Note that thermal results are often
expressed in number of moles n
rather than numbers of molecules N.
This is especially true in chemistry and biology. Such applications replace
the Boltzmann constant k with the
ideal gas constant R as follows:
.
In particular, this defines the gas
constantin terms of Avogadroவmberso that. Verify that this gives a familiar value for R.
Both forms are used interchangeably
in this outline.
The
great advantage of the mole concept is that moles are a common denominator
for several important quantities including masses, numbers of molecules, gas
volumes, and coefficients in chemical reactions (stoichiometric
coefficients).
Here is the relation of mass to moles:
As an example, consider that we
have 36 g of water, .We find the
molecular mass by looking at a periodic table. The mass number, more often called the molecular weight, is used
for MW. We find the number 1.0 for
H and number 16.0 for O. The molecular mass is then . Substituting for n shows that we have 2 molesof water.
Expressing numbers of molecules N is easy when the number of moles is known,
.
Substituting from our example of 2 moles of water, we get molecules.
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. Verify that this gives a familiar value for R. 
.
. Substituting for n shows that we have 2 moles
