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Atomic Masses & the MOLE…
• Neon is a gas that can be found in
the atmosphere.
– Dry air contains about 0.002% Ne
– That’s 500,000,000,000,000,000
atoms of neon every breath
• Scientists can deal with atoms quantitatively because they know some
fundamental properties of the atoms
of each element
• Masses of atoms expressed in grams
are extremely small.
– An atom of Oxygen -16
literally weighs
0.0000000000000000000000266 g
-For most calcs in chemistry
it is easier to use a relative
atomic mass.
- For relative masses, an
atom was arbitrarily chosen as
the standard, by which all other
masses are compared
I. Atomic Mass
A. Relative Mass is when you
measure the mass of all
atoms based on the
measurement of one
particular atom.
1.C-12 atom acts as the standard to
compare all other atoms
2. A single C-12 atom was assigned
a mass of 12 atomic mass units
(amu)
– 1 amu is exactly 1/12 of the mass of
a C-12 atom
– Carbon has 12 nucleons therefore,
the mass of a proton = 1 amu
3. The masses of all other atoms are
based on the mass of 1 amu
– H has 1 proton= 1 amu
– He has 2 protons and nuetrons= 4
amus
A proton weighs
1.007276 amu
A neutron weighs
1.008665 amu
II. Average Atomic Mass
A. Most elements exist in nature as
isotopes
• 75% of all of the Cl atoms found in
nature are the isotope Cl-35
• 25% of the all of the Cl atoms found
in nature are the isotope Cl-37
1.Average atomic mass is the mass on
the PT and is the average of all of the
naturally occurring isotopes of an
element
Example:
We have 25 marbles that each
weigh 2 g and 75 marbles that
weigh one gram. What is the
average atomic mass for these
marbles?
2. Calculating average atomic masses:
a. Cu
69.17% Cu-63 has a mass of 63 amu,
30.83% Cu-65 has a mass of 65 amu.
• It’s calculated by multiplying the atomic
mass of each isotope by its abundance
and adding the results.
Cu-63
Cu-65
(0.6917)(63 amu)
+ (0.3083)(65 amu)
63.6 amu
• The reported average atomic mass of
naturally occurring Cu is 63.55 amu.
Your Turn:
b. Practice #1.
Gallium consists of two isotopes of masses
• 68.95 amu and 70.95 amu with
abundances of 60.16% and 39.84%,
respectively. What is the average atomic
mass of gallium?
•
•
••
c. Practice #2.
Naturally occurring element X exists in
three isotopic forms:
X-28 (27.977 amu, 92.21%
abundance),
X-29 (28.976 amu, 4.70% abundance),
X-30 (29.974 amu, 3.09% abundance)
. Calculate the atomic weight of X.
•
B. Relating Mass to the number of
Atoms
• It is impractical to get caught up into
working with 1 atom’s mass because
usually you working with a large
number of atoms.
• Scientists were challenged to figure
out a way to define a collection of
particles
– And which could still be described in
terms of a relative mass
1. The average C atom with an atomic
mass of 12.0 amus is 12 times
heavier than the average H atom
a.So 100 C atoms are 12 times
heavier than 100 H atoms
b. any # of C atoms would be 12
times heavier than the same # of H
atom
• If we assume we can relate the
relative masses from the PT in the
terms of grams
– With the literal masses of an atom
(g) for each atom we use we seem
to get the same number of atoms


