Avogadro’s Number

Amedeo Avogadro was one of the most brilliant scientists of the 19th century.   He was born in Italy on August 9, 1776 and died on his 80th birthday on August 9, 1856. Avogadro studied the behavior of gasses and realized that the properties of a gas such as volume and pressure at a known temperature depended on the number of gas particles, not the type of gas molecule.
avogadro_amedeo

Avogadro proposed that the weight of a sample of gas at a known volume, pressure and temperature was related to the weight of the individual molecules of the gas.

 

 

 

In 1909, a French Physicist named Jean Perrin, proposed that a scaling factor could be found relating the weight of 1 molecule of a gas to its volume and suggested this scaling factor be named after his predecessor, Avogadro.  jean_perrin_1926

The value of this scaling factor could not be measured untill the 1950’s.

In the 1950’s, methods became available which allowed scientists to obtain extremely pure samples of Carbon-12.  Using X-ray diffraction, exact measurements were made of the spacing of Carbon atoms in Graphite.

Artwork of the crystal structure of graphite showing parallel layers of hexagonally arranged carbon atoms. Graphite as used in pencil lead, lubricants, and structural components that need strength and lightness.
Artwork of the crystal structure of graphite showing parallel layers of hexagonally arranged carbon atoms. Graphite as used in pencil lead, lubricants, and structural components that need strength and lightness.

 

 

 

graphite-x-ray-diffractionartists rendering of graphite crystal

 

 

 

 

 

X-Ray Diffraction pattern from single crystal graphite. The arrangement of the bright spots shows the hexagonal structure of the graphite crystal. The spacing of the bright spots can be related back to the  spacing between individual atoms.

In the 1990’s new techniques such scanning-tunneling microscopy were developed which allow us to directly image the atoms on the surface of a crystal.scanning-tunneling-graphite

 

Notice the hexagonal arrangement of the Carbon atoms in graphite.

 

 

Avogadro’s Number:

Knowing that Carbon 12 has 6 protons and 6 neutrons for a total of 12 Atomic Mass Units, scientists set about to make an ultra pure sample of Carbon-12, they measured out exactly 12.000…. grams and grew a single crystal of graphite.  By measuring the volume of the crystal and knowing the exact spacing of the carbon atoms (from x-ray diffraction), they were able to determine the exact number of Carbon atoms in 12 grams of graphite.  This number was calculated to be:

N = 6.022 x 10^23 and was the first accurate measurement of Avogadro’s number.

The Mole:

Avogadro’s number turned out to be a very useful number. The name mole (or mol) is used to denote the 1 molecular weight of a substance.   The names mol and mole are used interchangeably.

For example, 1 mol of Carbon contains 6.022 x 10^23 atoms of Carbon and weighs 12 grams.  1 mol of water weighs 18 grams and contains 6.022 x 10^23  molecules of H2O.

If you know the weight of a sample and its chemical composition, you can find the number of moles in a sample.
Simply total up the elements in a compound, multiply each by their atomic weight to get the molecular weight of the compound.
Next divide the weight of the sample by the molecular weight of the molecule.
example: 18 grams of H2O is 1 mole
example  36 grams of H2O is 2 moles
(notice the relation between MOLEcular weight and the unit MOLE)

Find the weight of 1 mole of each of these chemicals.
Hint: Total up the molecular weights of each component.
H2
He
12C
H2O
Al2O3

Find the weight of 2 moles of each of these chemicals.
Hint: Total up the molecular weights of each component, multiply by 2.
H2
He
12C
H2O
Al2O3