Chapter 3/9
Chemical Reactions and
Quantities
The Mole
Calculations Using Molar Mass
MOLE CONCEPT
So far we were in the microscopic world of atoms
and molecules. But it is very important that chemists
be able to measure and observe, in order to gather
data.
To do this we must take sufficient quantities of
atoms and molecules.
How many atoms or molecules must the chemists
take?
Let us not bother about the numbers but instead
call this amount a mole.
Oxygen was the best candidate to define a mole.
•The most universal atom at the time was
oxygen.
•About 50% of the earth crust is oxygen.
•Oxygen can react with all the other atoms.
Let us weigh 32 grams of oxygen gas (O2) and define
this amount of molecules as one mole of oxygen gas
molecules.
If we react this amount with the following atoms and
the weight of the products obtained were as given,
how much will one mole of the atoms of Fe, H, and
S weigh?
2 Fe + O2
2 FeO ;
2 H2 + O2
2 H2O ;
S + O2
SO2 ;
144 grams FeO
36 grams H2O
64 grams SO2
2Fe + O2
2 FeO ;
2 H2 + O2
2 H2O ; (36 grams - 32 grams)/4
= 1g (H)
S + O2
(144 grams - 32grams) /2
= 56g (Fe)
SO2 ; (64 grams - 32 grams)
= 32g (S)
So chemists agreed that the number of
molecules in 32 grams of gaseous
oxygen should be known as a mole of
molecules.
By reacting other atoms with oxygen
chemists were able to determine how
much a mole of all other atoms weigh.
The purpose of the mole concept was to scale
up the quantity of atoms and molecules so
that we can conduct experiments.
It was only later that Amedeo Avogadro
found that one mole of oxygen gas is
compromised of 6.022x10²³ molecules, give
and take a few molecules.
In his honor this number is known as
Avogadro's Number.
So we often say that a mole of an element or
compound contains Avogadro's number of
particulars.
Q: How would you describe a stinky chemist?
A: Mole-odorous
Collection Terms
1 trio
=
3 singers
1 six-pack Cola
=
6 cans Cola drink
1 dozen donuts
=
12 donuts
1 gross of pencils
=
144 pencils
A Mole of Particles
Contains 6.02 x 1023 particles
1 mole C
= 6.02 x 1023 C atoms
1 mole H2O
= 6.02 x 1023 H2O molecules
1 mole NaCl = 6.02 x 1023 Na+ ions and
6.02 x 1023 Cl– ions
Q: How does Avogadro write to his friends?
A: By e-mole!
More Examples of Moles
Moles of elements
1 mole Mg
= 6.02 x 1023 Mg atoms
1 mole Au
= 6.02 x 1023 Au atoms
Moles of compounds
1 mole NH3
= 6.02 x 1023 NH3 molecules
1 mole C9H8O4 = 6.02 x 1023 aspirin molecules
Avogadro’s Number (N) = 6.02 x 1023
How big is this?
• If 6.02 x 1023 hydrogen atoms were laid side by
side, the total length would encircle the earth
about a million times.
• The mass of 6.02 x 1023 Olympic shotput balls
is about equal to the mass of the Earth.
• The volume of 6.02 x 1023 softballs is about
equal to the volume of the Earth.
Learning Check M1
Suppose we invented a new collection unit
called a mep. One mep contains 8 objects.
A. How many paper clips in 1 mep?
1) 1
2) 4
3) 8
B. How many oranges in 2.0 meps?
1) 4
2) 8
3) 16
C. How many meps contain 40 gummy bears?
1) 5
2) 10
3) 20
Solution M1
Suppose we invented a new collection unit
called a mep. One mep contains 8 objects.
A. How many paper clips in 1 mep?
3) 8
B. How many oranges in 2.0 meps?
3) 16
C. How many meps contain 40 gummy bears?
1) 5
Q: How would you describe Avogadro's room while he was a
teenager?
A: A Molar mess
Using Avogadro’s Number in Calculations
How many particles are in 3.0
moles of Al?
Review Conversion Factors
• Make a T-chart
•Put whatever information the problem gave
you in the top left
•Put the units of whatever you were given in
the bottom right of the T
•Put the units of what you want to find in the
top right.
