the Mole and Molar Mass

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CHEMICAL
QUANTITIES
All Roads Lead to the Mole
Chemical Quantities
Dozen: Baker as Mole: Chemist
• Measuring doughnuts:
o 1 dozen = 12 doughnuts (count)
o 1 dozen = 500 g doughnuts (mass)
o 1 dozen = 1 box doughnuts (volume)
• Measuring steam (H2O gas):
o 1 mole = 6.02 x 1023 H2O molecules (count)
o 1 mole = 18.0 g H2O (mass)
o 1 mole = 22.4 L H2O (volume) at STP
Count Amedeo
Avogadro
• 1776-1856
• Lawyer who became interested in math and
physics
• Discovered that equal volumes of different
gases contained an equal number of particles.
• 9 years after his death, Joseph Loschmidt
determined a constant and named it after
Avogadro.
AVOGADRO’S CONSTANT
23
= 6.02 x 10
Not to be confused
with the delicious
fruit
AVOGADRO’S CONSTANT
23
= 6.02 x 10
1 mole = 6.02 x 1023 particles
1 mole = molar mass (grams)
1 mole (of a gas at STP) = 22.4 L
The MOLE is to chemists as the
DOZEN is to bakers.
Believe it or not, students all over the country celebrate
National Mole Day!
National Mole Day Foundation, INC.
Mole Day
5 Pound Bag of Sugar contains 6.6 moles
Of C12H22O11
1 Liter bottle of Water contains 55.5
moles H20
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.
6.02 x 1023 Watermelon Seeds: Would be
found inside a melon slightly larger than
the moon.
6.02 x 1023 Pennies: Would make at least
7 stacks that would reach the moon.
6.02 x 1023 Donut Holes: Would cover the
earth and be 5 miles (8 km) deep.
Volume
Mass
Formula Units
Ions
R.P.
Molecules
Atoms
Types of Representative Particles
• Molecules (breaks down into atoms)
• Atoms
• Formula Units (breaks down into ions)
• Ions
Naming Representative
Particles
Pure
Substance
Element
Monotomic
Charged
Neutral
ION
ATOM
Compound
Polyatomic
Molecular
Ionic
MOLECULE
MOLECULE
FORMULA
UNIT
Naming Representative Particles
Examples: Name the representative particle for each substance given. For
each molecule, state how many atoms are present. For each formula unit,
state how many ions make up the ionic compound.
H+: ION
Cl2: MOLECULE – 2 ATOMS per molecule
C2H6: MOLECULE – 8 ATOMS
Cu(NO3)2: FORMULA UNIT – 3 IONS per Form.U.
Al: ATOM
NaCl: FORMULA UNIT – 2 IONS per Form.U.
Mole
R.P. Calculations
1 mole = Avogadro’s Number = 6.02 x 1023 R.P.’s
6.02  1023 R.P.
1 mol
1 mol
6.02  10 23 R.P.
R.P.
R.P. Example 1:
How many moles are in 1.4 x 1022 molecules of H2O?
1.4  10 molecules H 2 O
22
1mol

23
6.02  10 molecules H 2 O
 0.023 mol H 2O
R.P. Example 2:
How many representative particles are in 2.6 mol CO2?
2.6 mol CO 2 6.02  10 molecules CO 2

1 mol CO 2
23
 1.6 10 molecules CO2
24
R.P. Example 3:
How many atoms are in 5.2 mol CO2?
5.2 mol CO 2 6.02  10 molecules CO 2
3 atoms


1 mol CO 2
1 molecule CO 2
23
 9.4 10 atoms
24
Molar Mass
… a.k.a. Molecular Weight (MW)
molar mass = mass of 1 mole of substance
Molar mass can be determined by adding
up the atomic masses from the periodic
table.
MW Example 1:
Find the MW of CH4.
= 1C + 4H
= 12.01 + 4(1.01)
= 16.05 g/mol
MW Example 2:
Find the MW of Mg(OH)2.
=Mg + 2O + 2H
=24.31 + 2(16.00) + 2(1.01)
=58.33 g/mol
MW Example 3:
Find the MW of MgSO4•7H2O.
=Mg + S + 4O + 7(H2O)
=24.31 + 32.07 + 4(16.00) + 7(18.02)
=246.52 g/mol
What is the mass of one mole of table salt
(NaCl)?
a) 22.99 g
b) 35.45 g
c) 58.44 g
d) 100.00 g
Atomic mass Na = 22.99 g/mol
Atomic mass Cl = 35.45 g/mol
Mole
Mass Calculations
1 mole = molar mass (MW) in grams
molar mass (g)
1 mol
1 mol
molar mass (g)
Mass
Mass Example 1:
Mass Example 1: How many grams are in
7.20 moles of dinitrogen trioxide?
Dinitrogen trioxide = N2O3
MW of N2O3 = 2N + 3O = 2(14.01) + 3(16.00) = 76.02 g/mol
1 mole = 76.02 g N2O3
7.20mol N 2 O 3
76.02g

