Calculation Of Equilibrium Composition Research Articles

Calculation of Equilibrium Compositions of Biochemical Reaction Systems Involving Water as a Reactant

In the thermodynamic treatment of reactions involving water as a reactant in dilute aqueous solutions, the activity of water is taken as unity in expressions for equilibrium constants, but the calculation of equilibrium constants using tables involves the standard Gibbs energy of formation of water. This convention, which is quite satisfactory for simple systems, causes problems in the thermodynamics of biochemical reaction systems in dilute aqueous solutions. One reason is that the identification of components in these systems is very important, and this involves the use of conservation matrixes and stoichiometric number matrixes. These matrixes can be interconverted, and this is especially useful in computer programs for calculating equilibrium compositions. When water is a reactant in a system of reactions, there is a sense in which oxygen atoms are not conserved because they can be brought into reactants or expelled from reactants without altering the activity of water in the solution. These problems can be avoided by using a Legendre transform to define a further transformed Gibbs energy that provides the criterion for spontaneous change and equilibrium when a(H2O) = 1. The equations that are derived here are illustrated by equilibrium calculations on a system of three enzyme-catalyzed reactions in the citric acid cycle. This system of reactions also illustrates the fact that the mechanisms of enzyme-catalyzed reactions may introduce constraints in addition to element balances.

Isothermal vapor–liquid equilibria of benzene-dimethylformamide and toluene-dimethylformamide systems using a small modified ebulliometer

A small modified ebulliometer, whose structure is both simple and rational, has been proposed for the reliable measurement of vapor–liquid equilibrium. The ebulliometric method was used to determine isothermal VLE data for the dimethylformamide-benzene binary system at 343.2, 353.2, and 363.2 K and for the dimethylformamide-toluene binary system at 353.2, 363.2, 373.2, and 383.2 K. The parameters of the NRTL and Wilson models for the two binary systems have been obtained by calculating equilibrium compositions of the liquid and vapor phases with the experimental equilibrium temperatures, pressures and feed compositions. They were expressed as a function of the temperature from 343.2 to 363.2 K and from 353.2 to 383.2 K. Correlation results were satisfactory. Meanwhile, the major factors influencing the value of the mean evaporation coefficient, f ̄ , of the ebulliometer were investigated and the effect of the error f ̄ of on the value of calculated equilibrium liquid and vapor compositions was examined. The results will allow a wide application of this ebulliometer to the determination of reliable VLE data.

Calculation of Equilibrium Compositions of Large Systems of Biochemical Reactions

A more global view of the thermodynamics of a system of biochemical reactions can be obtained by specifying concentrations of coenzymes such as adenosine triphosphate and adenosine diphosphate. These calculations are facilitated by use of conservation matrices that can be arranged in such a way that the coenzymes are components. In calculations at specified pH in dilute aqueous solutions, neither hydrogen atoms or oxygen atoms are conserved, and so the applicable conservation matrices are calculated from stoichiometric number matrices that omit the stoichiometric numbers for H2O. For a system of biochemical reactions, the number of components is generally greater than the number of elements other than hydrogen and oxygen because of constraints that arise in the mechanisms of the enzyme-catalyzed reactions. When concentrations of coenzymes are specified, the system can be described as being made up of pseudoisomer groups, each made up of one or several reactants. The values of apparent equilibrium constants K‘ ‘ for reactions between the pseudoisomer groups can be calculated if the standard transformed Gibbs energies of formation of the reactants are known at the desired pH or the apparent equilibrium constants K‘ are all known. These concepts and equations are applied to glycolysis plus the citric acid cycle, and it is shown that quantitative thermodynamic calculations can be made by working with 7 reactants, rather than 32, and 5 reactions, rather than 20.

Gibbs energy minimization in gas + liquid + solid systems

An algorithm is described for the calculation of equilibrium compositions of multiple highly nonideal liquid and solid solutions, as well as pure stoichiometric phases, coexisting with a mixture of ideal gas species at fixed temperature and pressure. The total Gibbs free energy of the system is approximated as a quadratic function of the compositions of the gas phase and stable condensed phases, in an orthogonal basis set of pure elements. Only changes in thermal energy and energy related to pressure-volume work are considered. The total Gibbs energy is minimized directly by use of both the slope and the curvature of the Gibbs energy surface with respect to the gas and condensed phase compositions in the basis elements. The algorithm described has been implemented in a computer code for the calculation of condensation sequences for cosmic nebular gases enriched in dust. Machine, compiler and library requirements for performing these calculations in the C programming language are compared. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 247–256, 2000

IVTANTHERMO for Windows — database on thermodynamic properties and related software

A new version of the software package IVTANTHERMO for Windows intended for thermodynamic modelling of complex chemically reacting systems is described. The package includes an extensive database on thermodynamic properties of individual substances, programs for the database handling and a program, which allows the calculation of equilibrium composition and thermodynamic properties of the system to be examined. The software is intended for scientists, chemical engineers and students.

