Michael Edmiston wrote:
>
> .... multiplying these percentages by the masses
> and summing,
> we get the average atomic mass of natural oxygen as:
>
> 15.99941
>
> and this is the number I find on my periodic table.
>
> If we figure the molecular mass of O2 by
> simply doubling this number, we get:
>
> 31.99881
>
> .... If we do the statistics [for the various flavors
> of O2 molecule] we actually get:
>
> 31.99881
>
> which is the same number as obtained by simply
> doubling the average atomic mass found on
> the periodic table.
>
> Think about this for a minute.
I don't think I need to think about it for very long.
The result has got nothing to do with statistics; the
statistical calculation could be not quite right (and
indeed *is* not quite right) and the same result still
holds. There's a sum rule in action here. The physical
principle here is that in chemical reactions,
_mass is conserved_ to a very high degree of precision.
Starting from that principle, the rest is just arithmetic.
Averaging is a linear operation. Finding the mass of a
molecule by summing the mass of the constituents is a
linear operation. As my friend Yann once said to me:
"They're both linear. I suspect they commute."
(As to why I needed to be told that, readers can use
their imagination.)
> Chemists [have] been
> doing it right. The atomic masses on the periodic table
> are the weighted averages (weighted by natural abundance)
> of the atomic masses (not mass numbers) of the naturally
> occurring isotopes of the elements. It is specifically done
> this way to allow us to find average natural molecular
> masses by simply adding the atomic masses listed
> in the periodic table.
Well, some chemists sometimes do it right. But meanwhile it
is also true that there are some tremendous misconceptions
running around.
1) Perhaps the mother of all conceptions in this area is
the notion that there is any such thing as "THE" natural
abundance.
In particular, for years there were two different scales
for measuring atomic mass, a "chemical" scale based on the
so-called natural mixture of oxygen isotopes, and a
"physical" scale based on 16O. Some people kept on using
the former for years past the point where it was clear
that place-to-place variations in "THE" natural abundance
made the scale irreproducible and self-inconsistent. An
complicated political process led to replacing both scales
with the current 12C scale in 1961.
Reference: Encyclopedia B.
2a) Also, we ought not assume that the reagent-grade stuff
in the stock bottle conforms to the "NATURAL" abundance.
For one example, it turns out that for very scary reasons,
certain parties have on hand a lot of lithium enriched in
7Li (or, more to the point, significantly depleted in 6Li).
They got the bright idea that they would sell it in the
reagent market. Your typical periodic table quotes the
natural atomic mass of lithium with a precision of 0.002,
which is already markedly worse precision than for other
common elements ... but even so you can get "reagent" lithium
that is outside those error bars by a factor of 10 or 20,
resulting in relative errors on the order of half a percent
or so!
2b) Even leaving aside cases where the abundance has been
willfully doctored, there are industrial processes that
unintentionally fractionate the isotopes ... for example
the nitrogen in synthetic fertilizers is waaay outside
the error bars for the "natural" abundance.
2c) Even leaving aside all human intervention, there are
natural processes that fractionate chromium and thallium
waaay outside the "official" error bars.