THE MOLE
Unit 7
How Scientists Keep Track of Atoms
• One way to measure how much substance
available is to count the # of particles in that
sample
– However, atoms & molecules are extremely
small
– Also, the # of individual particles in even a
small sample is very large
– Therefore, counting the # of particles is not
a practical measure of amount
• To solve this problem, scientists developed
the concept of the mole
– It’s the “chemical counting unit”
• Just as a dozen eggs equals 12 eggs, a mole
= 602,000,000,000,000,000,000,000
– It is equal to that number no matter what
kind of particles you’re talking about
– It could be represent marbles, pencils, or
bikes
– usually deals with atoms and molecules
• The word “mole” was introduced about 1896
by Wilhelm Oswald, who derived the term
from the latin word moles meaning a “heap”
or “pile.”
• The mole, whose abbreviation is “mol”, is
the SI base unit for measuring amount of a
pure substance.
• The mole, as a unit, is only used to count
very small items
– Represents a # of items, so, we can know
exactly how many items are in 1 mole
• The experimentally determined number a
mole is called, Avogadro’s Number.
– Or 6.02x1023
• The term representative particle refers to the
species present in a substance
– Usually atoms
– Molecules
– Or formula units (ions)
REPRESENTATIVE PARTICLES & MOLES
ATOMIC
NITROGEN
ATOM
N
6.02x1023
NITROGEN
GAS
MOLEC.
N2
6.02x1023
WATER
MOLEC.
H20
6.02x1023
CALCIUM
ION
ION
Ca2+
6.02x1023
CALCIUM
FLUORIDE
FORMULA
UNIT
CaF2
6.02x1023
How Do We Use The Mole?
• We’d never use the mole to describe
macroscopic or real world objects.
– 1 mole (6.02x1023) of watermelon seeds
would be found inside a watermelon the size
of the moon.
– 1 mole (6.02x1023) of donut holes would cover
the earth and would be 5 miles deep.
• Since the mole is such a huge number of
items, it is only used to describe the amount
of things that are very, very small.
– 1 mole (6.02x1023) of water molecules would
barely fill a shot glass
Using the mole in calculations #1
What number of moles of Mg is equivalent to
1.806x1024 atoms of Mg?
*Remember*
1 mol Mg = 6.02x1023 atoms Mg
1 mole Mg
=
X mole Mg
6.02x1023 atoms Mg 1.806x1024 atoms Mg
(6.02x1023 atoms Mg)(X mole Mg) =
(1.806x1024 atoms Mg)(1 mole Mg)
(6.02x1023atmMg)(X)=(1.806x1024atms•molsMg)
X = 3.0 moles
(6.02x1023atmMg)
(6.02x1023atmMg)
Using the mole in calculations #2
If we had 2.5 moles of sugar, how many
molecules of sugar is that equal to?
*Remember*
1 mol sugar = 6.02x1023 molecules sugar
1 mole sugar
6.02x1023molec sugar
=
2.5 moles sugar
X molec sugar
(1mole sugar)(X molec sugar) =
(6.02x1023 molecs sugar)(2.5 mole sugar)
(1molsugar)(X) = (1.505x1024molecs•mols sugar)
X = 1.51x1024 molecules of sugar
(1molsugar)
(1molsugar)
• What if I asked you how many atoms are in
a mole of a compound?
– you must know how many atoms are in a
representative particle or cluster of the
compound.
• To do this you must know the chem formula
– For example, each molecule of CO2 is
composed of 1 C + 2 O’s = 3 atoms
• 1 mole of carbon dioxide molecules contains
avogadro’s number of carbon dioxide
molecules.
– Thus a mole of CO2 contains three times
avogadro’s number of atoms
• To find the # of atoms in a mol of a
compound,
– You 1st determine the # of atoms in a
representative particle of that compound
– And then multiply that # of atoms by
avogadro’s #
Using the mole in calculations #3
How many atoms of carbon are in 2.12 mols
of propane molecules (C3H8)?
