Avogadro’s Number and moles

In 1811 Amedeo Avogadro proposed the volume of a gas is dependent on the number of atoms of gas at a fixed temperature and pressure.  If more gas is added at this fixed temperature and pressure, the volume will increase due to more atoms being added.  He proposed this was the same for all gases.

Avogadro’s proposal lay dormant for approximately 50 years when other scientists began to see the value of his work.  Namely the relation between the mass (grams) of an element in a container and the number of atoms of the element in that mass.

The number of atoms in a volume of gas was first determined by Johann Josef Loschmidt in 1865.  Other attempts to determine the number followed.

Atomic weights were known at this time and it was decided to determine the number of atoms in the mass of an element equal to it’s atomic weight.  For example, how many helium (He) atoms would be in 4.0026 g grams of He?  4.0026 is the gram atomic weight of He.  The experimentally determined number has changed over the years as measurement methods improved.  The currently accepted value is 6.022 X 1023 atoms.  This is a very large number .  Written out it would be 602200000000000000000000.  The exponent representation (6.022 X 1023) is more convenient to use. (See Exponents and Exponents for help with exponents)

Other examples.  There are 6.022 X 1023 atoms of C in 12.0107 grams of C.  12.0107 is the gram atomic weight of C. There are 6.022 X 1023 atoms of Al in 26.9812 grams of Al.  26.9816 is the gram atomic weight of Al.

The number 6.022 X 1023 was given the name Avogadro’s Number by Jean Perrin in 1901.

In 1902 Ostwald proposed the term “mole” as another way to express Avogadro’s Number.  So a mole of carbon ( C ) would have a mass of 12.0107 g and contain 6.022 X 1023 atoms of carbon.  This definition adds units to atomic weight values and a name change to gram atomic weights.

The relative atomic weight of carbon 12.0107 would become the gram atomic weight of carbon 12.0107 g/mole.

For any element, the mass of that element equal to its gram atomic weight would be 1 mole of that element and that mass would have 6.022 X 1023 atoms of that element.

The gram atomic weight of an element is a conversion factor between any mass of an element weighted on a balance and the number of moles of that element.  The number of moles of an element is a representation of the number of atoms of that element.

The unit mole is comparable to unit dozen.  It represents a number.  A dozen represents 12 of something.  A mole represents 6.022 X 1023 of something.

A dozen eggs would be 12 eggs, likewise a dozen doughnuts would be 12 doughnuts.  A mole (Fe) of iron would be 6.022 X 1023 atoms of iron, likewise a mole of electrons would be 6.022 X 1023 electrons.

Just as one could have 0.5 (1/2) dozen eggs, one could have 0.5 (1/2) mole of copper (Cu).  It is possible to have any fraction or any multiple of a mole of a chemical.

 

Calculations involving moles (Review conversion factors in the Math Skills section under the Basics tab.)

Example 1
A piece of copper (Cu) weighs 14.886 g.  How many moles of Cu would be in this mass?  How many atoms of Cu would be in this mass?

From the Periodic Table, the gram atomic weight of Cu is 63.546 g/mole.  The conversion factor for copper (Cu) is 63.546 g Cu =  1 mole Cu. This can be expressed as:

63.546 g Cu   or   1 mole Cu
   1 mole Cu             63.546 g Cu

In this problem we want moles to be the final unit, the conversion factor would be:

1 mole Cu
63.546 g Cu

The calculation would be:

                  14.886 g  x 1 mole Cu    = 0.234 mole of Cu
63.546 g Cu

The number of atoms of Cu would be:
0.234 moles x 6.022 X 1023 atoms/mole = 1.409 x 1023 atoms

Example 2

If a beaker contained 0.75 mole of Fe (iron) and a second beaker contained 0.75 mole of Al (aluminum), would the number of atoms of Fe be less than, same as or greater than the number of atoms of Al in the second beaker?  The mole unit represents the number of entities, in this case atoms of Fe and Al.  Since the mole values are the same, the number of atoms of both metals would be the same.

The second part of the example.  Would the mass of Fe in the first beaker be less than, same as or greater than the mass of Al in the second beaker?

To get the answer to this question, one needs to make a calculation similar to the calculation in Example 1 because this requires a conversion from moles to grams. To do this, the student needs to use a conversion factor for Fe and one for Al.

The conversion factor for Fe is:  55.845 g of Fe = 1 mole of Fe.

In this problem, the conversion factor would be:

55.845 g Fe
1 mole Fe

the calculation would be:

0.75 moles Fe x 55.845 g Fe = 41.88 g
1 mole Fe

The conversion factor for Al is 26.982 g of Al = 1 mole of Al.  The calculation would be:

0.75 moles Al x 26.982 g Al = 20.24 g
1 mole Al

The mass of Fe in the first beaker is greater than the mass of Al in the second beaker because the mass of Fe atoms is greater than the mass of Al atoms.  The GAW (gram atomic weight) of Fe is greater than the GAW of Al.

The conversion between grams and moles is the most frequent calculation that will be done in this class.  Rarely will the number of atoms be calculated.  It is important however to establish that a mole represents a number of entities.  One can talk about a mole of protons, a mole of electrons, a mole of atoms, a mole of ions (to be defined later) and a mole of molecules (to be defined later).