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9Wschodnioeuropejskie Czasopismo Naukowe (East European Scientific Journal) #3(55), 2020 61
ХИМИЧЕСКИЕ НАУКИ
УДК: 547.662. 66.011
Ziyadullaev A.E.
Doctorate of 3-course of the Tashkent Chemical Technology Institute Nurmonov S.E. Doctor of technical sciences, professor, Faculty of ^emistry of the National University of Uzbekistan
Parmonov A.B.
Lecturer at the Faculty of Chemistry of National University of Uzbekistan
Jumartova U.U. Student of 2-course of the Faculty of Chemistry National University of Uzbekistan Mavloniy M.I.
Head Laboratories Institute of Microbiology Academy of Sciences of the Republic of Uzbekistan, Doctor of Biological Sciences, academician
MATHEMATICAL PROCESSING OF THE RESULTS OF SYNTHESIS OF VINYL ETHERS OF
CYANURIC ACID
Зиядуллаев А. Э.
Докторант 3-курса Ташкентский химико- технологический института
Нурманов С.Э.
Доктор технических наук, профессор, факультет химия Национального университета Узбекистана
Парманов А.Б.
Преподаватель химического факультета Национальный Университет Узбекистана Жумартова У.У.
Магистрантка 2-курса химического факультета Национальный Университет Узбекистана
Мавлоний М.И.
Зав. Лаборатории Институт Микробиологии Академия наук Республики Узбекистан, доктор биологических наук, академик
МАТЕМАТИЧЕСКАЯ ОБРАБОТКА РЕЗУЛЬТАТОВ СИНТЕЗА ВИНИЛОВЫХ ЭФИРОВ
ЦИАНУРОВОЙ КИСЛОТЫ
Аннотация. В статье приведены результаты исследования процесса гомогенного каталитического винилирования 2,4,6-тригидрокси 1,3,5-триазина ацетиленом на основе высоко-основны систем: ДМСО, ДМФА; гидроксидов лития, натрия и калия. Определено, что в процессе синтеза образуются моно-, ди- и три-виниловые эфиры триазин. Найдены оптимальные параметры процесса, определено влияние продолжительности проведения реакции и температуры, количества и скорости подачи ацетилена, природы катализаторов и растворителей на выход целевых продукта. Структура синтезированных виниловых эфиров подтверждена данными ИК, :Н, 13С-ЯМР спектральные анализов. Полученные разработаны математическими моделями и методами. Анализ полученных экспериментальных результатов химического процесса показал их соответствие с теоретическими данными. Разработаны диаграммы результатов энергии активации и динамика изменения кинетических параметров, а также приведи графики аналитических функций.
Определена значение выхода продуктов: показало, что при температуре 80-120 оС продолжительности реакции 6 часов выход виниловых эфиров циануровый кислоты увеличивается: (12,218,2) моно-винилового эфира, (14,6-21,8) ди-винилового эфира и (12,4-22,6) % три- винилового эфира соответственно. Установлена, что дальнейшее повышение температуры реакции (140 оС) приводит к умещению выхода продуктов до 16,4; 16 и 10,8 % соответственно для моно-, ди- и три-виниловых эфиров. Установлено, что оптимальным режим от проведения экспериментов является: продолжительность 6 часов, температура 120 оС, количество катализатора относительно кислот 10 % от массы кислоты, скорость
62 Wschodnioeuropejskie Czasopismo Naukowe (East European Scientific Journal) #3(55), 2020 ----подачи ацетилена 4,5 л/сек. Вылены условия максимального выхода общая винилового эфира (62.6%) циануровой кислоты.
