CHAPTER 5
THE MOLE
The mole (mol) is one of the
seven base units in the SI system.
It measures the amount of
substance.
The form in which a substance
exists is its “representative
particle”.
Representative particles can be
atoms, ions, molecules, formula
units, or anything else.
Just as one dozen is 12
representative particles,
a mole is 6.02 x 1023
representative particles.
602,000,000,
000,000,000,
000,000!!!!!
Examples:
1 mole Fe = 6.02 x 1023 atoms of Fe
1 mole H2O molecules = 6.02 x 1023 molecules of water
1 mole Na+ ions = 6.02 x 1023 Na+ ions
1 mole eggs = 6.02 x 1023 eggs
6.02 X 1023 Watermelon Seeds:
Would be found inside a melon slightly larger than the moon.
6.02 X 1023 Donut Holes:
Would cover the earth and be 5 miles (8 km) deep.
6.02 X 1023 Pennies:
Would make at least 7 stacks that would reach the moon.
6.02 X 1023 Grains of Sand:
Would be more than all of the sand on Miami Beach.
6.02 X 1023 Blood Cells:
Would be more than the total number of
blood cells found in every human on earth.
Diatomic Elements
Certain elements are only stable
in pairs or with other elements in
a compound. These elements are
called the diatomic elements.
There are 7 diatomic elements:
Hydrogen, bromine, oxygen,
nitrogen, chlorine, iodine,
and fluorine
(Memory trick: HOBrFINCl
twins or 7th Heaven)
Avogadro’s Number
6.02 x
is called Avogadro’s
number. It is named after
Amadeo Avogadro who did work
in the 1800’s that allowed
6.02 x 1023 to be calculated.
23
10
The mole is the “chemist’s
dozen”. It is a convenient way to
count extremely large numbers of
atoms, molecules or ions.
New Conversion Factor!
1 mole = 6.02 x 1023
representative particles
We work these problems using
dimensional analysis.
#1. How many moles are
25
1.20 x 10 atoms of phosphorous?
1.20 x 1025 atoms P 1 mol P
6.02 x 1023 atoms
= 19.9 mol P
#2. How many atoms are in
0.750 mol of Zn?
0.750 mol Zn
6.02 x 1023 atoms Zn =
1 mol Zn
4.52 x 1023 atoms Zn
Q: What did Avogadro teach his students
in math class?
A: Moletiplication
#3. How many molecules are in
0.400 mol N2O5?
0.400 mol N2O5 6.02 x 1023molecules =
1 mole N2O
2.41 x 1023 molecules
#4. How many moles are contained
24
in 1.20 x 10 molecules CO2?
1.20 x 1024 molec CO2
= 1.99 moles CO2
1 mol CO2
6.02 x 1023 molecules
#5. How many ammonium ions are in
0.036 mol ammonium phosphate?
0.036 mol (NH4)3PO4 6.02 x 1023 f. u. (NH4)3PO4
1 mole (NH4)3PO4
3 NH4+
1 f.u. (NH4)3PO4
= 6.5x 1022 NH4+
#6. How many total carbon atoms are in
a mixture of 3.00 mol acetylene (C2H2)
and 0.700 mol carbon monoxide?
3.00 mol C2H2 6.02 x 1023 molec C2H2 2 C atoms
1 mol C2H2
= 3.61 x 1024 atoms C
1 molec C2H2
0.700 mol CO 6.02 x 1023 molec CO 1 C atom
1 mol CO
1 molec CO
= 4.21 x 1023 atoms C
3.61 x 1024 atoms + 4.21 x 1023 atoms =
4.03 x 1024 atoms C
Gram atomic mass (gam)
-atomic mass of an element in
grams
-mass of one mole of atoms of a
monatomic element
-use the periodic table and take
masses to 0.1 g
Example:
23
C =12.0 g = mass of 6.02 x 10 atoms
12.0 g/mol is the gram atomic
mass of carbon
Gram molecular mass (gmm)
-mass of one mole of a molecule
-sum of the atomic masses of
each atom in the molecule
1 mol H2O: 2 mol H
1 mol O
=2 x 1.0 g H/mol = 2.0 g
=1 x 16.0 g O/mol = 16.0 g
18.0 g H2O
#7. What is the gram molecular
mass of CH3OH?
C 1 x 12.0 = 12.0
H 4 x 1.0 = 4.0
O 1 x 16.0 = 16.0
32.0 g
Gram formula mass (gfm)
-mass of one mole of an ionic
compound
-sum of the atomic masses of
each atom in a formula unit
#8. What is the gfm of
magnesium phosphate?
Mg3(PO4)2
3 mol Mg 3 x 24.3 g = 72.9 g
2 mol P 2 x 31.0 g = 62.0 g
8 mol O 8 x 16.0 g =128.0 g
262.9 g
Gram formula mass is a generic
term and can be used for either
ionic or molecular compounds.
