1mole
=602,214,150,000,000,000,000,000 Avogadro's Number

The number of carbon-12 atoms in 12
grams of unbound carbon in the ground state.

Avogadro's number, the number
of particles in a mole, can be experimentally determined
by first "counting" the number of atoms in a
smaller space and then scaling up to find the number of
particles that would have a mass equal to the atomic or
molecular mass in grams. Here is some real data from
which Avogadro's number can be determined.

X-Ray diffraction studies show that gold consists of
a repeating atomic arrangement where the repeating unit
(called a cell unit) is a cube containing 4 gold atoms.
Each side of the cube has a length of 4.08x10^{-8}
cm. The density of gold is 19.3 g / cm^{3} and
its atomic mass is 197.

v= side^{3}= (4.08 x 10^{-8}cm)^{3}=
6.79 x 10^{-23}cm^{3}

197g

X

1 cm^{3}

X

4 atoms

=6.013 x 10^{23 }atoms/mole
(pretty close)

mol

19.3g

6.79 x 10^{-23}cm^{3}

The History of the Term"Mole"

The Avogadro constant is named after the early nineteenth
century Italian scientist Amedeo Avogadro, who is credited
(1811) with being the first to realize that the volume of a gas
(strictly, of an ideal gas) is proportional to the number of
atoms or molecules. The French chemist Jean Baptiste Perrin in
1909 proposed naming the constant in honor of Avogadro. American
chemistry textbooks picked it up in the 1930's followed by high
school textbooks starting in the 1950s.

The unit "mole" was introduced into
chemistry around 1900 by Ostwald, and he originally defined this
unit in terms of gram. Gram is a unit of mass; but what is the
mole a unit of? Ostwald did not say;^{3} however,
several years later, he did make it clear that the concept of
mole should be linked to the ideal gas. ^{4}

^{3}"...the molecular weight of a substance,
expressed in grams, shall henceforth be called mole [. . . das
in Grammen augedruckte [. . .] Molekulargewicht eines Stoffes
soll fortan ein Mol heissen]" Ref. 7).

^{4} "That amount of any gas that occupies a
volume of 22414 mL in normal conditions is called one mole [eine
solche Menge irgendeines Gases, welche das Volum von 22412 ccm
im Normalzustand einnimt nennt man ein Mol]"

References
Ref. 7. Ostwald, W. Grundriss der allgemeinen Chemie;
Leipzig: Engelmann, 1900, p. 11

Ref. 8. Ostwald, W. Grundriss der allgemeinen Chemie,
5th ed.; Dresden: Steinkopff, 1917, p. 44

Given that the volume of a grain of sand is
approximately 10^{-12} m^{3}, and given that the
area of the United States is about 10^{13}m^{2},
it therefore follows that a mole of sand grains would cover the
United States in approximately one centimeter of sand.

A human body contains very roughly one hundred trillion
cells; there are roughly six billion people on Earth; so the
total number of human cells on the planet is approximately
100×10^{12}*6×10^{9}=6×10^{23}, which
is very close to one mole.

Since the Earth has a radius of about 6400 km, its volume is
approximately 10^{21} m^{3}. Since about 500
large grapefruit will fit in one cubic meter, it therefore
follows that a mole of grapefruit would have approximately the
same volume as the Earth.

If you had exactly one mole of sheets of paper, you
could make one million equal stacks from sea level on the earth
that would pass the sun.

If you had a mole of pennies, you could give out enough money
to everyone in the world so that they could spend a million
dollars every hour, day and night, for the rest of their lives.

If you wanted to use trial and error to find the
combination to an e-mail password that contained exactly six
alphanumeric characters, it would take you up to 6^36 different
tries, which is approximately 10^{28}, which is over
17,000 moles.