Windsor University
School of Medicine
QUANTITIES, MOLES &
EQUATIONS
CONVICTIONS ARE MORE DANGEROUS THAN LIES.
NIETZSCHE
Ch 4.1
J.C. Rowe
LEARNING OBJECTIVES
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to understand molecular and formula masses and be
able to relate them to real quantities
to understand the mole and be able to use it
quantitatively
to understand molar mass and be able to use it to
convert between grams and moles of a substance
to understand how to calculate and use percent
composition
to understand the difference
between empirical and molecular formulas and be
able to calculate both from chemical analyses
MOLECULAR AND FORMULA MASSES
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the sum of the mass of all elements in a chemical
formula is the mass of that formula or its formula
mass (formula weights).
the sum of the mass of all elements in a molecule is
the mass of that molecule or its molecular mass.
(molecular weight)
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Molecular formula of vitamin C is C6H8O6
Thus molecular mass is (6 x 12.0)+(8 x 1.0)+(6 x
16.0) =
= 72.0 amu + 8.0 amu + 96.0 amu =176.0 amu
when we are in the lab, how do we weigh out 176.0
amu? What is an amu relative to a mass that a lab
balance can weigh? This is where the definition of
the mole is handy!
Actual Atomic Mass (Ar)
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Ar =
(Element)
Mass of one C-12
C-12 = 2.00 x 10-26 kg
Oxygen = 2.66 x 10-26 kg
Bromine = 1.33 x 10-25 kg
Silver = 1.8 x 10 10-25 kg
x 12
MOLE
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We can measure masses in amu but how do we
relate that to mass in grams?
Since the masses of atoms are too small to be able
to weigh individually on a balance, we measure a
"gaggle, gross, bunch, dozen" of atoms on the
balance.
In other words, we define a quantity of atoms which
have the same numerical mass in grams as the
numerical mass in amu.
So how many atoms does it take to make, say,
1.00 g of H?
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We know the mass of an H atom is about 1.7 x 10-24 g
Using dimensional analysis:
1.0 g H x 1 atom H ~= 6.0 x 1023 atoms of H
1.7 x 10-24 g H
12.0 g C x 1 atom C ~= 6.0 x 1023 atoms of C
2.0 x 10-23 g C
Why did I choose 1.0 g of H and 12.0 g of C? Notice
that these respective numerical values are the same
numerical values of the masses of these atoms in amu:
H = 1.0 amu and C = 12.0 amu from the periodic
table
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Also notice the number of atoms required in both
cases--6.0 x 1023 atoms--is the same!
This is showing us a pattern—
if we want to equate the mass of any atom on the
periodic table in amu to its respective mass in
grams, we need 6.0 x 10 23 of the atoms for it to
work.
Pick any atom on the periodic table:
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Br, atomic mass 80 amu from the periodic table:
How many atoms of Br does it take to make
80 grams of Br?
6.0 x 1023 atoms = 80 grams of Br
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Mn, atomic mass 55 amu from the periodic table:
How many atoms of Mn does it take to make
55 grams of Mn?
6.0 x 1023 atoms = 55 grams of Mn
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K, atomic mass 39 amu from the periodic table:
How many atoms of K does it take to make
39 grams of K?
6.0 x 1023 atoms = 39 grams of K
If we did the calculations above more exactly the
actual number would be 6.022 x 1023 and ……
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we define that number as a mole -- therefore, 1 mole
of any element = 6.022 x 1023 atoms of that element.
You've used equalities like this before, it is just another
definition of an equality:
1 dozen of anything (donuts, for example) = 12 of anything
(donuts)
 1 mole of anything ( atoms, molecules or donuts, for example) =
6.022 x 1023 atoms, molecules, or donuts (a lot of donuts!)
 1 mole of cows = 6.022 x 1023 cows
 1 mole of Y atoms = 6.022 x 1023 Y atoms
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this number 6.022 x 1023 is a very important number
and is called AVOGADRO'S NUMBER- memorize it!
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Let's review some of the relationships that we have
discussed:
6.022 x 1023 atoms = one mole of atoms
1 atom C = 12.0 amu, and 1 mole C atoms = 12.0 g
1 molecule CO = 28.0 amu, and1 mole CO molecules
= 28.0 g
1 atom O = 16.0 amu, and 1 mole O atoms = 16.0 g
1 molecule O2 = 32.0 amu, and1 mole O2 molecules
= 32.0 g
Let's review some of the relationships
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1 mole C = 12.0 g = 6.022 x 1023 C atoms
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1 mole CO = 28.0 g = 6.022 x 1023 CO molecules
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1 mole O = 16.0 g = 6.022 x 1023 O atoms
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1 mole O2 = 32.0 g = 6.022 x 1023 O2 molecules
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1 mole cows = 6.022 x 1023 cows
MOLAR MASS
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From this information we can define something
called the molar mass (MM) of an atom:
from the equality, 1 mole C = 12.0 g C we get
the molar mass of C or 12.0 g C = MM
1moleC
Likewise, if the formula mass of vitamin C, C6H8O6,
is 176.0 amu, then the mass in grams of 1 mole of
vitamin C molecules is 176.0 g
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1 mole C6H8O6 = 176.0 g C6H8O6 and from that
we get the
The molar mass of C6H8O6 is 176.0 g C6H8O6
1 mole C6H8O6
or 176.0 g C 6H8O6 =MM
1 mole
How many moles of vitamin C are
contained in 5.00 g of vitamin C?
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We use molar mass just like a conversion factor in
solving problems using dimensional analysis:
Begin with the given amount of 5.00 g and use
the conversion factor (MM) to cancel grams and
obtain the required moles
-remember, Our two conversion factors
1 mole
=
176.0g C6H8O6
176.0 g C6H8O6
1 mole
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5.00 g vitamin C x 1mole = 0.0284 mole vitamin C
176.0 g vitamin C
The difference between moles and molecules
is one of scale, for example:
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if we completely decompose one molecule of
vitamin C, C6H8O6, (take it apart into its constituent
elements) what do we have?
6 carbon atoms
8 hydrogen atoms
6 oxygen atoms
if we completely decompose one mole of
vitamin C what do we have?
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6 moles carbon atoms (or 6 x 6.022 x 1023 C atoms)
1 mole C atoms
8 moles hydrogen atoms (or 8 x 6.022 x 1023 H atoms)
1 mole H atoms
6 moles oxygen atoms (or 6 x 6.022 x 1023 O atoms)
1 mole O atoms
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THE MOLAR MASS IS ALWAYS THE RATIO OF THE
MASS (gram mass from the periodic table) OF AN
(atom, molecule or formula) TO ONE MOLE OF THE
(atom, molecule or formula) AND IS USED TO
CONVERT BETWEEN MASS AND MOLES
Hint for solving chemistry problems
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Atom
Mole
1
3
Molecules
2
Mass (in gram)
(1) formula
 (2) Avogadro number ( 6.022x1023)
 (3) molecular weight (M.W.)
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Luther Eisenhardt
It is the attitude of mind developed in the student as he
proceeds with his studies, and not primarily the
information he acquires, which determine the character
and extent of his education.