Page 38 - Radiochemistry and nuclear chemistry

Nuclei, Isotopes and Isotope Separation 27

factor is about 2.5. Bacteria behave similarly, with coli bacteria showing an enrichment
factor for deuterium of 3.9.
Inasmuch as some of the hydrogen atoms are not exchanged readily due to the inertness
of their chemical bonds, the isotopic fractionation which involves the easily exchangeable
hydrogen atoms in these biological processes must have even larger enrichment factors for
deuterium and tritium than their measured values would indicate.
The peculiarity of biological material to prefer certain isotopes has led to studies of how
biological material behaves in an isotopic environment which differs substantially from that
found in nature. Normally it is found that the organisms wither away and lose their ability
to reproduce. Carp cannot survive a higher D20 concentration than 30%, but, on the other
hand, some organisms show a strong growth, and some microorganisms have been found
to be able to live in pure D20 or H2180. It has been possible to raise mice with only 13C
in their organism (fed on 13C algae). Exchanging natural 14NH3 for 15NH3 seems to have
little effect on biological systems.
In all of these investigations it should be noted that even when we characterize an isotopic
effect as large, it is still quite small by normal reaction criteria except for hydrogen
isotopes. For all but the very lightest elements we can assume in most chemical experiments
that there is no isotope effect. This assumption forms a basis of the use of radioactive
tracers to study chemical systems.

2.7. Isotope effects in chemical kinetics

The reason why higher organisms cannot survive when all light hydrogen atoms are
replaced by deuterium is to be found not so much in a shift of chemical equilibria as in a
shift in reaction rate leading to a fatal lowering of the metabolic rate when light isotopes
are replaced by heavier.
In contrast to chemical equilibria, chemical reaction rates depend on the concentration of
the reactants and transition states but not on the product. The concentration of the transition
states depends on the activation energy for its formation and the frequency for its
decomposition into the products. These factors can be derived from the partition function
which, as mentioned above, differ slightly for molecules of different isotopic composition.
Let us consider the reaction

A + BC ~ AB + C (2.36)

The rate constant is given by the expression

d[A]/dt = k[A][BC] (2.37)
The reaction is assumed to take place over an intermediate compound ABC, usually denoted
ABC # where the # indicates a short-lived transition state. According to the transition state
theory, derived by H. Eyring, J. Biegeleisen, and others, it is assumed that the intermediate
complex undergoes internal vibrations, with such an energy E v that the bond is broken
along the vertical line in the complex ABIC, leading to the fragments AB and C. The rate
of reaction is the rate at which the complex ABC # decomposes into the products. It can