Unit 7 – Chemical
Quantities & The
Mole
Day 1: Mole Math
We use a unit called the mole , or mol ,
to measure the amount of a
substance. The mole can represent
mass (grams), volume (liters), or
amount (particles).
**You must ALWAYS go through the MOLE!**
1 mole = molar mass or atomic mass
1 mole = 22.4 Liters
1 mole = 6.02 x 1023 particles
Avogadro's number: 6.02 x 1023 particles and is also
called a Mole .
12
• One dozen = _________
items.
36
• 3 dozen cookies = _______
cookies
• 0.5 dozen doughnuts = _________
doughnuts
6
• A “dozen” is a counting unit equal to 12 of any
object.
• A “Mole” is a counting unit equal to 6.02 x 1023 of
any object, even really small ones like atoms,
molecules, or formula units.
What is so special about 6.02 x 1023 ? Why do
scientists use that number?
• Conversion factor
• Allows us to manipulate many small particles, as if
they were one whole part.
Example Conversion Factors:
• 1 mole = 6.02 x 1023 particles (atoms, molecules, or formula
units)
• 1 mole of copper = 6.02 x 1023 atoms of copper.
• 1 mole of CuCl2 = 6.02 x 1023 formula units of CuCl2
• 1 mole of CO2 = 6.02 x 1023 molecules of CO2
• The amount of a substance containing Avogadro’s number of any
kind of chemical unit is called a mole of that substance.
• One mole of K contains 6.02 x 1023 atoms.
• One mole of NaOH contains 6.02 x 1023 formula units.
Molar Mass
Molar mass is the mass of one mole
of a substance.
Other names for molar mass include…
*formula mass
*gram formula mass
Molar Mass
• One _____________of
any element will have a
mole
mass in grams corresponding to the value of its
atomic mass
____________________.
12.011 g/mol
– 1 mol carbon = __________
28.014 g/mol
– 1 mol nitrogen = ___________
– (its atomic mass from the periodic table = 1
mole)
Diatomic Elements never exist alone in
nature!!!
*Trick for remembering the 7 diatomics *
Molar Mass of Compounds
mol of any molecule/compound
• One ________
will have a mass in grams corresponding to
the value of its molar mass (the sum of the
masses of the elements that compose it).
http://app.discoveryeducation.com/search?Ntt=moles
Example: Water, H2O
Element
H
O
Molar Mass
1.008
15.999
# of Atoms
X
X
2
1
Total
2.016 g
15.999 g
18.015 g/mol
This is the mass of 1 mol of water!
Ex. Ca(NO3)2
Ca: 40.078 x 1 = 40.078
N: 14.007 x 2 = 28.014
O: 15.999 x 6 = 95.994
-------------164.086 g/mole
Sample Problems
K2CO3
Potassium carbonate ___________
# of K atoms:
39.098 x 2 = 78.196
# of C atoms:
12.011 x 1 = 12.011
# of O atoms:
15.999 x 3 = 47.997
+
+
138.204 g/mol
___________________
K2CO3
Sample Problems
(NH4)2SO4
Ammonium sulfate  _____________
# of N atoms: 14.007 x 2 =
x
28.014
+
# of H atoms:
1.008
8 = 8.064
# of S atoms:
32.066 x 1 = 32.066
# of O atoms:
15.999 x 4 = 63.996
+
+
132.140 g/mol
_________________________
(NH4)2SO4
Practice
1. What is the atomic mass of sodium?
2. Calculate the molar mass of Al2(SO4)3
3. Calculate the molar mass of nitrogen (hint:
diatomic!?!?).
Mole Highway
NOTES:
To convert between units, follow the highway.
Notice, there is no shortcut from grams to
liters or between any of the three units
surrounding the mole.
This means you have to convert to moles
before converting to another unit!
Draw the Mole Road Map!!
Molar mass:
• called gram atomic mass when single element is used.
• called gram formula unit when ionic compound is used.
• called gram molecular unit when molecular compound or diatomic
molecules used.
• Diatomic molecules are atoms that bond with themselves. There are
SEVEN of these that you need to remember: Br2 I2 N2 Cl2 H2 O2 F2
(Remember this by the name “BRINClHOF”)
Determine the number of moles in….
• 25 g sodium
25 g Na
1 mol Na
22.990 g Na
Molar mass of Sodium =
Na = 1 x 22.990 = 22.990 g
=
1.1 mol Na
Determine the number of moles in….