Abstract. In article results by investigation of catalytic homogeneous vinylation of 2,4,6-trihydroxy-1,3,5-triazine (cyanuric acid) by acetylene on the base high-based system: DMSO, DMF; hydroxides of lithium, potassium and sodium. It was determined that in process of synthesis mono-, two- and three-vinyl ethers of cyanuric acid have been formed. Optimal parameters of investigated process were determined: influence of duration of reaction temperature and rate of feeding acetylene, nature of using catalysts and solvents on yield of forming products. Structure of the synthesized vinyl ethers was been proved by data of such methods IR, 1H, 13C-NMR spectral analyzes. Obtain results were treated wish using mathematical models and methods. Analysis of obtained experimental results of investigated chemical process has shown corresponding to theoretical data. Diagrams of results of activation energy and dynamics of changing of kinetic parameters have been elaborated and also graphs of analytical functions are also presented. Values of products yields have been determined: it was shown that at temperature of 80-120 oC for and duration of reaction 6 h, yield of vinyl ethers of cyanuric acid have increased: (12.2-18.2) of mono-vinyl ether, (14.6-21.8) two-vinyl ether and (12.4 - 22.6) % three-vinyl ether, correspondence. It was determined that further increase of temperature (140 oC) has carried out to he creasing of yields of products to 16.4; 16 and 10.8 % correspondence for mono-, two- and thee-vinyl ethers. It was determined that optimal optimal regime for carrying out of experiments was: duration of reaction 6 hours, temperature 120 oC, quantity of catalyst relatively of initial reagent (cyanuric acid) - 10 mas %, (from it's mass) and rate feeding of acetylene 4.5 l / sec. The conditions for the maximum yield of total vinyl ester (62.6%) of cyanuric acid were determined.
Ключевые слова: ацетилен, винилирование, виниловый эфир, циануровой кислоты, моно,- ди- и три винил цианурат.
Key words: acetylene, vinylation, ethers of cyanuric acid, mono, - two- and three vinyl cyanurates.
INTRODUCTION
Obtaining complex compounds with the participation of cyanuric acid is becoming relevant in the world industry. The formation of certain cyanuric acid derivatives due to the exchange of a hydrogen atom and sulfur containing compounds by oxygen substitution has been theoretically studied [1]. Also, with the participation of cyanuric acid and melamine, supramolecular clusters were obtained [2-5]. The use of cyanuric acid and some of its homologs is becoming more promising in metallurgy. It should be emphasized that due to the content of the hydrogen atom in the composition of cyanuric acid, it has a special tendency to form the Hamilton complex [6,7]. Because of these properties, cyanuric acid has gained importance for the biochemical and pharmaceutical industries [8-12].
Currently, vinyl esters and ethers are widely used in various industries: including as biological active substances in medicine; monomers for the production of polymers and plastic materials; inhibitors in the oil and gas industry; crosslinking agents in the manufacture of rubber and rubber; adhesives in
microelectronics; various solvents in the textile industry [13-15].
Cyanuric acid and its derivatives are widely used in various industries. The introduction of a vinyl group into a cyanuric acid molecule has increased its biological activity and expands the scope of its using [16-18]. Mathematical processing the results obtained in chemical reactions, finding a mathematical formula for the course of such processes is important at elaboration of technology and determining the technological parameters of the synthesis of organic compounds [19].
In this paper is presented the mathematical processing of the obtained experimental results by catalytic vinylation of cyanuric acid with acetylene.
EXPERIMENTAL
The least squares method has allowed the experimental data to select such analytical function that passes as close to the experimental points as possible. In the general case, the problem can be formulated as follows. Let result of the experiments in a certain experimental dependence y (x), was obtained which in
X Xi *2 xn-1 xn
У У1 У 2 Уз Уп-1 Уп
It is necessary to build an analytical dependence f(x,a1,a2, ...,ak), that most accurately describes the results of the experiment. To building function parameters f(x,a1,a2,.,ak) the least squares method. Was used which is concluded that
function f(x,a1,a2,.,ak) it in necessaries, by such method so that the sum of the squared deviations of the measured values yt from calculated Yt = f(x, a1,a2,..., ak) would be the smallest (Fig. 1):
S(ai,a2,...,ak) = Yi=i[Уt - Yi] = I1f=i[yi - f(x,ai,a2,... ,ak)]2 ^min
(1)
Y A
vi
3
O >1 X2 x5 «I xn
X
Process temperature
Fig 1. Analytical dependence of product yield on temperature
The task consists of two stages:
1. By use it's the results of the experiments, to determine the appearance of the selected dependence.
2. Choose the coefficients of dependence Y = f(x,ai,a2, ...,ak). Mathematical, the problem of selecting the coefficients of dependence is reduced to determining the coefficients at from the condition (1).
The sufficient condition for the minimum function S(ai,a2, ...,ak) (1) is the equality to zero of all its partial derivatives. Therefore, the problem of finding the minimum of function (1) is equivalent to solving a system of algebraic equations:
da!
