1202
INDUSTRIAL AND ENGINEERING CHEMISTRY
VOL. 29, NO. 10
soil 35 of Table I1 and was the only vegetation growing there when the examination was made. Sample 38A is alfalfa which was being eaten by a cow definitely suffering from the selenium poisoning (Figure 1). The milk from this cow contained 0.6 p. p. m. of selenium, which made up about 6 p. p. m. of the milk solids. Incidentally, this cow, as well as two bulls also suffering from the same trouble, was a newcomer into the valley. Some of the members of the herd of some fifty cattle showed evidence of the disease to a much smaller extent. The samples of vegetables sold in the city market are significant. Of the nine samples analyzed, all but two are definitely seleniferous, and these may not have been grown in the valley.
When we consider that more than 4 parts per million of selenium in a dry diet are definitely injurious (3)and that the people of Irapuato live largely on their local produce, it is clear that this location is an excellent one to study the effect of selenium in foods upon humans. Since selenium may be present in all the vegetables, milk, and meat consumed ( I ) , the citizen of Irapuato is likely to be affected by selenium from even his prenatal days. To what extent the evident ill health of the inhabitants is due to selenium in their food is problematical but is worthy of study,
Conclusions
In making the field examination here reported the Mexican Government was represented by Jose Figueroa; without his local knowledge and energetic assistance the collection of m% terials would have been almost impossible. The laboratory examinations were made by &. T. Williams and H. W. Lakin of the Soil Chemistry and Physics Research Division of the Bureau of Chemistry and Soils.
I n the area of seleniferous soils about Irapuato the toxic agent is evidently deposited in the soils from the waste product of the mines about Guanajuato. No similar situation exists, so far as is known, in the United States. The condition in Irapuato seems less serious than would be the case if selenium-loving plants, capable of enriching the soil with available selenium, were present. In this area irrigation as practiced is not a remedial measure ( I ) , partially because the region is semihumid and therefore does not require continuous irrigation and partially because of the presence of selenium in the water. This point may be important in connection with the use of drainage waters from seleniferous areas for irrigation in other places.
Acknowledgment
Literature Cited (1) Byers, H. G., U.S. Dept. Agr., Tech. Bull. 530 (1936). (2) Franke, K.W., Rice, T. D., Johnson, A. G., and Schoening, H. W., Ibid., Circ. 320 (1934). (2) Munsell, H. E., Ibid., Tech. BUZZ. 534 (1936). REcEIVBD
J d Y 21, 1937. 8
Investigating Time-Temperature Effects upon Properties
of Reactants W. M. BREITMANN 20, Riga Prospect,Ap. 38, Leningrad, U. S. S. R.
T
HE control of the chemical conversion of matter is the
province of chemical kinetics, which studies in a dynamic aspect reactions that “static” chemistry investigated in detail over a century ago. Modern chemical industry urgently needs a technic that will make it possible to predict the effect of varying time and temperature conditions in a reaction upon the properties of the product. It is therefore natural to seek an empirical generalization that will enable us to control the chemical conversion of a substance by studying its physical and chemical properties during the course of the reaction. Certain regularities discovered by chemical kinetics can be used for this purpose. When the composition of the starting mixture remains constant, the properties of the products obtained are governed by the time and temperature conditions prevailing during the course of the reaction. Because instantaneous heating and, subsequently, cooling of a reaction mixture is always impossible, we may consider that every large-scale chemical process is proceeding a t a variable temperature. This is particularly
true when the reaction evolves or takes up heat. I n many cases the inevitable temperature variations are such as to make it difficult or even impossible to obtain products with the required properties. The present work is an attempt to find a method of investigation that will relate the physicochemical properties of the product to time and temperature variations during the reaction.
