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