Nonequilibrium Fractionation and Isotopic Transport

At the Earth’s surface, isotopic disequilibrium is far more common than isotopic equilibrium. Although isotopic equilibrium is approached in certain instances, numerous constituents of the lithosphere, hydrosphere, atmosphere, and biosphere are simply not in mutual isotopic equilibrium. This condition is consistent with the complex and dynamic conditions typical of the Earth’s surface, particularly the large material fluxes, the rapid changes in temperature, and the biological mediation of chemical systems. Fortunately, several aspects of isotopic disequilibrium may be understood in terms of elementary physical laws. For homogeneous phases such as gases or well-stirred liquids, or for cases where spatial gradients in isotopic contents are not of primary interest, then the principles of elementary kinetics can be applied. For cases where isotopic gradients are important, the laws of diffusion are applicable. If two phases are out of isotopic equilibrium, they will progressively tend to approach the equilibrium state with the passage of time. This phenomenon occurs by the process of isotopic exchange, and its rate may be understood by examining isotopic exchange reactions from the viewpoint of elementary kinetic theory. In particular, consider the generalized exchange reaction where A and B are two phases that share a common major element, and A* and B* represent the same phases in which the trace isotope of that element is present. The present analysis is simplified if the exchange reaction is written so that only one atom is exchanged, in which case the stoichiometric coefficients are all unity. For reaction 4.1, kinetic principles assert that the forward and reverse reactions do not, in general, proceed at identical rates, but rather at the rates indicated by the quantities kα and k written by the arrows, multiplied by the appropriate concentrations terms. Assuming that the reaction is first order, then the reaction progress, represented by the quantity dA*/dt, may be expressed by the difference between these forward and reverse rates, as follows: . . . dA*/dt = kα(A)(B*) − k(A*)(B) (4.2) . . . In order to evaluate the exchange process more completely, is important to carefully chose a consistent set of concentrations for substitution equation 4.2.