Development af Equations Consider the equation of polymolecular reaction, and for the sake of simplicity let us assume that the amounts of different constituents present are equivalent:
where z = amount of substance converted t time a = original amount of substance IC p: reaction constant n order of reaction The reaction constant depends, as is known, on temperature: IC = Mf(T)
where M = a coefficient of proportionality T absolute temperature =1
(2)
OCTOBER, 1937
0
/
INDUSTRIAL AND ENGINEERING CHEMISTRY
2
3
4
5
6
7
8
9
/
1203
0
t FIGURE1. CHANGEOF S , T , 10e SPONDINO
03 - 1_
T
WITH THE
CHANQES IN 2f sat, 2 f Tdt, 2f 10ae
CORRE-
- 106 T dt
I
0
ax
- = M(a
Consequently
dt
- z)"f(T)
(3)
By integration of (3) : 1
a - [M(n - l)Jf(T)dt]= and by simplification: 2
=
= +[ff(T)dtl
(3-4)
20
25
30
FIGURE2. CHANGE OF TEMPERATURE WITH TIME DURING THREEBOILINGS OF LINSEED OIL IN THE RAIN APPARATUB USEDIN THE LINOLIDUM INDUSTRY
I
I
(3B)
On the other hand, the physico-chemical properties, u, of a mixture are a function of the amount of the converted substance x: Q
= f(z)
(4)
Consequently, the physico-chemical properties will be related to time and temperature as indicated by the following equation: u = F[Sf(T)dtI
(5)
A practical difficulty in using Equation 5 may arise because the chosen function f may happen to depend upon temperature, so that the form of function F will also depend upon temperature. However, we may always choose a temperature range within which the experimentally determined form of function F will be practically constant. Let us assume that P I is correct within certain temperature limits as defined by the expression: Ta > To,i > Ti
For other temperature ranges, such as: Ta > TQ,I > T2 .................... ....................
Tn > To,,-1
or the functions Fa,
...,F,, -
will be correct.
will determine the form of a given function that will be correct within the given temperature range. Consequently, the value of the property u can always be presented as a series: e
+
+ .... +
Fi[[Sf(To,i)dtl KIJf(To,zJdtl Fn-z[Sf(To,n-z)dtl Fn-l[Jf(To,n-l)dt] (6)
. . a * +
5
/O
/5
20
25
30
t FIGURE 3. CHANGE IN SPECIFIC GRAVITY WITH TIMEIN LINSEED OILDURING TXREEBOILINGS IN THE RAIN APPARATUS
The use of this series makes it possible to express the effect of time and temperature variation upon the property of the product, with any desired degree of approximation. It is known that the reaction constant of simple rnonomolecular, bimolecular, and most of the catalytic reactions increases with temperature according to the Arrhenius law:
> Tn-I
It will then be necessary to divide the whole temperature range into a number of sections (n - 1 in all), and each section
Q
I
I
0
--Ma
We may assume thatf (T)= M I ~T ,where M I and M2 represent constants. Then by substitution ill Equation 5 we have: (7)
Kinetic theory gives for the reaction constant k an expression analogous to the Arrhenius equation:
INDUSTRIAL AND ENGINEERING CHEMISTRY
1204
VOL. 29, NO. 10
54
I
2 !
FIGURE 5. CHANGE IN SPECIFIC GRAVITY OF LINSEE~ OIL AS RELATEDTO THE MAGNITUDE(2f X d t ) OBSERVEDDURINQ THREEBOILINGS IN THE RAINAPPARATUS FIQURE 4. CHANQE IN VISCOSITYOF LINSEEDOIL THREE BOILWQS IN TEXERAINAPPARATUS
DURINQ
24
0
/ooo
500
1500
2000
2flo3e -&t -.
/ooo
0
FIQURE 8. CHANGE IN VISCOSITYOF LINSEED OIL AS RELATED
2000
2/sdt
TO
FIGURE 6. CHANGE IN VISCOSITY OF LINSEED Om AS RELATED THE MAGNITUDE(2fS&) OBSERVEDDURING THREE BOILINQS IN THE RAINAPPARATUS
THE
- -10'
MAGNITUDE(2J108e T dt) OBSERVED DURING THREE BOILINGS IN THB RAINAPPARATUS
TO
--E
IC = Ce RT where E = energy of activation R = gas constant C = constant times the square root of T The optimum approximation can be obtained by using the expression:
0
500
/ooo
/so0
2000
~/oJe-&t FIGURE7.