^=0
da2
(2)
dS dak
=0
If the parameters ai are introduced in dependence Y = f(x,ai,a2, ...,ak) linearly, then system (3) consisting from k linear equations with k unknowns will be obtained:
'TH=i2[yi - f(x, a.1,0.2, TH=i2[ji - fix, ai,a2,
Yii=i2[yi- fix, ai,a2,
■,a*)]£=0(3)
In general, a system of equations for calculating parameters ai polynomial k - 1-st degree Y = Y1ki=1 aixl-1 has the form:
a±n + a2 Z?=iXi + a3 YH=ix} + -+ak Z?=iXk-1 = Yi?=iyi ai Yu=i Xi + a2 Ya=i x2 + a-z^ixf + ■■■+ ak Yu=i xk = 12=1 xy (4)
ai Y!i=ixt + a2 Y!i=ixt+i + a3 Y!i=ixt+2 + ■■■ + ak Yi=ix?k 2 = Y,f=ixtyi
System (4) can be written in matrix form:
Ca = g, (5)
Elements of the matrix C and vector g are calculated by the formulas:
i
n _ \ ' i+j-2 Ci,j = ^ xk ,
k=i
i = 1,...,k + 1,j = 1,...,k + 1, (6)
gi = rk=iykxik-i,i = 1.....k + 1. (7)
Having solved system (4), parameters of dependence Y = ai + a2x + a3x2 + —+ ak+ixk can be determined.
RESULTS AND DISCUSSION The influence of the nature of the solvent and catalyst, the temperature and the feed rate of acetylene on the formation of vinyl compounds on the base of cyanuric acid has been investigated. Cyanuric acid vinyl compounds were synthesized by catalytic vinylation involving acetylene owing to its active hydrogen atoms [20].
DMSO, DMF were used as a solvent, and LiOH, NaOH, and KOH as catalysts. In this case, the formation of mono-, two- and three-vinyl ethers of cyanuric acid was established. The results showed that
Wschodnioeuropejskie Czasopismo Naukowe (East European Scientific Journal) #3(55), 2020
64
with an increasing of the amount of catalyst, the yield of products has increased.
The activation energy and reaction rate were calculated in order to determine the kinetic parameters
of the synthesis of mono-, two- and three vinyl ethers of cyanuric acids (table 1).
Table 1.
Kinetic parameters of the synthesis of mono, two, three-vinyl ethers of cyanuric acid
The duration of the reaction, hour Temperature, °C Product yield: Average reaction rate
% mol/l % / hour mol / l.h
Synthesis mono-vinyl ether of cyanuric acid
6 80 12,2 0,99 4,41 0,22
100 16,7 1,35 6,03 0,30
120 18,2 1,47 6,57 0,32
140 16,4 1,32 5,92 0,28
Synthesis two-vinyl ether of cyanuric acid
6 80 14,6 1,19 5,28 0,26
100 18,6 1,51 6,73 0,34
120 21,8 1,78 7,89 0,40
140 16,0 1,30 5,27 0,29
Synthesis three-vinyl ether of cyanuric acid
6 80 12,4 1,01 4,48 0,22
100 14,8 1,20 5,33 0,26
120 22,6 1,86 8,15 0,42
140 10,8 0,88 3,89 0,20
Using the tables, it is possible to elaborate a mathematical model of the reactions. Mathematical model and has been composed an analytic function for each table has been found. According to the results, the
1-table model:
most effective reaction is the reaction, the duration of which is 6 hours. For brevity, mathematically a model of these reactions in presented:
ti 80 100 120 140
Ui 12.2 16.7 18.2 16.4
S(ai,a.2,...,ak) = ^[ui-Ui]2 = ^[ui - f(ti,ai,a2,a3,a4)]2 ^ min
i=i i=i
f(ti,ai,a.2,a3,a4) = % + a2tt + a3tt2 + a^3
From (2) we obtain system (8) from 4 linear equations with 4 unknowns:
Td=i2[ui -ai- a.2ti - a.3ti2 - a^3] = 0 Y1Ui2[ui -a.i-a.2ti- a3ti2 - tt3] tt = 0 Y,1=i2[ui - ai- a.2ti - a3ti2 - a^3] t^2 = 0 £t=i2[Ui -a.i + a.2ti + a3ti2 + a^3] ti3 = 0
From here we get the system:
4ai + a2 Y.Ui k + % ZUi t2 + a4 Ya=i t3 = Y.Ui Ui ai Yd=i + a2 Yd=i t^ + a3 Y,4=i t3 + a4 Y,4=i t4 = Y,4=i tiUi ai Zl=i t2 + a2 Z4=i t3 + a3 Z4=i t? + a4 Y4=i tf = Z4=i tfa ai Z4=i t3 + a2 Z4=i t? + a3 l?=i if + ak+i Z?=i t? = Zti t^i
In matrix form, system (9) can be written as:
4 440 ( 50400 \5984000
440 50400 5984000 73248 •104
50400 5984000 73248 •104 919424 •W5
5984000 73248 •104
919424 •W5 11777664 •W6
(8)
63,5 7126 1 828600 99397600
4
4
i,;... Wschodnioeuropejskie Czasopismo Naukowe (East European Scientific Journal) #3(55), 2020 65 Having solved system (9), we determine the dependence parameters
a1 = -29,8; a2 = 0,715;a3 = -18,75 • 10-4; a4 = -62,496 • 10-7
and function f = -29,8 + 0,715x - 18,75 • 10-4x2 - 62,496 • 10-7x3.
Now using the Maple18 program, it is possible to construct a graph of this function and a diagram of the
results (Fig. 2).
Process temperature.0C ' Process temperature.0 c
Fig 2. The in fluense of temperature on the yield of mono-vinyl ester of cyanuric acid; (a) experimentally;
(b) the results of mathematical processing.
ti 80 100 120 140
Vi 4,41 6,03 6,57 5,92
Ui 12.2 16.7 18.2 16.4
S(ai,a2,...,ak) = - Ui]2 = - f(ti,di,ai,a2,a3,a4)]2 ^ min
=i =i
f(ti,idi,ai,a2,a3,a4) = a^ + a2^2 + a3tidi + a4d2 From (2) we obtain system (10) from 4 linear equations with 4 unknowns:
f Z4=I2[U, - (uiti + a2ti2 + a3tidi + a4^i2)]ti = 0 Z4=i2[Ui - (aaiti + a2ti2 + a3tißi + a4ß2)] t? = 0 Z4=i2[Ui - (ait i + a2ti2 + a3tidi + a402)] tfa = 0 Z4=i2[U - (aiti + a2ti2 + a3tidi + a402)] V2 = 0
From here the following system will be obtained:
10)
ai Z4=i tf + a2 Z4=i tf + a3 Z4=i Wi + a4 Z4=i W = £4=^
i 2 =i 3 =i 4 =i =i
ai Z4=1+ a2 Z4=114 + a3 Z4=i tfa + a4 Z4=i t^d,2 = £4=^2
ai Z4=i tfVi + a2 Z4=i tfa + a3 Z4=i tfa2 + a4 Z4=i W3 = ZU Utrf.
(11)
Ui Z4=i ti$i2 + a2 Z4=i t^i2 + a3 Z4=i tA3 + ak+i Z4=i Vi4 = Z=i UiVi
^i1- i" i n „, .0 2
System (11) can be written in matrix form:
50400 5984000 299164 15278,222
I 5984000 73248 •W4 35885360 1796560,84 \
( 299164 35885360 1796560,84 91864,57586 )
\15278,222 1796560,84 91864,57586 4791,802388/
7126 828600 42315,46 2204,85599
Having solved system (11), the dependence parameters ai = 0,151887768503185; a2 = -8,17174362595097 •10-6;a3 = -0,0222409649173869; a4 = 0,432874298761817 and function f(ti,di,ai,a2,a3,a4) = 0,151887768503185tt - 0,0000817174362595097tt2 -0,0222409649173869 tii9i + 0,432874298761817d2 have been determined.
