O
46.07 g
Mass % of H =
Mass of H in 1 mol C2H6O 6.048 g x 100% = 13.13%
Mass of 1 mol C2H6O = 46.07 g
Mass of O in 1 mol C2H6O = 16.00 g x 100% = 34.73%
Mass % of O = Mass of 1 mol C2H6O
46.07 g
Percent Composition
• To review, by weight, ethanol contains
52.14% carbon, 13.13% hydrogen, and
34.73% Oxygen
• Or, 52.14% +13.13% + 34.73% = 100%
What is Mass Percent?
percent
• The ________by
mass of an Answer Bank
Total
element in a compound or
________
Percent
molecule
Element
adding
mole
• Mass % is calculated by
masses
comparing the mass of a single
total mass
element to the _____
(molar mass) of the compound
Practice:
• Find the weight percent of oxygen in water
H2O:
Practice:
• First calculate the molar mass of H2O:
Mass of 2 mol of hydrogen (H)= 2 x 1.008 g = 2.016 g
Mass of 1 mol of oxygen (O) = 1 x 16.00 g = _______
16.00 g
Mass of 1 mol of (H2O): = 18.016 g
• A sample of water weighs 20.56 grams. How
many moles of water are in 20.56 grams of water?
20.56 grams H2O
1 mol of H2O
18.016 grams H2O
= 1.14 mol H2O
Summarize:
• _____ _____is the mass in grams of one
mole of a substance
• To calculate Molar mass, you would add
up the ____ ______for each element that
make up a molecule
• The percent by mass of an element in a
compound is called it’s ______ ______
• Calculate the percentage of nitrogen in
nitrogen dioxide NO2