A universal thermodynamic model of calculating mass action concentrations for structural units or ion couples in aqueous solutions and its applications in binary and ternary aqueous solutions

A universal thermodynamic model of calculating mass action concentrations for structural units or ion couples in ternary and binary strong electrolyte aqueous solution was developed based on the ion and molecule coexistence theory and verified in four kinds of binary aqueous solutions and two kinds of ternary aqueous solutions. The calculated mass action concentrations of structural units or ion couples in four binary aqueous solutions and two ternary solutions at 298.15 K have good agreement with the reported activity data from literatures after shifting the standard state and concentration unit. Therefore, the calculated mass action concentrations of structural units or ion couples from the developed universal thermodynamic model for ternary and binary aqueous solutions can be applied to predict reaction ability of components in ternary and binary strong electrolyte aqueous solutions. It is also proved that the assumptions applied in the developed thermodynamic model are correct and reasonable, i.e., strong electrolyte aqueous solution is composed of cations and anions as simple ions, H2O as simple molecule and other hydrous salt compounds as complex molecules. The calculated mass action concentrations of structural units or ion couples in ternary and binary strong electrolyte aqueous solutions strictly follow the mass action law.

Calculating models of mass action concentrations for NaBr(aq), LiNO_3(aq), HNO_3(aq), and KF(aq) binary solutions

The calculating models of mass action concentrations for electrolyte aqueous solutions NaBr-H2O, LiNO3-H2O, HNO3-H2O, and KF-H2O have been developed at 298.15 K and their molalities ranging from 0.1 mol/kg to saturation according to the ion and molecule coexistence theory as well as mass action law. The calculated mass action concentration is based on pure species as the standard state and the mole fraction as the concentration unit, and the reported activities are usually based on infinite dilution as the standard state and molality as the concentration unit. Hence, the calculated mass action concentration must be transformed to the same standard state and concentration unit. The transformation coefficients between calculated mass action concentrations and reported activities of the same component fluctuate in a very narrow range. Thus, the transformed mass action concentrations not only agree well with reported activities, but also strictly obey mass action law. The calculated results show that the new developed models can embody the intrinsic structure of investigated four electrolyte aqueous solutions. The results also indicate that mass action law has its widespread applicability to electrolyte binary aqueous solutions.

Applicability of law of mass action to distribution of manganese between slag melts and liquid iron

According to the law of mass action and the coexistence theory of slag structure, the distribution of manganese between MnO FeO SiO 2 and MgO MnO FeO SiO 2 slag melts as well as liquid iron was analyzed. It is shown that K ′ Mn and K MnO are only dependent on temperature and don’t change with basicities and compositions of slag melts. So the distribution of manganese between the above mentioned slag melts and molten iron obeys the law of mass action. But analysis of experimental results from other sources shows that K ′ Mn and K MnO really change with basicities of slag, which is probably arisen from not approaching equilibrium under low basicity slag melts.

CALCULATING MODEL OF MASS ACTION CONCENTRATIONS FOR Cd-Sb ALLOY MELT

According to the Cd-Sb alloy phase diagram, resistivity, heat capacity, partial molar entropy and viscosity,the structural units of this alloy melt have been determined as Cd and Sb atoms as well as Cd3Sb2, Cd4Sb3 and CdSb compounds.Based on these structural units and the coexistence theory of metallic melt structure involing compound formation,a calculating model of mass action concentrations has been deduced.The calculated mass action concentrations Ncd are in good agreement with measured activities acd. The Gibbs standard free energy of formatioin for above three compunds have been obtained too.

Calculating model of mass action concentrations for Ag-Au-Cu melts

Based on phase diagrams and measured activities, the calculatingmodel of mass action concentrations for het- erogeneous meltsAg-Au-Cu was formulated. Calculated results agree with the improvedresults of recent research work, Showing that the model formulatedcan reflect the structural characteristics of these melts. In thismodel, without the help Of any empirical parameters, only threeequilibrium constants are used, hence it is simple, lear, andfavorable to the sim- Plification of calculation.