Molar mass or molecular weight
are terms also used to mean the
same thing.
#9. What is the molar mass of
ammonium sulfate?
(NH4)2SO4
2 mol N 2 x 14.0 = 28.0
8 mol H 8 x 1.0 = 8.0
1 mol S 1 x 32.1 = 32.1
4 mol O 4 x 16.0 = 64.0
132.1 g
Mole – Mass Conversions
New Conversion factor!
1 mol = gfm
#10. Find the mass in grams of
3.32 mol of K.
3.32 mol K
39.1 g K
1 mol K
2
= 1.30 x 10 g K
#11. Find the mass in grams of 15.0
mol of sulfuric acid.
H2SO4
H 2 x 1.0 = 2.0
S 1 x 32.1 = 32.1
O 4 x 16.0 = 64.0
98.1 g
15.0 mol H2SO4 98.1 g H2SO4
1 mol H2SO4
= 1470 g H2SO4
#12. Find the number of moles in
187 g of aluminum.
187g Al
1 mol Al
27.0 g Al
= 6.93 mol Al
#13. Find the number of moles in
11.0 g of methane (CH4).
CH4 = (12.0 + 4.0 = 16.0 g)
11.0 g CH4 1 mol CH4
16.0 g CH4
= 0.688 mol CH4
#14. Calculate the number of molecules
present in 4.29 g of nitrogen dioxide.
4.29g NO2 1 mol NO2 6.02 x 1023 NO2 molec
46.0g NO2 1 mol NO2
= 5.61
x 1022 molecules NO2
#15. Calculate the number of moles
of sulfur atoms present in 2.01g of
sodium sulfide.
2.01g Na2S 1mol Na2S 1 mol S atoms
78.1g Na2S 1 mol Na2S
= 0.0257 mol S atoms
#16. Calculate the mass in grams of
2.49 x 1020 carbon dioxide molecules.
2.49 x 1020 CO2 molec 1 mol CO2
6.02 x 1023 CO2 molec
44.0 g CO2
1mol CO2
= 0.0182 g CO2
#17. Calculate the grams of carbon in
12.2 mol of sucrose, C12H22O11.
12.2 mol C12H22O11 12 mol C
12.0g C
1 mol C12H22O11 1 mol C
=1760 g C
Molar Volume of a Gas
The volume of a gas is usually
measured at 0oC and 1
atmosphere of pressure.
This is called standard
temperature and pressure (STP).
-At STP, one mole of any gas has
a volume of 22.4 L.
-22.4 L is called the molar
volume of a gas.
-22.4 L of a gas at STP contains
6.02 x 1023 particles of the gas.
-22.4 L of a gas has a mass equal
to the gfm of the gas.
New conversion factor!
1 mol of any gas at STP = 22.4 L
(for gases only)
#18. What is the volume (liters)
at STP of 0.960 mol of methane,
CH4?
0.960 mol CH4
=21.5 L CH4
22.4 L CH4
1 mol CH4
#19. At STP, how many moles
are in 0.542 mL of neon gas?
0.542 mL Ne 1 L Ne
1 mol Ne
1000 mL Ne 22.4 L Ne
= 2.42 x 10-5 mol Ne
Gas Density
If we know the density of a gas in
g/L at STP, we can calculate the gfm
of the gas (or visa versa)
22.4 L/mol x density(g/L) = gfm
#20. The density of nitrogen gas
at STP is 1.25 g/L. Find the gfm
of nitrogen gas.
22.4 L 1.25 g
1 mol
1L
=28.0 g/mol N2
#21. Calculate the density of
sulfur dioxide gas at STP.
SO2 = 64.1 g/mol
64.1gSO2 1 mol SO2
1 mol SO2 22.4 L SO2
= 2.86g/L
Percent Composition
(remember: percent = part
divided by total x 100)
percent by mass of each element
in a compound
# of grams of the element per 100
grams of the compound
#22. Find the % composition for a compound that
is formed from 222.6 g of Na and 77.4 g O.
222.6g Na + 77.4 g O = 300.0 g total
222.6 g Na x
300.0g total
100
= 74.2% Na
77.4 g O
x
300.0g total
100
= 25.8% O
OR solve for percent
composition from the chemical
formula:
% mass = grams of element in 1 mol of cmpd x 100
gfm of compound
#23. What is the percent
composition of calcium acetate?
Ca(C2H3O2)2
Ca 1 x 40.1 = 40.1
C 4 x 12.0 = 48.0
H 6 x 1.0 = 6.0
O 4 x 16.0 = 64.0
158.1 g
Ca = (40.1/158.1) x 100 =25.4% Ca
C = (48.0/158.1) x 100 = 30.4%C
H = (6.0/158.1) x 100 =
3.8%H
O = (64.0/158.1) x 100 = 40.5%O
100.1
CALCULATING
EMPIRICAL FORMULAS
Empirical formula - lowest whole
number ratio of the elements
in a compound
- may or may not be the same as
the molecular formula.
