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The Mole
Q: how long would it take to spend a mole of $1 coins if
they were being spent at a rate of 1 billion per second?
Background: Atomic Masses
• Look at the “atomic masses” on the periodic table. What
do these represent?
– E.g. the atomic mass of C is 12 (atomic # is 6)
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We know there are 6 protons and 6 neutrons
Protons and neutrons have roughly the same mass.
So, C weighs about 12 u (atomic mass units).
– TB: why is the atomic mass not exactly 12 on the periodic table?
• What is the actual mass of a C atom?
– Answer: approx. 2 x 10-23 grams (protons and neutrons each
weigh about 1.7 x10-24 grams)
Two problems:
1. Atomic masses do not convert easily to grams
2. They can’t be weighed (they are too small)
The Mole
With these problems, why use atomic mass at all?
- Atomic masses give information about # of p+, n0, e–
It has been found that
1g H, 12g C, or 23g Na have 6.02x1023 atoms
6.02 x
23
10
= a “mole” or “Avogadro’s number”
• “mol” is used in equations, “mole” is used in writing;
– one gram = 1 g, one mole = 1 mol.
• Unit used to measure the amount of molecules/individual
particles in a substance
Mollionaire!
Q: how long would it take to spend a mole of
$1 coins if they were being spent at a rate of
1 billion per second?
A: $ 6.02 x 1023 / $1 000 000 000
= 6.02 x 1014 payments = 6.02 x 1014 seconds
6.02 x 1014 seconds / 60 = 1.003 x 1013 minutes
1.003 x 1013 minutes / 60 = 1.672 x 1011 hours
1.672 x 1011 hours / 24 = 6.968 x 109 days
6.968 x 109 days / 365.25 = 1.908 x 107 years
A: It would take 19 million years
Comparing sugar (C12H22O11) & H2O
Same
1 gram each
1 mol each
No, they have dif. No, molecules
volume?
densities.
have dif. sizes.
Yes, that’s what
No, molecules
mass?
grams are.
have dif. masses
No, they have dif.
Yes.
# of moles? molar masses
No, they have dif. Yes (6.02x1023
# of
in each)
molecules? molar masses
No, sugar has
# of atoms?
No
more (45:3 ratio)
Molar mass
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The mass of one mole is called “molar mass”
E.g. 1 mol Li = 6.94 g Li
This is expressed as 6.94 g/mol
What are the following molar masses?
S 32.06 g/mol SO2 64.06 g/mol
Cu3(BO3)2 308.27 g/mol
Calculate molar masses (to 2 decimal places)
CaCl2
Cu x 3 = 63.55 x 3 = 190.65
(NH4)2CO3 B x 2 = 10.81 x 2 = 21.62
O2
O x 6 = 16.00 x 6 = 96.00
308.27
Pb3(PO4)2
C6H12O6
Molar mass
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The mass of one mole is called “molar mass”
E.g. 1 mol Li = 6.94 g Li
This is expressed as 6.94 g/mol
What are the following molar masses?
S 32.06 g/mol SO2 64.06 g/mol
Cu3(BO3)2 308.27 g/mol
Calculate molar masses (to 2 decimal places)
CaCl2
110.98 g/mol (Cax1, Clx2)
(NH4)2CO3 96.11 g/mol (Nx2, Hx8, Cx1, Ox3)
O2
32.00 g/mol (Ox2)
Pb3(PO4)2 811.54 g/mol (Pbx3, Px2, Ox8)
C6H12O6 180.18 g/mol (Cx6, Hx12, Ox6)
Converting between grams and moles
• If we are given the # of grams of a compound
we can determine the # of moles, & vise-versa
• In order to convert from one to the other you
must first calculate molar mass
m
m=nxM
n
M
n=mM
• This can be represented in an “equation triangle”
m (g)
n (mol)
Formula M (g/mol)
Equation
HCl
36.46
9.1
0.25
m= n x M
H2SO4 98.08 53.15 0.5419
n= m  M
NaCl 58.44
207
3.55
m= n x M
Cu
63.55
1.27 0.0200
n= m  M
Converting between grams and number
of particles (atoms, molecules, compounds, etc.)
• Once you know the amount of a substance (n),
you can then calculate the number of particles
(N) by going back to our first equation triangle
that includes Avagadro’s number (NA)
N
n
NA
m
n
N
M
n
NA
• Determine the number of molecules of water in an ice
cube of mass 12.6 g.
1st – convert m  n
2nd – convert n  N
A little more tricky
• Calculate the number of atoms in 1.00 g of nitrogen.
• Calculate the number of chloride ions in 22.2 g of
CaCl2
Homework! 
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Pg. 226 #2,3
Pg. 228, 230, 231 – odd numbers
Pg. 235 #31,33
Pg. 237, 239, 242 – odd numbers