4
4
Wschodnioeuropejskie Czasopismo Naukowe (East European Scientific Journal) #3(55), 2020
2-table model:
ti 80 100 120 140
Ui 14.6 18.6 21.8 16
S(ai,a.2,...,ak) = ^[ui-Ui]2 = ^[ui - fit^ai, 0.2,0.3, a.4)]2 ^ min
=i =i
fit^ai, 0.2,0.3,0.4) = ai + 0.2^ + a3ti2 + a4ti3 From (2) system (12) of 4 linear equations with 4 unknowns was obtained:
Ti=i2[ui - ai- a.2ti - 03ti2 - 04ti3] = 0
Y14=i2[ui -a.i-a.2ti- a3ti2 - tt3] tt = 0 Tl4=i2[ui - ai- a.2ti - 03ti2 - 04^] t^2 = 0
X4=i2[Ui - ai + a.2ti + 03ti2 + 04ti3] ti3 = 0
From here the following system can be obtained:
4ai + 02 ZUi tt + 03 ZUi tf + 04 Y,4=i tf = Y,4=i Ui
ai Z4=i k + 02 Z4=i t2 + 03 Z4=i tf + 04 Z4=i t4 = Z4=i №
ai Z4=i tf + 02 Z4=i tf + 03 Z4=i t4 + 04 Z4=i ti = Z4=i tfu.i ,ai Z4=i tf + 02 Z4=i t4 + 03 Z4=i tf + ak+i Z4=i tf = YH=i tfui
(12)
(13)
System (13) in matrix form can be written as:
/ 4 440
/ 440 50400
( 50400 5984000
\5984000 73248 •W4
50400 5984000 73248 •104 919424 •W5
5984000 73248 • 104
919424 • 105 11777664•106
71 7884 ( 906960 107649600
4
4
Solving the system (13), parameters dependence ai = 154,6 ;a2 =-4,67666; a3 = 0,05025; =
a 4
0,0001708336 and function f = 154,6 - 4,67666x + 0,05025x2 + 0,0001708336x3., can been determined.
Now, using the program Maple18, a graph of this function and a diagram of the results can been determined (Fig. 3).
r Process temperatureC ' Process temperatureC
Fig. 3. Effect of temperature on the yield two-vinyl ether of cyanuric acid: (a) experimentally; (b) the results of mathematical processing
ti 80 100 120 140
5,28 6,73 7,89 5,27
Ui 14.6 18.6 21.8 16
^ min
S(ai,a2,...,ak) = - U^2 = ^[Ui - f(ti,di,ai,a2,a.3,a4)]'
=i =i
f(fi,'^i,ai,a2,a3,a4) = aiti + a2k2 + a3ti^i + a4$i2
From (2) system (14) from 4 linear equations with 4 unknowns will be obtained.
f Z4=i2[Ui - (a^i + a2ti2 + a3tidi + a4Td2)]ti = 0
Z4=i2[Ui - (aiti + a2ti2 + a3tidi + 04^)] ti2 = 0
Z4=i2[Ui - (aiti + a2ti2 + a3tidi + a4fi2)] t^ = 0 Z=i2[Ui - (aiti + a2ti2 + a3tidi + a4d2)]d2 = 0
From here we get the system:
ai Z4=i tf + 0.2 Z4=i 13 + «3 Z4=i tfdi + 04 Z4=i kd2 = Z4=iUiti ai Z4=i tf + a2 Z4=i t4 + a3 Z4=i tfa + 04 Z4=i t^di2 = Z4=iUit2 ai Z4=i tf$i + a2 Z4=i tfa + a3 Z4=i t^2 + 04 Z4=i t&3 = Z4=i Uitidi Ui Z4=i kd2 + a2 Z4=i tfd2 + a3 Z4=i ttfi3 + ak+i Z4=i fy4 = Z=i rf
(14)
(15)
System (15) can be written in matrix form
/ 50400 5984000 318000 18118,02 \
/ 5984000 73248 •W4 37528160 2072129,84 \
( 318000 37528160 2072129,84 121689,0917 )
18118,02 2072129,84 121689,0917 7475,309905
7884 906960 51129,88 3050,93476
Having solved system (15), the dependence parameters ai = 0,18257393692835; a2 = -3,05057318158219 • 10-4; a3 = -0,0174143349854603; a4 = 0,333673055662075 and function f(ti,di,ai,a2,a3,a4) = 0,18257393692835 tt - 3,05057318158219 • 10-4ti2 -0,0174143349854603tidi + 0,333673055662075d2 can be determined.
