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T. Y. Gumerov, O. A. Reshetnik CALCULATING COMPOSITION AND EQUILIBRIUM CONSTANTS OF HETERONUCLEAR COMPLEXES IN SYSTEM Al(III)-Cr(III)-H2O-OH-Cl"
Ключевые слова: потенциометрическое титрование, полиядерные и гетероядерные соединения, модельные системы.
Исследованы кривые потенциометрического титрования растворов AlCl3, CrCl3 и их смесей в области рН 3 - 12.
Keywords: Potentiometrie titration, polynuclear and heteronuclear compounds, modeling a system.
We obtained experimental curves of Potentiometrie titration of solutions AICI3, CrCI3 and their mixes with pH 3 -12.
Mathematical model of system Al(III)-Cr(III)-H2O-OH--CI-, which reflects its real equilibrium processes, is quite important for solving scientific and technical problems. They include calculation of equilibrium constants, determination of areas with compounds, synthesis of compounds from water solutions, processing of technological solutions, waste water purification and etc. Main principles of modeling of complex balances in systems metal ions - water - ligands were explained by R.A. Yusupov in works [1-3].
In works by E.G. Vinokurov and others [4-6], a research was conducted on stoichiometry of compounds and chemical balances in water chromic sulphate solutions (III) in a wide range of concentration of chromic sulphate (III) and pH solutions. A mathematical balance model was tested in these works to describe experimental data about how solutions' initial pH values depend on initial salt content, how conductivity, transmission density and viscosity of solutions depend on initial salt content and pH solutions. Authors indicated that mathematical model of equilibrium processes is important for optimization of chroming solutions' composition. However, the approach to modeling of complex balance systems used in work [4] has some disadvantages: residues are not taken into account; different equations of mass balance are used to describe experimental data obtained by different methods.
In our opinion, when creating a mathematical model of a complex balance system it is necessary to have a large experimental database received by different research methods, as well as wide theoretic and methodic base and software. When modeling systems with a possible formation of heteronuclear compounds situation becomes more indefinite than when we model systems metal salt-water-ligands. It should be stressed here that requirements to reliability of mathematical models of some systems are considerably increasing. At the first step of calculations we simply sum the values of two systems. Difference between the values of simple summation and values of the system with heteronuclear compounds let receive reliable data about stoichiometry of heteronuclear compounds, and equilibrium constants between them. When modeling and calculating stoichi-ometry and equilibrium constants, one should constantly base on visualized assessment of harmonization of theory and experiment. At the simple summation of values the assessment is based on experimental data of several systems (AI(III)-H2O-OH- -CI-- system 1, Cr(III)-
H2O-OH--CI--system 2). When we study heteronuclear compounds, the evaluation is conducted using data of experiment on system Al(III) - Cr(III)-H2O-OH—CI--system 3. Formation of residues is one of the main problems in systems modeling. The above mentioned conditions of solutions' saturation determine areas of residue formation, for example, the last condition determines gradual metal oxidation as pH solution values grow. If the area of residues formations coin cides with the area where main residue's component exists in significant mole fractions, then curves of potentiometric titration (CPT) do not differ from CPT, where residues are not taken into consideration. Otherwise there's a significant difference in the form of CPT on borders of residue areas. Ionic strength of solutions should be regarded as a secondary factor when calculating equilibrium constants. Calculations using ionic strength of solutions should be conducted after reliable data on complex system's mass balance and evaluation of equilibrium constants are available. In other case the situation is possible when systematic parameter seem to be calculated more precise due to additional factor. Besides, artificial inclusion into system of highly concentrated additional substances in order to keep ionic strength of solutions causes risk of system's pollution and formation of additional complex compounds [7]. So, determination of equations of system's mass balance and equilibrium processes between them, evaluation of equilibrium constants basing on visualized calculations let minimize the number of compounds in the system, which are initially included in the software. At the last stage of data processing automatic calculations let rather precisely and reliably describe experimental data and get values of system parameters and their confidence intervals.