Calculation of equilibrium composition and establishing time in a mixture of three hydrogen isotopes

A mathematical model describing the kinetics of establishing equilibrium is developed. Equilibrium concentrations of isotopic molecules for gas mixtures used in muon catalyzed fusion research are calculated.

Influence of thermodynamic and thermochemical data errors on calculated equilibrium composition

AbstractInfluence of thermodynamic data errors upon the results of calculation of equilibrium composition of complex chemically reacting systems is examined. Two possible approaches (sensitivity analysis and statistical approach) are described. The examples showing significance of the error influence are presented.

Calculation of equilibrium composition in combustion products

For a specific combustion problem involving calculations of several species at equilibrium, it is much simpler to write a special computer program and calculate the concentrations, rather than to use a generalized computer program. To calculate these concentrations, one must solve a set of non-linear algebraic equations. This work describes a procedure in which the Newton-Raphson method and the successive substitution method are combined. It was found that for this type of problem, the quantity of unknowns and the nature of the equations, are such that, by adopting the two procedures simultaneously, a much faster and reliable convergence is achieved. This study also shows what possible species should be considered for these calculations.

Calculation of equilibrium composition in combustion products

AbstractFor a specific combustion problem involving calculations of several species at equilibrium, it is much simpler to write a special computer program and calculate the concentrations, rather than to use a generalized computer program. To calculate these concentrations, one must solve a set of non‐linear algebraic equations. This work describes a procedure in which the Newton‐Raphson method and the successive substitution method are combined. It is was found that for these types of problems the value of unknowns and the nature of the equations are such that by adopting the two procedures simultaneously a much faster and reliable convergence is achieved. This study also shows what possible species should be considered for these calculations.

An effective equation of state for dense matter with strangeness

An effective equation of state which generalizes the Lattimer-Swesty equation for nuclear matter is presented for matter at supernuclear densities including strange baryons. It contains an adjustable baryon potential energy density, based on models of local potentials for the baryon-baryon interactions. The features of the equation rely on the properties of nuclei for the nucleon-nucleon interactions, and mainly on experimental data from hypernuclei for the hyperon-nucleon and hyperon-hyperon interactions. The equation is used to calculate equilibrium compositions and thermodynamic properties of high density matter with strangeness in two astrophysical contexts: neutron star matter (transparent to neutrinos) and proto-neutron star matter (opaque to neutrinos). The effective equation of state reproduces typical properties of high density matter found in theoretical microscopic models. Of these, the main result is that hyperons appear in both types of matter at about twice the nuclear saturation density, and that their appearance significantly softens the equation of state. The range of maximal masses of neutron stars found in a comprehensive parameter survey is 1.4--1.7 M ⊙. Another typical result is that the maximal mass of a proto-neutron star with strange baryons is higher than that of an evolved neutron star (opposite to the case of nuclear matter), setting the stage for a “delayed collapse” scenario.

Analysis of carbine formation in a cyanided layer and methods for calculating equilibrium compositions of saturating atmospheres

It is known that one of the defects of a carburized (cyanided) layer is a carbide network, which worsens considerably the characteristics of parts. The present paper is devoted to the causes of its formation in a cyanided layer in steel 35G2. The boundaries of deposition of carbon black and the carbon potential in a cyaniding furnace are calculated. The effect of the alloying elements and the carbon content in steels 08kp and 35G2 on the final distribution of carbon in the diffusion layer is determined. The equilibrium composition of a saturating atmosphere that provides cyaniding without deposition of carbon black in the functional zones of the furnace or carbide formation (as a network or as a solid layer) on the surface of the metal is calculated.