1 atom
23

15.999g

6
.
0235
*
10
atoms
 23 
 2.6561*10 g 
Counting Atoms


1 atom
23

1.00797g

6
.
0231
*
10
atoms
 24 
 1.6735 *10 g 


1 atom
23


12.0115g
 6.0235 *10 atoms
 23 
 1.9941*10 g 
Counting Atoms
• The number of atoms that are in the
relative masses of elements identical
in grams to the atomic masses on the
PT is called Avogadro’s Number
• And is defined as a mole
• The mole becomes a counting unit
much like the dozen.
– 1 dozen eggs = 12 eggs
– 1 mole of eggs =
Counting Atoms
• The word “mole” was introduced by
Wilhelm Oswald, who derived the
term from the word moles meaning
a “heap” or “pile.”
– We are just defining the pile as containing 6.02x1023 items
– Because it is such a huge number of
items we usually reserve the mole for
atoms or molecules
1 mole is always = 6.02 x 1023 items
Counting Atoms
• The mole, whose abbreviation is
“mol”, is the SI base unit for measuring amount of a pure substance.
– The mole is the chemist’s six-pack or
dozen. Many objects in our everyday
lives come in similar counting units.
• 1 ream = 500 sheets of paper
• 1 pair of socks = 2 socks
• 1 cube = 24 cans
REPRESENTATIVE PARTICLES & MOLES
Atomic
Nitrogen
Atom
N
6.02x1023
Nitrogen
gas
Molec.
N2
6.02x1023
Water
Molec.
H 2O
6.02x1023
Calcium ion
Ion
Ca2+
6.02x1023
Calcium
Fluoride
Formula
unit
CaF2
6.02x1023
Counting Atoms
• We will learn in the near future that
when a chemist reasons through a
chemical reaction (recipe) they think
in terms of X number of mols of this
compound reacts with Y number of
mols of this compound.
– So we need to know how to calculate
the number of molecules or atoms
are involved in that X number of mols
Counting Atoms
Using the mole in calculations #1
How many moles of Magnesium
is 1.25 x 1023 atoms of Magnesium?
unit equality:
1 mol Mg = 6.02 x 1023 atoms Mg
Counting Atoms
The desired conversion is:
atoms moles
1.25x1023 atoms Mg
1 mole Mg
6.02x1023atoms Mg
= .208 mol Mg
Your Turn:
• To make sure adequate amounts of product AB
is being made during a rxn you might need
3.33 mols of A reacting with 2.68 mols of B.
How many atoms of A are reacting with how
many atoms of B?
• If you burn sugar (C12H22O11) in pure oxygen
you produce carbon dioxide and water as
products. To burn 6.02x1023 molecules of
sugar you also need 7.22x1024 molecules of
oxygen and you produce 6.62x1024 molecules
of water and 7.22x1024 molecules of carbon
dioxide. How many mols are reacted or
produced for each component of the rxn?
Counting Atoms
• Now suppose you want to determine
how many atoms are in a mol of a
compound or molecule
– To do this you must know how many
atoms are involved in the molecule.
• To determine the number of atoms
represented in a molecule requires
knowing the chemical formula
– Eg, each molecule of Carbon Dioxide
(CO2) is composed of 3 atoms
Counting Atoms
• 1 mole of Carbon Dioxide contains
Avogadro’s number of Carbon
Dioxide molecules.
– Thus a mole of CO2 contains three
times Avogadro’s # of atoms
Counting Atoms
Using the mole in calculations #2
How many atoms of Carbon are in
2.12 mols of Propane (C3H8)?
unit equalities:
1 mol C3H8 = 6.02x1023 molecules C3H8
1 molecule C3H8 = 3 atoms C
Counting Atoms
The desired conversions are:
moles  molecules  atoms
2.12
mols
C3H8
6.02x1023
molecules C3H8
3 atoms C
1 mole C3H8
1 molecule
C3H8
=3.83x1024 atoms C
Your Turn:
• Back to burning sugar, 1 mol of sugar
(C12H22O11) was burned with 12 mols of
oxygen (O2) to produce 11 mols of water
(H2O) and 12 mols of Carbon dioxide
(CO2). How many total atoms of oxygen
are burned in the reaction (reactants),
and how many total atoms of oxygen are
produced in the reaction (products)?
Counting Atoms
• We can also relate mass to the
number of atoms and the mole.
– Relative atomic masses and the mol
can be used to develop a method of
measuring the amount of a sample.
• If we had a pile of C atoms that
weighed 12 g and a pile of H atoms
that weighed 1g
– each pile would contain the same
number of atoms or 6.02x1023 atoms
Counting Atoms
• The gram atomic masses of any
2 elements (since they are relative to
C) must contain the same # of atoms
– A pile of any atom that corresponds
to its average atomic mass from the
PT contains exactly 6.02x1023 atoms
of that element.
• And is equal to how much 1 mole of that
sample would weigh in grams
Counting Atoms
• What this allows us to do is to use the
mass off of the periodic table to
represent the mass of 1 mole (or
6.02x1023 atoms) of that element
– 1 mol of C atoms weighs 12.01 g
– 1 mol of H atoms weighs 1.008 g