Universal thermodynamic model of calculating the mass action concentrations of omponents in a ternary strong electrolyte aqueous solution and its application in the NaCl-KCl-H_2O system

A universal thermodynamic model of calculating the mass action concentrations of components in a ternary strong electrolyte aqueous solution has been developed based on the ion and molecule coexistence theory,and verified in the NaCl-KCl-H2O ternary system at 298.15 K. To compare the difference of the thermodynamic model in binary and ternary strong electrolyte aqueous solutions,the mass action concentrations of components in the NaCl-H2O binary strong electrolyte aqueous solution were also computed at 298.15K. A transformation coefficient was required to compare the calculated mass action concentration and reported activity because they were obtained at different standard states and concentration units. The results show that the transformation coefficients between calculated mass action concentrations and reported activities of the same components change in a very narrow range. The calculated mass action concentrations of components in the NaCl-H2O and NaCl-KCl-H2O systems are in good agreement with the reported activities. This indicates that the developed thermodynamic model can reflect the structural characteristics of solutions,and the mass action concentration also strictly follows the mass action law.

APPLICABILITY OF THE MASS ACTION LAW IN COMBINATION WITH THE COEXISTENCE THEORY OF METALLIC MELTS INVOLVING COMPOUND TO BINARY METALLIC MELTS

Based on the atomicity and molecularity as well as the consistency ofthermodynamic properties and activities of metallic melts with their structures, the coexistencetheory of metallic melts structure involving compound has been suggested. According to this theory,the calculating models of mass action concentrations for different binary metallic melts have beenformulated. The calculated mass action concentrations agree well with corresponding measuredactivities, which confirms that the suggested theory can reflect the structural characteristics ofmetallic melts involving compound and that the mass action law is widely applicable to this kind ofmetallic melts.

Applicability of mass action law to sulphur distribution between slag melts and liquid iron

According to the mass action law and the coexistence theory of slagstructure, the calculating models of mass action concentration for CaO-MgO-FeO-Fe_2O_3-SiO_2,CaO-MgO-MnO-FeO-Fe_2O_3-P_2O_5-SiO_2 and CaO-MgO-MnO-FeO-Fe_2O_3-Al_2O_3-P_2O_5-SiO_2 slag melts areformulated and sulphur distribution between the slag melts and liquid iron is treated. It is foundthat CaO, MnO and FeO promote desulphurization, while MgO is detrimental to desulphurization. Inaddition, the sulphur distribution coefficients between the slag melts and liquid iron andpresented.

Calculating Models of Mass Action Concentrations for Fe-P and Cr-P Melts and Optimization of Their Thermodynamic Parameters

Based on the phase diagrams, reliable reference experimental data and the coexistence theory of metallic melts structure involving compound formation, calculating models of mass action concentrations for Fe-P and Cr-P melts have been formulated. At the same time, some of their thermodynamic parameters have been optimized. The calculated results not only agree well with the measuredvalues, but also obey the mass action law rigorously, this in turn shows that these models can reflect the structural characteristics of corresponding melts.

Calculation Models of Mass Action Concentrations for Metallic Melts Involving Monotectic

Based on the phase diagrams, measured activities as well asDeltaG(m) and DeltaG(xs), calculating models of mass action concentrations for metallic melts involving monotectic have been formulated. The calculated results agree with practice on the whole, showing that the models deduced generally can reflect the structural characteristics of these melts. The metastable compounds formed in the melts are of the types A(2)B(3), AB(2), A(2)B(3) or AB and A(2)B(3)+AB etc..