An algorithm for multiphase equilibrium calculations for systems containing polymers

A comprehensive algorithm has been developed for multiphase equilibrium computations in multicomponent systems. The algorithm includes stability analysis and calculation of equilibrium compositions by a combination of a multiphase direct substitution method and Gibbs energy minimization. The algorithm has been specially designed to handle the numerical complexities that are characteristic of systems containing large (polymeric) and small molecules. Such complexities include a very strong composition dependence of equilibrium ratios (K-factors) as well as frequent occurrence of extremely low equilibrium concentrations and fugacity or activity coefficients.

An efficient method for the calculation of chemical equilibrium composition in multicomponent gas mixtures

AbstractThe determination of the composition of multi‐component mixtures is the basis by which a number of technical and physical problems in the field of power and process engineering are modelled. In order to calculate chemical states of equilibrium in the gas phase, a calculation method will be presented which is founded on a minimization of the Gibbs enthalpy. This method is characterized by a high reliability in convergency, considerable independence of starting vectors and by a moderate requirement for programming. These characteristics are achieved by a transformation of variables which results in numerically more favourable solutions to the non‐linear equation system. Calculated equilibrium compositions (including dissociation and ionisation) for a stochiometric mixture of hydrogen and oxygen in a temperature range of 300–12000 K and a pressure of 105 Pa as well as the application of the method will be demonstrated.

Constraints in biochemical reactions

Chemical reactions satisfy element and charge conservation equations, but generally do not satisfy additional independent conservation equations. Biochemical reactions at a specified pH satisfy conservation equations for elements in addition to hydrogen, but they often satisfy additional independent conservation equations because of the coupling of reactions through the enzymatic mechanism. The enzyme may couple together two or more biochemical reactions so that only the sum of the coupled reactions is catalysed. The biochemical reactions that are coupled together may, or may not, share reactants, but the type of coupling discussed here is stoichiometric. Since chemical equations and biochemical equations are mathematical equations, linear algebra provides the means for determining the number and types of constraints involved in the enzymatic mechanism. Constraints in addition to element balances indicate missing reactions. The identification of conservation equations is essential for calculations of equilibrium compositions using computer programs that minimize the transformed Gibbs energy at a specified pH subject to the conservation equations that apply.

Nonstoichiometric algorithm of calculations of simultaneous chemical and phase equilibria. 1. Influence of a method modeling nonideality of systems on the calculated equilibrium composition at low pressure

A nonstoichiometric algorithm for the calculation of simultaneous chemical and phase equilibria (CPE) in multicomponent nonideal systems is presented. This algorithm provides an implementation of the intermediate method for nonideal systems based on the ideal-system BNR algorithm (Smith and Missen, 1982). This implementation is used for calculation of CPE of strongly nonideal systems (the mixtures in esterification of acetic acid with ethanol or methanol), and the results obtained for different methods modeling the system nonideality (ASOG, original UNIFAC, UNIFAC modified by Larsen, the Wilson equation, regarding or disregarding organic acid association in the vapor phase) are compared. It is shown that the differences in calculated equilibrium compositions resulting from the different nonideality models are extremely significant. The method of verification of calculated equilibrium composition is presented

Approximate Stoichiometry for Rich Hydrocarbon Mixtures

The stoichiometry of lean mixtures can readily and accurately be determined from the assumption that all the carbon oxidizes to carbon dioxide and all the hydrogen oxidizes to water. This assumption is valid up to an equivalence ratio ([sigma]) of 0.8 and can be used with little error up to [sigma] = 1. The composition of the products of a hydrocarbon burnt in air under the foregoing assumption can be obtained from simple carbon, hydrogen, oxygen and nitrogen balances. Given the composition, one can determine the energy released and/or the adiabatic flame temperature. For rich mixtures, the foregoing assumption, of course, is not valid. Hence, there is no easy way to determine the stoichiometry of the products of a rich mixture. The objective of this note is to present an equation' which will allow one to readily determine the composition of the products of rich hydrocarbon mixtures. The equation is based on equilibrium composition calculations and some assumptions regarding the characteristics of hydrocarbons. The equation gives approximate results. However, the results are sufficiently accurate for many situations. If more accuracy is wanted, one should use an equilibrium combustion program like the one by Gordon and McBride.

