Re: Fundamental physical properties

[David Bowman <dbowman@tiger.gtc.georgetown.ky.us>]

Joe Darling wrote:
> The mole seems to be a reflection of having defined the kilogram, and
> hence the gram, and then finding that there are Avogadro's number of
> carbon-12 atoms in 12 g of carbon-12 atom's.  It is a fundamental constant
> of nature, but related to the definition of the unit of mass.

and Roger Pruitt responded with:
> It seems to me that the simplest definition of the mole is that it is
> Avogadro's number of anything. A mole of carbon-12 atoms thus has a mass of
> 12 grams. A mole of oxygen molecules occupies a volume of 22.4 liters at
> STP. Chemists make the definition of a mole hard by defining it in terms of
> mass on one page and volume of gases on another, etc. The common denominator
> is that a mole is a count of something in the same way that a pair, a dozen
> and a gross are counts.

I think Joe is closer to the essence here.  Although Roger is correct that
Avagadro's number is a big positive integer it is clear that the value of
that big counting number crucially depends on the ratio of the mass of the
standard kilogram to the mass of a C-12 atom.  Thus Joe is correct that a
mole is "a reflection of having defined the kilogram".  Avagadro's number is
a peculiar number in that it is a dimensionless number whose value is
determined by a standard maintained unit (which has dimensions of mass.)
If a redefinition of the kilogram was made tomorrow because a new modernized
standard definition was agreed upon, and the precise size of the kilogram
changed somewhat because of this redefinition, it is clear that Avagadro's
number *would* change accordingly.  Pure numbers like pi, 4 and a dozen do
not have this property.

I disagree with Joe's last statement above though.  I do not consider that
there is anything fundamental about a mole. When I get a longer stretch of
uncommitted time later I would like to expand on this and to respond to the
rest of Joe's post in this issue.  Stay tuned.

David Bowman
dbowman@gtc.georgetown.ky.us