scholarly journals A model of carbon dioxide dissolution and mineral carbonation kinetics

2009 ◽  
Vol 466 (2117) ◽  
pp. 1265-1290 ◽  
Author(s):  
Mark J. Mitchell ◽  
Oliver E. Jensen ◽  
K. Andrew Cliffe ◽  
M. Mercedes Maroto-Valer
Keyword(s):  
Carbon Dioxide ◽  
Mass Action ◽  
Mineral Carbonation ◽  
Leading Order ◽  
Full System ◽  
Mass Action Law ◽  
Gaseous Carbon Dioxide ◽  
Equilibrium Concentrations ◽  
Kinetics Of ◽  
Independent Parameters

The kinetics of the dissolution of carbon dioxide in water and subsequent chemical reactions through to the formation of calcium carbonate, a system of reactions integral to carbon sequestration and anthropogenic ocean acidification, is mathematically modelled using the mass action law. This group of reactions is expressed as a system of five coupled nonlinear ordinary differential equations, with 14 independent parameters. The evolution of this system to equilibrium at 25 ° C and 1 atm, following an instantaneous injection of gaseous carbon dioxide, is simulated. An asymptotic analysis captures the leading-order behaviour of the system over six disparate time scales, yielding expressions for all species in each time scale. These approximations show excellent agreement with simulations of the full system, and give remarkably simple formulae for the equilibrium concentrations.

scholarly journals Spectrophotometric study of competitive complexation equilibria involving overlapped spectral responding species: Determination of the stability constant of bismuth-pyrophosphate complex

2012 ◽  
Vol 10 (6) ◽  
pp. 1875-1881
Author(s):  
Tsvetanka Nedeltcheva ◽  
Andriana Surleva ◽  
Liliya Nikolova ◽  
Rahila Borissova ◽  
Stela Georgieva
Keyword(s):  
Stability Constant ◽  
Spectrophotometric Study ◽  
Mass Action ◽  
Competitive Reaction ◽  
Species Determination ◽  
Complex Formation Equilibria ◽  
Mass Action Law ◽  
Multivariable Regression ◽  
Equilibrium Concentrations ◽  
The Stability

AbstractSpectrophotometric study of competitive complex formation equilibria involving overlapped spectral responding species applying a simple and versatile algorithm was carried out. The algorithm involves multivariable regression for calculation of equilibrium concentrations from multiwavelength data and mass action law for the stability constant calculation. The used regression functions are part of common statistical software. Stability constants and complex stoichiometry of competing equilibria were simultaneously determined. The species concentration profiles at several spectral overlapping and α-coefficient of competing reaction were obtained. Non-absorbing bismuth — pyrophosphate (PPh) system was studied as a competitive reaction of bismuth — 4-(2-Pyridylazo) resorcinol (PAR) complex. The formation of Bi-PPh complex with 1:1 stoichiometry was proved in the studied concentration region (CBi = 1×10−5 mol L−1; CPPh = 5×10−6 − 1×10−4 mol L−1). The stability constant of the complex at pH 1 and µ = 1.0 have been determined: logβ = 4.2±0.2.

scholarly journals Development of a Simple Kinetic Mathematical Model of Aggregation of Particles or Clustering of Receptors

Life ◽  
2020 ◽  
Vol 10 (6) ◽  
pp. 97
Author(s):  
Andrei K. Garzon Dasgupta ◽  
Alexey A. Martyanov ◽  
Aleksandra A. Filkova ◽  
Mikhail A. Panteleev ◽  
Anastasia N. Sveshnikova
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Cluster Formation ◽  
Quantitative Description ◽  
Membrane Receptors ◽  
Mass Action ◽  
Mass Action Kinetics ◽  
Clustering Model ◽  
Mass Action Law ◽  
Kinetics Of

The process of clustering of plasma membrane receptors in response to their agonist is the first step in signal transduction. The rate of the clustering process and the size of the clusters determine further cell responses. Here we aim to demonstrate that a simple 2-differential equation mathematical model is capable of quantitative description of the kinetics of 2D or 3D cluster formation in various processes. Three mathematical models based on mass action kinetics were considered and compared with each other by their ability to describe experimental data on GPVI or CR3 receptor clustering (2D) and albumin or platelet aggregation (3D) in response to activation. The models were able to successfully describe experimental data without losing accuracy after switching between complex and simple models. However, additional restrictions on parameter values are required to match a single set of parameters for the given experimental data. The extended clustering model captured several properties of the kinetics of cluster formation, such as the existence of only three typical steady states for this system: unclustered receptors, receptor dimers, and clusters. Therefore, a simple kinetic mass-action-law-based model could be utilized to adequately describe clustering in response to activation both in 2D and in 3D.

38.—Development of Ideas concerning the Carbon Dioxide System in Sea Water up to 1940.

