8
A. Theoretical and Instrumental Background
Qualitatively, many observed deviations from the simple equilibrium
processes can be interpreted as consequences of the various isotopic
components having different rates of reaction.
Isotope fractionation measurements taken during irreversible
chemical reactions always show a preferential enrichment of the lighter
isotope in the products of the-reaction. The nature of this fractionation
stems from the lower ground-state vibration frequency of the heavy
isotope. Hence, more energy is required to destroy a molecule bearing
the heavy isotope.
The transition-state theory provides the framework for any theory
of kinetic isotope effects. This theory is based on the idea that a chemical
reaction proceeds from some initial state to a final configuration by a
continuous change and that there is some critical intermediate configuration called the activated complex or transition state.
It is further assumed that there is a small number of activated molecules in equilibrium with the reacting species and that the rate of reaction
is controlled by the rate of decomposition of the activated species.
The isotope fractionation introduced in the course of a unidirectional
reaction may be considered in terms of the ratio of rate constants for the
isotopic substances.
For the two competing isotopic reactions
K,
d
K2
Al-----+Bl an
A2-----+B2
the ratio of rate constants, KdK2' for the reaction of light and heavy
isotopic species is expressed, as in the case of equilibrium constants, in
terms of two partition function ratios, one for the two isotopic reactants
species, and one for the two isotopic species of the activated complex
(for a more detailed discussion see MELANDER, 1960).
The third class of processes that can lead to isotope fractionation are
also due to physico-chemical effects. To this category belong the following
phenomena: Evaporation and condensation, crystallization and melting,
absorption and desorption, diffusion and thermodiffusion. Of special
interest in stable isotope geochemistry are the evaporation-condensation
processes. Some of these phenomena are not necessarily different from (1)
and (2) and could be also discussed there.
Differences in the vapor pressures of isotopic compounds lead to
fractionations. For example, from the vapor pressure data for water it is
evident that the lighter molecular species are preferentially enriched in
the vapor phase, the extent depending upon the temperature. Such an
isotopic separative process has been treated theoretically in terms of
batch distillation of a liquid under equilibrium conditions (Rayleigh
distillation). Any isotopic reaction carried out in such a way that the
products are isolated immediately after formation from the reactants will
A. Theoretical and Instrumental Background
Qualitatively, many observed deviations from the simple equilibrium
processes can be interpreted as consequences of the various isotopic
components having different rates of reaction.
Isotope fractionation measurements taken during irreversible
chemical reactions always show a preferential enrichment of the lighter
isotope in the products of the-reaction. The nature of this fractionation
stems from the lower ground-state vibration frequency of the heavy
isotope. Hence, more energy is required to destroy a molecule bearing
the heavy isotope.
The transition-state theory provides the framework for any theory
of kinetic isotope effects. This theory is based on the idea that a chemical
reaction proceeds from some initial state to a final configuration by a
continuous change and that there is some critical intermediate configuration called the activated complex or transition state.
It is further assumed that there is a small number of activated molecules in equilibrium with the reacting species and that the rate of reaction
is controlled by the rate of decomposition of the activated species.
The isotope fractionation introduced in the course of a unidirectional
reaction may be considered in terms of the ratio of rate constants for the
isotopic substances.
For the two competing isotopic reactions
K,
d
K2
Al-----+Bl an
A2-----+B2
the ratio of rate constants, KdK2' for the reaction of light and heavy
isotopic species is expressed, as in the case of equilibrium constants, in
terms of two partition function ratios, one for the two isotopic reactants
species, and one for the two isotopic species of the activated complex
(for a more detailed discussion see MELANDER, 1960).
The third class of processes that can lead to isotope fractionation are
also due to physico-chemical effects. To this category belong the following
phenomena: Evaporation and condensation, crystallization and melting,
absorption and desorption, diffusion and thermodiffusion. Of special
interest in stable isotope geochemistry are the evaporation-condensation
processes. Some of these phenomena are not necessarily different from (1)
and (2) and could be also discussed there.
Differences in the vapor pressures of isotopic compounds lead to
fractionations. For example, from the vapor pressure data for water it is
evident that the lighter molecular species are preferentially enriched in
the vapor phase, the extent depending upon the temperature. Such an
isotopic separative process has been treated theoretically in terms of
batch distillation of a liquid under equilibrium conditions (Rayleigh
distillation). Any isotopic reaction carried out in such a way that the
products are isolated immediately after formation from the reactants will