1. 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?
2. 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)
• We know there are 6 protons and 6 neutrons
• Protons and neutrons have roughly the same
mass. So, C weighs 12 u (atomic mass units).
• 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)
3. The Mole
With these problems, why use atomic mass at all?
1. Masses give information about # of p+, n0, e–
2. It is useful to know relative mass
E.g. Q - What ratio is needed to make H2O?
A - 2:1 by atoms, but 2:16 by mass
• It is useful to associate atomic mass with a
mass in grams. It has been found that
1g H, 12g C, or 23g Na have 6.02x1023 atoms
• 6.02 x 1023 is a “mole” or “Avogadro’s number”
• “mol” is used in equations, “mole” is used in
writing; one gram = 1 g, one mole = 1 mol.
• Do Q1-6. Challenge: 1st slide (use reasonable units)
4. Assignment
• 1. Why do we use the unit the mole?
• 2. What is a mole equal to?
• 3. Write out the number referred to a mole in expanded
form.
• 4. How many particles would 3.00 moles of CO2
represent? How many total atoms is that?
• 5. How many particles would 0.500 moles represent?
• 6. a) If there is 1 dozen oranges in a box and a box
weighs 1.43 kg, how much does each orange weigh?
• b) If 1.00 moles of hydrogen atoms are in a container.
How much does each individual atom weigh?
5. The Mole: Answers
1. A mole is a number (like a dozen). Having
this number of atoms allows us to easily
convert atomic masses to molar masses.
2. 6.02x1023
3. 602 000 000 000 000 000 000 000
4. 3.00 x 6.02x1023 = 18.06x1023 or 1.81x1024
(note: there are 3 moles of atoms in one
mole of CO2 molecules. In other words,
there are 5.42x1024 atoms in 3.00 mol CO2)
5. 3.01x1023
6. a) 1.43 kg 12 = 0.119 kg per orange
b) 1.01 g 6.02x1023 = 1.68 x 10–24 g
6. 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
7. Comparing sugar (C12H22O11) & H2O
No, sugar has
more (45:3 ratio)
Yes (6.02x1023
in each)
Yes.
No, molecules
have dif. masses
No, molecules
have dif. sizes.
1 mol each
Yes, that’s what
grams are.
mass?
No, they have dif.
molar masses
# of moles?
No, they have dif.
molar masses
# of
molecules?
No
# of atoms?
No, they have dif.
densities.
volume?
1 gram each
Same
8. Molar mass
• 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 SO2
Cu3(BO3)2
32.06 g/mol 64.06 g/mol
308.27 g/mol
Calculate molar masses (to 2 decimal places)
CaCl2
(NH4)2CO3
O2
Pb3(PO4)2
C6H12O6
Cu x 3 = 63.55 x 3 = 190.65
B x 2 = 10.81 x 2 = 21.62
O x 6 = 16.00 x 6 = 96.00
308.27
9. Molar mass
• 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 SO2
Cu3(BO3)2
32.06 g/mol 64.06 g/mol
308.27 g/mol
Calculate molar masses (to 2 decimal places)
CaCl2
(NH4)2CO3
O2
Pb3(PO4)2
C6H12O6
110.98 g/mol (Cax1, Clx2)
96.11 g/mol (Nx2, Hx8, Cx1, Ox3)
32.00 g/mol (Ox2)
811.54 g/mol (Pbx3, Px2, Ox8)
180.18 g/mol (Cx6, Hx12, Ox6)
10. 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
g = mol x g/mol
mol = g g/mol
• This can be represented in an “equation triangle”
g
mol g/mol
g= g/mol x mol
0.25
HCl
53.15
H2SO4
3.55
NaCl
1.27
Cu
Equation
mol (n)
g
g/mol
Formula
9.1
36.46
mol= g g/mol
0.5419
98.08
g= g/mol x mol
207
58.44
mol= g g/mol
0.0200
63.55
11. Mass, Moles and Molar Mass
• n = m/mm
• m= n x mm
• mm= m/n
• n= number of moles
• m= mass in grams
• mm= molar mass in g/mol
• Some textbooks use M to symbolize molar mass as opposed to mm…I avoid
M for molar mass since in the next unit M is used to symbolize
molarity…two meaning for one letter…
m
n mm
12. Moles, # Entities, Avogadro’s #
• n = N/NA
• N= n x NA
• NA= N/n
• n= number of moles
• N= number of entities
– (atoms, molecules, particles, ions)
• NA= Avogadro’s number
= 602 sextillion
• Since there is n in both triangles, the first and the second triangle
link together.
N
n NA
13. Simplest and molecular formulae
Consider NaCl (ionic) vs. H2O2 (covalent)
Cl Na
Na Cl
Cl
Cl
Na
Na
• Chemical formulas are either “simplest” (a.k.a.
“empirical”) or “molecular”. Ionic compounds
are always expressed as simplest formulas.
• Covalent compounds can either be molecular
formulas (I.e. H2O2) or simplest (e.g. HO)
Q - Write simplest formulas for propene (C3H6),
C2H2, glucose (C6H12O6), octane (C8H14)
Q - Identify these as simplest formula, molecular
formula, or both H2O, C4H10, CH, NaCl
14. Answers
Q - Write simplest formulas for propene (C3H6),
C2H2, glucose (C6H12O6), octane (C8H14)
Q - Identify these as simplest formula, molecular
formula, or both H2O, C4H10, CH, NaCl
A - CH2
A - H2O is both simplest and molecular
C4H10 is molecular (C2H5 would be simplest)
CH is simplest (not molecular since CH can’t
form a molecule - recall Lewis diagrams)
NaCl is simplest (it’s ionic, thus it doesn’t
form molecules; it has no molecular formula)
CH CH2O C4H7