1972 ◽  
Vol 72 (1) ◽  
pp. 381-387 ◽  
Author(s):  
John Lyman
Keyword(s):  
Physical Chemistry ◽  
Carbon Dioxide ◽  
Boric Acid ◽  
Sea Water ◽  
Pure Water ◽  
Weak Acid ◽  
Sea Salt ◽  
Mass Action ◽  
Mass Action Law

SynopsisMarcet reported in 1822 that sea salt contained lime, and several investigators confirmed its presence in sea water in the 1830s. Darondeau found dissolved CO2 in sea water in 1838, and von Bibra in 1851 considered sea water to be slightly alkaline. Tornöe in 1880 pointed out that this condition required part of the CO2 to be bound chemically, and Hamberg applied the mass action law to the CO2-system in sea water in 1885. For nearly 50 years, however, despite the development of the concepts of pH and activity, attempts to apply the law in detail failed, first because the behaviour of H2CO3 and HCO3− as weak acids is strikingly different in pure water, sea water or NaCl solutions, and secondly because the presence and role of another weak acid, boric acid, was not recognised fully until 1933. Investigators often attributed their failures to some mysterious ability of the sea to disregard or evade the laws of physical chemistry. Buch in 1933 and 1938 finally laid this hobgoblin to rest, and his results are still accepted with only minor modifications.

scholarly journals Kinetics methods for clinical epidemiology problems

2015 ◽  
Vol 112 (46) ◽  
pp. 14150-14155 ◽  
Author(s):  
Alexandru Dan Corlan ◽  
John Ross
Keyword(s):  
Clinical Epidemiology ◽  
Meta Analysis ◽  
Reaction Rates ◽  
Mass Action ◽  
Reaction Systems ◽  
Disease Epidemiology ◽  
Mass Action Law ◽  
The Individual ◽  
Kinetics Of ◽  
Stochastic Kinetics

Calculating the probability of each possible outcome for a patient at any time in the future is currently possible only in the simplest cases: short-term prediction in acute diseases of otherwise healthy persons. This problem is to some extent analogous to predicting the concentrations of species in a reactor when knowing initial concentrations and after examining reaction rates at the individual molecule level. The existing theoretical framework behind predicting contagion and the immediate outcome of acute diseases in previously healthy individuals is largely analogous to deterministic kinetics of chemical systems consisting of one or a few reactions. We show that current statistical models commonly used in chronic disease epidemiology correspond to simple stochastic treatment of single reaction systems. The general problem corresponds to stochastic kinetics of complex reaction systems. We attempt to formulate epidemiologic problems related to chronic diseases in chemical kinetics terms. We review methods that may be adapted for use in epidemiology. We show that some reactions cannot fit into the mass-action law paradigm and solutions to these systems would frequently exhibit an antiportfolio effect. We provide a complete example application of stochastic kinetics modeling for a deductive meta-analysis of two papers on atrial fibrillation incidence, prevalence, and mortality.

Modified mass action law-based model to correlate the solubility of solids and liquids in entrained supercritical carbon dioxide

2001 ◽  
Vol 910 (1) ◽  
pp. 119-125 ◽  
Author(s):  
Jose C. González ◽  
Mercedes R. Vieytes ◽  
Ana M. Botana ◽  
Juan M. Vieites ◽  
Luis M. Botana
Keyword(s):  
Carbon Dioxide ◽  
Supercritical Carbon Dioxide ◽  
Mass Action ◽  
Mass Action Law ◽  
Supercritical Carbon

scholarly journals Macroscopic currents of ionic channels using Mass Action Law: A mathematical model

2021 ◽  
Vol 2 (5) ◽  
pp. 7493-7514
Author(s):  
Torres Jácome Julián ◽  
Martagon-Domínguez Juan Mauricio ◽  
Montes Pérez Areli ◽  
Montiel-Jaen Guadalupe ◽  
García-Garibay Otto ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Ionic Channels ◽  
Mass Action ◽  
System Of Equations ◽  
Law Of Mass Action ◽  
Voltage Dependent ◽  
Mass Action Law ◽  
Experimental Protocols ◽  
Pass Through ◽  
Kinetics Of

In this work it proposes a mathematical model for ion channels based on two concepts, the Hodgkin and Huxley's as well as the Law of Mass Action in addition, we consider the kinetics of channels as a dynamic process of Markov`s chain. With the previous premises, a system of differential equations is proposed that when it is solved, all properties of the macroscopic currents are determined. The activation, deactivation, inactivation, and recovery of the inactivation concepts remain as processes that are part of a chemical reaction. With this system of equations, all the experimental protocols used in electrophysiology to characterize macroscopic currents can be modeled. Another advantage is that the model allows, with the same system of equations, to determine the properties of voltage-dependent channels regardless of the type of ion that pass through in the channel.

Studies on Activator Formation in Human Plasma with Streptokinase

1973 ◽  
Vol 30 (02) ◽  
pp. 381-392
Author(s):  
M Martin ◽  
Keyword(s):  
Human Plasma ◽  
Plasminogen Activator ◽  
Mass Action ◽  
Activator Concentration ◽  
Kinetic Effect ◽  
Mass Action Law

SummaryThe plasminogen-streptokinase complex called “activator” was present in diluted plasma in the form of a largely dissociated mixture. More than ⅞ of the streptokinase and plasminogen molecules were available for further activator formation.The activator is probably a dissociated complex of the formulaStreptokinase + Plasminogen ⇄ Activator.The fact that an increase in activator concentration by x times is obtained by multiplying either the streptokinase content by the factor y or the plasminogen concentration by the same factor y would point to a kinetic effect along the lines of the mass action law.

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