• 85 g H2SO4
85 g H2SO4
1 mol H2SO4
98.078 g H2SO4
Mass in grams of H2SO4 =
H = 2 x 1.008 = 2.016
S = 1 x 32.066 = 32.066
O = 4 x 15.999 = 63.996
Add to get molar mass of 98.078 g
=
0.87 mol H2SO4
Determine the number of grams in….
• 2.5 moles of sodium
2.5 mol Na
22.990 g Na
I mol Na
Molar mass of Sodium =
Na = 1 x 22.990 = 22.990 g
= 57 g Na
Determine the number of grams in….
• 0.50 moles of H2SO4
0.50 mol H2SO4
98.078 g H2SO4
I mol H2SO4
Mass in grams of H2SO4 =
H = 2 x 1.008 =
S = 1 x 32.066 =
O = 4 x 15.999 =
Add to get molar mass of 98.078 g
= 49 g
H2SO4
How many moles are there in 27 g of
ethanol (C2H5OH)?
27 g
1 mol
46.069 g
Mass of C2H5OH:
C = 2 x 12.011=
H = 6 x 1.008=
O = 1 x 15.999=
Add these all up for mass in grams = 46.069 g
= 0.59 mol
Homework page 7
Show all work and units to receive full credit.
Representative
Particles  Moles
It’s a quantity, and it’s a BIG one.
6.02 x 1023 and is
• Avogadro’s Number = ______________
Mole
also called a _______.
• Like a “pair” or “dozen,” a “mole” represents a
set number of things; in chemistry, those
“things” are particles.
For example:
12 items
• 1 dozen =
______
• 3 dozen =
______
36 cookies
6 doughnuts
• .5 dozen =
______
It’s a quantity, and it’s a BIG one.
So, a “dozen” is a counting unit equal to
__12__of any object.
Likewise, a “Mole” is a counting unit
6.02 x 1023 of an object,
equal to _____________
even really small ones like
atoms
molecules or
____________,
____________,
formula units
_____________.
What’s so special about 6.02 x 1023?
• Why do scientists use that number?
– A conversion factor.
– Allows us to manipulate many small particles,
as if they were one whole part.
– For elements on the periodic table, there is a 1 to 1
relationship between the mass of a single atom (in amu)
and the mass of 1 Mole of the same species of atom (in
grams).
– Remember, Mole is a quantity…6.02 x 1023 particles.
What’s so special about 6.02 x 1023?
Atomic Number
(number of protons)
Using the periodic table, we’ve learned that an Argon atom
has a mass of 39.95 amu.
Unfortunately, manipulating a single atom of any element
isn’t reasonable, so taking its individual mass isn’t
possible.
Atomic Mass
(average number of
protons and neutrons)
Ar
1 Atom of Argon
However, we do have the Mole…
•So, a 39.95 g sample of
Argon contains 6.02 x 1023
atoms…that’s Avogadro’s
Number, the MOLE!
•It’s a 1 to 1 relationship
between a single atom in
amu and a Mole of atoms
in grams.
1 Mole of Argon
Representative Particles
• A representative particle is the
smallest unit of a substance.
Types of Particles
atoms
• Monatomic elements = _______________
• Diatomic elements = _________________
molecules
• Ionic compounds = _________________
formula units
molecules
• Covalent compounds = ______________
atoms
• Ions = _________________
molecules
• Acids = _________________
Avogadro’s number, which is
6.02 x 1023
________________,
represents the
number of “chemical units” in one mole
of any substance. For the monatomic
elements, the “chemical unit” is an
atom
__________.
1 mol of any chemical =
6.02 x 1023 particles.
______________
Examples
• 1 mol CaCl2 =
6.02 x 1023 formula units
• 1 mol Ca2+ =
6.02 x 1023 atoms
• 1 mol HCl (aq) =
• 1 mol P2O5 =
• 1 mol Ca =
• 1 mol Cl2 =
6.02 x 1023 molecules
6.02 x 1023 molecules
6.02 x 1023 atoms
6.02 x 1023 molecules
Sample problems
1. How many moles are in 4.50 x 105 atoms
of manganese?
4.50 1025 atoms Mn
1 mol Mn
6.02  1023 atoms Mn
= 74.8 moles Mn
Sample problems
2. How many atoms are found in 3.27 mol
of magnesium?
3.27 mol
6.02 
23
10 atoms
1 mol
= 1.97  1024 atoms
Sample problems
3. Chalk is composed primarily of calcium
carbonate. How many particles are in 3.4 moles
of calcium carbonate?
