July 1950
INDUSTRIAL AND ENGINEERING CHEMISTRY
certain of the alumina forms represent increasing degrees of crystallinity in a transitional phase, their diffraction patterns may be interpreted as resulting from mixtures of several of the aluminas discussed here. x-Alumina, y-alumina, and ?-alumina have a lower order of crystallinity than the other forms. Chi is readily distinguished because of the diffuse line at about 2.13 A., which occurs in patterns of none of the other forms and which disappears when chi transforms t o gamma. The differences between patterns of eta and gamma are more subtle. They may be distinguished by differences in relative intensity and sharpness of lines, by the line a t 4.6 A. for eta, and b y a marked splitting for gamma of a line which appears a t 1.985 A. for eta. Interplanar spacings for the various forms of alumina are listed in Table I. These spacings and intensities are characteristic of the forms, no matter what starting materials are used. The only differences between powder patterns of a given phase are in line breadth, because of the small size of crystallites in the low temperature forms. y-, p, and x-aluminas always exhibit line broadening. x-Alumina gives a particularly diffuse pattern, even when it persists to relatively high temperatures. &Alumina shows slight broadening; 9- and K-aluminas exhibit practically no line broadening. CONCLUSIONS
Seven crystalline modifications of nearly anhydrous alumina are formed from pure alumina hydrates: alpha, gamma, delta, eta, theta, kappa, and chi.
1403
The basic sequences of transformations occurring in dry air or steam when the alumina hydrates are heated to successively higher temperatures are: a-Trihydrate goes t o a-monohydrate, t o x-, t o y-, to K-, to &, to a-alumina. 0-Trihydrate goes t o a-monohydrate, t o 7,t o 8, t o a-alumina. a-Monohydrate goes t o y-, t o 6-, t o e-, to oralumina. p-Monohydrate goes to a-alumina. The transformation temperatures depend upon time of heating, atmosphere, and hydrate particle size and purity. Of the pure alumina forms, only yalumina has a cubic, spinel type of crystal structure. Tentative tetragonal or orthorhombic lattices may be assigned t o several of the other forms, but this work has not progressed t o a state of certainty as yet. LITERATURE CITED
(1) Edwards, J. D., Frary, F. C., and Jeffries, Z., "Aluminum In-
dustry. Aluminum and Its Production," p. 164, New York, McGraw-Hill Book Co., 1930. ( 2 ) Frary, F. C., IND.ENG.CHEM.,38, 129 (1946). (3) Jellinek, M.H., and Fankuchen, I., Ibid., 37,158 (1945). (4) Ibid., 41,2259 (1949). (5) Russell, A. S.,and Cochran, C. N., Ibid., 42,1332 (1950). (6) Rteinheil, A.,Ann. Physik, 19,465(1934). (7) Taylor, R. J., J. SOC.Chem. I d . , 68,23 (1949). (8) Verwey, E.J. W., 2.Kristallog., 91,65 (1935). REC~IVE June D 4, 1949.
Kinetics of Methanol-Lactic Acid Reaction REACTION WITH 44% TECHNICAL ACID RALPH A. TROUPE' AND KENNETH A. KOBE, University Kinetic data for the reaction of methanol and lactic acid were determined in a series of experiments using 4470 technical grade lactic acid and absolute methanol in sealed tubes. Variables studied were temperature, concentration of mineral acid catalyst, and mole ratio of reactants. It was found that the kinetic data were represented by an equation of the form k9 =
X
( A - b ) ( A - b - xj w-here A - b is the original titratable acidity. In order to express the effect of the variables given above on the rate constant, k, i t was necessary to derive two empirical equations-one for catalyst concentrations below 0.417 %, the other for concentrations above 0.417%. This division was necessary because of the reaction of the sulfuric acid with impurities in the lactic acid. Average percentage deviation of the values of k calculated by these equations from the actual values of k was about 8.5%.