3 moles
particles
mole
=
Avogadro's Number
6.02 x 1023 particles
1 mole
or
1 mole
6.02 x 1023 particles
Each of
these can be
used as a
conversion
factor
3 moles 6.02 x 1023 particles
1 mole
Ans: 1.81 x 1024 particles
=
Learning Check M2
1. Number of atoms in 0.500 mole of Al
1) 500 Al atoms
2) 6.02 x 1023 Al atoms
3) 3.01 x 1023 Al atoms
2.Number of moles of S in 1.8 x 1024
S atoms
1) 1.0 mole S atoms
2) 3.0 mole S atoms
3) 1.1 x 1048 mole S atoms
Solution M2
1. Number of atoms in 0.500 mol of Al
3) 3.01 x 1023 Al atoms
2. Number of moles of S if a sample of S
contains 1.8 x 1024 S atoms
2) 3.0 mole S atoms
Q: Why did Avogadro stop going to a chiropractor on
October 24th?
A: He was only tense to the 23rd.
23
A Rice Analogy
Rufus’ favorite food is rice. But he rarely eats it even though
it is economical and easily prepared. He knows it is healthy
for him and he was told once that one serving is 12,000
grains.
So every time Rufus wants to eat rice he has to prepare 2
hr. ahead of time and count out 12,000 grains.
How can we help my friend Rufus?
Weighing can be used as a way to count!
A rice analogy
Rufus’ favorite food is rice. But he rarely eats it even though
it is economical and easily prepared. He knows it is healthy
for him and he was told once that one serving is 12,000
grains.
So every time Rufus wants to eat rice he has to prepare 2
hr. ahead of time and count out 12,000 grains.
How can we help my friend Rufus?
1 grain of rice weighs an average of 19 mg.
12000 grains 19 mg
1 grain
1g
1000mg
= 228 grams
How do we measure the mass of an object that is too
small to be seen?
Atomic Mass Unit
The atomic mass unit (amu) has been used as a
standard for a mass of an atom.
1 amu = 1.66 x 10-24 g = 1/12 mass of a 12C atom
1 proton = approx. 1 amu
Atomic mass gives us the mass of one atom.
• one atom of potassium 39K weighs 39 amu.
• one atom of zinc 65Zn weighs 65 amu.
Molecular mass gives us the mass of one molecule (mC)
•one water (H2O) molecule = 18 amu
(2-H, 1-O = 2amu + 16amu)
•one glucose (C6H12O6) molecule = 144 amu
(6C, 12H, 6O = [6 C x12amu] + [12 H x 1 amu] +
[6 O x 16amu]
Question:
Why is the mass of carbon 12.011 amu according the
periodic table instead of just 12?
Why is the mass of chlorine 35.453 amu ?
Answer:
Atomic mass, as shown in the periodic table, is the
weighted average mass of all isotopes found in
nature.
Molar Mass

Number of grams in 1 mole of particles

Equal to the numerical value of the atomic
mass (from Periodic Table)
Review: Atomic Mass
The mass of the atom in atomic mass units (amu)
What value for the atomic mass is given for
carbon on the periodic table?
12.0 amu
What value for the atomic mass is given for
magnesium on the periodic table?
24.3 amu
How much do 6.02 x 1023 carbon atoms weigh if
one atom weighs 12.0 amu and 1 amu equals 1.66
x 10-24 g
6.02 x 1023 molecules
12.0 amu
1 molecule
1.66 x 10-24g
1 amu
= 12.0 grams
The MOLAR MASS is equal to the numerical
value of the atomic mass (from Periodic
Table)
1 mole of C atoms =
1 mole of Mg atoms =
1 mole of Cu atoms =
1 mole of C atoms =
1 mole of Mg atoms =
1 mole of Cu atoms =
12.0 g
24.3 g
63.5 g
6.02 x 1023 atoms
6.02 x 1023 atoms
6.02 x 1023 atoms
Q: How did Avogadro get through the desert?
A: He rode on a camole
Learning Check M3
Give the molar mass to 0.1 g
A. 1 mole of Br atoms
=
________
B. 1 mole of Sn atoms
=
________
Solution M3
Give the molar mass to 0.1 g
A. 1 mole of Br atoms =
79.9 g
B. 1 mole of Sn atoms =
118.7 g
Molar Mass of Compounds
Mass in grams of 1 mole of a compound is
equal numerically to the sum of the atomic
masses of the atoms in the compound.
