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.

Generalized law of mass action for a two-temperature plasma.

Abstract: The Zubarev formalism is applied to a two-temperature plasma to obtain the generalized law of mass action. This is done for arbitrary heat flow between the electrons and the internal states of the heavy particles on one hand and the kinetic degrees of freedom of the heavy particles on the other hand. In the case of zero heat flow the results previously reported are recovered. Applying the outcome of the calculation to a simple plasma of Rydberg atoms and ions, the Saha equation is changed. The difference can be expressed in a correction factor that depends on the mass ratio of the electron to the heavy particle, the difference in temperature, and the specific atomic structure. For argon plasmas the correction factor is small. For hydrogen plasma the results indicate a correction on the order of 10%, depending on the plasma conditions.

Modeling the onset of asphaltene flocculation at high pressure by an association model

Abstract: A new thermodynamic model was developed to calculate the onset of flocculation in crude oil systems similarly to the liquid-liquid equilibrium of polymer solutions. The key concept of the model is that asphaltene self-association leads to a polydisperse system of associates characterized by a size distribution function. Using continuous thermodynamics the mass action law is applied to the association equilibrium and an analytical expression for the size distribution function is derived. In contrast to polymer thermodynamics this distribution function depends on temperature, pressure, and concentration. For modeling the high pressure equilibrium the Sako-Wu-Prausnitz equation of state is applied. The model was tested on existing flocculation data for three systems of the type methane + i-octane + maltene + asphaltene with crude oils of different asphaltene contents. The amount of precipitant necessary to provoke flocculation was calculated in good agreement with the experimental data for all three...

Equilibrium studies on butane-1,4-diamine extraction with 4-nonylphenol

Abstract: BACKGROUND The extraction of butane-1,4-diamine (BDA) from aqueous solutions with undiluted 4-nonylphenol (4NP) has been studied at three temperatures (298 K, 310 K and 323 K) in a batch system. A reactive extraction model based on mass action law was applied to describe the experimental data. RESULTS The model developed describes the distribution of BDA between the 4NP phase and the aqueous phase, and the average stoichiometry of the complexation due to interactions between the two amine groups of BDA and 4NP, as well as the complexation constant were fitted to experimental data with good accuracy for each of the three temperatures, the largest error at the confidence limit of the estimated parameters being 6%. Using a Van't Hoff plot, the thermodynamic parameters of the equilibrium constant were determined and used to estimate that in a single stage with only S/F = 0.5, over 99% of the BDA can be extracted from a 1.146 wt% aqueous solution. High distribution ratios at low BDA concentrations hampered the effective recovery by back-extraction in a single stage, therefore multistage processing was considered and short-cut calculations revealed a maximum concentration factor of 3.6. CONCLUSION Good agreement between single stage equilibrium data and the model was obtained and the model developed was used in short-cut calculation of a coupled multistage forward and back-extraction process showing a maximum concentration factor of only 3.6, therefore an alternative, more effective recovery strategy, e.g. through anti-solvent addition is suggested. © 2013 Society of Chemical Industry

Repair of irradiated cells by Michaelis–Menten enzyme catalysis: the Lambert function for integrated rate equations in description of surviving fractions

Abstract: Michaelis–Menten second-order chemical kinetics is used to describe the three main mechanisms for surviving fractions of cells after irradiation. These are a direct yield of lethal lesions by single event inactivation, metabolic repair of radiation lesions and transformation of sublethal to lethal lesions by further irradiations. The mass action law gives a system of time-dependent differential equations for molar concentrations of the invoked species that are the DNA substrates as lesions, enzyme repair molecules, the product substances, etc. The approximate solutions of these coupled rate equations are reduced to the problem of finding all the roots of the typical transcendental equation $$ax\mathrm{e}^{-bx}=c$$ with $$x\ge 0$$ being a real variable, where $$a,b$$ and $$c$$ are real constants. In the present context, the unique solution of this latter equation is given by $$x=(1/b)W_0(bc/a)$$ where $$W_0$$ is the principal-branch real-valued Lambert function. Employing the concept of Michaelis–Menten enzyme catalysis, a new radiobiological formalism is proposed and called the “Integrated Michaelis–Menten” (IMM) model. It has three dose-range independent parameters ingrained in a system of the rate equations that are set up and solved by extracting the concentration of lethal lesions whose time development is governed by the said three mechanisms. The indefinite integral of the reaction rate is given by the Lambert $$W_0$$ function. This result is proportional to the sought concentration of lethal lesions. Such a finding combined with the assumed Poisson distribution of lesions yields the cell surviving fraction after irradiation. Exploiting the known asymptotes of the Lambert $$W_0$$ function, the novel dose-effect curve is found to exhibit a shoulder at intermediate doses preceded by the exponential cell kill with a non-zero initial slope and followed by the exponential decline with the reciprocal of the $$D_0$$ or $$D_{37}$$ dose as the final slope. All three dose regions are universally as well as smoothly covered by the Lambert function and, hence, by the ensuing cell surviving fractions. The outlined features of the proposed IMM model stem from a comprehensive mechanistic description of radiation-lesion interactions by means of kinetic rate equations. They are expected to be of critical importance in new dose-planning systems for high doses per fraction where the conventional linear-quadratic radiobiological modeling is demonstrably inapplicable.