3-table model:
6 80 12,4 1,01 4,48 0,22
100 14,8 1,20 5,33 0,26
120 22,6 1,86 8,15 0,42
140 10,8 0,88 3,89 0,20
ti 80 100 120 140
Ui 12.4 14.8 22.6 10,8
44
S(ai,a2, ..,ak) = ^^[ui-Ui']2 =^[Ui - f fa, a^ 02,03, a4)]2 ^ mm
Ui]2
=i =i f(ti,Oi, 02,03,04) = Oi + 02ti + 03ti2 + 04ti3
From (2) system (16) from 4 linear equations with 4 unknowns will be obtained:
Z4=i2[Ui -ai- a2ti - a3ti2 - a4ti3] = 0 z4=i2[Ui -0.i-a.2ti- 03ti2 - ti3] ti = 0
Z4>=i2[ui -ai- a2ti - a3ti2 - a4ti3} ti2 = 0 Z4=i2[Ui -ai + a2ti + a3ti2 + a4ti3] ti3 = 0
From here we get the system:
4
4
68 Wschodnioeuropejskie Czasopismo Naukowe (East European Scientific Journal) #3(55), 2020
4ai + a2 Z4=i ti + a3 Z4=i t2 + a4 Z4=i if = Z4=i u, ai Z4=i h + a2 Z4=i t2 + a3 t3 + a4 Z4=i t4 = Z4=i tiUi
ai Z4=i tf + a2 Z4=i ti + a3 Z4=i ti + a4 Z4=i t-i = Z4=i tfUi a Z4=i tf + a2 Z4=i tf + a3 Z4=i tf + ak + i Z4=i tf = Zn=i tfUi
(17)
System (17) in matrix form can be written as:
I 4
/ 440 ( 50400 \5984000
440 50400 5984000 73248 •104
50400 5984000 73248 •104 919424 •W5
5984000 73248 •104
919424 •W5 11777664•106
f 60,6 6696 ( 764480 89836800
Having solved system (13), we determine the dependence parameters ai = 556,8; a2 = -16,51167; a3 = 0,163; a4 = -0,000520834 and function f = 556,8 - 16,51167x + 0,163x2 - 0,000520834x3.
Now, using the program Maple18, we construct a graph of this function and a diagram of the results (Fig.4).
Fig.4. The effect of temperature on the yield of three vinyl esters of cyanuric acid; (a) experimentally;
(b) the results of mathematical processing:
ti 80 100 120 140
- 4,48 5,33 8,15 3,89
Ui 12.4 14.8 22.6 10,8
S(ai,a2,...,ak) = - Ui]2 = ^[ui - f(ti,idi,ai,a2,a3,a4)]
=i =i
f(ti,di,a1,a2,a3,a4) = a^ + a2ti2 + a3tidi + a4d2 From (2) system (18) from 4 linear equations with 4 unknowns will be obtained.
f z4=12[Ui - (aiti + a2tc2 + a3tidi + a4id2)]ti = 0 z4=12[Ui - (aiti + a2ti2 + a3tidi + a4-d2)] t? = 0 Z4=i2[Ui - (aiti + a2ti2 + a3ti$i + a4-2)] tfà = 0 .Z4=i2[Ui - (aiti + a2ti2 + a3tißi + a^d-2)]^2 = 0
(18)
From here we get the system:
ai Z4=i tf + a2 Z4=i tf + a3 Z4=i tfà + a4 Z4=i t—2 = Z4=iUiti ai Z4=i tf + a2 Z4=i tf + af Z4=i iffy + a4 Z4=i t^2 = ^=^2 ai Z4=i tfa + a2 Z4=i tftii + af Z4=i tfa2 + a4 Z4=i t—3 = Z4=i Uitidi Ui Z4=i ti$i2 + a2 Z4=i t2-d2 + af Z4=i t-3 + ak+i Z4=i $i4 = Z=i Ui-d2
System (19) can be written in matrix form:
4
4
/ 50400 / 5984000 ( 275576 \14535,716
5984000 73248 • 104 32381120 1665612,72
275576 32381120 1665612,72 95537,32172
14535,716 1665612,72 95537,32172 ) 5850,815511
6696 764480 40317,04 23333,89986
Having solved system (19), we determine parameters of the dependence ai = 0,15863913854156; a2 = -8,94907004671319 • 10-4; a3 = 0,00740573017296242; a4 = 0,138615079939314 and function
f(ti,di,a1,a2,a3,a4) = 0,15863913854156tt - 8,94907004671319 0,00740573017296242titii + 0,138615079939314d2.
