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 12C

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

12C

 

 

 

 

In Avogadro number, dalton and gram, after to have defined the Avogadro number like the number of atoms of 12C contained in 12 grams of 12C, 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 12C contained in 12 grams of 12C.

 

In other words given the two following definitions:

 

1)     The dalton is the twelfth part of the mass of an atom of 12C

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 12C contained in 12 grams of 12C.

 

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 12C = 12 N u of atoms of 12C

 

Since 12 dalton they are the mass of an atom of 12C, Avogadro number must necessarily be the number of atoms of 12C contained in 12 g of 12C

 

The two definitions:

      Avogadro number is the number of atoms contained in 12 g of 12C

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

 

HOME