I
N ANY fundamental process, pure research may uncover many important details, but nonetheless the task of evaluating technical grade reactants is necessary t o obtain complete data on the process. Thus, while the primary purpose of this investigation of the kinetics of the methanol-lactic acid reaction was to obtain an empirical relation for the reaction rate using pure reactants ( S ) , data concerning the reaction rate of 4470 technical grade acid with methanol are of industrial importance. 1
Present address, University of Louisville, Louisville, Ky.
of Texas, Austin, Tex.
At the time the investigations on the rate of the reaction of the 44% technical acid mere made, it was planned t o compare the reaction rates of 85% reagent grade acid and 4470 technical grade acid. Because of many requests from industry, the d a t a on the 44% technical grade acid have also been correlated into an empirical relationship expressing the effect of the process variables-temperature, catalyst concentration, and ratio of reactants-on the specific reaction rate constant. Other data presented are variation of density of the reaction mixture with temperature and composition, and equilibrium constants for esterification. RATE OF REACTION
Materials. Du Pont technical grade 44% lactic acid, analyzing 44.03% titratable acidity (as lactic acid), was used in these laboratory investigations. No total acidity (by saponification) was determined experimentally for this material as the presence of impurities made this determination unreliable. The total acidity was obtained from the relation between total and titratable acidity as reported by Watson (4). Absolute methanol, analyzing 100% by density and boiling point determinations, was employed in these experiments. Analytical reagent grade sulfuric acid analyzing 97.03YGsulfuric acid was used as a catalyst. Determination of Densities. To determine the densities of the reaction mixtures a t the temperatures of reaction, the method reported for the first part of this work ( 3 ) was used. As in the
INDUSTRIAL AND ENGINEERING CHEMISTRY
1404
TABLEI. DENSITYOF REACTIOX MIXTURESAT TEMPERATURES
Vol. 42, No. 7
VARIOUS
Temp., Indicated Apprent True Density 0 C. Volume, Mi. Density, d' d , G./MI. A. Calibration with Water; Weight Water, 99.6960 Grams 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
100.00 100.10 100.20 100.35 100.52 100.70 100.95 101.10 101.35 101.60 101.85 102.15 102.42 102.70 103.12 103.35
0.99696 0.99596 0.99497 0.99348 0.99180 0.99007 0.98758 0.98611 0,98368 0.98216 0.97885 0,97598 0,97340 0,97076 0.96680 0,96464
Equation d = (1.00214
B.
99.95 101.12 102.60 104.20 105.90
1.09168 1.07910 1,07079 1.04715 1,03050
Reaction Mixture M / L = 2.0; 20 40 60 80 100
D.
0.00004367t)d'
Reaction Mixture M / L = 1 . 0 ; Weight of Mixture, 109,1140 Grams 20 40 60 80 100
C.
-
0.99823 0,99707 0.99567 0.99406 0.99224 0,99025 0.98807 0.98573 0.98324 0.98059 0.97781 0.97489 0.97183 0.96865 0.96530 0.96192
100.05 101.32 103.00 104.70 106.55
1.09306 1.07950 1,06297 1 ,04573 1.02820
1.05308 1.03988 1,02292 1.00631 0.98880
1.05440 1.04029 1.02245 1.00495 0.98660
Reaction Mixture M / L = 4.0; Weight of Mixture, 99.8330 Grams 20 25 40 60 80
100
100.08 100.35 101.60 103.32 105.20 107.25
0.99753 0.99484 0,98260 0.96625 0.94898 0.93087
E. Reaction Mixture M / L = 8 . 0 ; Weight of Mixture, 93.6940 Grams 20 40 60 80 100
100 .oo 101.68 103.62 105.65 107.92
0.93694 0.92146 0.90421 0.88683 0.86813
0,93813 0.92182 0.90378 0.88562 0.86620
-
0.00004367t)d'