10-4tt2
+
CONCLUSION
After analyzation of kinetic parameters of the synthesis of cyanuric acid vinyl esters, the average reaction rate was determined and it's activation energy was calculated. Using mathematical modeling, analysis of graphs of analytical functions and diagrams of kinetic parameters of synthesis it is possible to establishe that at a reaction time of 6 hours and a temperature of 120 ° C the yields of vinyl esters have reached a maximum values: mono- vinyl 18.2%, di-vinyl 21.8%, and tri-vinyl - 22.6%.
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UDC 541.123.6
Usmonov Muhammadsalim Bozorovich
PhD, Associate Professor Tajik State Pedagogical University
PHASE EQUILIBRIA IN THE NA, CA// SO4, F- H2O SYSTEM AT 75°C
Abstract. The phase equilibria in the Na, Ca //SO4, F - H2O system at 75°C were investigated by the translation method. The closed phase diagram for the system was constructed based on the obtained data.
Keywords: translation method - phase equilibria - component -geometric images.
Knowledge of the laws of phase equilibria of the Na, Ca // SO4, F - H2O system is necessary to establish optimal conditions for the separation of sulfate and fluoride salts of sodium and calcium from natural and technological solutions containing these salts.
As an analysis of the literature [1] shows, this system has not been investigated so far. We studied it using the translation method, which follows from the principle of compatibility of structural elements n and (n + 1) component systems in one diagram [2]. According to the translation method, structural elements of the diagrams of n-component systems increase their dimension by one unit and translated to the (n + 1) component composition in a transformed form when the next component is added to them (at constant temperature and pressure),. For example, in this case, invariant points of n - component systems at the (n + 1) component level turn into monovariant curves, and monovariant curves into divariant fields, etc. Transformed geometric images, according to their topological properties, at the level of (n + 1) component
composition, intersecting each other (observing the Gibbs phase rule) form geometric images of the system at this component level. Thus, the translation method will make it possible to predict the possible phase equilibria of multicomponent systems (when moving from the n-component level to the (n + 1) component level) and theoretically construct their closed phase diagrams. A more detailed application of the translation method for predicting the structure of the phase equilibrium diagram in multicomponent water - salt systems was considered in literature [3-4].
The studied four-component system includes the following three-component systems: Na2SO4 - CaSO4 - H2O, NaF - CaF2 - H2O, NaF - Na2SO4 - H2O and CaF2 - CaSO4 - H2O.
There are 3, 1, 2 and 1 invaraint points in the Na2SO4 - CaSO4 - H2O, NaF - CaF2 - H2O, NaF -Na2SO4 - H2O and CaF2 - CaSO4 - H2O systems at 75°C respectively according to literature [5]. Table 1 gives the list and equilibrium solid phases at the ternary invariant points of the listed systems.
Table 1
Phase equilibria in the invariant points of the Na, Ca// SO4,F-H2O system
Invariant point Solid phase composition Invariant point Solid phase composition
Na2SO4 - NaF -H2O system NaF - CaF2 - H2O system
Е3 Wo+Shr Е3 Е4 Wo+Fo
Е2 Shr+Te Na2SO4 - CaSO4 - H2O system
CaF2 - CaSO4 -H2O system Е5 Те+Gb
Е3 Fo+ Gp Е6 Gb+ 5Ca№3
Е7 5Ca-Na-3+ Gp
Letter E in Table 1 and further denotes an invariant point with an superscript indicating the multiplicity of the point (system complexity) and subscript indicating the serial number of the point. Following notations were used: Te-tenarditis Na2SO4, Gb - glauberite
Na2SO4- CaSO4, Gp - gypsum CaSO4-2H2O, Wo -willomite NaF, Fo - fluorite CaF2, Shr - sheireritis Na2SO4-NaF, 5Ca-Na-3 - 5CaSO4-Na2SO4-3H2O.
Figure 1 shows phase equilibria diagram of the Na, Ca//SO4, F - H2O system at 75° C. Unfolded pyramid
