The paper refers to disproportionation of HIO and NaIO in aqueous media, in static and dynamic systems. The results of calculations, realized according to GATES/GEB principles, with use of an iterative computer progra...The paper refers to disproportionation of HIO and NaIO in aqueous media, in static and dynamic systems. The results of calculations, realized according to GATES/GEB principles, with use of an iterative computer program, are presented graphically. An example of the computer program with all physicochemical knowledge involved in the related algorithm is attached herewith.展开更多
A simple general relation P = Q + R + 1 between the number P of kinds of species, the number Q of charge and elemental/core balances and the number R of independent equilibrium constants is deduced, and its validity i...A simple general relation P = Q + R + 1 between the number P of kinds of species, the number Q of charge and elemental/core balances and the number R of independent equilibrium constants is deduced, and its validity is confirmed for non-redox and redox electrolytic systems, of different degree of complexity.展开更多
The formalism realised according to the Generalised Approach to Electrolytic Systems (GATES) is presented and applied to typical redox systems known from the laboratory practice. In any redox system, the Generalized E...The formalism realised according to the Generalised Approach to Electrolytic Systems (GATES) is presented and applied to typical redox systems known from the laboratory practice. In any redox system, the Generalized Electron Balance (GEB), perceived as the law of the matter conservation, is derivable from linear combination 2·f(O) – f(H) of elemental balances: f(O) for oxygen and f(H) for hydrogen. It is an equation linearly independent from other (charge and concentration) balances referred to an electrolytic redox system (aqueous media) of any degree of complexity, and named as the primary form of GEB and then denoted as pr-GEB. A compact equation for GEB is obtained from linear combination of 2·f(O) – f(H) with other (charge and concentration) balances. For a non-redox electrolytic system, of any degree of complexity, the balance 2·f(O) – f(H) is not an independent equation. In the derivation of GEB, all known components (species) of the system tested, taken in their real (i.e., hydrated) form, are involved in the balances, and none simplifying assumptions are needed. The redox systems are simulated with use of an iterative computer program.展开更多
The correct approach, based on the rules of conservation and detailed physicochemical/thermodynamic knowledge on the system considered is opposed to conventional approach to solubility and dissolution, based on stoich...The correct approach, based on the rules of conservation and detailed physicochemical/thermodynamic knowledge on the system considered is opposed to conventional approach to solubility and dissolution, based on stoichiometry of a reaction notation and on the solubility product (Ksp) of a precipitate. The correct approach is realized according to Generalized Approach to Electrolytic Systems (GATES) principles, with use of iterative programs applied for computational purposes. All the qualitative and quantitative knowledge is involved in the balances and independent expressions for the equilibrium constants. Three two-phase electrolytic systems with diversified chemical properties were selected carefully, from the viewpoint of their diversity. The results of calculations are presented graphically and discussed. The advantages of the GATES in resolution of two-phase (static) non-redox systems and one complex (dynamic) redox system are proved.展开更多
A complex example of electrolytic redox system involving 47 species, 3 electron-active elements and five (3 am-phiprotic + 2 aprotic) co-solvents, is presented. Mixed solvates of the species thus formed are admitted i...A complex example of electrolytic redox system involving 47 species, 3 electron-active elements and five (3 am-phiprotic + 2 aprotic) co-solvents, is presented. Mixed solvates of the species thus formed are admitted in the system considered. It is proved that the Generalized Electron Balance (GEB) in its simplest form obtained according to the Approach II to GEB is identical with the one obtained for aqueous media and binary-solvent system, and is equivalent to the Approach I to GEB.展开更多
Two complex dynamic non-redox systems are considered as examples, providing interdependent linear equations. A simple and efficient linear combination method that leads the system of equations to the identity, 0 = 0, ...Two complex dynamic non-redox systems are considered as examples, providing interdependent linear equations. A simple and efficient linear combination method that leads the system of equations to the identity, 0 = 0, is used for this purpose. These examples are clear confirmations of the general property differentiating non-redox and redox electrolytic systems. This property is involved with linear dependence or independence of 2·f(O)-f(H) on charge and elemental/core balances for elements/cores ≠H, O, where f(H) and?f(O) are elemental balances for H and O, respectively.展开更多
A uniform procedure is suggested for calculation of the pHt value(s) separating equilibrium solid phases in pH scale, at an excess of the precipitating agent. The pHt value, related to pairs of precipitates formed fro...A uniform procedure is suggested for calculation of the pHt value(s) separating equilibrium solid phases in pH scale, at an excess of the precipitating agent. The pHt value, related to pairs of precipitates formed from the species ??and ?, fulfils the relation , where F is a constant value involving pKso’s for solubility products (Kso’s) of these precipitates, and the equilibrium data, related to the species composing these precipitates.展开更多
