The Mole

1
The Mole

• The following provides an overview of moles and
  the skills necessary for performing mole
  conversions

2
Definition of a Mole

• A dozen is a number that has been given a name.
  The same can be said for a mole. The only
  difference is that the number defined as a mole
  is very, very, very, very, very, very, very
  ,very, very, very, very, very, very, very, very,
  very, very, big!!!
• 1 mole 6.02 x 1023
• (602,000,000,000,000,000,000,000)
• Avogadros Number

3
Is A Mole Really That Big?

• If an atom were the size of a marble and one
  mole of marbles were spread over the surface of
  the Earth, our planet would be covered by a 50
  mi-thick layer.

4
Is A Mole Really That Big?

• A new supercomputer can count all of the people
  in the United States in one-quarter of a second,
  but it would take almost two million years for it
  to count one mole of people at the same rate.

5
Is A Mole Really That Big?

• If you made 40,000 (4,000,000 pennies) every
  second at your job that you had been working at
  since the formation of earth 4.5 billion years
  ago, you would not yet have earned Avogadros
  number of pennies.

6
So How is a Mole Helpful?

• Scientists obviously cant mass quantities of
  chemicals in amu because an amu is far too small.
  When scientists work with a substance like H2O,
  they cant deal with single molecules we cant
  see or mass 2 atoms of hydrogen and one atom of
  oxygen. Scientists obviously have to work with
  much larger quantities. To solve this problem,
  scientists use the mole. To be useful the mole
  has to be somehow related to amu. Officially,
  the mole (symbol mol) is the SI term for the
  amount of substance containing as many elementary
  particles as there are atoms in 0.012 kg of
  carbon-12 (which is about 6.02 x 1023atoms)

7
Where do you find how much a mole of something
weighs?

• The atomic mass given on the periodic table is
  not only the mass of one atom of that element,
  but it is also the mass (in grams) of 1 mole of
  the atoms of that element. Therefore, since the
  mass of one carbon atom is 12 amu, the mass of
  one mole of Carbon atoms would be 12 grams. When
  dealing with a molecule or compound you simply
  calculate the molecular/formula mass using the
  periodic table, and this (like with atoms) is not
  only the mass of one molecule/compound, but it is
  also the mass (in grams) of 1 mole of the
  molecule/compound. Therefore, since the mass of
  one molecule of ozone (O3) is 48 amu, the mass of
  one mole of ozone molecules would be 48 grams.

8
How much does it weigh?
You may want to use your periodic table!

• 1 mole of Oxygen
• 1 mole of Sodium
• 2 moles of Carbon
• 3 moles of Hydrogen
• 1 mole of H2O

16 grams
23 grams
24 grams
3 grams
18 grams
9
Mole Map
This map is to help you navigate mole problems
Atoms, Molecules, Particles, Etc.
Moles
Mass (Grams)
Excuse me, how do I get to Atoms?
If you use the map, you wont get lost!!!
Just start at grams, go straight through moles
and you will get to atoms.
10
Sample One Step Problem

• Calculate the mass of 7.5 moles of Carbon.
• Use the map to help figure it out

Moles
Atoms, Molecules, Particles, Etc.
Mass (Grams)
What is the starting point in this problem?
What is the final destination in this problem?
How many steps/fractions will it take you to get
there?
11
One Step Problem

• Calculate the mass of 7.5 moles of Carbon.
• 7.5 moles of C ? grams of C

grams of C
(7.5 moles of C) (1)
(____________) ( )
12
90 grams of C
mole of C
1
4 Since you are aware that it is necessary to
travel to grams you can simply place that unit
on the top of the fraction. To determine the
mass of a mole of carbon you use the periodic
table. In this case, one mole of carbon has a
mass of 12 grams. You plug these numbers into
the fraction, letting the units guide you. You
have now transitioned from moles to grams.
6 Finally, multiply across the top, multiply
across the bottom, and divide the product of the
top by the product of the bottom. This will give
you the final answer, which in this case is 90
grams of C.
1 Since you have already found the starting
point, final destination, and the number of steps
it will take, you should now write down a little
reminder of all of this information.
2 Place your starting point over one. In this
case you will be placing 7.5 moles of carbon
over one.
3 Multiply between fractions and make sure the
bottom unit of the new fraction is the same as
the top unit of the previous fraction. In this
case the unit is mole of carbon.
5 Now that you have arrived at your final
destination (grams) you can simply cancel all
other diagonal units.
Use 1 Mole 6.02x1023
Use Periodic table
12
Sample Two Step Problem