Calculating Model of Mass Action Concentrations for Fe-Cr-P Melts and Optimization of Thermodynamic Parameters

According to the results of research on the thermodynamic propelles of Fe-Cr, Fe-P and Cr-P melts, the measured achvihes of Fe-Cr-P melts from reference sources as well as the coexistence theory of metallic melts structure involving compound formation, a calculating model of the mass action concentrations for Fe-Cr-P melts has been formulated and some of its thermodynamic parameters have been optimized. The calculated mass action concentrations agree with the measured achvities, which shows that this model can reflect the structural reality of Fe-Cr-P melts.

Calculating models of mass action concentrations for structural units or ion couples in RbCl-H_2O binary system and RbCl-RbNO_3-H_2O ternary system

Thermodynamic models of calculating mass action concentrations for structural units or ion couples in RbCl-H2O binary and RbCl-RbNO3-H2O ternary strong electrolyte aqueous solutions were developed based on the ion and molecule coexistence theory at 298.15 K.A transformation coefficient is needed to compare the calculated mass action concentration and the reported activity because they are obtained at different standard states and concentration units.The results show that the transformation coefficients between the calculated mass action concentrations and the reported activities of the same structural units or ion couples in RbCl-H2O binary and RbCl-RbNO3-H2O ternary strong electrolyte aqueous solutions change in a very narrow range.The transformed mass action concentrations of structural units or ion couples in RbCl-H2O binary system are in good agreement with the reported activities. The transformed mass action concentrations of RbCl and RbNO3 in RbCl-RbNO3-H2O ternary solution are also in good agreement with the reported activities,aRbCl and 3RbNOa,with different total ionic strengths as 0.01,0.05,0.1,0.5,1.0,1.5,2.0,3.0 and 3.5 mol/kg,respectively.All those results mean the developed thermodynamic model of strong electrolyte aqueous solutions can reflect structural characteristics of RbCl-H2O binary and RbCl-RbNO3-H2O ternary strong electrolyte aqueous solutions and the mass action concentration also strictly follows the mass action law.

CALCULATING MODELS OF MASS ACTION CONCENTRATIONSFOR MATTES (Cu_2S-FeS-SnS)INVOLVING EUTECTIC

Based on the facts that cations and anions of molten salts and binary basic oxide solid solutions do not separate from each other as well as that the electric conductivities of mattes are greater than that of salts and basic oxide solid solutions, the calculating models of mass action concentrations for binary and ternary mattes involving eutectic have been formulated. The results of calculation agree well with the values measured;this in turn shows that the calculating models can reftect the structural characteristics of the mattes concerned.

Calculating Models of Mass Action Concentrations for Ni-Mn and Co-Mn Melts and Optimization of Their Thermodynamic Parameters

According to phase diagrams, measured activities as well as the coexistence theory of motallic melts structure involving compound formation, the calculating models of mass action concentrations for Ni-Mn and Co-Mn melts are formulated and their thermodynamic parameters are optimized. As a result, the calculated mass action concentrations agree well with the corresponding measured activities, showing that these models can reflect the structural characteristics of both Ni-Mn and Co-Mn melts.

Novel Insight into the Preparation of Ti-6Al-4V Alloy Through Thermite Reduction Based on the Mass Action Concentration

Based on the mass action concentration theory,a novel thermodynamic analysis for the raw material ratio in the procedure of preparing Ti-6Al-4V alloy by aluminothermic reduction process is proposed in this paper,which is originated from TiO_(2),Al particles,and V_(2)O_(5) as feedstocks,and the relevant equilibrium thermodynamics was calculated through this new method.The results show that the range of aluminum addition coefficient in raw material to experiment should be controlled within 61.5%-100%,which can significantly reduce the number of experimental groups.This method is ready to regulate the matter of excessive aluminum content in reactants for materials preparation,especially for those reactions including elements that are effortless to combine with aluminum to form the corresponding intermetallics or alloys.In addition,it can also be used in general metallurgy or material preparation process to effectively predict the composition and proportion of equilibrium components under certain conditions.