of these substances and the difficulty of analyzing for them in the solution containing the technical grade acid. That this omission introduces a negligible error can readily be seen. Corrections for the amount of polymer present in the equilibrium samples were made based on a method previously reported ( d ) , using a curve showing the relation between titratable and total acidity a t equilibrium. All titration values obtained were corrected for the acidity of the catalyst present by using the information on rates of reaction between methanol and sulfuric acid previously reported ( 3 ) . EFFECT OF VARIABLES OK RATE
previous work a thin-walled Cassia flask of 100-ml. capacity, with a graduated neck of 10-ml. capacity, was employed and was first calibrated with water. The equation for the relationship between true and apparent densities based on this calibration is d = (1.00214
Figure 1. Density of Reaction Mixtures
Weight of Mixture, 105.3615 Grams
(1)
where d is the true density in grams per ml.; d' is the apparent density; and t i s the temperature in O C. Densities of the reaction mixtures were then determined by filling the flask to the zero mark a t 20' C. with a weighed amount of the reaction mixture. The stopper was sealed in the neck of the flask because some of the reaction temperatures were higher than the boiling point of the mixture. Volumetric readings were taken on the flask which had been placed in a constant temperature bath. Inserting the apparent density found in this manner into Equation 1, the true value of density was calculated (Table I, Figure 1). This method of density determination assumes that the volume change during reaction is negligible. Reaction of Lactic Acid and Methanol. The lactic acid, methanol, and sulfuric acid were weighed into separate flasks in the proper proportions. The contents of these flasks were then chilled in a n ice bath, combined, and thoroughly mixed. Approximately 8-ml. samples of the mixture were sealed in soft glass ampoules and placed in a constant temperature bath. At intervals ampoules were removed from the bath, chilled in an ice bath, and broken open. Weighed aliquots were analyzed by titration t o the neutral red end point using standard sodium hydroxide solution. This titration determined only the titratable acidity. No attempt was made t o determine the amounts of polylactylic acids present because of the relatively small amounts
D a t a for the reaction of the technical 4470 lactic acid with methanol are given in Table 11. Figures 2, 3, and 4 show the effect of temperature, catalyst concentration, and ratio of reactants on the rate of reaction of this acid with methanol. An examination of these curves shows that, for a mole ratio of methanol to lactic acid of approximately 4 and a temperature of 100" C., small amounts of catalyst have little effect on the rate of reaction. This is quite apparent for catalyst concentrations from 0 to 0.25y0 sulfuric acid, inclusive. The mixture with 0.5% catalyst shows a definite increase in rate over those mixtures having less catalyst. The lack of catalytic activity of the sulfuric acid, when present in small amounts, is undoubtedly due to its reaction with impurities in the technical grade lactic acid.
I
I
i
1
I
I
TIME. HCURS
Figure 2.
Effect of Temperature on R a t e of Reaction of 44% Crude Lactic Acid and Methanol
I
July 1950
INDUSTRIAL AND ENGINEERING CHEMISTRY
TABLE 11. REACTION RATEDATAFOR CRUDE 44% LACTICACIDAND Time, Hours
looo
Titratable Acidity M1. 0.1 N Base/G. Sbln. HOLao plus catalyst HOLac C.; 0.0943% HzSO4; M / L
HOLac Converted, Moles/100 G. Conversion, % Soln. 1.005; L p 0.435
0.0 0.5 1.0 2.0 3.5 5.0 6.0
0.0 0.5 1.o 2.0 3.0
4.0 6.0 8.0
100" C.; 0.101% HzSO4; M / L = 2.05; L 37.21 37.00 33.18 33.08 0.0342 30.23 0.0677 30.33 26.32 0.1068 26.42 25.03 0.1197 25.13 0.1387 23.23 23.13 21.90 0.1510 22.00 0.1585 21.25 21.15 100'
0.0 1.0 2.0 3.0 4.0 6.0 8.0 24.0
-
9:14 14.9 21.4 27.4 28.7 28.9
.
