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Lecture 4 Professor Hicks
Inorganic Chemistry (CHE151)
The Mole
• The mole is a counting unit like couple,
dozen, gross etc.
1 mole of anything = 6.02 1023 of that thing
• 6.02 1023 is called Avogadro’s number
Amedeo AvogadroAmedeo Avogadro
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Avocado/Avogadro
Amedeo AvogadroAmedeo Avogadro
Avocado Avogadro
Counting units
• Used to express large numbers conveniently
• Why is 12 a counting unit?
• Dozens, 12 inches/foot, 12 hour clocks etc.
• Remember Avogadro’s number also a counting unit
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Avogadro's Number
as a counting unit
• 6.02 x 1023 = one mole like 2 = 1 couple; 12 = 1 dozen; 144= 1 gross
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6.02 x 1023 amu
• another way to express
large numbers like:
- scientific notation
- unit prefixes
counting unit size
couple 2
dozen 12
gross 144
mole 6.02 x1023
the mole is big because atoms are very small
1 mole neutrons
Example: Convert 1.75 x 1017 gold atoms into units
of moles of gold atoms
Example: Convert 1055 bagels
into units of dozens of bagels
1055 bagels x
1 dozen bagels =12 bagels
1 dozen bagels
12 bagels = 87.9 dozen bagels
old unit
( number of bagels)
new unit
( dozens of bagels) conversion
factor
1.75 x 1017 gold atoms x 1 mole gold atoms
6.02 x 1023 gold atoms = 2.91 x 10-7
moles gold atoms
old unit
number of gold atoms new unit
moles of gold atoms conversion
factor
1 mole gold atoms = 6.02 x 1023 gold atoms
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moles
of atoms number
of atoms
multiply
Avogadro's
number
divide
Avogadro's
number
dozens
of bagels
number
bagels
multiply
by 12
divide
by 12
Avogadro's number is
also a conversion factor
3.5 x 1022 amu x 1.0 g
6.02 x1023 amu = 0.058 g
old unit conversion factor
new unit
amu grams
6.02 x1023 amu = 1.0 g (Avogadro's number)
like 1 pound = 453.59 g
1 km = 0.62137 miles
2.54 cm = 1 inch
Example: Convert 3.5 x 1022 amu into grams.
5
Molar Mass 1 mole
phosphorus
molar mass
phosphorous = 30.974
grams
mole
molar mass
mass of one mole P atoms
atomic mass
average mass of one P atom
like the mass of a dozen donuts
like the mass of a single donut both reflect how heavy a
substance is but in different units
Why did they make Avogadro’s
number (the number of amu in a
gram) the counting unit used in
chemistry (the mole)?
6
amu grams
divide by
Avogadro's
number
number
atoms
number
moles divide by
Avogadro's
number
30.97 amu
atom 30.97 grams
mole
Atomic
mass
Molar
mass
6.02 x 1023 amu = 1.0 gram
6.02 x 1023 atoms = 1.0 mole atoms
as mass conversion factor
as a counting unit
Molar mass is a conversion factor
0.487 mole He atoms x 4.00 g helium
1 mole helium atoms = 1.95 g helium
old unit
moles conversion factor
molar mass
new unit
grams
mass moles
7
Molar mass is a conversion factor
1.23 grams arsenic × 1 mole arsenic atoms
74.922 grams arsenic
= 1.64 x 10-2 moles
of arsenic atoms (or
You could just say
moles of arsenic) old unit
grams conversion factor
1 / molar mass new unit
moles
Here honey have some arsenic
with your tea. BTW I just took out
a large life insurance policy on you
3 ways to describe amounts of an element like
grams & pounds; liters & mL; inches & cm etc.
Mass Moles Number
atoms
multiply
molar
mass
divide
molar
mass
divide
Avogadro's
number
multiply
Avogadro's
number
amu grams Avogadro's number
also converts
amu to grams
divide
Avogadro's
number
multiply
Avogadro's
number
8
What is the mass in grams of 19.00 amu?