The article provides experimental data applied to the determination of carbonate alkalinity (CAM) according to modified Gran II functions. CAM is related to the mixtures NaHCO3 + Na2CO3 and Na2CO3 + NaOH. In addition ...The article provides experimental data applied to the determination of carbonate alkalinity (CAM) according to modified Gran II functions. CAM is related to the mixtures NaHCO3 + Na2CO3 and Na2CO3 + NaOH. In addition to the determination of equivalence volumes, one of the main novelties of the proposed method is the possibility of determining the activity coefficient of hydrogen ions (γ). Moreover, CAM can be used to calculate the dissociation constants (K1, K2) for carbonic acid and the ionic product of water (KW) from a single pH titration curve. The parameters of the related functions are calculated according to the least squares method.展开更多
The Generalized Electron Balance (GEB), together with charge balance and concentration balances, completes the set of equations needed for resolution of electrolytic redox systems. The general formulae for GEB were ob...The Generalized Electron Balance (GEB), together with charge balance and concentration balances, completes the set of equations needed for resolution of electrolytic redox systems. The general formulae for GEB were obtained according to Approach II to GEB, i.e., on the basis of the equation 2?f(O) ? f(H) obtained from elemental balances: f(H) for H, and f(O) for O. Equivalency of the Approach II and the Approach I to GEB was proved for an aqueous solution and a binary-solvent system. On this basis, a compact form of GEB was derived.展开更多
Formulation of the simplex matrix referred to n-D space, is presented in terms of the scalar product of vectors, known from elementary algebra. The principles of a simplex optimization procedure are presented on a sim...Formulation of the simplex matrix referred to n-D space, is presented in terms of the scalar product of vectors, known from elementary algebra. The principles of a simplex optimization procedure are presented on a simple example, with use of a target function taken as a criterion of optimization, where accuracy and precision are treated equally in searching optimal conditions of a gravimetric analysis.展开更多
This paper refers to inflection point—the fundamental property of S-shaped curves. In this paper, the inflection points are related to pH titration curve pH = pH(V), and to the curve s = s(pH) involved with surface t...This paper refers to inflection point—the fundamental property of S-shaped curves. In this paper, the inflection points are related to pH titration curve pH = pH(V), and to the curve s = s(pH) involved with surface tension, s.展开更多
The solubilities (s, mol/L) of different oxyquinolinates (oxinates, MeL2) are calculated using the formulae obtained according to elementary algebra, with the use of Excel spreadsheets. The calculations are involved w...The solubilities (s, mol/L) of different oxyquinolinates (oxinates, MeL2) are calculated using the formulae obtained according to elementary algebra, with the use of Excel spreadsheets. The calculations are involved with solution of algebraic equation of the third degree, obtained on the basis of concentration balances. The root of this equation, , is then inserted into the charge balance, and resolved according to zeroing procedure. In principle, the calculations are related to aqueous media. Nonetheless, the extension on liquid-liquid extraction systems is also proposed.展开更多
The isohydricity (pH constancy) as the property referred to mixtures of acids or bases, is illustrated on a simple example of the solutions: HL (C0, mol/L) and HL (C mol/L) mixed according to titrimetric mode (pH titr...The isohydricity (pH constancy) as the property referred to mixtures of acids or bases, is illustrated on a simple example of the solutions: HL (C0, mol/L) and HL (C mol/L) mixed according to titrimetric mode (pH titration). A new derivation of the Michalowski formula C0=C+C2·10PK1 expressing this property is presented, and its applicability for determination of pK1 = – logK1 value is indicated. The principle of the isohydric method of pK1 determination is also outlined.展开更多
文摘The paper refers to disproportionation of HIO and NaIO in aqueous media, in static and dynamic systems. The results of calculations, realized according to GATES/GEB principles, with use of an iterative computer program, are presented graphically. An example of the computer program with all physicochemical knowledge involved in the related algorithm is attached herewith.
文摘A simple general relation P = Q + R + 1 between the number P of kinds of species, the number Q of charge and elemental/core balances and the number R of independent equilibrium constants is deduced, and its validity is confirmed for non-redox and redox electrolytic systems, of different degree of complexity.
文摘The formalism realised according to the Generalised Approach to Electrolytic Systems (GATES) is presented and applied to typical redox systems known from the laboratory practice. In any redox system, the Generalized Electron Balance (GEB), perceived as the law of the matter conservation, is derivable from linear combination 2·f(O) – f(H) of elemental balances: f(O) for oxygen and f(H) for hydrogen. It is an equation linearly independent from other (charge and concentration) balances referred to an electrolytic redox system (aqueous media) of any degree of complexity, and named as the primary form of GEB and then denoted as pr-GEB. A compact equation for GEB is obtained from linear combination of 2·f(O) – f(H) with other (charge and concentration) balances. For a non-redox electrolytic system, of any degree of complexity, the balance 2·f(O) – f(H) is not an independent equation. In the derivation of GEB, all known components (species) of the system tested, taken in their real (i.e., hydrated) form, are involved in the balances, and none simplifying assumptions are needed. The redox systems are simulated with use of an iterative computer program.