– 1 mol of W atoms weigh 183.8 g
Counting Atoms
• This new version of mass from the
periodic table is called the gram
molar mass, or molar mass.
– Molar Mass = mass of 1 mole of
atoms/molecules/or formula units in
grams
• abbreviated = MM
• units = grams/mol
Counting Atoms
• We get the mass of 1 mole of any
element off of the Periodic Table
• So how do we figure out the mass of
a mole of a compound rather than
just an element?
– To answer that question you must
have the formula of the
compound.
Counting Atoms
What is the mass of 1 mole of Sulfur
Trioxide (SO3) A.K.A. Molar Mass?
The formula of a compound tells you how
many atoms of each element combine to
make the representative particle of that
compound.
Formula
Model
Formula
Model
Counting Atoms
• You can calculate the mass of a molecule of SO3 by adding the MM of
each of the atoms in the molecule
– The mass of 1 mole of S is 32.1g.
– The mass of 3 atoms of O is 3 times
the MM of a single O atom,
or (3)(15.99g) = 47.97g
– So MM of 1 molecule of SO3
is 32.1g + 47.97g = 80.1 g/mol
Counting Atoms
What is the MM of glucose (C6H12O6)?
(6C’S)(12.011g/mol) = 72.066g/mol
(12H’S)(1.008 g/mol) = 12.096g/mol
(6O’S)(15.99 g/mol) = 95.94g/mol
180.1g/mol
1 mole of C6H12O6 or
6.02x1023 molecules of the compound –
it would weigh 180 grams
Practice Time:
• Determine the mass of 1 mole (Molar
mass) of each of the following:
–
–
–
–
–
Zn
Gd
Zn(C2H3O2)2
(NH4)3PO4
C12H22O11
Counting Atoms
Using the mole in calculations:
How many grams are in 9.45 mol
of Dinitrogen Trioxide (N2O3)
The only connection to N2O3 and its mass
is how much 1 mol of the compound
weighs. But, using it as a comparison
we can calculate the mass of 9.45 mol.
Counting Atoms
Step 1: Determine the mass of 1 mol
of N2O3
(2N’s)(14.01g) = 28.02g
(3O’s)(15.99g) = 47.97g
75.99g
If 1 mole of N2O3 weighs 75.99g than how
much will 9.45 mols of N2O3 weigh?
Counting Atoms
Step 2: Convert the given moles to
grams using the Molar mass
equality.
9.45 mol N2O3
75.99 g N2O3
1 mol N2O3
=718 g N2O3
Counting Atoms
Find the number of moles of
92.2g of Iron (III) Oxide (Fe2O3)
The only connection to the mass of Fe2O3
and how that corresponds to mols is how
that 1 mol of the compound weighs a certain
# of grams. Using that we can figure out
how many moles weigh 92.2 g
Counting Atoms
Step 1: Determine the mass of 1 mol of
Fe2O3
(2Fe’s)(55.85g) = 111.7g
(3O’s)(15.99g) = 47.97g
159.67g
If 1 mole of Fe2O3 weighs 157.67g than how
many mols will weigh 92.2 g of Fe2O3?
Counting Atoms
Step 2: Convert the given mass to mols
using the Molar mass equality
92.2 g Fe2O3
1 mol Fe2O3
159.67 g Fe2O3
=.577mol Fe2O3
Practice Time:
• Vitamin C (C6H8O6), cannot be stored by
the body and therefore, must be present
in the diet. If an orange contains 70 mg
of Vit C how many oranges are necessary
to consume 2.5 mols of Vit C?
Counting Atoms
• Another generality about the mole is
that with matter in the gas phase we
can develop another equality.
– Under the same conditions, equal
volumes of gases contain equal
numbers of particles.
– 1 mol of a gas will occupy the same
volume as 1 mol of any other gas
under the same conditions.
Molar Volume of a Gas
1 mole of any gas
under the specific
conditions of 0°C
and 1 atm (STP)
will occupy a
volume of 22.4 L.
6.02x1023
6.02x1023
molecules of O2 molecules of CO2
Counting Atoms
What volume, in Liters, does 0.60 mol
of SO2 gas occupy at STP?
The only connection to the volume of any
gas and how that corresponds to mols is
that 1 mol of a gas occupies 22.4 Liters of
space. Using that we can figure out the
volume of 0.60 mols of a gas at STP.
Counting Atoms
Step 1: Use the equality 1 mol = 22.4 L
to do the conversion
0.60 moles SO2
22.4 L SO2
1 mole SO2
= 13 L SO2
Practice Time:
• The Snoopy balloon featured at the
Macy’s Thanksgiving Day Parade has a
volume of 15650 ft3. How many moles of
Helium are required to fill it up @ STP?
Counting Atoms
If you have a 35.67g piece of Chromium metal on your car, how many
atoms of Chromium do you have?
• You are given mass and asked for
number of particles
• Let’s get some strategy
Counting Atoms
• 1st convert given mass into moles
• To do this we use the molar mass (MM)
of Cr which on the PT is 51.996g/mol
• Then we need to convert from mols to
atoms using Avogadro’s number.
1 mole Cr 6.02x1023 atoms
35.67g Cr
51.996g Cr
1 mole Cr
=
23
4.130x10 atoms
of Cr
Calculate the Missing Info…
Formula
CH4
H2SO4
Molar
Mass
Moles
Mass
1.5
mol
79.0 g
9.03x1023
molecules
CO
Cu(NO3)2
Particles
93.8 g
Gas Vol.
@ STP