Two
equivalent definitions of Avogadro number
A
possible definition of the kilogram
By Cesare Curti
Two definitions are equivalent when from the
first it comes down the second and vice versa We will demonstrate that the two following
definitions: 1)
Avogadro
number is the number of atoms contained in 12 g of ^{12}C 2)
Avogadro
number is the equivalent in dalton of the gram are equivalent. 
Used symbols 



Avogadro number 
N 
dalton kilodalton 
u Ku 
gram kilogram 
g Kg 
carbon 12 
^{12}C 


In Avogadro number,
dalton and gram, after to have defined the Avogadro number like the number
of atoms of ^{12}C contained in 12 grams of ^{12}C, we have
demonstrated that Avogadro number has also the meant one of equivalent in
dalton of the gram.
Now, inversely, we will define the number of
Avogadro as the equivalent in dalton of the gram and demonstrate that it has
also the meant one of number of atoms of ^{12}C contained in 12 grams
of ^{12}C.
In other words given the two following
definitions:
1)
The
dalton is the twelfth part of the mass of an atom of ^{12}C
2)
Avogadro
number is the equivalent in dalton of the gram
it is easy to demonstrate that the Avogadro
number is also the number of atom of ^{12}C contained in 12 grams of ^{12}C.
It can be reasoned in the following way: 1 gram is equivalent to N dalton, 2 grams
are equivalent to 2N dalton,.., 12 grams are equivalent to 12N dalton. It can therefore be written:
12 g of atoms of ^{12}C = 12 N u of
atoms of ^{12}C
Since 12
dalton they are the mass of an atom of ^{12}C, Avogadro number must
necessarily be the number of atoms of ^{12}C contained in 12 g of ^{12}C
The
two definitions:
Avogadro number is the number of atoms
contained in 12 g of ^{12}C
and
Avogadro number is the equivalent in dalton of
the gram
they
are therefore equivalents.
If the
Avogadro number is defined like the equivalent in dalton of the gram, we
can write:
1 g = N u
and
immediately we can write also:
1Kg = N Ku
This last
relation could become a new definition of the kilogram, independent from the standard
of Sèvres and having a character of
generality similar to that one of the definitions of meter and second adopted
in the International System.
The National Institute of Standard and Technology (NIST) is exploring the possibility to define the kilogram by means of the constant of Avogadro. [1]
Bologna,
sabato 10 febbraio 2001 (tradotto in inglese giovedì 1 marzo 2001)
Revised
2/2003