Units of measure of atomic, molecular and molar masses. Demonstration of a significant equality between two units of measure:

n daltons/atom = n grams/mole

otherwise:

n daltons/molecule = n grams/mole

 

by Cesare Curti

 

 

 

 

We demonstrate the following equality

 

                1 dalton  x elementary entity-1  = 1 gram x mole-1

 

In other words we demonstrate that the two units of measure “dalton x natural unit-1” e “gram x mole-1” they are only nominally different.

“Natural unit” is synonymous with “elementary entity”

 

 

 

                                    Used symbols

 

 

 

Avogadro number……………………………

N

dalton  ……………………………………….

kilodalton …………………………………..

u

Ku

gram ……………………………………........

kilogram …………………………………….

g

Kg

mole …………………………………………

kilomole …………………………………….

natural unit (or elementary entity) of amount of substance

1000 ee ………………………………………                                  

mol

Kmol

ee

Kee

 

 

 

 

The molar masses are usually measured in g mol-1 or Kg Kmol-1. The atomic masses can be measured in dalton atom-1: if it is a question of the mass of one isotope, is necessary to specify its own mass number. If the mass number is not specified it can be understood that the atomic mass is the average atomic mass. Analogous the molecular masses can be expressed in dalton molecule-1. In more generalized manner, the mass of a natural unit of amount of substance (atom, aggregate of atoms or of other elementary entity) can be measured in u ee-1 or Ku Kee-1.

Using two of already enunciated definitions (under repeated) of Avogadro number, can easy be demonstrated the following equality:

 

1 dalton x natural unit-1  = 1 gram x mole-1

or, using the symbols:

1 u ee-1 = 1 g mol-1

 

For the demonstration it can be proceeded in the following way:

 

1)      In Avogadro number, dalton and gram we have demonstrated that the number of Avogadro is the equivalent in dalton of the gram  (N u g-1)

2)      In Amount of substance and its unit of measure. A third definition of the Avogadro number we have defined the Avogadro number like the equivalent, in natural units of substance amount, of the mole (N ee mol-1)

 

We multiply 1 (dalton x natural unit -1)  for N (natural units x mole-1)  and divide for N (dalton x gram-1) :

 

 

1 u ee-1  = 1 u ee-1  N ee mol-1  N-1 u-1 g

 

Becoming simpler:

 

1 u ee-1 = 1 g mol-1

 

It can therefore be concluded that the two units of measure u ee-1  and g mol-1  are only nominally different.

 


 

Questions and answers

 

Question: the atomic mass of the argon is 39.948 u atom-1 ; calculate the molar  mass of the argon in g mol-1

Answer:  the atomic mass of the argon is 39.948 u atom-1 N atom mol-1  N-1  u-1  g = 39.948 g mol-1

 

Question:  the molecular mass of the water is 18.005 u molecule-1; calculate the molar mass of the water in g mol-1.

Answer:   the molar mass of the water is  18.005 u molecule-1  N molecule mol-1  N-1  u-1  g = 18.005 g mol-1

 

Question:  the molar mass of the ethanol is 46.069  g mol-1; calculate the molecular mass of the ethanol in u molecule-1

Answer:  the molecular mass of the ethanol is 46.069 g mol-1 N u g-1  N-1 mol molecule-1 = 46.069 u molecule-1

 

Question: the mass of one natural unit of sodium chloride  is 58.443 u ee-1 ; calculate the molar mass of sodium chloride in g mol-1

Answer: the molar mass of  sodium chloride  is  58.443 u ee-1  N ee mol-1  N-1 u-1 g  =  58.443 g mol-1

 


Bologna, sabato 5 maggio 2001

 

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