We used solutions A1C13 (Terms of Reference 38-102612-88) and CrCf, (State Standard 4473-78). During potentiometric titration of metals' water solutions with solution NaOH («analytically pure») we used digital ionomer I-130.2M. As a measure electrode we used glass electrode ESL-43-07, as a reference electrode - chloride-silver electrode EVL-1M1. Ionomer was tuned to standard buffer solutions with pH = 9,18 and pH = 1,68 (Na2B4O7- 10H2O (0,01%) and KH3(C2O4)2-2H20 (0,05 M) correspondingly). We also used magnetic drive for mixing and a steel rod in capronic shell as a mixer.
Table 1 - Composition of compounds and values of stability constants in system Al(III),Cr(III) - H2O - OH- - Cl"
Composition of compounds Code Constants Vaiues of draded constants of noH
M (Al(III), Cr(III)), stability (lgP) and constants and
L (OH) solubilty (pKs)
Al(III) Cr(III)
Al(III) Cr(III) Cl- Cl-
Basic series of ML B1 K1 KC1 7.7 6.7 1.00
compounds -B ML2 B2 K2 KC2 7.7 6.7 2.00
ML3 B3 K3 KC3 3.8 3.4 3.00
ML3s B3S K3S KC3S 7.2 6.8 3.00
ML4 B4 K4 KC4 2.0 3.0 4.00
Polynuclear M2L P1.0 KPB0XB1 2.3 - 0.50
compounds - P M4L3 P2.0 KP2B0XB1XB2 - 15.5 0.75
M3L5 P2.3 KPB1X2B2 15.2 18.0 1.67
M3L5s P2.3S KPB1X2B2S 0.5 - 1.67
M6L12 P2.5 KPB2X5B2 33.0 28.0 2.00
M6L12s P2.5S KPB2X5B2S 21.0 21.0 2.00
M2L5 P2.6 KP2B2XL 10.0 - 2.50
M2L5s P2.6S KP2B2XLS 1.4 - 2.50
M3L8 P2.7 KP3B2X2L 16.0 - 2.67
M4L11 P2.8 KP4B2X3L 22.0 - 2.75
Heteronuclear Al2L4CrL G2.1 KG2B2XBC1 15.3 1.67
compounds - G Al2L4Cr2L4 G2.4 KG2B2X2BC2 25.0 2.00
Al2L4Cr2L4s G2.4S KG2B2X2BC2S 9.0 2.00
AlL3CrL2 G2.5 KGB2XBC2XL 16.0 2.50
AlL3CrL3 G2.6 KGB2XBC2X2L 18.0 3.00
0.5
I
0.75
I
1.50 1.67 2 I I I
2.5 2.67 2.75 J III I
4 n™ [ n _J I fiuirtiiiaflf
- riu::nhju
K3 (K3S1
KC1
AIL; m
CiLj CiUE
12-
Th?
stoichiomstry bvm3talion
K4
EC4
AIL,"
{baaic series)
n £
O
&SI srlc :£=C = 1
Fig. 1 - Scheme of balances in systems Al(III),- H2O - OH- - Cl-, Cr(III) - H2O - OH- - Cl- and Al(III),Cr(III) H2O - OH- - Cl-
Titration was carried out at a fixed speed of mixing and adding drops of solution NaOH of a specific concentration. At the end of each titration interval between drops (from 30 to 120) we measured volume of
titrant solution and evaluated pH of solution. During titration the system is close to balance, which is shown by overlay of titration curves, presented in coordinates nL = f (pH) (initial concentration of metal salt is the
same, concentrations of titrant are different), and comparison with curves of residual concentration of metal salt, as well as changing time of titration.
