Mass action law

About: Mass action law is a research topic. Over the lifetime, 168 publications have been published within this topic receiving 2684 citations.

Mass Transfer Mechanism of Ion Exchange in Fixed Bed Columns

Abstract: In this work, the binary ion exchange of Zn2+−Na+ ions has been studied by a column technique using a NaY zeolite as the cation exchanger. The experimental data (breakthrough curves) for the binary system were obtained at total concentrations of (1, 2, and 3) meq·L−1. The mass action law was used to represent the ion exchange equilibrium. To represent the ion exchange in the column, two models were used. In the first model, the rate-controlling step of mass transfer was considered only in the solid phase. The experimental results were represented by a Linear Driving Force (LDF) model. In the second model, resistance to mass transfer in series in the solid phase and the external liquid film was considered. Both models described ion exchange in the fixed-bed column properly. However, in the initial part of the breakthrough curve, the dual resistance model fit better.

The widespread applicability of the mass action law to metallurgical melts and organic solutions

Abstract: With the mass action law as the dominant principle, general models of mass action concentrations have been formulated by using measured activities as practical basis and criterion, and using phase diagrams, the coexistence theory of metallic melts (atoms and molecules), the coexistence theory of slag melts (molecules and ions), the model of inseparable cations and anions of molten salts and mattes, and the all molecule model of some organic solutions as the scientific basis for determination of the structural units of each solution. Calculated mass action concentrations for the above-mentioned five solutions (over the whole composition range without any application of the activity coefficient) agree well with measured activities of corresponding solutions, this in turn shows that the mass action law has its widespread applicability to metallurgical melts and organic solutions.

Investigation of Extraction of 4-Oxopentanoic Acid by N,N-Dioctyloctan-1-amine in Six Different Diluents: Equilibrium Study

Abstract: The present equilibrium study deals with the reactive extraction of 4-oxopentanoic acid [levulinic acid] from an aqueous solution by N,N-dioctyloctan-1-amine [tri-n-octylamine (TOA)] at a constant concentration of 0.573 kmol·m–3 in a wide range of diluents such as [n-decane, decane-1-ol, n-decane + decane-1-ol (1:1 v/v), toluene, 4-methylpentan-2-one (MIBK), and dichloromethane (DCM)] at isothermal conditions ((298 ± 1) K). The physical extraction of levulinic acid with pure diluents is also carried out. The effect of acid concentration (0.10 mol·kg–1 to 0.75 mol·kg–1) and type of diluent on the recovery of levulinic acid from aqueous solution are determined. Mathematical modeling based on mass action law is used to estimate overall equilibrium constants (KE), stoichiometry of reaction, and individual equilibrium constants (K11 and K21) for 1:1 and 2:1 complexes between acid and TOA. Further, the experimentally determined distribution coefficients (KD) are correlated predicted ones by the linear solvation...

Prediction of the critical reduced electric field strength for carbon dioxide and its mixtures with copper vapor from Boltzmann analysis for a gas temperature range of 300 K to 4000 K at 0.4 MPa

Abstract: The influence of copper vapor mixed in hot CO2 on dielectric breakdown properties of gas mixture at a fixed pressure of 0.4 MPa for a temperature range of 300 K–4000 K is numerically analyzed. First, the equilibrium composition of hot CO2 with different copper fractions is calculated using a method based on mass action law. The next stage is devoted to computing the electron energy distribution functions (EEDF) by solving the two-term Boltzmann equation. The reduced ionization coefficient, the reduced attachment coefficient, and the reduced effective ionization coefficient are then obtained based on the EEDF. Finally, the critical reduced electric field (E/N)cr is obtained. The results indicate that an increasing mole fraction of copper markedly reduces (E/N)cr of the CO2–Cu gas mixtures because of copper's low ionization potential and large ionization cross section. Additionally, the generation of O2 from the thermal dissociation of CO2 contributes to the increase of (E/N)cr of CO2–Cu hot gas mixtures fr...

Fluctuations and mass action law breakdown in statistical thermodynamics of small systems

Abstract: The statistical equilibrium of chemical reaction of the type PQ⇄P+Q, taking place within small but macroscopic closed vesicle, is considered using statistical physics approach. It is shown, that mass action law, being the result of mean‐field‐type approximation, breaks down for sufficiently small vesicle volume and/or equilibrium constant of reaction, when mean number of free ‘‘P’’ particles, 〈p〉, within the vesicle becomes of order one or less. At the same time, the Nernst equation is shown to be applicable for systems of arbitrary volume and it gives the relation ΔF∼−ln〈p〉 for free energy ‘‘payment’’ for one ‘‘P’’ particle liberation from the vesicle. Due to fluctuations the true 〈p〉 and (−ΔF) values are essentially lower than corresponding mass action law predictions. The same effect of fluctuations leads to essential random inhomogeneity in the ensemble of vesicles, prepared under equivalent macroscopic conditions, and to non‐Gaussian distributions of these vesicles over total number of particles with...