Ex. H2O is both the empirical &
molecular formula.
H2O2 is a molecular formula.
HO is the empirical formula for H2O2.
Steps to calculate empirical
formula:
1. Find moles of each element.
2. Set up mole ratio.
3. Simplify mole ratio (divide by
smallest). If your answers are
not in whole numbers, you must
multiply by 2,3,4,or 5 to get
whole numbers.
4. Use mole ratio as subscripts in
the formula.
If given % composition, assume
100 g of compound.
Percent to mass,
Mass to moles,
Divide by small,
Multiple ‘til whole!
#24. A compound is 79.8% C and
20.2% H. Find its empirical formula.
79.8gC 1mol C = 6.65 mol C
12.0 g C
20.2 g H 1 mol H = 20.0 mol H
1.01 g H
C:H 6.65: 20.0 = 1 : 3.0
6.65 6.65
CH
#25. An oxide of aluminum is formed by the
complete reaction of 4.151g of aluminum with
3.692 g of oxygen. Calculate the empirical
formula for this compound.
4.151g Al
1 mol Al = 0.1537 mol Al
27.0 g Al
3.692g O 1 mol O = 0.23075 mol O
16.0 g O
Al:O 0.1537 : 0.23075 = 1 : 1.5 = 2 : 3
0.1537 0.1537
Al2O3
Molecular formulas are the actual
formulas. They may be the same
as the empirical formula or a
multiple of it.
To find the multiple (n), take the
gram formulas mass (gfm) and
divide by the empirical formula
mass (efm):
n = gfm
efm
Multiply each subscript in the
empirical formula by n to get the
molecular formula.
#26. A white powder is analyzed and found to
have the empirical formula P2O5. The compound
has a molar mass of 283.9 g. What is the
compound’s molecular formula?
P2O5 = 142.0 g/mol
gfm/efm
283.9/142.0 = 2
2(P2O5) = P4O10
Ex. Complete combustion (reaction with O2) of a
sample of propane gas (contains only C & H)
produced 2.641 g of CO2 and 1.442 g of water as the
only products. Find the empirical formula for
propane.
2.641g CO2
1 mol CO2 1 mol C = 0.0600 mol C
44.0 g CO2 1 mol CO2
1.442g H2O 1 mol H2O 2 mol H = 0.160 mol H
18.0g H2O 1 mol H2O
C:H 0.0600 : 0.160 = 1 : 2.67 (*3) = 3 : 8
0.0600 0.0600
C3H8
A Mole Is a Unit
A mole is an animal that burrows in the ground,
Or a spot on your chin that you gotta shave around.
But there's another kind of mole of interest to me,
That's the kind of mole they use in chemistry.
Chorus: A mole is a unit, or have you heard,
Containing six times ten to the twenty-third,
That's a six with twenty-three zero's at the end,
Much too big a number to comprehend.
Say you had a mole of pennies to distribute 'round the
world,
Give to each of the five billion grownups, boys, and girls,
There wouldn't be a single person down and out of luck,
Cause everybody in the world would get a trillion bucks.
Or say you had a mole of paper and stacked it toward the
sky,
Paper's awful thin, but that pile would get so high.
It'd reach up into outer space, in fact I think you'd find,
It'd go up to the moon and back, eighty billion times.
Chorus: A mole is a unit, or have you heard,
Containing six times ten to the twenty-third,
That's a six with twenty-three zero's at the end,
Much too big a number to comprehend.
Suppose a mole of marshmallows fell upon the planet,
Over each square inch of land and sea, think that you
could stand it?
That layer would be twelve miles high and of course
block our sun,
We're talking close to five million trillion tons.
Well, maybe we could save ourselves if we all started
eaten',
One marshmallow each second, not two 'cause that'd be
cheatin',
With forty five billion people munching, how long do you
think it'd take?
Forty million years, and that's without a bathroom break.
Chorus: A mole is a unit, or have you heard,
Containing six times ten to the twenty-third,
That's a six with twenty-three zero's at the end,
Much too big a number to comprehend.
But say you had a mole of atoms, would the pile be
immense,
Should I say the answer now or leave you in suspense?
Well, atoms are so very small, very small, you
understand,
You could hold a mole of atoms in the palm of your hand.
So shake a little sugar in the middle of your palm,
Now you don't want to spill it, so try and stay calm.
You hardly can imagine and barely realize,
There're more atoms in that sugar than stars up in the
sky.
Chorus: A mole is a unit, or have you heard,
Containing six times ten to the twenty-third,
That's a six with twenty-three zero's at the end,
Much too big a number to comprehend.