M l and
Moles
d Numbers
N b
There are times when we want to deal with the actual number
of atoms or molecules in a sample,
p , not jjust in the total amount
of moles. To do this you need the relationship
1 mole = 6.022x1023 things.
This number seems a bit arbitrary and is called Avogadro’s
number. You do not need to memorize this number because I
include it on a sheet of constants I distribute with all of my
tests.
M l and
Moles
d Numbers
N b
Avogadro’s number is a very big number. It is useful for
calculation involvingg atoms and molecules,, but it is a really
y
bad number to use for counting things that are any bigger that
atoms or molecules.
Let’s work a couple of problems to try to get a feel how big
this number is. First, what is the volume of 1 mole or
6.022x1023 molecules of water?
M l and
Moles
d Numbers
N b
What is the volume of 1 mole or 6.022x1023 molecules of
water?
Using the molar mass of water = 1(16) + 2(1.008) = 18.002g
you can quickly come up with the fact that
1 mole of water x (18.002 g/1mole) = 18.002 g of water
Remembering that water has a density of 1 or 1 g = 1 ml
You can take this a bit farther
18.002 g of water x (1 ml/1g) = 18.002 ml of water
(that is a little over a tablespoon!)
M l and
Moles
d Numbers
N b
Now how many molecules of water are there in this 18 g of
water?
18 g x (1 mole/18g) x (6.022x1023 molecules/mole)
= 6.022x1023 molecules
M l and
Moles
d Numbers
N b
Now let’s try it the other direction. How many atoms are there
in a ngg of Mercury?
y
First do you remember how much a ng is?
n = nanonano so this is 1 nanogram of Mercury
a nano is 1x10-9
so 1 ng = 1x10-9 g or .000000001 g
M l and
Moles
d Numbers
N b
How many atoms are there in a ng of Mercury?
Mercury (Hg) has an atomic mass of 200.6g so that will
convert grams to moles, and we have Avogadro’s number
6 022x1023 atoms = 1 mole,
6.022x10
mole so we have all the conversion
factors we need to finish the problem.
1x10 − 9 g 1 mole Hg 6.022 x10 23 atoms
1 ng Hg ×
×
×
1 ng
200.6 g Hg
1 mole
= 3x1012 atoms
t
M l and
Moles
d Numbers
N b
How many atoms are there in a ng of Mercury?
So even though we are dealing with only .000000001 g of
Mercury still have 3x1012 or 3,000,000,000,000 atoms.
Like I said earlier, 6.022x1023 is a BIG number.