0.380
10:3 17.8 28.1 31.5 36.2 39.7 41.7
100° C.; 0.0% HaSOr; M / L
4.00;
L
100" C.; 0.145% HaSOk; M / L = 4.00;
-
0.3065
L
0.0 2.0 4.0 8.0 12.0 24.0 48.0
ld.'17 17.65 28.70 35.30 41.00 47.20 49.00 60.05 100' C.; 0.1022% Hz604; M / L = 7.87;
L
= 0.2225
0.0 0.5 1.0 2.0 3.0 4.0 8.0 12.0 24.0 100' C.; 0.098% HzSO4; M / L
=a
7.87; L
-
0.0 1.0 2.0 3.0 4.0 6.0 8.0 10.0 36.0 0.0 0.5 1.0 2.0 3.0 4.0 6.0 8.0 24.0
0.3065
0.0 0.5 1.0 2.0 3.0 4.0 6.0 8.0 24.0
0.222
METH.4NOL
Titratable Acidity, M1. 0.1 N Base/G. S o h . HOLac HOLao Converted, Time, plus Moles/100 G. Conversion, Hours catalyst HOLao Soh. 70 40' C.; 0.1194% HzS04; M/L = 3 . 8 ; L = 0.313 0.0 30.79 30.55 4.0 29.94 29.76 0.0079 2.'52 8.0 29.19 29.04 0.0151 4.82 12.0 28.38 28.24 0.0231 7.38 24.0 26.56 26.43 0.0412 13.15 35.0 25.18 25.05 0.0550 17.60 48.0 23.75 23.63 0.0692 22.10 72.0 22.22 22.10 0.0845 27.00
c.;
0.260% HzSO4: M / L = 4.00; L = 0.306 30.33 29.80 23.79 23.52 0 * 0628 20.'5 20.40 20.13 0.0967 31.6 18.21 17.94 0.1186 38.7 16.53 16.26 0.1354 44.3 15.07 14.81 0.1499 49.0 13.77 13.51 0.1629 53.2 11.61 11.35 0.1845 60.3
1405
30.06 28.54 27.35 25.45 23.37 20.13 16.50
29.86 28.43 27.25 25.35 23.27 20.03 16.40
0.0i43 0.0261 0.0451 0.0659 0.0983 0.1346
4.67 8.55 14.75 21.60 32.10 44.00
80' C.; 0.0955% &Sod; M / L = 3.78; L = 0.314 30.83 30.63 28.01 27.91 o.oij2 8.65 0.0492 15.65 25.81 25.71 24.22 24.12 0.0651 20.75 0.0780 24,80 22.93 22.83 20.83 20.73 0.0990 31.50 19.35 19.25 0.1138 36.20 18.27 18.17 0.1246 39.70 12.73 0.1790 57.00 12.83 100' C.; 0.0968% HzSOI; M / L = 3.95; L = 0.3085 30.31 30.11 26.76 26.66 0.0345 11.2 0.0601 19.5 24.20 24.10 0.0910 29.5 21.11 21.01 18.89 0.1122 36.4 18.99 0.1268 41.0 17.53 17.43 0.1480 47.6 15.41 15.31 0.1577 51.0 14.44 14.34 11.85 11.75 0.1836 59.5
Although the minimum amount of sulfuric acid catalyst is between 0.25 and 0.5% (Figure 3), noticeable decomposition occurred with sulfuric acid concentration of 0.570 and greater. Noticeable decomposition also occurred at 100' C. when the mole ratio of methanol to lactic acid dropped below 4,regardless of the catalyst concentration. Naturally the more prolonged t h e heating the more pronounced was the decomposition. I n the series of curves based on the ratio of reactants, Figure 4, the &mole ratio curve intersects the other curves of lower r s tio. This work was repeated with the same unusual results. I n this experiment the precipitate, which forms in the reaction
looo C.; 0.0 1.0 2.0 4.0 6.0
0.0 0.5 1.0 2.0 4.0 6.0
1.038% HaSOr; M/L = 4.05; L = 0.302 31.61 29.49 15.02 13.96 o.i& 5 i .*so 58.60 11.77 0.1771 12.83 0.1792 59.40 12.62 11.56 0.1809 60.00 12.46 11.40
100O C.; 0.476% H&Od; M / L 31.05 80. 08 25.20 24.72 22.01 21.53 18.81 18.33 15.17 14.69 13.32 12.84
25' C.; 0.0978% HsSOr; M / L 30.14 29.94 30.02 29.82 29.76 3.0 29.96 4.0 29.91 29.71 29.56 8.0 29.74 28.70 28.54 24.0 27.61 27.47 48.0 26.84 26.72 72.0 25.73 96.0 25.84 24.71 24.81 120.0 23.45 23.35 168.0
0.0 1.0
3.90;
L
0.3085
O.&i6 0.0855 0.1175 0.1539 0.1724 p
4.02; L o.bji2 0.00175 0.0023 0.00375 0.0140 0.0247 0.0322 0.0422 0.0523 0.0659
lf.'35 27.70 38.05 49.85 56.00 0.3065 0.k9 0.57 0.75 1.22 4.55 8.05 10.50 13.75 17.00 21.50
TIYL
-wns
Figure 3. Effect of Catalyst Concentration on Rate of Reaction of 44% Crude Lactic Acid and Methanol
