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10(C-O-C) group, the vinyl band 862 cm-1 area deformation vibration of the =CH2 group, 2929 and 1438 cm-
1 area the valence oscillations of the CH group, 1654 sm-1 in the area, the valence vibration signal (-CH = CH2) was observed.
IR-spectrum of 2,4,6-trieth (vinyloxy) -1,3,5-triazine: 2,4,6-tritium (vinyloxy) in the IR spectrum of -1,3,5-triazine of carbonyl group (C = O) the valence vibration signal was in the field 1791 cm-1, and the valve vibration signals of the C = N group of the ring were in the 1400 cm-1 area. In the 1056 cm-1 area was the valence vibration signal of the ether (C-O-C) group, vinyl band 761 cm-1 area deformation vibration band CH2, 3053 and 1463 cm-1 area = CH valence oscillations; 1693 sm-1 in the area, was observed the valence vibration signal (-CH = CH2).
PMR spectrum of 2,4,6-trieth (vinyloxy) -1,3,5-triazine: 2,4,6-tritium (vinyloxy) in the PMR spectrum of -1,4,5-triazine in the vinyl group (-CH = CH2) quartet signal of one proton (-CH =) is 7.41 m.p. in the field, the duplex-duplex signals of two protons (= CH2) are 5.03 and 5.06 m. areas. Three-vinyl ether of cyanuric acid in the 13C spectrum signals of carbon atoms in the 2,4,6-position in the triazine ring at 166 m. in the field, the carbon of the vinyl group is 145.5 (-CH=) and 94.6 (=CH2) ppm areas.
CONCLUSION
After analyation of kinetic parameters of the synthesis of cyanuric acid vinyl ethers, the average reaction rate was determined and it's activation energy was calculated. Using analysis of graphs of analytical functions and diagrams of kinetic parameters of synthesis it is possible to established that at a reaction time of 2, 4, 6 hours and a temperature of 140 ° C the yields of vinyl ethers have reached a maximum values: mono-vinyl, in
2 h, 75,2; di-vinyl, in 4 h, 81,2 and in 6 hours 89,6 %.
References
1. E.H. Wiebenga and N.F. Moerman. Crystal structure of cyanuric acid // Nature 141. 122 (1938). https://doi.org/10.1038/141122b0
2. T. Yilmaz and Z. Yazar. Determination of cyanuric acid in swimming pool water and milk by differential pulse polarography // Clean - Soil Air Water. 2010. -38. -P. 816-821. https://doi.org/10.1002/clen.201000071
3. E. Canelli. Chemical, bacteriological, and tox-icological properties of cyanuric acid and chlorinated isocyanurates as applied to swimming pool disinfection // Am. J. Pub. Health.1974. -64. -P. 155-162.
4. V.I. Mur. 2,4,6-trichloro-1,3,5-triazine and its future applications // Russ. Chem. Rev. 1964. -33: -P. 120-121.
5. G. Giampaolo, P. Andrea and D. L. Lidia. 1,3,5-triazine: A versatile heterocycle in current applications of organic chemistry // Curr. Org. Chem. 2004. -8. -P. 1497-1519.
6. T.R. Aslamazova, V.A. Kotenev, N.Yu. Lomovskaya, and A.Yu. Tsivadze. Prot. Met Phys. Chem. Surf. 2014. vol.-50. №-5. -P. 620-627.
7. D.L. Flamm and O. Auciello. Plasma deposition, treatment, and Etching of Polymers the Treatment and Etching of Polymers // New York. Elsevier. 2012.-P. 124-127
8. A.B. Parmanov, S.E. Nurmanov, Beata Kolesinsko, Tomash Maniecki, O.E. Ziyadullayev. Homogeneous vinylation of 2-hydroxy-2-phenylethanical acid. Azerbaijan chemical journal. -Azerbaijan, -2019, № 4. P. 32-34. DOI: https://doi.org/10.32737/0005-2531-2019-4-32-34.
9. Parmanov A.B., Nurmonov S.E., Abdugafu-rov I.A., Ziyadullaev O.E., Mirkhamitova D.X. Synthesis of vinyl ester of lactic acid. Eurasian Union of Scientists. Russia. № 7 (64) / 2019 P. 51-56. DOI: https://doi.org/10.31618/ESU.2413-9335.2019.2.64.227
10. А.Э. Зиядуллаев, С.Э. Нурманов, У.У. Жумартова, А.Б. Парманов. Теоретические основы реакции гомогенного каталитического винилирования циануровой кислоты // Журнал Евразийский союз ученых, Россия № 9 (66) 2019. 2 часть. 37 - 41 с. DOI: 10.31618/ESU.2413-9335.2019.2.66.304
SOLVING DIRECT AND INVERSE PROBLEMS FOR AUTOCATALYTIC REACTIONS
Bondarchuk I.
