Showing papers on "Mass action law published in 2010"

The Michaelis-Menten-Stueckelberg Theorem

Abstract: We study chemical reactions with complex mechanisms under two assumptions: (i) intermediates are present in small amounts (this is the quasi-steady-state hypothesis or QSS) and (ii) they are in equilibrium relations with substrates (this is the quasiequilibrium hypothesis or QE). Under these assumptions, we prove the generalized mass action law together with the basic relations between kinetic factors, which are sufficient for the positivity of the entropy production but hold even without microreversibility, when the detailed balance is not applicable. Even though QE and QSS produce useful approximations by themselves, only the combination of these assumptions can render the possibility beyond the "rarefied gas" limit or the "molecular chaos" hypotheses. We do not use any a priori form of the kinetic law for the chemical reactions and describe their equilibria by thermodynamic relations. The transformations of the intermediate compounds can be described by the Markov kinetics because of their low density ({\em low density of elementary events}). This combination of assumptions was introduced by Michaelis and Menten in 1913. In 1952, Stueckelberg used the same assumptions for the gas kinetics and produced the remarkable semi-detailed balance relations between collision rates in the Boltzmann equation that are weaker than the detailed balance conditions but are still sufficient for the Boltzmann $H$-theorem to be valid. Our results are obtained within the Michaelis-Menten-Stueckelbeg conceptual framework.

Ion Exchange Equilibrium Prediction for the System Cu2+−Zn2+−Na+

Abstract: In this work, ion exchange experimental data were obtained in batch operation for the binary systems Cu2+−Na+, Zn2+−Na+, and Zn2+−Cu2+ and for the ternary system Cu2+−Zn2+−Na+. The ionic exchanger employed was the cationic resin Amberlite IR 120. The experimental data for the binary systems and the ternary system were obtained at total concentrations of (1, 3, and 5) mEq·L−1. The total exchange capacity of the Amberlite IR 120 resin was obtained by the column technique. All experiments were carried out at 25 °C. To model the ion exchange equilibrium, the Mass Action Law was used. The model considered both ideal and nonideal behavior to represent the experimental data. The nonideality in the solution phase and in the resin phase was described by Bromley’s model and by Wilson’s model. Wilson’s model interaction parameters and the thermodynamic equilibrium constants were obtained from the experimental data for each binary system, from which ternary system ion exchange equilibrium was predicted. On the basis ...

A thermodynamic model of calculating mass action concentrations for structural units or ion couples in NaClO4-H2O and NaF-H2O binary solutions and NaClO4-NaF-H2O ternary solution

Abstract: A thermodynamic model of calculating mass action concentrations for structural units or ion couples in NaClO4-H2O and NaF-H2O binary solutions and NaClO4-NaF-H2O ternary strong electrolyte aqueous solutions was developed based on the ion and molecule coexistence theory (IMCT). A transformation coefficient was needed to compare the calculated mass action concentration and the reported activity, because they were usually obtained at different standard states and concentration units. The results show that transformation coefficients between the calculated mass action concentrations and the reported activities of the same components change in a very narrow range. The transformed mass action concentrations of structural units or ion couples in NaClO4-H2O and NaF-H2O binary solutions agree well with the reported activities. The transformed mass action concentrations of structural units or ion couples in NaClO4-NaF-H2O ternary solution are also in good agreement with the reported activities in a total ionic strength range from 0.1 to 0.9 mol/kg H2O by the 0.1 mol/kg step with different ionic strength fractions of 0, 0.2, 0.4, 0.5, 0.6, 0.8, and 1, respectively. The results indicate that the developed thermodynamic model can reveal the structural characteristics of binary and ternary strong electrolyte aqueous solutions, and the calculated mass action concentrations of structural units or ion couples also strictly follow the mass action law.