Avogadro number, dalton and gram

 

by Cesare Curti

 

 

To transform daltons into grams is like to transform centimetres into meters.á Number 100 is the equivalent in centimetres of the meter just like Avogadro number is the equivalent in daltons of the gram

 

ááááá

ááááááá Used symbols

 

 

 

Avogadro number

á N

dalton

á u

gram

á g

carbon 12

12C

 

 

 

 

The masses of atoms commonly are expressed in atomic mass unit or dalton [1]. The dalton is defined in this way:á the dalton is the twelfth part of the mass of an atom of 12C

From this definition (later called definition 1) comes down immediately that the mass of an atom ofá 12C is 12 u.

 

More equivalent definitions of Avogadro number can be given.á One of they is following:á N is the number of atoms contained in 12 g of 12C

From this last definition (later called definition 2) it comes down immediately that 12 g of 12C contain N atoms.

 

Using the two previous definitions it is easy to demonstrate that 1 g is equivalent to N u.á It can be reasoned in this way:á 12 g of 12C contain N atoms of 12C (for definition 2) every one of which have a mass of 12 u (for the definition 1). It can therefore be written:

 

12 g of atoms of 12C = 12N u of atoms of 12C

 

The mass is independent from the species of the substances and simplifying:

 

1 g = N u

 

Therefore it has been demonstrated that the Avogadro number is the equivalent in dalton of the gram.á Consequently 1/N is the equivalent in grams of the dalton.

Gram and dalton are both mass measure unit and therefore the Avogadro number, like over defined, is a pure number or if one is preferred, non-dimensional properties. The National Institute of Standard and Technology (NIST) defines instead the Avogadro constant NA [2]:

 

NA = 6.022 141 99(47) 1023á mol-1

 

N and NA have the same numerical value, experimentally determinable by means of many independent ways.

Later on we will use:

 

N = 6.022 1023 u g-1

 


 

Questions and answers

 

Question:á twenty-five grams to how many daltons correspond?

Answer:áá twenty-five grams correspond toá 25 g N u g-1 = 25 gá 6.022á 1023 ug-1 = 1.506 1025 u

 

Question:á one million of daltons to how many grams correspond?

Answer:á one million of daltons correspond to 106 uá N-1 u-1gá = 106 uáá 6.022-1 á10-23 u-1gá = 1.661 10-18 g

 

Question:á which is the mass in grams of 1 atom of 12C?

Answer:á the mass in grams of a 12C atom isá 12 uá N-1 u-1gáá = 12 uáá 6.022-1 á10-23 u-1gá =á 1.993 10-23 g

 


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Bologna, giovedý 25 gennaio 2001

 

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