Useful Info:
1 mol C3H8 = 6.02x1023 molecules C3H8
1molecule C3H8 = 3 atoms of C
1st we need to see how many molecules of
propane we have if we have 2.12 moles.
1 mole C3H8
6.02x1023molec C3H8
=
2.12 moles C3H8
X molec C3H8
(1molecC3H8)(X)=(1.276x1024molec•molsC3H8)
(1 molec C3H8)
(1 molec C3H8)
X = 1.276x1024 molecules of C3H8
2nd we need to see how many atoms of C if we
have 1.276x1024 molecs of C3H8.
1 molecule C3H8
3 atoms of C
=
1.276x1024 molec C3H8
X atoms C
(1molec C3H8)(X)=(3.83x1024molec • atoms C)
(1 molec C3H8)
(1 molec C3H8)
X = 3.83x1024 atoms of Carbon
How we measure moles…
• Do you know how to measure out 3 moles
of sugar or salt or water?
– The mole is a counting unit, so we would
have to count out 6.02x1023 particles of
each substance. (no thank you)
• There are 2 ways we can use to measure
out a number of moles of a substance.
– Measure it in grams (a mass)
– Or measure it in liters (a volume)
Using mass to measure moles…
• One of the units we can use to measure out
a particular amount of moles is to weigh it
out in grams?
– The only problem with this method is that 1
mol of books will weigh more than 1 mol of
pencils, since each book is heavier.
– What if 1 mol of pencils weighs 500Gtons
and 1 mol of books weighs 1x106Gtons.
• How much would 3.0 mols of pencils and 3
mols of books weigh?
– 500 Gtons * 3 mols = 1500 Gtons pencils
– 1x106 Gtons * 3 mols = 3x106 Gtons
Using mass to measure moles…
• To be able to measure out 1 mol of a
substance we would need access to the
known mass in grams of 1 mol of any
substance in question
– We would need a data table that provided all
of these masses since every substance
involved would have its own mass.
• Remember, we don’t use the mole to count
anything but atoms, molecules, etc.
– So we need a table that provides the mass 1
mole would weigh for every combination of
atoms known to man.
Using mass to measure moles…
• It just so happens that the periodic table
provides us with some of that information.
– The masses of each atom on the table is the
equivalent to the mass of 1 mole of that atom
– Every type of atom known to humankind is
on that table.
• The mass on the periodic table is called the
molar mass (units of g/mol), because it
represents the mass of 1 mol of that atom
– 1 mole of Mg atoms weighs 24.305 g
– 1 mole of C atoms weighs 12.011 g
Using mass to measure moles…
• That works well for atoms off of the periodic
table, but how do we deal the molar masses
of molecules and compounds?
– Each of those compounds and molecules is
composed of a combination of atoms
– We have the molar masses for all of the
atoms on the periodic table
• We need to be able to add up the total
weight of all of the atoms in the compound
or molecule given its formula.
– For ex, what is the molar mass of H2O?
• We just add the molar masses of each of the
atoms that make up the molecule
• From the PT, we find that the molar mass of
1 mole of Hydrogen atoms is 1.0079 g.
–We have 2 Hydrogen atoms per molecule of
H2O, so our Hydrogen atoms total 2 * 1.0079
g or 2.0158 g per mole
• The mass of 1 mole of oxygen atoms is 15.999
g.
–We have only 1 atom of oxygen per mole-cule
of H2O so our total mass of oxygen is 1 *
15.999 g or just 15.999 g per mol
• Therefore 1 mole of H2O molecs would
weigh, 2.0158g+15.999g= 18.0148g
Ex #2: Calculating molar masses using
chemical formulas
What is the mass of 1 mole of C6H12O6?
• The overall mass of 1 mole of C6H12O6 will
be the molar mass of 6 Carbons + the
molar mass of 12 Hydrogens + the molar
mass of 6 Oxygens.