Examples of CPT of solutions Al(III), Cr(III), AI(III) + Cr(III) by solution NaOH are shown on pictures 2-4 in the article Calculating composition and equilibrium constants of heteronuclear complexes in system Al(III)-Cr(III)-H2O-OH-Cl-- by method of po-tentiometric titration. Gumerov T.U. , Yusupov R.A. Dobrynina A.F., Barabanov V.P. // Euopean journal of natural history. Chemical sciences. 2006. №6, p 105.
On the CPT areas are marked, which begin with a sharp rise (step) and ends with a slower growth of nL (plateau). On picture we have: I - area of formation of polynuclear compounds with the function of formation with ligand nL < 2; II - area of formation of hydrocomplexes and polynuclear hydro-complexes nL > 2 and < 3; III - area of formation of negative hydrocomplexes with excessive ligand (OH-). The above mentioned is typical for all experimental data. Heteronuclear compounds are also forming in areas I and II.
The CPT form in case shown can be explained by several reasons. Inclination of CPT's step reduces in area I when initial concentration of metal ion grows. It happens due to decreasing value of stoichiometric coefficient of metal ion for compounds formed in this area of pH solution. Inclination at the plateau in area I, when concentration of metal ion is low, is probably caused by gradual formation of several complex compounds with slightly larger nL. In area II of the CPT the step shifts to alkaline area, when concentration of metal ion becomes higher. Moreover, inclination of the step reduces, proving that the stoichiometric coefficient of metal ion decreases. It can be explained by the following: neutral hydro-complex or polynuclear hydro-complexes with nL > 2 and < 3 are displaced from area I by polynuclear compounds with nL = 2 due to their high stability. If there were no polynuclear hydro-complexes with nL < 2 in the system, then, if concentration of metal ion grew, CPT in area II would move to acid area due to formation of residues of neutral metal hydroxide. The above described situation can only take place when concentration of metal ion is less than 10-4 mol/l. The same case is presented where rise in area I depends on initial concentration of Al(III) (CAl(III)); when CAL(III) increases, the step moves to acid area with pH value ranging from 4,6 to 3,4, inclination of the step decreases (due to smaller nL), which is typical for all systems.
Principles of equilibrium constants' indexing
Indexation of a complex compound:
K - Graded equilibrium constant of a complex compound. Concentration of complex compound is marked by the same symbol, but without letter K.
X - sign of addition (signs «+» or «-» cannot be used due to their incompatibility for programming purposes).
B - the most stable series of complex compound called the basic series of complex compound (in this article it is hydro-complexes). The number to the right of symbols B or BC shows the number of compounds in these series (for example: BO - Al3+; B1 - AlOH2+; B2
- Al(OH)2+; BCO - Cr3+ and etc. The number to the left of symbol В or ВС shows the number of adjoining particles.
С - concomitant series of complex compound.
Р - polynuclear compounds.
G - heteronuclear compounds.
Areas I are different in systems 2 and 1, as there's an incline, and they reach n = 2 when pH = 9. Apparently, this incline can be explained by formation of several polynuclear compounds, whose nL slightly increase when value of pH solution goes up. It comes as a result of gradual displacement of chloride ions from internal coordination sphere. The step in area II moves from acid to alkaline area, when CAL(III) concentration grows; step I for system 1 depends on concentration and moves to acid area with pH 4,6 - 3,6, when CAL(III) value increases; inclination of step's rise declines. In system 2 residues begin to form when pH = 6,7 and CCr(III) = 5,77-10-3 mol/l. In system 3 residues begin to form when pH = 5,3 and pH = 4,05, Са(ш) = 5,77-10-3 mol/l. Residues forming in systems 1 - 2 are polynuclear compounds, and in system 3 they are heteronuclear compounds.