Postgraduate student, Department of Chemistry, Tomsk State University Bondarchuk S.
Doctor of Physical and Mathematical Sciences, Professor, Department of Biology and Chemistry, Tomsk State Pedagogical University
Abstract
This article proposes a new method and algorithm for identifying the kinetic parameters of autocatalytic reactions through solving inverse problems. The proposed method can be classified as integral. A simple algorithm and code is presented, which is easy to test and which is based on the MS Excel Solver add-on without using macros of Visual Basic. A detailed description of the implementation of the algorithm and the results of determining the kinetic parameters for identifying the kinetic parameters of typical autocatalytic reactions are given.
Keywords: chemical kinetics, autocatalytic reaction, inverse problems, spreadsheet.
Autocatalysis (autocatalytic reaction) is a reaction, the rate of which increases due to the formation of a catalyst during the process, the final product as its concentration increases. The rate of the autocatalytic reaction in the initial period increases, and then begins to decrease according to a decrease in the spent reagents. The kinetic curve of the autocatalytic reaction has the form of a sigmoid (S-shaped curve).
An example of autocatalysis is the reaction of io-dination of acetone in an acidic environment CH3COCH3 + I ^ CH3COCH3I + HI,
when at the first stage the ketone is converted to enol, and then the latter reacts with iodine to form final products. As the reaction proceeds, the content of hy-droxonium ions increases, which causes an acceleration of the reaction [1, 2].
k
The autocatalytic reaction M^P can occur in other cases when the so-called seed is present in the system initially, a certain amount of the substance that is a product of this reaction. During the autocatalytic reaction, there is an induction period when the catalyst product accumulates in the system.
It should be noted that product T is not a catalyst in the exact concept of this term, since, in particular, during the reaction, its concentration continuously increases.
For the constant k, the rate constant of the limiting stage, the kinetic equation of the first-order autocata-lytic reaction with respect to reagent <A and product T can be written as
^=-kAP ,t = 0: A = A0,P = P0 .(1)
Given the law of matter conservation A0 - A = P0 + P, the kinetic equation of the autocatalytic reaction can be rewritten in the form
dA
— = -kA(Ao + Po
■A). (2)
Separation of variables and the use of the method of uncertain coefficients leads to equality
~:{a+ An + Pn - a).
1
A(Ao+Po-A)
¿o + Po\A
From this equation after integration can obtain expressions for the reactant and product concentrations
A0 + P0
A =-^-0-0-, (3)
p
1+^^exp((Ao + Po)kt) 0 Ao + Po
P = Ao+Po-A =
A
-,(4)
1 + ^°exp(-(A0+P0)kt)
and clearly express the value of the rate constant through time and, for example, reactant concentration
k =
1
(¿o + Po)t
ln
Ao(Ao + Po
TA—a--1)
(5)
Example 1. To determine the time dependences of the concentrations of the reagent, product, and reaction rate for the autocatalytic reaction
k
in the first orders of magnitude for the components with the following initial data: fc=0.2, ^0=0.8, P0 =0.001 [1].
The required dependencies are formulated according to equations (3), (4) and (2) in columns C, D and E for the initial data A0, P0 (cells H4 and H5) with the reaction constant recorded in cell H6 (Figure 1). The required calculated dependences are shown in the same Figure 1. Change in concentrations and reaction rate with time (calculation results) are shown in Figure 2.
A B C D E I- G H
1 =H$10/ (1+H$S/H$4*EXP(H$10*H$6*B4)| |
1= $H$10-C4j;iH$6*C4*(H$10-C4) |
2
3 I A P idA/dt
4 0 0,800 fcO.OOl kl,60E-04 0,8
5 5 0,799 0,002 3,55E 04 po= 0,001
6 10 0,796 0,005 7.86E-04 <r= 0,2
7 15 0,790 0,011 1,73E 03
8 20 0,777 0,024 3.72E-03
9 25 0,750 0,051 7.71E 03
10 30 0,695 0,106 1.48E-02 A. + Po= • 0,801
11 35 0,598 0,203 2.43E-02
12 40 0,4S6 0,345 3,15E-02 ■ H4.HS
13 45 0,298 0,503 3.00E 02
14 SO 0,168 0,633 2.13E-02
15 55 0,085 0,716 1.22E-02
16 60 0,041 0,760 6.19E-03
17 65 0,019 0,782 2.94E-03
18 70 0,009 0,792 1.35E-03
19 75 0,004 0,797 6.15E-04
20 80 0,002 0,799 2,78E-04
21 85 0,001 0,800 1.25E-04
22 90 0,000 '0,801 ▼ 5,61E-OS
Figure 1. Spreadsheet of the solution to the direct problem of autocatalysis
0 15 30 45 60 75 t
Figure 2. Change in concentration and reaction rate versus time. The values of the rate increased by 25 times
Example 2. Using a given dependence of the
change in reagent versus time, determine the reaction
rate constant and the seed concentration for an auto-
k
catalytic reaction of the sheme P.