Development and application of continuous thermodynamics for complex chemical equilibria calculations

For the calculation of complex chemical equilibria of multicomponent mixtures containing species whose Gibbs free energies of formation depend very regularly on the structure of the molecules involved, statistical methods of continuous thermodynamics can successfully be put into use. Homologous series of n-alkanes and n-alkenes are examples of such systems. In this case the Gibbs free energy of formation is a linear function of the number of C atoms in the molecules. The application of statistical methods of continuous thermodynamics enables not only the calculation of equilibrium composition but also provides facilities for the demonstration of very interesting and striking regularities in behavior. In the case studies the increasing complexity of the system is considered. In most simple versions all chemical species constitute one homologous series only (alkanes or alkenes). In a more refined version the system is treated as a mixture of two ensembles (alkanes and alkenes). Furthermore, some individual components are added, such as hydrogen, carbon oxide, carbon dioxide and the first members of every homologous series.

An Equilibrium Analysis of Some Chlorinated Hydrocarbons in Stoichiometric to Fuel-rich Post-flame Combustion Environments

The equilibrium composition of product gases from the combustion of chlorinated hydrocarbons (CHC) has been studied for varying ratios of C, H, Cl, and O under stoichiometric to fuel-rich conditions. An interactive, PC-compatible FORTRAN program, STANJAN, was utilized in conjunction with thermochemical data sources to calculate equilibrium compositions of gas mixtures as a function of temperature. The predicted results, when judiciously interpreted, assist in the understanding of the potential for formation of residual organic substance emissions (ROSEs) in post-flame environments of an incinerator. Arguments are presented for the potential formation of chlorinated species, which are stable at ambient temperature, if locally fuel-rich mixtures penetrate into the lower temperature zones of an incinerator. ROSEs that have been observed in field tests of incinerators burning chlorinated compounds are predicted to form under the fuel-rich condition. Furthermore, when the equivalence ratio is greater than unity by even a slight amount, the degree of chlorination of product gases increases markedly when the Cl/H ratio also exceeds unity. In that case, time, temperature, turbulence and an overall fuel-lean stoichiometry may not be sufficient to guarantee elimination of measurable levels of chlorinated products. Possible implications of the equilibrium calculations are discussed. Further systematic studies with additional CHCs, nitrogen-, sulfur-, and heavy metal-bearing compounds are recommended as well as continued efforts to carry out kinetic studies.

Application of Soot Formation Model: Effects of Chlorine

Abstract Soot formation in the combustion of hydrocarbon fuels is the net effect of competition between molecular weight growth and destruction mechanisms involving free radicals. Chlorine addition to the fuel can alter the concentrations of radicals in a manner that enhances soot formation. In diffusion flames and purely pyrolysis systems, the presence of chlorine increases the fractional conversion of carbon to soot, while in premixed flames and well-stirred combustion the presence of chlorine lowers the critical equivalence ratio for the onset of soot formation. These effects tend not to be of major importance in premixed and well-stirred systems unless substantial amounts of chlorine are added. The chlorine has a strong tendency to go to HO, which may or may not significantly lower the concentration of H atoms, and in turn affect the concentrations of OH and O, depending on whether the atomic Cl/H ratio is comparable to or much less than unity. The observed effects of chlorine on soot formation are qualitatively consistent with expectations based on the knowledge of soot formation, the known rate coefficients of the hydrogen and chlorine analogs of the key radical reactions, and calculated equilibrium compositions with and without chlorine present.

Application of chemical thermodynamics to the description of processes of special inorganic materials preparation

The paper reviews the possibilities of chemical thermodynamics for the description of processes for preparing special inorganic materials with exactly defined final properties. The first part is devoted to general conditions of thermodynamic equilibrium, and describes a procedure for calculating the equilibrium composition of multiphase and multicomponent systems by minimizing the total Gibbs energy of the system while satisfying mass balance conditions. A stoichiometric algorithm convenient especially for equilibrium composition calculations of simple systems is described. Special attention is paid to input data needed for equilibrium calculations. Data characterizing the thermodynamic properties of individual pure substances are discussed, as are data describing the nonideal behaviour of multicomponent condensed phases. The second part of the paper gives a summary of some applications of chemical thermodynamics to the description of processes of special inorganic materials preparation. Case studies on thermodynamic analysis are described for three industrial processes: (1) chemical vapour deposition of titanium carbonitride, (2) growth of Si-doped GaAs single crystals by Bridgman's method, and (3) refining of technical boron nitride by reductive chlorination. The results of equilibrium calculations for all the three systems are in very good agreement with available experimental data.