6 Carbons = 6 * 12.011 g = 72.066 g
12 Hydrogens = 12 * 1.0079 g = 12.095 g
6 Oxygens = 6 * 15.999 g = 95. 994 g
180.16 g/mole
• Even though for compounds and molecules
we have to calculate a molar mass using the
periodic table, they are considered given or
known values.
• We can use these molar masses in
calculations in which we are either give
moles and asked for its mass equivalent or
given mass and asked for its mole
equivalent.
– If we are given an element we just use the
mass from the periodic table
– If we are given a formula instead we just
calculate the molar mass of the molecule
using the masses from the periodic table.
Using the mole in calculations #4
How much would
9.45 moles of N2O3 weigh?
1 mole N2O3
9.45 moles N2O3
=
2(14.007g)+3(15.999g)
X g N 2 O3
Using the mole in calculations #4
How much would
9.45 moles of N2O3 weigh?
1 mole N2O3
9.45 moles N2O3
=
76.011g N2O3
X g N 2 O3
(1mole N2O3)(X g N2O3) =
(9.45 moles N2O3)(76.011g N2O3)
(1mol N2O3)(X) = (718 g • mols N2O3)
(1 mol N2O3)
(1 mol N2O3)
X = 718 grams of N2O3
Using the mole in calculations #5
We have 92.2g of FeO, how many moles is the
equivalent of the given mass?
1 mole FeO
X mols FeO
=
1(55.847g)+1(15.999g)
92.2 g FeO
Using the mole in calculations #5
We have 92.2g of FeO, how many moles is the
equivalent of the given mass?
1 mole FeO
X mols FeO
=
71.846 g FeO
92.2 g FeO
(71.846g FeO)(X mols FeO) =
(1 mole FeO)(92.2 g FeO)
(71.846gFeO)(X) = (92.2 g•mols FeO)
(71.846gFeO)
(71.846gFeO)
X = 1.28 moles of FeO
Using volume to measure moles…
• The other unit we can use to measure out
mols is to measure a gas in Liters
– There is a standard volume that 1 mol of
any gas will occupy called molar volume.
– If we had 1 mol of Ne and 1 mol of CO2 they
would each contain 6.02x1023 particles, and
occupy the same volume under standard
conditions (0°C, 1 atm).
• At STP or standard temp & press; 1 mol of
any gas occupies 22.4 Liters of space
– 1 mol of He = 22.4 L of space
– 1 mol of N2 = 22.4 L of space
Using the mole in calculations #6
What volume, in Liters, would
.500
mols of CO gas occupy at STP?
*Remember*
1 mol CO = 22.4 L CO
1 mole CO
22.4 L CO
=
.500 mol CO
X L CO
(1mol CO)(X L CO)= (.500 mol CO)(22.4 L CO
(1mol CO)
(1mol CO)
X = 12.2 L of CO
Using the mole in calculations #7
If you have a 35.67g piece
of
Chromium metal on your car,
how many atoms of Chromium are
in this piece of metal?
• You are given mass and asked for
number of particles
• Let’s get some strategy
We are given
a mass
We are asked
for atoms
We are given
a mass
• It’s going to take
us 2 conversions,
we just need to
follow the arrows
• 1st we must convert our given mass of
Chromium to moles of Chromium
– So we need to use the periodic table to
calculate the mass of 1 mole of Chromium
1 mole Cr
51.996g Cr
=
X mol Cr
35.67g Cr
(51.996gCr)(X mol Cr) =
(35.67gCr)(1 mol Cr)
X = .6860 mol Cr
• 2nd we must convert our newly found moles
of Cr to atoms of Cr
– So we need to remember that 1 mole of
anything there are 6.02x1023 particles
6.02x1023 atoms Cr
1 mole Cr
=
X atoms Cr
.6860 mol Cr
(1 mol Cr)(X atoms Cr) =
(6.02x1023 atoms Cr)
(.6860 mol Cr)
X = 4.13x1023 atoms Cr