Showing papers on "Mass action law published in 1997"

Nonstoichiometry of Ce0.8Gd0.2 O 1.9 − x

Abstract: Oxygen nonstoichiometry of Ce{sub 0.8}Gd{sub 0.2}O{sub 1.9{minus}x} was gravimetrically measured at temperatures from 700 to 1,000 C and oxygen partial pressures between 10{sup {minus}24} and 1 atm. Based on the experimental data, the relationship between log x and log p{sub O{sub 2}}, (where x is the oxygen deficiency and p{sub O{sub 2}} the oxygen partial pressure) is discussed and partial molar enthalpy, {Delta}{bar H}{sub O}, and entropy, {Delta}{bar S}{sub O}, of oxygen are calculated. In the region of x {le} 0.04, x is proportional to the {minus}1/4 power of p{sub O{sub 2}} and {Delta}{bar H}{sub O}, and {Delta}{bar S}{sub O}, behave as in an ideal solution, showing that oxygen vacancies are doubly charged and defects in Ce{sub 0.8}Gd{sub 0.2}O{sub 1.9{minus}x} are randomly distributed. Thus, the mass action law is satisfied in the area x {le} 0.04.

Effects of Mass Action Equilibria on Fixed-Bed Multicomponent Ion-Exchange Dynamics

Abstract: A generalized parallel pore and surface diffusion model and associated dynamic simulation program have been developed for multicomponent fixed-bed ion-exchange processes. Both equilibrium and nonequilibrium mass action laws are used to describe stoichiometric ion exchange. Model equations are solved numerically for frontal, pulse, or sequential loading processes. Analytical solutions obtained from a local equilibrium theory for binary systems and experimental data of two multicomponent systems served as benchmarks for the numerical solutions. The results indicate that the parallel pore and surface diffusion model should be considered for nonlinear large-particle systems. A parametric study shows that a major difference in fixed-bed dynamics between mass action and Langmuir systems lies in the propagation of diffuse waves of multivalent ions. Generally, the higher the valence or mass action equilibrium constant, the more pronounced the tailing of diffuse waves, which results in apparent adsorption hysteres...

Mass transfer based on chemical potential theory: ZnSO4/H2SO4/D2EHPA

Abstract: A fundamental model based on chemical reaction kinetics and diffusional mass transfer for the extraction of zinc sulfate with di(2-ethyhexyl) phosphoric acid (D2EHPA) in n-heptane at 250 C was developed. Gradients of the chemical potential were used as the driving force for diffusion. Activity coefficients and their derivatives were calculated from the Pitzer equation in the aqueous phase, while the organic non-ideality was considered by the Hildebrand–Scott treatment. The Nerst–Planck equation was chosen for describing the diffusion of aqueous ions, paying special care to the formation of hydrogen sulfate. It was assumed that this fast ionic reaction can be described in terms of the mass action law in the bulk and film. For the multicomponent mass transfer of the organic species, the Maxwell–Stefan theory was adopted. A kinetic equation for the extraction of zinc with D2EHPA, which considers the adsorption of the D2EHPA molecules at the interface based on the Langmuir law, was suitable for our experimental data. Organic zinc concentration vs. time was obtained in a type of Lewis cell with vibrational mixing. Molar fluxes were calculated by fitting it with rational functions, which were analytically differentiated. Initial conditions of the experiments cover a wide range of the zinc (0.1 mM to 0.05 M), D2EHPA, and sulfuric acid concentration. Experimental fluxes could be well described by this model when chemical kinetics and mass transfer were considered. In particular, the resistance to mass transfer in the organic film is important.

Comparison between gibbs free energy minimization and mass action law for a multitemperature plasma with application to nitrogen

Abstract: This paper gives all the necessary physical equations to determine the composition and the thermodynamic properties in a multitemperature plasma utilizing two different methods: the first method is based on Gibbs free energy minimization and the second is based on the resolution of the mass action law. The lowering terms of the ionization potential and thermodynamic properties are given for a multitemperature plasma using the Debye-Huckel approximation. Numerical application is made to a nitrogen plasma.

Temperature dependence of luminescence spectra related to free carrier and exciton recombination in GaAs quantum wells

Abstract: We measure luminescence spectra in high quality GaAs quantum wells in the temperature range of 8 K to 290 K using photon counting techniques. Using these and a lineshape analysis of the spectra, we determine the spectrally integrated luminescence due to free electron-hole pairs and heavy and light hole excitons as a function of temperature. We obtain the temperature dependence of the first subband edge and the binding energies and linewidths of the heavy and light hole excitons. We compare the results with the theoretically expected behaviour. Also, we obtain a generalized relationship between free carrier and exciton densities and find conditions under which this reduces to the 2D mass action law often used to obtain an Arrhenius type behaviour.

Numerical method and composition at and out of chemical equilibrium in a multitemperature plasma. Application to a pure nitrogen plasma

Abstract: The disequilibrium between the temperatures (excitation, rotation, vibration, translation) in plasmas lead us to specific chemical potentials. Then, they are used to develop a mass action law in a multitemperature plasma. This mass action law enables us to determine the composition of a pure nitrogen mixture out of thermal equilibrium. The composition evolution versus time is determined from a kinetic method modified to take into account different temperature hypotheses. The composition and different thermodynamic properties of a pure nitrogen mixture are given at the chemical equilibrium, then versus time for various temperature hypotheses and thermal disequilibriums.

Simultaneously dissipative operators and the infinitesimal wrapping effect in interval spaces

Abstract: One of shortcomings of stepwise interval methods is the following The intervals determining the solution of a system are often expanded in the course of time irrespective of the method and step used (the {\em Moore effect}) We introduce the notion of general {\em interval spaces} and study the infinitesimal Moore effect (IME) in these spaces We obtain the local conditions of absence of the IME in terms of Jacobi matrices field The relation between the absence of IME and simultaneous dissipativity of the Jacobi matrices is established We study simultaneously dissipative operators in $\Bbb{R}^n$ A linear operator $A$ is {\em dissipative} with respect to a norm $\|\|$ if $\| \exp (At) \| \leq 1$ at all $t \geq 0$ For each norm, the dissipative operator form a closed convex cone An operator $A$ is {\em stable dissipative} if it belongs to the interior of this cone The family of linear operators $\{A_\alpha \}$ is called {\em simultaneously dissipative}, if there exists a norm with respect to which all the operators are dissipative We studied general properties of such families For example, let the family $\{A_\alpha \}$ be finite and generate a nilpotent Lee algebra and let for each $A_\alpha$ there exist a norm with respect to which it is dissipative Then $\{A_\alpha \}$ is simultaneously dissipative Let the family $\{A_\alpha \}$ be compact and generate solvable Lee algebra, and let the spectrum of each operator $A_\alpha $ lie in the open left half-plane Then $\{A_\alpha \}$ is simultaneously stable dissipative, ie there exists a norm with respect to which all $A_\alpha $ are stable dissipative We study the conditions of simultaneous dissipativity of the matrices of rank one and discussed their application to equations of {\em mass action law} kinetics