Unit 8 The Mole
23
6.02 X 10
The Mole
 A counting unit
 Similar to a dozen, except instead of
12, it’s 602 billion trillion
602,000,000,000,000,000,000,000
 Avogadro’s number= 6.02 X 1023 (in
scientific notation)
 This number is named in honor of
Amedeo Avogadro (1776 – 1856), who
studied quantities of gases and
discovered that no matter what the
gas was, there were the same number
of molecules present
Just How Big is a Mole?
 Enough soft drink cans to cover the
surface of the earth to a depth of over 200
miles.
 If you had Avogadro's number of
unpopped popcorn kernels, and spread
them across the United States of America,
the country would be covered in popcorn
to a depth of over 9 miles.
 If we were able to count atoms at the rate
of 10 million per second, it would take
about 2 billion years to count the atoms in
one mole.
One mole of $100 bills stacked one on top of another
would reach from the Sun to Pluto and back 7.5 million
times.
One mole of marbles would cover the entire Earth
(oceans included) for a depth of three miles.
Homework
 How long will it take to spend a mole of Lps.1.00 if
they were being spent at a rate of a billion per second?
The Mole
 1 dozen cookies = 12 cookies
 1 mole of cookies = 6.02 X 1023 cookies
 1 dozen cars = 12 cars
 1 mole of cars = 6.02 X 1023 cars
 1 dozen Al atoms = 12 Al atoms
 1 mole of Al atoms = 6.02 X 1023 atoms
Note that the NUMBER is always the same,
but the MASS is very different!
Mole is abbreviated mol (big difference!!)
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 NaCl formula units
(ionic compounds are not molecules so they are
called formula units)
6.02 x 1023 Na+ ions and
6.02 x 1023 Cl– ions
Avogadro’s Number as Conversion
Factor
6.02 x 1023 particles
1 mole
or
1 mole
6.02 x 1023 particles
Note that a particle could be an atom, ion, formula unit
OR a molecule!
Ex. 1 How many atoms are in 0.67mol of Al?
= 0.67 mol Al
6.02x 1023 atoms Al
1 mol Al
= 4.0 x 1023 atoms Al
Remember to round answer to correct number of
significant digits and don’t forget to write units
Ex. 2 A sample of gold contains 5.21 x1023 atoms
of gold, how many moles is this?
= 5.21x 1023 atoms Au
1 mol Au
6.02x 1023 atoms Au
= 0.865 mol Au
Remember to round answer to correct number of
significant digits and don’t forget to write units
Learning Check
1. Number of atoms in 0.500 mole of Ag
a) 500 Ag atoms
b) 6.02 x 1023 Ag atoms
c) 3.01 x 1023 Ag atoms
2.Number of moles of S in 1.8 x 1024 S atoms
a) 1.0 mole S atoms
b) 3.0 mole S atoms
c) 1.1 x 1048 mole S atoms
Learning Check
1. Number of atoms in 0.500 mole of Ag
a) 500 Ag atoms
b) 6.02 x 1023 Ag atoms
c) 3.01 x 1023 Ag atoms
2.Number of moles of S in 1.8 x 1024 S atoms
a) 1.0 mole S atoms
b) 3.0 mole S atoms
c) 1.1 x 1048 mole S atoms
Molar Mass
 The Mass of 1 mole (in grams)
 Equal to the numerical value of the average
atomic mass (get from periodic table)
1 mole of C atoms
=
12.0 g
1 mole of Mg atoms
=
24.3 g
1 mole of Cu atoms
=
63.5 g
 Units: grams/mole or g/mol
Other Names Related to Molar Mass
 Molecular Mass/Molecular Weight
 Formula Mass/Formula Weight
Learning Check!
Find the molar mass
(usually we round to the tenths place)
A. 1 mole of Br atoms =
B. 1 mole of Sn atoms =
79.9 g/mole
118.7 g/mole
Molar Mass of Molecules and
Compounds
The molar mass of a compound is equal to the
sum of the atomic masses of all the atoms in
the compound.
1 mole of CaCl2
= 111.1 g/mol
1 mole Ca x 40.1 g/mol =
40.1 g/mol
+ 2 moles Cl x 35.5 g/mol = 71.0 g/mol
= 111.1 g/mol CaCl2
Molar mass for calcium nitrate,
Ca(NO3)2
Ca :
N:
O:
1 atom x 40.1 g/mol = 40.1 g/mol
2 atoms x 14.0 g/mol = 28.0 g/mol
6 atoms x 16.00 g/mol = 96.0 g/mol
+
164.1 g/mol
Learning Check!