How many amu are there in 1.16 g?
9
How many phosphorous atoms are there in 6.66
moles of phosphorous (atoms)?
How many moles of iron (Fe) atoms are in 17.4
g of Fe?
10
How many grams of silver (Ag) are there in 5.3
moles of Ag (atoms)?
What is the mass in grams of 6.66 × 109 sodium
(Na) atoms?
11
How many carbon atoms are present in 2.718 g
of carbon (C)?
What is the mass in grams of a single atom of
Co-60?
12
1 mole NO2
molecules
6.02 x 1023
NO2 molecules
Mole concept for compounds
• As a counting unit the mole is also applied
to molecules, ions, and formula units
1 mole CaCl2
formula units
6.02 x 1023
CaCl2 formula units
Ca2+
Cl- Cl-
1 CaCl2
formula unit
Counting moles of wheels in moles cars
1 mole cars = 6.02 x 1023 cars
How many moles of wheels are in 1 mole of cars?
4 wheels
per 1 car
4 wheels
1 car
4 dozen wheels
1 dozen cars 4 moles wheels
1 mole cars
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Why do chemists use moles?
• Ratios of moles are the same as ratios of atoms
- 4 wheels per 1 car
- 4 dozen wheels per 1 dozen cars
- 4 moles wheels per 1 mole cars
• Amounts are easier to express without lots of
zeros
• Equivalent to counting atoms, but more
convenient
All
4 to 1
Molar mass of a compound
• Sum of all elements atomic masses
• Can be interpreted as either
- average mass in amu for each formula unit or
- grams for each mole of formula units
What is the molar mass of CaCl2?
Ca 1 x 40.078
2 Cl + 2 x 35.45
110.98 amu CaCl2
formula unit or
grams CaCl2
mole CaCl2
14
Molar mass (of a compound)
is (also) a conversion factor
0.789 moles NO2 molecules x = 36.29 g NO2
old unit
moles conversion factor
molar mass
new unit
grams
46.00 g NO2
1 mole NO2
mass moles
46.00 g/mol
NO2
N 1 x 14.02 g/mol
O 2 x 15.99 g/mol multiply
molar mass
Example. Convert 0.789 moles of NO2 into mass of NO2
When we refer to moles of a molecular compound it must be moles of
molecules so we do not need to say the word molecule
Molar mass (of a compound)
is (also) a conversion factor
6.66 grams C6H12O6 x 1 mole C6H12O6
180.10 grams C6H12O6 = 3.70 x 10-2 moles
C6H12O6 molecules old unit
grams conversion factor
1 / molar mass
new unit
moles
mass moles C 6 x 12.01
H 12 x 1.008
O 6 x 15.99
180.10 g/mol
C6H12O6
Example. Convert 6.66 grams of glucose C6H12O6 into moles of glucose
divide
molar mass
15
Mole concept for Molecular Elements
• Molecules of a molecular element can specified in
moles
• Note the language when referring to molecular
elements:
– If we say a mole of bromine or a mole of molecular
bromine we mean a mole of the diatiomic molecules
– Example: I reacted 2.5 moles of bromine mean
2.5 moles of Br2 were reacted
– If we mean to specify a number of bromine atoms
we must use the word atom
– Example 5.0 moles of SeBr2 molecules contains
10 moles of bromine atoms
Molar mass is a conversion factor
4.68 grams bromine x 1 mole bromine
159.808 grams bromine = 2.93x 10-2 moles
bromine (molecules)
old unit
grams conversion factor
1 / molar mass
new unit
moles
Br 2 × 79.904
159.808 g/mol
16
3 different units to describe amounts of a compound
like length of an object can be expressed in mm,
cm, inches, etc.
mass
compound
moles of
formula units,
molecules,
atoms,
or ions
number
formula units,
molecules,
atoms,
or ions
multiply
molar
mass
divide
molar
mass
divide
Avogadro's
number
multiply
Avogadro's
number
17
How many moles of molecular sulfur are in
165.123 grams of molecular sulfur?
