The collision theory reaction rate coefficient for power-law distributions

Abstract

Abstract:The collision theory for power-law distributions and a generalized collision theory rate coefficient is studied when the reactions take place in nonequilibrium systems with power-law distributions. We obtain the power-law rate coefficient and by numerical analyses we show a very strong dependence of the rate coefficient on the power-law parameter. We find that the power-law collision theory can successfully overcome the two difficulties of Lindemann-Christiansen mechanism. We take three reactions as examples to calculate the pre-exponential factor and yield the values that can be exactly in agreement with those measured in the experimental studies.

Potential of Brass to Remove Inorganic Hg(II) from Aqueous Solution through Amalgamation

“…Again,~100% of Hg was removed from the aqueous phase after 120 minutes. Differences in initial sorption rates follow the principals of collision theory, originally developed by Trautz (1916) (for recent work in that field, see e.g., Yin and Du, 2014). The reaction between Hg and brass is a second-order reaction, as the concentrations of both reactants (Hg and Cu/Zn alloy) change, when Cu/Zn amalgam is formed (see eq 2).…”

The power-law reaction rate coefficient for barrierless reactions

“…It was shown that the power-law rate coefficient increases as the temperature increases and there are differences, but not very significant, for different ν-parameters about ν=1. Nevertheless, different from the power-law rate coefficients for the bimolecular reactions [26], the unimolecular reactions [27] and the collision theory [28], because there are not the barriers the power-law rate coefficient Eq. (19) for the barrierless reactions does not have the factor of power-law ν-distribution and thus it is not very strongly dependent on the ν-parameter, as compared with those for the bimolecular and unimolecular reactions, and the collision theory.…”

The Generalized Reaction Rate Theories in the Systems with Power-Law Distributions

“…More important, analysis of the collision phenomena plays a central role in almost all investigations of structures of matters on microscopic scale. As a first step of the generalization of the collision theory rate formula to the nonequilibrium system presenting non-Arrhenius behavior, a simple system involving two gases, A and B, whose molecules behave as hard spheres characterized by the impenetrable radii R A and R B , was considered [21]. The collision between A and B occurs when their centers approach within a distance d AB , such that d AB = R A + R B .…”

“…By using the nonextensive velocity distribution [22], the collision theory reaction rate for systems presenting non-Arrhenius behavior was derived, and the new collision theory can overcome the difficulties in the Lindemann-Christiansen mechanism. The collision theory reaction rate coefficient for the power-law distribution was derived by [21],…”