A. Molar Mass of K2O = ? Grams/mole
B. Molar Mass of antacid Al(OH)3 = ? Grams/mole
Learning Check!
A. Molar Mass of K2O = ? Grams/mole
K : 2 x 39.1 = 78.2
O : 1 x 16.0 = 16.0
+
94.2 g/ mol
B. Molar Mass of antacid Al(OH)3 = ? Grams/mole
Al: 1 x 27.0 = 27.0
O: 3 x 16.0 = 48.0
H: 3 x 1.00 = 3.0
+
78.0 g/mol
Learning Check
Prozac, C17H18F3NO, is a widely used
antidepressant that inhibits the uptake of
serotonin by the brain. Find its molar mass.
(answer: 304 g/mol)
Calculations with Molar Mass
molar mass
Grams
Moles
To convert between grams and moles, use the
molar mass of the substance as a conversion
factor.
Converting Moles to 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
To convert between grams and moles,
Calculate the molar mass of the substance
1. Molar mass of Al
1 mole Al = 27.0 g Al
2. Conversion factors for Al
27.0g Al
1 mol Al
or
1 mol Al
27.0 g Al
3. Setup 3.00 moles Al
Answer
x
27.0 g Al
1 mole Al
= 81.0 g Al
Converting grams to moles
Acetylsalicylic acid is the chemical name for the
substance we commonly know as aspirin,
C6H4(OCOCH3)CO2H. How many moles of aspirin are
255g of aspirin?
255 g aspirin
? Mol aspirin
1. Molar mass of aspirin 1 mole = 180.0 g aspirin
2. Conversion factors for aspirin
180.0g
1 mol
or
1 mol
180.0 g
3. Setup 255 g aspirin
Answer
x
1 mole aspirin
180 g aspirin
= 1.42 mol aspirin
Learning Check!
The artificial sweetener aspartame (NutraSweet) formula C14H18N2O5 is used to
sweeten diet foods, coffee and soft drinks.
How many moles of aspartame are present in
225 g of aspartame?
Answer: 0.765 mol aspartame
Learning Check
 A recipe requires 0.629 mol of sucralose,
SPLENDA (C12H19Cl3O8). How many grams is this?
Answer: 250. g splenda
Conversions: particles  Grams
 6.02 X 1023 particles = 1 mole
AND
1 mole = molar mass (grams)
 We can convert between particles and
grams (Two step process)
 You can’t go directly from atoms to
grams!!!! You MUST go thru MOLES.
Calculations
molar mass
Grams
Avogadro’s number
Moles
particles
Everything must go through
Moles!!!
Atoms/Molecules and Grams
How many atoms of Cu are present in 35.4 g of Cu?
Plan: g Cu  mol Cu  atoms Cu
Step 1: converting g Cu to mol Cu using molar mass
35.4 g Cu
1 mol Cu = 0.5566 mol Cu
63.6 g Cu
Step 2: converting mol Cu to atoms Cu using
Avogadro’s number.
0.5566 mol Cu 6.02 x 1023 atoms Cu= 3.35x1023 atoms Cu
1 mol Cu
Atoms/Molecules and Grams
How many atoms of Cu are present in 35.4 g of Cu?
Plan: g Cu  mol Cu  atoms Cu
Combining step 1 and 2
35.4 g Cu 1 mol Cu 6.02 x 1023 atoms Cu= 3.35x1023 atoms Cu
63.6 g Cu
1 mol Cu
Atoms/Molecules and Grams
What is the mass of 5.54x1024 molecules of CO?
Plan: molecules CO mol CO  g CO
Step 1: converting molecules CO to mol CO using
Avogadro’s number.
5.54x1024 molecules of CO 1 mol CO
= 9.2026 mol CO
6.02x1023 molecules CO
Step 2: converting mol CO to g CO using molar mass
9.2026 mol CO
28.0 g CO
= 258g CO
1 mol CO
Learning Check!
How many atoms of K are present in 78.4 g of
K? (answer: 1.21 x 1024 atoms K)
Learning Check!
What is the mass (in grams) of 1.20 X 1024 molecules
of glucose (C6H12O6)? (answer:359 g glucose)