INDUSTRIAL AND ENGINEERING CHEMISTRY
1406
Vol. 42, No. 7
tion was not a simple f i s t , second, or third order reaction, it, seemed logical t,o attempt t o fit the data by the type relationship used to represent t,he data for t,he reagent material. This relationship as reported (3) is k8=
V I
0
iw5
0
2
1
3
4
TlME
5
6
7
8
HOURS
Figure 4. Effect of Mole Ratio of Reactants on Kate of Reaction of 44qo Crude Lactic Acid and Methanol
mixture (due to impurities in the technical grade acid), was of a different nature than that obtained in the runs a t other ratios; it appeared t o be more abundant and did not settle out easily. It is believed that this precipitate caused the unusual behavior in t,he reaction because ( a ) it remained in colloidal suspension and contributed to the xeight of the sample taken for analysis but not to the titration value, and ( b ) it may have interfered with the reaction itself by acting as an inhibitor. ORDER O F ESTERIFICATION REACTION
The data for the reaction of Myo technical grade lactic wid with methanol are given in Table 11. Since previous work on reagent grade 8 5 q lactic acid (3) had indicated that the reac-
TIME - H O U R S
Figure 5 ,
X
(A
- b)(A - b - X )
where A - b is the original titratable acidity; X is the amount of lactic acid converted in time, 8; 0 is the time of reaction; and k is a specific reaction rate constant. Plots of X / ( A - b - X) against time were made with X data obtained from the smoothed curves of per cent esterified and using the values of original titratable acidity for A - b (Figurcbs 5, 6, and 7). Reasonably straight lines were obtained in nearly every case up t o about 60YO of the equilibrium per cent react,ed. With reagent grade materials these curves fitted the data up to 90% or more of equilibrium ( 3 ) . It is not surprising, however, that the curves for technical grade 44Y0 acid do not hold over so wide a range. Two factors contribute to this. First, the 44'; acid contains more water a t the start, and hence the reverse reaction of hydrolysis becomes an important factor a t lower concentrations of ester. Secondly, as reported previously, tht: longer reaction times in some mixtures produced decomposition of the crude material. Therefore, the equation adequately represents the most important range of the data from a practical standpoint. Slopes of the curves were obtained by taking the average sloptl through the points in the straight line region and the origin. Unlike the runs with reagent grade lactic acid no induction periods were found with the higher ratios of methanol to lactic acid. I t is probable that, with t,he more dilute acid, this transition occurs at still higher ratios. The data for the derivation of k are given in Table 111. I n order t o obtain k in the units, liters per (mole)(minute), the quantity A - b must be expressed in moles per liter and 0 in niinutes. Since X / ( A - b - X) is a ratio, the units are immaterisl as long as they are consistent. Values of k (Table IV) were obtained by dividing the slopes of the lines in Figures 5, 6, and 7 by values of A - b, in moles per liter, which had been calculated from the original titratable acidity and the density values determined for the reaction mistures.