1 mole of CaCl2
= ? grams
1 mole Ca x 40.1 g/mole = 40.1 g
+ 2 moles Cl x 35.5 g/mole = 71.0 g
111.1 g = 1 mole CaCl2
1 mole of N2O4 =
? grams
2 moles N x 14.0 g/mole = 28.0 g
+ 4 moles O x 16.0 g/mole = 64.0 g
94.0 g = 1 moleN2O4
Learning Check M4
A. 1 mole of K2O
= ______g
B. 1 mole of antacid Al(OH)3
= ______g
Solution M4
A. 1 mole of K2O
2 K x 39.1 g/mole = 78.2 g
+ 1 O x 16.0 g/mole = 16.0 g
94.2 g = 1 mole K2O
B. 1 mole of antacid Al(OH)3
1 Al x 27.0 g/mole = 27.0 g
+ 3 O x 16.0 g/mole = 48.0 g
+ 3 H x 1.0 g/mole
= 3.0 g
78.0g = 1 mole Al(OH)3
Learning Check M5
Prozac, C17H18F3NO, is a widely used
antidepressant that inhibits the uptake of
serotonin by the brain. It has a molar mass
of
1) 40.0 g/mole
2) 262 g/mole
3) 309 g/mole
Solution M5
Prozac, C17H18F3NO, is a widely used
antidepressant that inhibits the uptake of
serotonin by the brain. It has a molar mass
of
3) 309 g/mole
17C (12.0) + 18H (1.0) + 3F (19.0) + 1N (14.0)
+ 1 O (16.0)
Molar Mass Factors for CH4
Methane CH4 known as natural gas is used
in gas cook tops and gas heaters. Express
the molar mass of methane in the form of
conversion factors.
Molar mass of CH4 =
16.0 g CH4
1 mole CH4
and
16.0 g
1 mole CH4
16.0 g CH4
Learning Check M7
Acetic acid CH3COOH is the acid in vinegar . It
has a molar mass of 60.0 g/mole.
1 mole of acetic acid
1 mole acetic acid
or
g acetic acid
=
____________
g acetic acid
1 mole acetic acid
Solution M7
Acetic acid CH3COOH is the acid in vinegar . It
has a molar mass of 60.0 g/mole.
1 mole of acetic acid
1 mole acetic acid
60.0 g acetic acid
=
or
60.0 g
60.0 g acetic acid
1 mole acetic acid
Calculations with Molar Mass
Moles
Number of grams
molar mass
Both Avogadro’s number and the
molar mass can be used as
conversion factors.
Let us look at both of these unit factors:
12.00 g Carbon-12
=1
1 mole of Carbon-12 atoms
1 mole carbon-12
=
1
23
6.022 x 10 atoms of carbon-12
These two give us the ability to….
Q: What does Avogadro put in his hot chocolate?
A: Marsh-mole-ows!
All About Mole Calculations
How many moles are in 22 grams of copper metal?
The Four Steps to Solving Mole Problems:
Step 1:
Looking at the diagram above (your roadmap), we can
see that we are going between grams and moles, which
is a one-step conversion. Furthermore, we can see that
we need to use the atomic mass of copper as our
conversion factor.
Step 2:
•Make a T-chart, and put whatever information the
problem gave you in the top left.
•Put the units of whatever you were given in the bottom
right of the T
•Put the units of what you want to find in the top right.
Step 3: Put the conversion factors into the T-chart in front
of the units on the right.
As we saw from the "map", the conversion factor between
grams and moles is the atomic mass of copper. Because we
measure atomic mass in grams, you need to put the atomic
mass in front of the unit "grams of copper". What do you put in
front of moles? Whenever you do a calculation of this kind,
you need to put "1" in front of moles, like you see here:
Step 4: Cancel out the units from the top left and
bottom right, then find the answer by multiplying all
the stuff on the top together and dividing it by the
stuff on the bottom.
In this case, you'd multiply 22 by one and divide the
result by 63.5. Your answer, 0.35 moles of copper:
And that's how you do a one-step problem of this
kind!
Moles and Grams
Aluminum is often used for the structure of
light-weight bicycle frames. How many grams
of Al are in 3.00 moles of Al?
3.00 moles Al
? g Al
Molar mass of Al
1 mole Al = 27.0 g Al
Setup
3.00 moles Al 27.0 g Al
1 mole Al
Answer
=
= 81.0 g Al
Learning Check M9
The artificial sweetener aspartame
(Nutri-Sweet) formula C14H18N2O5 is
used to sweeten diet foods, coffee and
soft drinks. How many moles of
aspartame are present in 225 g of
aspartame?
Solution M9
1. Molar mass of Aspartame C14H18N2O5
(14 x 12.0) + (18 x 1.01) + (2 x 14.0) + (5 x 16.0)
= 294 g/mole
2. Setup
225 g aspartame 1 mole aspartame
294 g aspartame
= 0.765 mole aspartame
Q: On which American mountain was Avogadro's face
carved in stone?
A: Mount Rushmole