For calculations, the Excel Solver add-on is used [3 - 6], where the variable is the sum of the concentrations of the reagent and the product (cell G10, Figure 3.) with a predefined value of 0.801 - a value slightly larger than A0 (adjusted for the seed).
In the course of preparation of the solution, the value Amin is determined - a restriction for the minimum value of the sum of the initial concentrations, which ensures the "presence" of the seed.
In the range of cells D4 :D10, kt are determined by relation (5), and their average value in cell D12.
The value of the functional is determined in cell D13 by N = 7; the values of are determined by the equation (coefficient of variation)
1
T(A0 +P0)= = M
through the Excel function STDEV.P (...).
This relation the functional in the form of a coefficient of variation is interpreted as follows: for the kinetic equation parameter corresponding to the initial data, the spread of the calculated values of some constant of this equation should be minimal. It should be noted that with this approach, the number of variables is reduced by one.
The solution is achieved using the Excel add-on Solver with the following parameters
• address of the cell ($D$13), where the formula of the functional - calculation of the objective function is located;
• optimization characteristic "To..." Min";
• variable cell address ($G$10) "By Changing Variable Cells for Solver";
• in the "Subject to the Constraints" window set the obvious restriction $G$10>=$G$3;
• flag the indicator "Make Unconstrained Variables Non-Negative";
• solution method "GRG Nonlinear".
Figure 3. Spreadsheet of solving the inverse problem of autocatalysis offirst-order reactions
In the case of arbitrary reaction orders for reagent A and product P, equation (1) has the form dA
— = -kAPipP^ dt
or, subject to the law of conservation of the quantity of substance, can be represented as
^=kAP1(A0+P0-A)P2 . (6)
Example 3. Based on a given dependence of the change in reagent versus time, determine the reaction rate constant, the concentration of the seed for the au-tocatalytic reaction, and the reaction orders by components.
As in the previous example, the solution search Excel add-on Solver is used for calculations, where the changing variable cells are the sum of the initial concentrations of the reagent and product, as well as the order of reactions for substances (cells I7:I9, Figure 4) with predefined values:
I7: Amin = 2.001 - a value slightly larger than A0 (adjusted for the seed);
I8, p1 = p2=1 - orders of reactions.
Since the orders of reactions are initially unknown, the explicit expression necessary for the calculations of the rate constant can be determined from the integral of equation (6)
A
_ . dA
k
The value of the integral I(x) for the integrand f(x) is calculated by the relation
n
Kx)~h^f(xi-1+h)
i = 1
2) n
= h^f( x0 + (i- 0.5)h ) ;
= 11
APi(A0 + P0 - A)P2
Numerical integration is carried out using the quadrature formula in accordance with midpoints rule.
preliminary, the integration steps h are determined in column D.
In the range of cells F5:F16, the ki values are determined by the above ratio, and in the cell F18, their average value is determined.
The value of the functional is determined by N = 12 kt values in the same way as in the previous example, in cell I11.
When it is activated in the add-on panel (the window "Subject to the Constraints"), the values $I$7>=$I$5 are set; $I$8=integer; $I$9=integer.
After starting the add-on Solver, where the objective function is determined by cell I11; the "By Changing Variable Cells" are cells I7:I9 the worksheet takes the form shown in Figure 4.
cells of the range E5: E16 are processed as array formulas
Figure 4. Spreadsheet of the solution of the inverse problem of autocatalysis of reactions of various orders
Thus, a new approach to the problems of identifying the kinetic parameters of autocatalytic reactions through solving inverse problems is presented, which can significantly reduce the amount of programming of computational algorithms and improve the accuracy of calculations. In the examples of determining the order
of reactions from experimental data, the algorithms for solving the problems as optimization are presented in sufficient detail when the spread of one of the identifiable unknown parameters of the mathematical model is minimized.
i=i
A
0
The mathematical apparatus required for mastering the method is quite simple (elementary integration and the method of separation of variables for solving ordinary differential equations). The implementation of the algorithm is carried out only by MS Excel spreadsheet tools without using macros.