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19
Calculate the number of C, H, and O atoms in
1.75 g of squaric acid, C4H2O4
20
Calculate the molar mass of a compound if
0.258 mole of it has a mass of 25.3 g.
Molarity (M)
• Unit of concentration
molarity = moles
liter
• Conversion factor from volume of
a homogenous solution to moles
molarity
moles
liter × liters
× volume
= moles
= # moles in that volume
21
molarity
divide
stoichiometric
number
mass
compound
moles of
formula units,
molecules,
atoms,
or ions
number
formula units,
molecules,
atoms,
or ions
multiply
molar
mass
divide
molar
mass
multiply
molar
mass
divide
molar
mass
divide
Avogadro's
number
multiply
Avogadro's
number
divide
Avogadro's
number
multiply
Avogadro's
number
equivalents
multiply by
volume liters M × V = # moles
Example: What is the molarity of glucose (C6H12O6) in a solution made by dissolving 100.0 grams of glucose in enough water to make 250.0 ml of solution
1) molarity has units of liters
convert mL liters 250.0 mL x 10-3 liter
1.0 mL = 0.2500 L
2) Convert mass C6H12O6 to moles
100.0 grams x 1 mole
180.16 grams = 0.5551 moles
Molarity = # moles
#liters =
0.5551 mol
0.2500 L = 2.220 M glucose
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Example: How many moles of NaCl are in
50.5 ml of a 0.250 M NaCl solution?
1) molarity has units of liters
convert mL liters
0.250 M NaCl x 0.0505 liters
50.5 mL x 10-3 liter
1.0 mL = 0.0505 L
= 0.0126 moles NaCl
x 0.0505 liters solution = 0.0126 moles NaCl 0.250 moles NaCl
liter solution
or if you write out the base units of molarity
23
How many moles of MgCl2 are present in 160.0 mL of
0.36 M MgCl2 solution?
How many moles of Mg2+ ions are in 160 mL?
How many moles of Cl- ions are in 160 mL?
24
How many grams of NaOH are present in 36.0 mL of a
2.50 M solution?
Calculate the volume in mL of a solution required to
provide the following:
(a) 2.14 g of sodium chloride from a 0.270 M solution
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Serial dilutions
• Homogenous solutions uniform throughout
1.000 gram
of blue compound
in 1000.000 mL of water
1.000 mL
+ 999.000 mL
water
1.000 mL
+ 999.000 mL
water
1.000 mL
contains
0.0000000001000 grams
(1.000 nanogram)
of blue compound
0.001000 grams
of blue compound
in 1000.000 mL
compared to a scale
that is limited to
0.001 g ( 1 mg)
0.00000100 grams
of blue compound
in 1000.000 mL
Dilution Formula MconcVconc = MdilVdil
concentrated
stock solution
Mconc = 12.0 M HCl
1) add 10 ml
HCl stock
Vconc = 0.010 lit
water
2) add water to
500 ml mark Mconc x Vconc = # moles HCl
12 M x 0.010 lit
= 0.12 moles HCl
added
500 ml flask
# moles HCl = # moles HCl
taken from stock after adding water
Used to prepare a dilute solution
from a concentrated stock solution
Mdil = MconcVconc
Vdil
12 x 0.010
0.50 = M = 0.24 M adding water did not change # moles
HCl but it did change molarity of HCl
Vdil = 0.50 lit
Mdil = 0.24 M
added
26
2.5 liters
Water is added to 125.0 mL of a 0.66 M NaNO2 solution
until the volume of the solution is exactly 250 mL. What
is the concentration of the final solution?
27
A 35.2-mL, 1.66 M KMnO4 solution is mixed with 16.7
mL of 0.892 M KMnO4 solution. Calculate the
concentration of the final solution.