3.4 mol
6.02 
23
10 formula
units
1 mol
= 2.0  1024 formula units
Moles of Chalk Lab
Homework page 10
Show all work and units to receive full credit.
Notes: Volume <-> Moles
• Warm-up:
1. How many atoms are in 0.75 mol of zinc?
Sample Problems
(SHOW ALL WORK & UNITS to receive full credit.)
1. The average lung capacity of a male is 6.0L. The average lung
capacity of a female is 4.7L. Assume the following:
If your TEACHER’s lungs are completely filled with oxygen, determine
the number of moles of oxygen gas in the lungs of your chemistry
teacher at STP.
2. At STP, how many moles are found in 54L of neon gas?
3. How many liters are found in 3.02mol of helium at STP?
Homework page 12
Empirical vs. molecular
Empirical formula
•
•
•
•
Is the simplest form of a formula
Is written in the lowest possible ratio
E.g., CH2O or CH
Will be reduced. May or may not
exist in this form in the real world.
Molecular formula
• Is the true formula or actual ratio of
the atoms in a compound.
• E.g., C2H4O2 or C6H6
• Will not be reduced. Formula
describes a substance as it actually
exists.
Empirical or Molecular?
• Na2O
empirical & molecular
___________________
• C3H6
molecular
___________________
• K2SO4
empirical & molecular
___________________
• C6H12O6
molecular
___________________
Keep in mind that for some compounds, its empirical
formula can also be its molecular formula.
Which pair has the same empirical
formula?
• Na2O and Na2O2
• C6H12O6 and CH2O
• C3H6 and C5H12
• C6H6 and C5H5
Calculating an Empirical Formula
1. Determine the mass of each element.
2. Convert the mass of each to moles. 
3. Find the mole to mole ratios of each element by
dividing the number of moles of each element by the
smallest number of moles.
4. If the ratio is not a whole number, multiply each
ratio by a factor to make them all whole numbers.
5. Write the formula using the mole ratio as the
subscript for the formula.
Find the empirical formula of 69.5% O &
30.5% N.
• Step 1: Divide % or grams by its atomic mass to
get moles of each element.
69.5 g O
1 mol O
15.999 g O
25.9 g N
1 mol N
14.007 g N
= 4.344 mole O
= 2.177 mole N
Find the empirical formula of 69.5% O &
30.5% N.
• Step 2: Divide smallest mole number in each
element to get ratio of that element.
4.344 mole O
2.177 mole
=2O
2.177 mole N
2.177 mole
=1N
Find the empirical formula of 69.5% O &
30.5% N.
• *This answer becomes the subscript for that
element; round to nearest whole number if .8
or higher or lower than .2.
Answer = NO2
Independent Practice:
1. Analysis of a compound shows that it contains
10.88g of calcium and 19.07g of chlorine.
Determine the empirical formula of this
compound.
Independent Practice:
2. One of the most commonly used white
pigments in paint is a compound of titanium and
oxygen that contains 5.99 g titanium by mass
and 4.01 g oxygen by mass. Determine the
empirical formula and name for this compound.
Independent Practice:
3. Used in the production of nylon, adipic acid is
an organic compound composed of 49.31% C,
43.79% O, and the rest is hydrogen. Determine
the empirical formula of adipic acid.
Calculating Molecular Formulas
• The molecular formula will have the
same ratio as the empirical formula.
• To determine a molecular formula,
we will multiply the empirical
formula by a whole number factor
(WNF).
Calculating Molecular Formulas
1. Empirical Formula = P2O5
Molar Mass= 283.88 g/mol
What is the molecular formula of this compound?
empirical mass = 141.943 g/mol
WNF =
283.88 g/mol
141.943 g/mol
(P2O5)2  P4O10
=2
2. Nitrogen and oxygen form multiple molecular
compounds together. One of these compounds is
used to fuel space shuttles and has the empirical
formula NO2. If the molar mass of this compound
is 92.02 g/ mol, what is the molecular formula?
• 3.Butane is commonly used in lighters. It is composed
of 17.37% hydrogen and 82.63% carbon . It has a
molar mass of 58.17 g/mol. What is the molecular
formula of butane?
**Fix typo in your packet, please.
4. Vitamin C is 40.91% C, 4.587% H, and the
remaining is oxygen. If the molar mass of
Vitamin C is about 180 g/mol, determine the
empirical and molecular formula.
Complete pages 20-21 for Homework!!!!