The document discusses the mole as a unit used to quantify atoms and molecules. It explains that atoms and molecules are too small to count individually, so they are grouped into moles containing 6.022 x 1023 particles. This allows for easier calculations involving large numbers of tiny particles. Examples show how moles can be used to determine the number of individual atoms or molecules present. The mole is analogous to counting items in dozens, and conversions between moles and individual particles use the mole-to-particle conversion factor.

1. Mole Conversions

2. Purpose
• Atoms and molecules are very, very small and very, very light. Rather than
counting individual atoms and molecules and having to deal with really
large numbers, we group them into chunks called moles. In this way, it will
be easier to deal with the quantities involved. For example, we can say
that there are 2.5 moles of water molecules in a glass of water. This is
much more reasonable than saying there are 1.505 x 1024 molecules of
water in the glass even though they both say the same thing. Similarly,
the mole allows us to deal with mass more easily, though this will not be
covered until a later lesson.

3. Atoms are too small to deal with individually
• A 2.5 g (gram) penny contains approximately 23000000000000000000000
(2.3 x 1022) atoms.
• The mass of one of the zinc atoms in a penny is approximately
0.000000000000000000000109 (1.09 x 10-22) grams.
• Neither of these numbers is easy to work with due to the very small size of
an atom.

4. To work with atoms and molecules, we deal in
quantities of moles
• Just like eggs are often dealt with in groups of 12 called dozens, atoms
and molecules are dealt with in groups of 602214150000000000000000
(6.022 x 1023) called a mole.
12 of anything = 1 dozen of that thing
602214150000000000000000 (6.022 x 1023) of anything = 1 mole of that thing
• Note: This is a really large number. The reason for this is that atoms are
so small.

5. Some simple examples:
• If you have 1 dozen grains of sand, you have 12 grains of sand.
• If you have 2 dozen grains of sand, you have 24 individual grains of sand.
• If you have 1 mole of sand grains, you have 602214150000000000000000
individual grains of sand.
• If you have 2 moles of sand grains, you have
1204428300000000000000000 individual grains of sand.
• Note: If you had 1 mole of sand grains on the United States, it would
cover it to a depth of approximately 1 cm. From this, you can see that we
should really only use moles when dealing with very, very small things like
atoms and molecules.

6. Stop and see the big idea:
1 mole of anything is equivalent to 602214150000000000000000 individual
items
or
1 mole = 6.022 x 1023
From now on, we will use the number in scientific notation now that you have
a good sense of the size of the number.

7. Atoms and Molecules are counted using moles
Atoms:
• 1 mole of carbon atoms is 6.022 x 1023 individual atoms of
carbon.
Molecules
• 1 mole of water molecules (H2O) is 6.022 x 1023 individual
molecules of H2O.
Carbon atom
Water Molecule

8. Mole Conversions use dimensional analysis
• Knowing 1 mole = 6.022 x 1023 atoms or molecules we can use it as a
conversion factor in dimensional analysis for conversions into and out of
moles for individual atoms or molecules.
1 𝑚𝑜𝑙
6.022 𝑥 1023 𝑎𝑡𝑜𝑚𝑠
𝑜𝑟
6.022 𝑥 1023
𝑎𝑡𝑜𝑚𝑠
1 𝑚𝑜𝑙
1 𝑚𝑜𝑙
6.022 𝑥 1023 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒𝑠
𝑜𝑟
6.022 𝑥 1023 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒𝑠
1 𝑚𝑜𝑙

9. Misconception Alert!
• The abbreviation for mole is mol
– mol means mole.
– Neither mol nor mole means molecule!

10. Let’s do some conversions with moles
• An aluminum can contains 0.471 moles of aluminum (Al) atoms. How
many aluminum atoms are in the can?
– Given: 0.471 mole Al
– Asked for: atoms of Al
– Relationship: 1 mole Al = 6.022 x 1023 atoms Al
– Solution:
0.471 𝑚𝑜𝑙 𝐴𝑙 𝑥
6.022 𝑥 1023 𝑎𝑡𝑜𝑚𝑠 𝐴𝑙
1 𝑚𝑜𝑙 𝐴𝑙
= 2.84 𝑥 1023 𝑎𝑡𝑜𝑚𝑠 𝐴𝑙

11. Pause and Practice
• A one liter bottle of water contains 106 moles of water. How many water
molecules are in the bottle?

12. Pause and Practice - Solution
• A one liter bottle of water contains 55.6 moles of water. How many water
molecules are in the bottle?
55.6 𝑚𝑜𝑙 𝐻2 𝑂 𝑥
6.022 𝑥 1023
𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒 𝐻2 𝑂
1 𝑚𝑜𝑙 𝐻2 𝑂
= 3.35 𝑥 1025
𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒𝑠 𝐻2 𝑂

13. Pause and Practice
• If the human body contains about 4 grams of iron, which is 4.31 x 1022
atoms of iron. How many moles of iron are in the human body?

14. Pause and Practice - Solution
• If the human body contains about 4 grams of iron, which is 4.31 x 1022
atoms of iron. How many moles of iron are in the human body?
4.31 𝑥 1022
𝑎𝑡𝑜𝑚𝑠 𝐹𝑒 𝑥
1 𝑚𝑜𝑙 𝐹𝑒
6.022 𝑥 1023 𝑎𝑡𝑜𝑚𝑠 𝐹𝑒
= 0.716 𝑚𝑜𝑙 𝐹𝑒

15. Now try the exercises.
• Remember:
1 mole of any substance = 6.022 x 1023 atoms or molecules