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Avogadro's number (NA) is the number of particles (atoms, molecules, or ions) in
a mole. Avogadro's number is approximately
6.022 × 1023 particles per mole of any substance.
This physical constant is named after the early 19th century Italian scientist Amedeo Avogadro. It appears that Jean
Baptiste Perrin was the first to name it. Perrin called it "Avogadro's constant" and it is still sometimes known by that
name. The numerical value was first calculated by Johann
Josef Loschmidt in 1865 using the kinetic gas theory. In the German language countries
the number is still sometimes referred to as Loschmidt's number.
Definition
Avogadro's number is formally defined as the number of carbon-12 atoms in 0.012 kg of carbon-12. Historically, carbon-12 was chosen as the reference substance
because its atomic weight could be measured particularly accurately.
Avogadro's number can be applied to any substance. It corresponds to the number of atoms or molecules needed to make up a mass
equal to the substance's atomic or molecular weight, in grams. For example, the atomic weight of iron is 55.847 amu, so Avogadro's
number of iron atoms (i.e. one mole of iron atoms) have a mass of 55.847 g. Conversely, 55.847 g of iron contains
Avogadro's number of iron atoms. Thus Avogadro's number also corresponds to the conversion factor between grams (g) and atomic mass units:
-
Numerical value
At present it is not technologically feasible to count the exact number of atoms in 0.012 kg of carbon-12, so the precise
value of Avogadro's number is unknown. The 1998 CODATA recommended value for Avogadro's
number is
-
where the number in parenthesis represents the one standard
deviation uncertainty in the last digits of the value.
A number of methods can be used to measure Avogadro's number. One modern method is to calculate Avogadro's number from the
density of a crystal, the relative atomic mass, and the unit cell length determined from x-ray crystallography. Very accurate
values of these quantities for silicon have been measured at the National Institute of Standards and Technology (NIST) and used to
obtain the value of Avogadro's number.
Connection to mass of protons and neutrons
A carbon-12 atom consists of 6 protons and 6 neutrons (which have approximately the same mass) and 6 electrons
(whose mass is negligible in comparison). One could therefore think that NA is the number of protons or
neutrons that have a mass of 1 gram. While this is approximately correct, the mass of a free proton is 1.00727 amu, so a mole of
protons would actually have a mass of 1.00727 g. Similarly, a mole of neutrons has a mass of 1.00866 g. Clearly, 6 moles of
protons combined with six moles of neutrons would have a mass greater than 12 g. So, you might ask how one mole of carbon-12
atoms, which should consist of 6 moles each of protons, neutrons, and electrons could possibly have a mass of only 12 g? What
happened to the excess mass? The answer is related to the equivalence of matter and energy discovered by Albert Einstein as part of the theory of
special relativity. When an atom is formed, the protons and
neutrons in the nucleus are bound together by the strong
nuclear force. This binding results in the formation of a low energy state and is accompanied by a large release of energy.
Since energy is equivalent to mass, the released energy corresponds to a loss in the mass of the nucleus relative to that of the
separated protons and neutrons. Thus, protons and neutrons in the nucleus have masses that are less (about 0.7 percent less) than
free protons and neutrons. The precise amount of mass loss is related to the binding energy of the nucleus and varies depending
on the type of atom.
One may therefore say that NA is approximately the number of nuclear neutrons or protons that
have a mass of 1 gram. This is approximate because the precise mass of a nuclear proton or neutron depends on the composition of
the nucleus.
Avogadro's number in life
Avogadro's number often yields practical reasonings in real life. For example, the fact that a finite number of atoms are in a given amount of a substance is one reason for scientific criticism of homeopathy, in which medicinal substances are often diluted to the extent that
Avogadro's number would imply that less than a single molecule remains.
See also
Further Reading
- Journal of Physical and Chemical Reference Data, 28 (1999) 1713.
External links
- Some Notes on Avogadro's Number, 6.022 x 1023
(historical
notes)
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