CHANGE IN SPECIFIC
GRAVITYO F
LINBEED 108 --
OIL
AS RELATEDTO THE MAQNITUDE(2J10ae T dt) OBSERVED DURING THREE BOILINGSIN THE RAINAPPARATUS
e
As a first approximation, we can assume that f ( T ) = T BI, where BIis a constant, representing approximately the lowest temperature limit of a given reaction. The use of this approximation tends to intensify the effect of temperature variations. Therefore, strange as it may seem, a fairly good description of the effect of time and temperature variations upon properties of the finished product may in some cases be obtained by establishing the relation of properties to the area of the timetemperature curve, where temperature is expressed in degrees Centigrade (B1= 273' C.): u = +(JSdt)
where S = temperature,
O
C.
INDUSTRIAL AND ENGINEERING CHEMISTRY
OCTOBER, 1937
Application
TABLEI. OPERATING CONDITIONS OF RAINAPPARATUS Run No. 1
No. of Working Days 1 2 3 4
started 12 : 10 12:lO 9:40 9:25
stopped 6:OO 5:20 4:OO 3:30
-Oil Time started 8:30 8:OO 8:30 8:30
-----Fan-
Time
Time
1 2 3
1:51 9:oo 10:40
5:55 5:oo 1:05
10:45 8:30 8:40
6:20 6:OO 4:40
3
1 2 3 4
3:30 9:oo 9:15
3:55 4:OO 4:OO
8:OO 8:OO 8:OO 1o:oo
5:OO 4:OO 4:OO 1:45
..
This field is peculiar in that the work is done on a large scale and the variations in temperature are considerable. For example, the oxidation of linseed oil was studied in the "rain" apparatus used in the linoleum industry. The total volume of the apparatus was 363.3 cubic meters, and 11.2 tons of oil were oxidized at one time. Table I gives data on the operating conditions of the apparatus. During some of the runs the fans in the apparatus were not operated. Therefore, when calculating the corresponding integrals, the arithmetical mean of their values was taken during the time when the fan was in operation and when it was idle; this was possible because oxidation of the oil takes place even when the fan is idle, as the air penetrates freely into the apparatus; however, in this latter case, practice has shown that the oxidation is slower. The variations in specific gravity and viscosity are shown in Table 11. The specific gravity was determined on Mohr's scale a t 15' C., and the error of each separate observation was .tO.OOl. The viscosity was measured with an Engler viscometer a t 50' C. The error of a single observation varied from *0.1' to d0.3OEngler. Table I11 and Figure 2 show the temperature variations occurring during different runs. When the properties of the product are plotted against boiling time (Figures 3 and 4))
PumpTime stopped 6:30 5:20 4:OO 3:30
2
Figure 1 indicates the comparative variations in T oabsolute and f Tdt, as well as the corresponding variations in
_108 _
108 -_
dt; this figure explains the S, f Sdt, 103e ,and .flOae high "sensibility" of the function 6 to temperature variations. The effect of temperature variations can be further intensified by giving to the function fl (T) a hyperbolic structure, such as:
Thus, when f ( T ) = Mle
Ma -_ )
we have
--
Ml
1205
TABLE11. VARIATIONS IN SPECIFIC GRAVITY AND VISCOSITY Working Days Expressed as Conaecutive
Nos.
