The Mole and History of The Term "Mole"
In 1811, Avogadro states that equal volumes of different gases at the same temperature contain
equal numbers of molecules.
Hydrogen gas is found to be 2 gram at 1 atm, 273 kelvin and 22.4 litre. At that time it is already
known that I mole of hydrogen gas actually has two hydrogen atoms. So as a standard, one mole
is defined as the number of atoms contained in 1 gram of hydrogen (or 2 grams of hydrogen gas).
To find the number of atoms in one mole, we need to find a relationship between the macroscopic
(volume, pressure, temperature) data and the microscopic (no. of molecules) data. This is
accomplished by the kinetic molecular theory and the ideal gas law. Kinetic molecular theory
gives us a relationship between the kinetic energy of a molecule from the temperature. The
collision of the molecules with the wall of the container is what gives us the pressure. Hence there
is a relationship between no.of molecules and the pressure. We know all ideal gas have the same
numbers of molecules in a constant pressure and volume, and we can substitute the conditions
for our standard 1 gram hydrogen to find Avogadro’s constant.
From the ideal gas law
PV=NK b T (1)
where K b is the Boltzmann constant and T the absolute temperature,
N=101325×0.0224/(273×1.3806×10 −23 )=6.022×10 23
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---------------------------------------------------------------------------------------------------------------------------------First chemists discovered the combining ratios of the elements by mass. Those are the atomic weights. e.g.
Na and Cl combine on a 1:1 ratio BY ATOM; BY MASS they combine on a 23 gram to 35.5 gram ratio.
This has to mean that an atom of Na weighs less than an atom of Cl.
The Atomic Weight scale was worked out by observations like these.
Next chemists decided to take the Atomic Weight of an element and define that many grams of it to be ONE
MOLE. That meant that 1 gram of H is a mole of H; 12 grams of C is a mole of C 23 grams of Na is a mole
of Na, etc.
Finally they measured how many atoms are in ONE MOLE. It comes out to be the number 6.023x1023
atoms Therefore 1 mole of substance = 6.023x1023 particles. This is called Avogadro's Number.
Mole Conversions Tutorial
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 / cm3 and its atomic mass is 197.
v= side3= (4.08 x 10-8cm)3= 6.79 x 10-23cm3
197g
1 cm3
4 atoms
X
X
mol
19.3g
6.79 x 10-23cm3
=6.013 x 1023 atoms/mole (pretty close)
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
From-http://dbhs.wvusd.k12.ca.us/webdocs/Mole/Origin-of-Mole.html
Real World Moles (wiki)
Given that the volume of a grain of sand is approximately 10-12 m3, and given that the area of the United States is
about 1013m2, 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 100×1012*6×109=6×1023, which is very close to one
mole.
Since the Earth has a radius of about 6400 km, its volume is approximately 1021 m3. 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 1028, which is over
17,000 moles.