MOLE CALCULATIONS
Moles & Representative Particles
In chemistry we work with large numbers of atoms and molecules because of
their minute size. It is not very practical for a chemist to count out atoms or
molecules so they use a unit called a mole. Just like a dozen is always 12, a
mole is always the same number, 6.02 X 1023. If you have one mole of atoms
or 1 mole of molecules or 1 mole of people, it is always 6.02 X 10 23. This
number is also called Avogadro's Number, named after the famous Italian
chemist Amedeo Avogadro, whose work lead to the determination of this
number. A common calculation in chemistry is converting between moles and
representative particles (atoms, molecules, or formula units). In this type of
calculation a conversion factor is used that relates moles and 6.02 X 1023. See
the examples below.
Example1
How many atoms of iron are in 4.75 moles of iron?
6.02 x 1023 atoms
4.75 moles of Fe X
--------------------- =
2.86 x 1024 atoms
1 mole
Example 2
How many moles are in 7.32 x 1023 molecules of water?
1 mole
7.32 x 1023 molecules H2O X -------------------------- = 1.22 moles H2O
6.02 x 1023 molecules
Moles & Mass
Chemists can also use the concept of the mole to count atoms without actually
taking the time to count them out individually. Atoms and molecules can be
counted by weighing them and then making a simple conversion. The periodic
table has the atomic masses of the elements listed and these weights can be
used to count atoms. The atomic mass of an element on the periodic table is
the weight of 1 mole of atoms. For example, the atomic mass of Fe is 55.8 on
the periodic table. If you weigh out 55.8 grams of Fe you will have 1 mole of
iron, or 6.02 x 1023 atoms. By using this method you can count atoms by
weighing them. The concept holds true for all of the atoms on the periodic
table. We can also apply this concept to compounds. If you want to count out
6.02 x 1023 molecules of water (1 mole) you could do so by weighing out 18.0
grams of water and you would have one mole. The 18.0 grams come from
adding up the weight of 2 hydrogens and 1 oxygen from the periodic table. The
mass of 1 mole of a substance, whether it is atoms, molecules, or formula units
is called the molar mass of a substance. Below you will find some examples
of how to calculate the molar mass of a substance.
Example 1
What is the molar mass of Na2SO4? To solve the problem you need to find the
weights of each type of atom in the compound from the periodic table and then
add them together.
Na 23.0g x 2 atoms = 46.0g
S 32.1g x 1 atom = 32.1g
O 16.0g x 4 atoms = 64.0g
---------142.1 grams / mole
Example 2
What is the molar mass of (NH4)2SO4?
N 14.0g x 2 atoms
H 1.0g x 8 atoms
S 32.1g x 1 atom
O 16.0g x 4 atoms
= 28.0g
= 8.0g
= 32.1g
= 64.0g
--------132.1 grams / mole
A very common calculation that is made in chemistry is converting between
mass (grams) and moles. This type of conversion can be made by using the
molar mass of a substance. Below are some examples of this type of
calculation.
Example1
How many grams of NaCl are in .487 moles of this compound?
This problem can be solved by finding the molar mass of NaCl from the
periodic table and then making a conversion factor using the molar mass and 1
mole.
58.5 grams
.487 moles NaCl x ---------------1 mole
= 28.5 grams of NaCl
Notice that the answer is rounded to 3 significant figures since we started with
3 significant figures and the molar mass from the periodic table contains 3
significant figures.
Example 2
How many moles are in 238.6 grams of Cu(NO3)2?
1 mole
238.6 grams Cu(NO3)2 x -------------187.6 grams
= 1.272 moles Cu(NO3)2
Moles & Volume of Gas
We have now seen how moles can be related to representative particles (atoms,
molecules, formula units) and how they can be related to mass (grams).
Because of experiments performed by Avogadro we are also able to relate
moles to the volume of a gas. Avogadro found through experiments that equal
volumes of gases at the same temperature and pressure will have the same
number of particles (atoms or molecules). This is now know as Avogadro's
Hypothesis. This means that if we have 1 mole of a gas at the same
temperature and pressure as another gas, they should have the same volume.
Since the volume of gases change with pressure and temperature, chemists had
to determine one temperature and pressure that would be considered the
standard when measuring gases. That temperature was determined to be 0°
Celsius and the pressure was determined to be 1 atmosphere (the average air
pressure at sea level). This temperature and pressure are now known as
standard temperature and pressure (STP). Chemists have found
experimentally that if you have 1 mole of gas at standard temperature and
pressure (STP) it will always have the same volume, 22.4 Liters. The type of
gas does not make a difference in this number even though the size and mass of
the particles in gases may differ. This is because gases are mostly empty space
so the size of their particles have little effect on their volume. This gives us
another relationship to moles and allows us to make another type of conversion
using moles. We can make a conversion factor relating 1 mole of a gas at STP
and 22.4 Liters. Below you will find some examples of how to use this
conversion.
Example 1
What is the volume of He (in Liters) of 2.33 moles of He at STP?
22.4 liters
2.33 moles He x ---------------- =
1 mole
52.2 liters of He
Example 2
How many moles of gas are in a 2.00 Liter bottle containing O2 if the gas is at
STP?
1 mole
2.00 L O2 x ---------------- =
O2
22.4 liters
0.0893 moles of O2 or 8.93 x 10-2 moles of