文摘The correct approach, based on the rules of conservation and detailed physicochemical/thermodynamic knowledge on the system considered is opposed to conventional approach to solubility and dissolution, based on stoichiometry of a reaction notation and on the solubility product (Ksp) of a precipitate. The correct approach is realized according to Generalized Approach to Electrolytic Systems (GATES) principles, with use of iterative programs applied for computational purposes. All the qualitative and quantitative knowledge is involved in the balances and independent expressions for the equilibrium constants. Three two-phase electrolytic systems with diversified chemical properties were selected carefully, from the viewpoint of their diversity. The results of calculations are presented graphically and discussed. The advantages of the GATES in resolution of two-phase (static) non-redox systems and one complex (dynamic) redox system are proved.
文摘A complex example of electrolytic redox system involving 47 species, 3 electron-active elements and five (3 am-phiprotic + 2 aprotic) co-solvents, is presented. Mixed solvates of the species thus formed are admitted in the system considered. It is proved that the Generalized Electron Balance (GEB) in its simplest form obtained according to the Approach II to GEB is identical with the one obtained for aqueous media and binary-solvent system, and is equivalent to the Approach I to GEB.
文摘Two complex dynamic non-redox systems are considered as examples, providing interdependent linear equations. A simple and efficient linear combination method that leads the system of equations to the identity, 0 = 0, is used for this purpose. These examples are clear confirmations of the general property differentiating non-redox and redox electrolytic systems. This property is involved with linear dependence or independence of 2·f(O)-f(H) on charge and elemental/core balances for elements/cores ≠H, O, where f(H) and?f(O) are elemental balances for H and O, respectively.
文摘A uniform procedure is suggested for calculation of the pHt value(s) separating equilibrium solid phases in pH scale, at an excess of the precipitating agent. The pHt value, related to pairs of precipitates formed from the species ??and ?, fulfils the relation , where F is a constant value involving pKso’s for solubility products (Kso’s) of these precipitates, and the equilibrium data, related to the species composing these precipitates.
文摘The article provides experimental data applied to the determination of carbonate alkalinity (CAM) according to modified Gran II functions. CAM is related to the mixtures NaHCO3 + Na2CO3 and Na2CO3 + NaOH. In addition to the determination of equivalence volumes, one of the main novelties of the proposed method is the possibility of determining the activity coefficient of hydrogen ions (γ). Moreover, CAM can be used to calculate the dissociation constants (K1, K2) for carbonic acid and the ionic product of water (KW) from a single pH titration curve. The parameters of the related functions are calculated according to the least squares method.
文摘The Generalized Electron Balance (GEB), together with charge balance and concentration balances, completes the set of equations needed for resolution of electrolytic redox systems. The general formulae for GEB were obtained according to Approach II to GEB, i.e., on the basis of the equation 2?f(O) ? f(H) obtained from elemental balances: f(H) for H, and f(O) for O. Equivalency of the Approach II and the Approach I to GEB was proved for an aqueous solution and a binary-solvent system. On this basis, a compact form of GEB was derived.
文摘Formulation of the simplex matrix referred to n-D space, is presented in terms of the scalar product of vectors, known from elementary algebra. The principles of a simplex optimization procedure are presented on a simple example, with use of a target function taken as a criterion of optimization, where accuracy and precision are treated equally in searching optimal conditions of a gravimetric analysis.
文摘This paper refers to inflection point—the fundamental property of S-shaped curves. In this paper, the inflection points are related to pH titration curve pH = pH(V), and to the curve s = s(pH) involved with surface tension, s.
文摘The solubilities (s, mol/L) of different oxyquinolinates (oxinates, MeL2) are calculated using the formulae obtained according to elementary algebra, with the use of Excel spreadsheets. The calculations are involved with solution of algebraic equation of the third degree, obtained on the basis of concentration balances. The root of this equation, , is then inserted into the charge balance, and resolved according to zeroing procedure. In principle, the calculations are related to aqueous media. Nonetheless, the extension on liquid-liquid extraction systems is also proposed.
文摘The isohydricity (pH constancy) as the property referred to mixtures of acids or bases, is illustrated on a simple example of the solutions: HL (C0, mol/L) and HL (C mol/L) mixed according to titrimetric mode (pH titration). A new derivation of the Michalowski formula C0=C+C2·10PK1 expressing this property is presented, and its applicability for determination of pK1 = – logK1 value is indicated. The principle of the isohydric method of pK1 determination is also outlined.