Calculating Model of Mass Action Concentrations for Mn-C Melts and Optimization of Thermodynamic Parameters

Based on the phase diagram, the coexistence theory of the metallic melt structure involving compoundformation and the regularity of melts containing saturated phase, a calculating model of mass action concentrationsfor Mn-C melts was formulated. According to the activities (or activity coefficients AM. and γc.), obtained by theUnified Interaction Parameter Model (UIPM), the thermodynamic parameters G and G at higher temperatures (1628～1873 K) were optimized by the repeated try and error method. It is testified that G G(873～1273 K) and G (298～1623 K), obtained at lower temperatures, can also be used at the above-mentionedhigher temperatures. The calculated N. and N agree well with ac. and ac obtained by UIPM. This result showsthat the deduced model can reflect the structural reality of Mn-C melts.

Carbon Solubility and Mass Action Concentrations of Fe-Cr-C Melts

An empirical equation of carbon solubility in Fe-Cr-C melts is regressed based on the experimental data from references. Acalculating model of mass action concentrations for these melts is formulated on the basis of the coexistence theory of metaIlic melts in-volving compound formation, the phase diagram of Cr-C system as well as thermodynamic data of Fe-Cr-C melts. According to the mod-el, the standard Gibbs free energies of formation of CrC and Cr3C2 are obtained. Satisfactory agreement between the calculated and me-asured values shows that the model can reflect the structural characteristics of Fe-Cr-C melts.

A Back Look on the Binary Phase Diagrams of Metals from the Mass Action Law and the Coexistence Theory of Metallic Melts

According to the mass action law and the coexistence theory of metallic melts, the mass action concentrations of Cu-Mg, Bi-Tl and Ni-Al melts involving compound formation have been calculated. The calculated results show that, except the ultimate case of pure element, when two elements are present in the melts, all structural units (atoms and molecules) without exception will be present in the melts, i.e., their concentrations may change from great to small, but they will not vanish into nothing, and only under such conditions, the calculated results both agree with practice and obey the law of mass action. In view of that over considerable wide composition range, the activities of both elements of the three solid binary alloys mentioned above have been measured, this seems in contradiction with the present relevant phase diagrams, in which the structural units are determined by composition range, so the latter needs further investigation and consideration.

A NEW APPROACH TO THE CURVE FITTING OF IN VITRO RADIOASSAYS BASED ON THE MASS ACTION LOW

A new curve fitting method with its mathematical models derived from the mass action law is presented which is applicable to several in vitro radioassays including RIA and RBA. Experiments revealed that the robustness of this method is better than the conventional methods like Woolf plot in RBA and 4- parameter logistic plot in RIA. However, the robustness of this method is only relative: in some cases of RIA and RBA, the bias of the results may still be too large to be acceptable. Further improvement is expected to be studied.

Quantum Statistics in Physical Chemistry, the Law of Mass Action and Epicatalysis

The law of mass action, based on maxwellian statistics, cannot explain recent epicatalysis experiments but does when generalized to non-maxwellian statistics. Challenges to the second law are traced to statistical heterogeneity that falls outside assumptions of homogeneity and indistinguishability made by Boltzmann, Gibbs, Tolman and Von Neumann in their H-Theorems. Epicatalysis operates outside these assumptions. Hence, H-Theorems do not apply to it and the second law is bypassed, not broken. There is no contradiction with correctly understood established physics. Other phenomena also based on heterogeneous statistics include non-maxwellian adsorption, the field-induced thermoelectric effect and the reciprocal Hall effect. Elementary particles have well known distributions such as Fermi-Dirac and Bose Einstein, but composite particles such as those involved in chemical reactions, have complex intractable statistics not necessarily maxwellian and best determined by quantum modeling methods. A step by step solution for finding the quantum thermodynamic properties of a quantum composite gas, that avoids the computational requirement of modeling a large number of composite particles includes 1) quantum molecular modeling of a few particles, 2) determining their available microstates, 3) producing their partition function, 4) generating their statistics, and 5) producing the epicatalytic parameter for the generalized law of mass action.