Time of Day
Time of Treatment, t
Viscoaity, W
2f Sdt
HOUTS
where m is a constant. It will be recalled that chain kinetics of chemical reactions introduces an amendment in the Arrhenius temperature law in the form of a multiplier (2) : 1
2 4 6 8 9.5
0 69 166 376 589 714
0.9350 0.9349 0.9380 0.9411
8:OO 1o:oo 12:oo 2:oo 4:OO 5:20
10 12 14 16 18 19.3
880 932 1038 1307 1528 1648
738 814 908 1135 1325 1440
0.9488 0.9506 0.9533 0.9568 0.9597 0.9607
4.0 4.3 4.6 5.5 6.2 6.8
8:30
12:oo 2:oo 4:OO
19.3 20.8 22.8 24.8 26.8
1648 1742 1954 2141 2297
1440 1620 1706 1882 2045
0.0602 0.9612
7.0 7.3 8.0 9.2
4
8:30 9:30
26.8 27.8
2297 2332
2045 2082
0.9704 0.9714
1
10:45 12:45 2:45 4:46 6:30
2 4 6 7.75
0 76 228 418 584
0.9360 0.9359
8:30 10:30 12:30 2:30 4:30 6:OO
7.75 9.75 11.75 13.75 15.75 17.25
625 823 1116 1390 1617 1710
584 765 985 1204 1395 1497
0.9455 0.9494 0.9543 0.9580 0.9611 0.9630
8:40 10:40 12:40 2:40 4:40
17.25 19.25 21:25 23.25 25.25
1710 1810 2021 2130 2225
1497 1582 1767 1876 1961
0.9623 0.9659 0.9668 0.9703 0.9700
9.0 9.9 11.4
387
0
0.9333 0.9401
2.85 3.3
1
2
--V a - b
RT
Therefore it is probable that Equation 11 is more universal than Equation 8 :
When using these expressions in practice, it is best to apply methods of approximate integration. Thus, when the number of temperature measurements is n 1 and the time element is a = t/n, we can assume:
+
3
2
3
In order to simplify the calculations, we can assume the coefficient of the algebraic sum in Equathis assumption is tion 12 to be unity instead of admissible since the form of the functional relation is implicit. The method will now be illustrated by a practical application. For this purpose, experimental data by the writer ( I ) will be taken from papers on changes occurring in vegetable oils during oxidation and polymerization.
Enoler Run 1 0 45 129 418 688 866
1
8:30 10:30 12:30 2:30 4:30 6:OO
1o:oo
8:OO 5:OO
0
0
0
9
Run 2 0 150 262 502 625
Run 3 0 489
..
....
0.9703 0.9707
o:iiia 0.9450
2.9 2.9 2.9 3.3 3.8 4.2
... .... ..
2.8 3.1 3.2 3.7 3.9
3.8 4.2 4.8
... ...
7.0
... ...
2
4:OO
17
1211
948
0.9535
5.5
3
4:OO
25
1880
1598
0.9631
7.7
4
1:45
28.75
2045
1763
0.9662
9.8
INDUSTRIAL AND ENGINEERING CHEMISTRY
1206
VOL. 29, NO. 10
TABLE 111. TEMPERATURN VARIATIONS
2
3
2
quite different curves are obtained for the different runs. This is natural because of the temperature variations that took place in the different runs. When the properties of the product are related to the area of the time-temperature curve (Centigrade) through Equation 9 (Table II), it is possible to draw for all runs smooth curves (Figures 5 and 6) which relate the properties of the product to the time and temperature conditions during the run:
3’98 33502s - 2f Sdt
+ 2.8
5=
A somewhat better relationship is obtained when Equation 7 is used, as shown in Table I1 and Figures 7 and 8. In this cas’e, the relation of the properties of the product to time and temperature can be expressed as follows: 108
= 183
x
10-6 42.f(10%-T
dt)
-_
2J’lOSe dt, which we may call L, is a criterion of the property of the product obtained. Therefore, we know that, in order to produce oxidized linseed oil with a viscosity of 7 ” or 12” Engler, we must specify that the oil be treated for such a time and a t such temperatures that L = 1500 or 2000,respectively. It is therefore possible to predict the properties of the Droduct which will be obtained by determining the
(14)
nrhere D specific gravity W = viscosity, ” Engler
D
In Equations 10’ 15 and 16 it can be seen that the quantity
+ 1650 + 0.8596 (15)
Acknowledgment The writer wishes to express his gratitude to N. N. Semyonov and to I?. N. Pavlov who very kindly went over the manuscript.
Literature Cited (1) Breitmann, W. M.,“Plastmassi,” p. 404, Leningrad, 1935. (2) Semyonov, N.N., 2. physik. Chem., B2, 169 (1929). RBcEIvED
July 29, 1936.