 547g N 2 O 3
1.00mol
Mass Example 2:
Mass Example 2: Find the number of moles
in 92.2 g of iron(III) oxide, Fe2O3.
Iron (III) oxide = Fe2O3
MW of Fe2O3 = 2Fe + 3O = 2(55.85) + 3(16.00) = 159.70 g/mol
1 mole = 159.70 g Fe2O3
92.2g Fe 2 O 3 1.00mol

 0.577mol Fe 2 O 3
159.70g
What is the mass of 3.7 moles of NaCl?
a) 16 g
b) 58 g
c) 220 g
d) 6.0 x 1023 g
3.7 mol NaCl 58.44 g NaCl

 216.2 g
1
mol
What is the mass of one mole of water
(H2O)?
a) 1.01 g
b) 16.00 g
c) 32.32 g
d) 18.02 g
Atomic mass H = 1.01 g/mol
Atomic mass O = 16.00 g/mol
Mass of one mole of H2O = 2(1.01) + 16.00 = 18.02 g
How many moles are in 152 g of water?
a) 0.118 mol
b) 8.44 mol
c) 2736 mol
d) 6.02 x 1023 mol
152g H 2O
1m ol

 8.44m ol
1
18.0 g H 2O
Mole
Volume Calculations
1 mole = 22.4 L of gas at STP
STP = standard temperature and pressure (0 °C & 1 atm)
22.4 L
1 mol
1 mol
22.4 L
Volume
Volume Example 1:
Volume Example 1: Determine the volume,
in liters, of 0.600 mol of SO2 gas at STP.
0.600mol SO2 (g) 22.4L

1 mol
 13.4L SO2
Volume Example 2:
Volume Example 2: Determine the
number of moles in 33.6 L of He gas at
STP.
33.6L He(g)
1 mol

22.4 L
 1.50 mol He
Density
Density = Mass / Volume
When given the density of an unknown
gas, one can multiply by the molar
volume to find the MW. The MW can
allow for identification of the gas from a
list of possibilities.
Density Example (part A):
The density of an unknown gas at STP is
2.054 g/L. (a) What is the molar mass?
density  molar volume  molar mass
2.054g 22.4L

 46.01g/mol
L
1mol
Density Example (part B):
The density of an unknown gas is 2.054 g/L.
(b) Identify the gas as either nitrogen, fluorine,
nitrogen dioxide, carbon dioxide, or ammonia.
MW = 46.01 g/mol (from part a)
Nitrogen = N2 = 2(14.01) = 28.02 g/mol
Fluorine = F2 = 2(19.00) = 38.00 g/mol
Nitrogen dioxide= NO2= 14.01 + 2(16.00) = 46.01 g/mol
Carbon dioxide = CO2 = 12.01 + 2(16.0) = 44.01 g/mol
Ammonia = NH3 = 14.01 + 3(1.01) = 17.04 g/mol
Mixed Mole Conversions
1 mole = 6.02 x 1023 RP’s = MW = 22.4 L of gas @STP
All Roads Lead to the Mole.
Always convert to units of moles first
when converting between grams, liters,
and representative particles.
Mixed Mole Example 1:
How many carbon atoms are in a 50.0-carat
diamond that is pure carbon? Fifty carats is the
same as 10.0 g.
10.0g
1 mol
6.02 10 23 atoms


12.01g C
1 mol C
 5.0110 atoms C
23
Mixed Mole Example 2:
How many atoms are in 22.0 g of water?
22.0g H 2 O
1 mol 6.02 10 molecules 3 atoms



18.02g
1 mol
1 molecule
23
 2.20 10 atoms
24

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