References
1. Korobov V.I., Ochkov V.F. Chemical Kinetics: Introduction with Mathcad / Maple / MCS / Moscow, Hotline-Telecom, 2015. 384 p.
1. Kolpakova N.A., Romanenko S.V., Kolpakov V.A. A task book in chemical kinetics: tutorial (2nd ed.): Tomsk Polytechnic University. Publishing House of Tomsk Polytechnic University, 2013. 246 p.
3. Bondarchuk I.S., Fedorova V.A. Algorithms for the identification of kinetic parameters of elementary reactions // "Prospects for the development of fundamental sciences". In materials of the XI International Conference of Students and Young Scientists. National
Research Tomsk Polytechnic University, 2014. P. 555557.
4. I.S. Bondarchuk, I.A. Kurzina, S.S. Bondarchuk, The Methodology of Solving Problems in Physical Chemistry by Using Solver MS Excel // Higher Education Today, 2014. 9, P. 22-24.
5. Ivan S. Bondarchuk, Sergei S. Bondarchuk, and Boris V. Borisov, Identification of kinetic triplets by results of derivatographic analysis // MATEC Web Conf., "Heat and Mass Transfer in the Thermal Control System of Technical and Technological Energy", 2018. V. 194, 01010. https://doi.org/10.1051/ matecconf/ 201819401010.
6. Bondarchuk S.S., Bondarchuk I.S., Kurzina I.A., Fedorova V.A. Methodology for solving the problems of physical chemistry with the SOLVER MS EXCEL tool // "Level training of specialists: e-learning and open educational resources". Materials of the I Russian Scientific and Methodological Conference. National Research Tomsk Polytechnic University, 2014. P. 178-180.
ГЛУБИННЫЕ ПРИЧИНЫ ЕДИНОГО ОБЩЕПРИРОДНОГО НАСЛЕДСТВЕННО -
ПЕРИОДИЧЕСКОГО ЗАКОНА
Григорьев М.А.
директор ООО Кадряковского Медицинского Лечебного центра «Саулык» РТ Канд. медицинских наук, врач
ROOT CAUSES OF THE ORIGINAL AND PERIODIC LAW OF A SINGLE EVOLUTIONARY
PROCESS
Grigoryev M.
Candidate of Medical Science, doctor, director of Kadryakovskiy medical treatment center "Saulyk", Republic of Tatarstan.
Аннотация
На сегодня нам известны механизм и следствие наследственных законов Г. Менделя и периодических законов химических элементов Д.И. Менделеева, однако не известны глубинные причины наследственной изменчивости и периодичности. В настоящий момент целый ряд ученых придерживается той точки зрения, что, в то время как причину возникновения всех солнечных феноменов следует искать внутри Солнца, распределение их во времени и на поверхности светила можно приписывать влиянию планет. Однако внутренняя структура Солнца и причины солнечной активности на сегодня тоже неизвестны.
Автор, несколько видоизменяя принцип Галилея, что не видимое тело устроено так же, как видимое, рассчитал параметры внутренней структуры Солнца. Этот принцип звучит так: «Изучай видимую разрыхленную наружную структуру тела, а квантованно уменьшенная невидимая уплотненная внутренняя его структура устроена спирально послойно подобно так же, как и наружная». Природа едина, если достоверно изучены биологические процессы, то подобные же процессы и происходят и в неорганическом мире. Молекула информационного или матричного РНК переписывает код с молекулы ДНК и несет его с помощью транспортного РНК к синтезирующим рибосомам клетки, где рибосомная РНК компонует подобные же, количественными порциями и очередностями аминокислот. В результате, возникающих многоходовых межкомпонентных комбинации РНК, образуются сложные ДНК подобные полипептиды белка. Подобным же образом синтезируются элементарные частицы и атомы химических элементов, только вместе РНК работает нейтрино.
Планеты дискретно вращаясь по периметру яйцеобразных орбитальных котлов Солнца, как по гипотенузе треугольника Пифагора, проходят за одно и то же время разные пути по этой дискретной искривленной и разделенной на многие отрезки гипотенузе, в зависимости от радиуса(катета) сегмента котлов.
При этом формируется афелий и перигелий планеты на минимальных и максимальных искривлениях орбитального котла Солнца. Причиной движения планет по прямому пути, а не по закруглённому, является искривление орбиты планет, где прямой и отраженный свет идет по тому пути, который занимает меньше
