6
A. Theoretical and Instrumental Background
Summarizing, we have seen that the energy of isotopic substances
depends on the vibrational frequencies of the molecules, which in turn
depends on the masses of the atoms in the molecules.
III. Isotope Fractionation Processes
The partitioning of isotopes between two substances with different
isotope ratios is called isotope fractionation. The main phenomena
producing isotope fractionation are:
1) isotope exchange reactions
2) kinetic processes, mainly depending on differences III reaction
rates of isotopic molecules;
3) fractionations due to other physico-chemical effects.
1) Isotope exchange includes processes with very different
mechanisms. In the following, the term "isotope exchange" is used for
all processes in which ordinary changes in the chemical system do not
occur, but in which the isotope distribution changes between different
chemical substances, between different phases, or between individual
molecules.
Let us consider a typical exchange reaction, an equilibrium process,
which may be written as
aAl +bB2~aA2 +bB1
where A and B are molecules having any element as a common
constituent. The subscripts 1 and 2 indicate that the molecules contain
only the light or heavy molecule, respectively. Using statistical mechanics,
the equilibrium constant K may be expressed in terms of the partition
functions Q.
K= Q A 2/ QB2 .
QAI
QBI
This means that the equilibrium constant K is the quotient of two
partition function ratios, one for the two molecules of A, and one for B;
in other words, a calculation of the partition functions allows the calculation of equilibrium constants for chemical reactions. The partition
function Q of a molecule is defined by
Q = L g;; EnikT
where the summation extends over all the allowed energy levels En of the
molecules and gn is the statistical weight of the nth level En. BIGELEISEN
and MAYER (1947) and UREY (1947) have demonstrated that, for the
calculation of partition function ratios of isotopic molecules (except