Theoretical curves of potentiometric titration (TCPT) were calculated using software EQ, which was developed at department of KSTU. Program MINIEQL [8] does not allow calculating stoichiometry of compounds and equilibrium constants in the systems that we study, as three conditions of residues solubility are not taken into account and due to simplified approach to equations of mass balance. The initial stage includes manual visualized evaluation of equilibrium constants which allows developing logic for their automatic calculation. Otherwise, there is a big chance to get local answers. For manual calculations, it is necessary to have an experimental database with a wide range of values of initial metal ion concentrations, because when concentration is low there are mainly compounds of basic series, and at high concentrations - polynuclear hydro-complex compounds. It is also necessary to have a scheme of basic compounds of balance system taking into account possible mechanisms of equilibrium processes (see picture 1). At the first step of calculations we recommend to include only compounds of basic series into the equation of mass balance of metal ion and ligand (OH-). Here the following regularity was found: values of all stability constants of compounds of basic series till neutral complex are equal, and stability constants of negative-charged compounds have values which are smaller by 5-8 orders. It is determined by different mechanisms of their formation: in the first instance they are formed by hydrolyze, in the second -by addition of OH-. At the next step of calculations we select values of stability constants of compounds of basic series, so that TCPTs move to area with higher pH in reference to experimental curves. Constant values of negative-charged complexes of basic series are selected till experimental and theoretic curves coincide in area III. Then, polynuclear hydro-complexes with the highest values of the formation function of metal should be included into the mass balance; and changing values of equilibrium constants we aim at alignment of TCPT and ECPT. Value of differences and inclination of titration curves at different concentrations of metal
ion in area I depend, first of sll, on stoichiometric coefficient of metal ion. The larger is the coefficient, the bigger is inclination of TCPT. If steps in area II disappear, we move to the 2nd iteration and increase constant values of basic series. It will lead to necessity to reduce values of stability instants of polynuclear hydro-complex with the largest value of formation function of metal. If TCPT and experimental CPT (ECPT) do not coincide well, then for curves showing titration of highly concentrated solutions polynuclear compounds with smaller пм and nL need to be added into equation of mass balarce. Iterations should be continued until theoretic and experimental curves of potenti-ometric titration align.
Existence of heteronuclear compounds in system 3 is proved by the fact that ECPTs of system 3 (see picture 4) do not coincide with a simple sum of TCPTs in systems 1 and 2 when initial concentrations of metal ions are the same. Alignment of ECPT and TCPT for system 4 can be only reached if five heteronuclear compounds are taken account (they are shown on picture 1 and values of their equilibrium constants are shown in table 1). As we cаn see in table 1, values of equilibrium constants for system 2 significantly differ from those in system 1: stability constants of complex compound of basic series have values which are smaller by an order, and polynuclear compounds M4L3 and M3L5 are more stable. Investigation of this fact is not the topic of this article. Equilibrium constants for heteronuclear compounds have a wide range of values, so there is no sense to discuss the reasons of why the constant values in system 3 differ.
We developed a mathematical model of system Al(III), Cr(III) - H20 - OH- - a- that let evaluate and сalculate equilibrium constants and stoichiometry of
compounds, which are present in solution and residues, basing on experiments on potentiometric titration. In the system that we studied it was showed that there are heteronuclear compounds of significant mole fractions. Equilibrium constants wеre evaluated.
References
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9 Gumerov, T.U. Features recovery Cr (VI) to Cr (III) in wastewater treatment. T.U. Gumerov, K.Y. Shvink // Life Safety, Moscow: New technologies - 2009. V. 1. №1. - P. 35-37.
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© Т. Ю. Гумеров - к.х.н. доцент кафедры технологии пищевых производств КНИТУ, tt-timofei@mail.ru; О. А. Решетник -д.т.н., профессор, зав. каф. технологии пищевых производств КНИТУ.
© T. U. Gumerov - Candidate of Siences (Ph.D.) in Ingineering, Docent (Associated Professor) of the Department of Technology of Food Productions from Faculty of Food Technology in Kazan National Research Technological University, tt-timofei@mail.ru; O. A. Peshetnik - Doctor of Technical Sciences, Professor, supervisor of the of the Department of Technology of Food Productions from Faculty of Food Technology in Kazan National Research Technological University.