• How many atoms are in 45.8 grams of Na?
• Use the map to help figure it out

Moles
Atoms, Molecules, Particles, Etc.
Mass (Grams)
What is the starting point in this problem?
What is the final destination in this problem?
How many steps/fractions will it take you to get
there?
13
Two Step Problem

• How many atoms are in 45.8 grams of Na?
• 45.8 grams ? atoms of Na

mole of Na
(45.8 grams of Na) (1)
(_____________) ( )
1
(________________) ( )
atoms of Na
6.02x1023
grams of Na
mole of Na
1
23
1.20 x 1024 atoms of Na
4 Since you are aware that it is necessary to
travel to atoms, according to the Mole Map,
you must stop at moles first. Therefore you
should place that unit on the top of the
fraction. To determine the mass of a mole of
sodium you use the periodic table. In this case,
one mole of sodium has a mass of 23 grams. You
plug these numbers into the fraction, letting the
units guide you. You have now transitioned from
grams to moles.
2 Place your starting point over one. In this
case you will be placing 45.8 grams of sodium
over one.
3 Multiply between fractions and make sure the
bottom unit of the new fraction is the same as
the top unit of the previous fraction. In this
case the unit is grams of sodium.
1 Since you have already found the starting
point, final destination, and the number of steps
it will take, you should now write down a little
reminder of all of this information.
5 Now that you have arrived at moles it will be
necessary to continue your travels to atoms since
moles is not your final destination. Once
again, you need to multiply between fractions and
make sure the bottom unit of the new fraction is
the same as the top unit of the previous
fraction. In this case the unit is mole of
sodium.
8 Finally, multiply across the top, multiply
across the bottom, and divide the product of the
top by the product of the bottom. This will give
you the final answer, which in this case is
1.20x1024 atoms of sodium.
6 Since you are at moles, it is now possible
for you to travel to atoms therefore you should
place that unit on the top of the fraction. To
determine the number of atoms in a mole of sodium
you simply use 1 mole 6.02x1023. You plug
these numbers into the fraction, letting the
units guide you. You have now transitioned from
moles to atoms.
7 Now that you have arrived at your final
destination (atoms) you can simply cancel all
other diagonal units.
Use 1 Mole 6.02x1023
Use Periodic table
14
Sample Problem That Requires Some Prep Work
Before Converting

• Calculate the mass of two moles of the compound
  Ca(NO3)2.
• What is different about this problem when
  compared to the others?

Ca(NO3)2 - it is not an atom
Ca 40g x 1 40 g/mol N 14g x 2 28 g/mol O
16g x 6 96 g/mol 1 mole of Ca(NO3)2 164 g
You should calculate the molar mass using your
periodic table prior to using your map and
subsequently converting
Now that you know the molar mass of Ca(NO3)2 you
can use your map and convert
15
Sample Problem That Requires Some Prep Work
Before Converting

• Calculate the mass of two moles of the compound
  Ca(NO3)2.
• Use the map to help figure it out

Moles
Atoms, Molecules, Particles, Etc.
Mass (Grams)
What is the starting point in this problem?
What is the final destination in this problem?
How many steps/fractions will it take you to get
there?
16
Continuation of Problem After Prep Work is
Complete

• Calculate the mass of two moles of the compound
  Ca(NO3)2.
• 2 moles of Ca(NO3)2 ? grams of Ca(NO3)2
• 1 mole of Ca(NO3)2 164 g

grams of Ca(NO3)2
(2 moles of Ca(NO3)2) (1)
(__________________) ( )
164
mole of Ca(NO3)2
1
328 grams of Ca(NO3)2
4 Since you are aware that it is necessary to
travel to grams you can simply place that unit
on the top of the fraction. To determine the
mass of a mole of Ca(NO3)2 you have already used
your periodic table and you calculated a mass of
164 grams. You plug these numbers into the
fraction, letting the units guide you. You have
now transitioned from moles to grams.
1 Since you have already done some preliminary
work and determined the mass of a mole of
Ca(NO3)2, found the starting point, final
destination, and the number of steps it will
take, you should now write down a little reminder
of all of this information.
2 Place your starting point over one. In this
case you will be placing 2 moles of Ca(NO3)2
over one.
3 Multiply between fractions and make sure the
bottom unit of the new fraction is the same as
the top unit of the previous fraction. In this
case the unit is mole of Ca(NO3)2.
5 Now that you have arrived at your final
destination (grams) you can simply cancel all
other diagonal units.
6 Finally, multiply across the top, multiply
across the bottom, and divide the product of the
top by the product of the bottom. This will give
you the final answer, which in this case is 328
grams of Ca(NO3)2..
Use 1 Mole 6.02x1023
Use Periodic table