Chemistry Reference
In-Depth Information
time averages over these continuous variations. Sameness of molecular kind would
then presuppose a time scale appropriate to this averaging so that even from the
microscopic perspective, substance concepts don
t apply for arbitrarily short times.
But there are complications. According to this notion, methane is a paradigma-
tically symmetric molecule with a tetrahedral structure and no chiral features.
But there is a small but measurable dipole moment in the vibrational ground state
due to rotational motion, which reduces the molecular tetrahedral symmetry to axial
symmetry, as a result of which molecules rotating in the same sense as the electric
vector of light differ in polarisability from molecules rotating in the counter
direction. The difference is small, but not beyond the limits of measurement.
Consequently, “ordinary methane is properly regarded as optically inactive not
because of the intrinsic inactivity of the molecules but because it is an enantiomeric
mixture” (Atkins and Gomes
1976
, p. 519). The substance is not optically inactive
because the molecules are all the same, but because of the distribution of different
kinds of molecules. The perfect geometric structures captured by time averages
are not quite the structures of real molecules even for appropriately long intervals
of time.
The averaging process at issue in this last example brings to the fore the
significance of the amount of material. The notion of substance is a macroscopic
concept, applicable to macroscopic quantities. A microscopic criterion of sub-
stancehood would be one applicable to a sufficiently large collection of
microentities. Mislow and Bickart (
1977
), p. 2 characterise “ensembles of achiral
molecules [whose properties] result from statistical cancellations of local chiral
effects” as stochastically achiral, and go on to extend the notion to include systems
at equilibrium consisting of chiral molecules which rapidly enantiomerise on the
time scale of observation. Above -230
C, for example, the distinction between
the two gauche conformations of butane is lost when thermal motion is sufficient to
overcome rotational barriers and the enantiomers interconvert, but below this
temperature the conformers apparently constitute two different substances.
Absence of measurable chirality doesn
'
t, however, imply stochastic achirality.
Quoting from a 1932 article of W. H. Mills, Mislow and Bickart (
1977
), p. 3 note
that “when 10,000,000 dissymmetric molecules are produced under conditions
which favour neither enantiomorph, there is an even chance that the product will
contain an excess of more than 0.021 % of one enantiomorph or the other.
It is practically impossible for the product to be absolutely optically inactive”.
Moreover, as percentage excess decreases with increasing size of sample, the
number of molecules in excess increases and along with it the probability of
obtaining a strictly racemic sample decreases. Such deviations from achirality
may be beyond the powers of our observational resources, but their occurrence is
ubiquitous. Thus, the actual molecular composition of macroscopic quantities of
matter may be complex, depriving us of a simple rule relating number of substances
and molecular structure. An apparently optically inactive mixture needn
'
tbea
50:50 mixture of corresponding enantiomers, and a 50:50 mixture of corresponding
enantiomers might be a single substance, not two.
'