2
-
Relation between X / ( A b - X) and Time at Different Temperatures
Catalyst concentration, approximately 0.1 %; approximately 4
m o l e ratio.
(2)
Figure 6.
-
4
TIME
YOURS
-
Relation between X / ( 4 - b X)and Time for Different Catalyst Concentrations
Temperature, 100' C.; m o l e ratio, approximately 4
INDUSTRIAL AND ENGINEERING CHEMISTRY
July 1950
1407
TABLE111. DATAFOR DERIVATION OF k Temperature Series Time, X hours ( A b X) 1000 C. 0.5 1.0 2.0 3.0 4.0 6.0 8.0
-
-
Catalyst Series Time, X hours ( A b X) 1.038% &so4
- -
1.0 2.0 3.0 4.0 6.0 8.0
4.0 8.0 12.0 24.0 35.0 48.0
Figure 7.
Relation between X / ( A - b - X ) and Time for Various Mole Ratios of Reactants
Temperature, 100'' C.; catalyst concentration, approximately 0.1 % EQUATION FOR RATE CONSTANT
I t was found that k varied with the catalyst concentration, the temperature, and the mole ratio of methanol to lactic acid. In esterifications of this kind (1) the rate constant is usually proportional t o the concentration of the mineral acid used. Such was found to be the case in the first part of this work (3). When the data for the 4470 technical lactic acid were plotted in this manner, Figure 8, the data fell on two straight lines. For cataIvst concentrations UD to 0.417% sulfuric acid the value of k was essentially constant at 0.001283 liters per (mole)(minute). Above this value k was linear with catalyst concentration, as noted in the discussion of Fieure 3. Two relationships may therefore be derived for this plot:
-
1.0 3.0 4.0 8.0 24.0 48.0 72.0 :;::1 168.0
1.0 2.0 3.0 4.0 6.0 8.0 40" C. 0.0266 0.0520 0,0818 0.1559 0.2196 0.2928 25O C. 0.0040 0.0059 0.0075 0.0127 0.04905 0.899 0.1205
g:0.2822 ",:!
1.587
0.476% 0.5 1.0 2.0 4.0 6.0
60' C. 2.0 4.0 8.0 12.0 24.0
HzSO4 0.2168 0.3971 0.6410 1.048 1.3427
0.26% HzSOa 0.2670 0.4804 0.6611 0.8327 1.0120 1 ,2058
0.145% HzSOi 0.5 0.2209 2.0 0.4177 3.0 0.5671 4.0 0.7265 6.0 0.9464 8.0 0.9967 0.0968% 0.5 1.0 2.0 3.0 4.0 6.0 8.0
HzSO4 0,1294 0.2494 0.4331 0,5940 0.7274 0.9667 1.0998
- 0.005334
1.0 2.0 3.0 4.0 6.0 8.0
0.1917 0.3570 0.5340 0.6729 0.9486 1.1590
M/L 3.95 0.5 1.0 2.0 3.0 4.0 6.0 8.0 I M / L 2.06 0.1185 0.2233 2.0 0.4058 3.0 0.4784 4.0 0.5997 6.0 0.6895 8.0 0.7494 0.5 1.0
M / L 1.005 0.1033 1.0 0.1904
0.5 2.0
3.5 5,o
6.0
0.2810 0.3911 0.4152 0.4204
0 . 0 % HzSOi 0.1235 1.0 0,2202 2.0 0.3997 3.0 0.5405 4.0 0.6485 6.0 0.8977 8.0 1.0714
plot of k against M I L . F~~a temperature of may be expressed by the equation
c. this line
k = 0.0001755(M/L) 0.0005807 ( 5 )
+
(4)
where C is the concentration of sulfuric acid catalyst in per cent of the total mixture. The location of the point of intersection of these curves will probably vary with the source of crude acid as it is undoubtedly a function of the impurities present. Because 0.1% sulfuric acid exerts no catalytic effect on the reaction, it was not necessary t o obtain k on a catalyst-free basis in finding the effect of mole ratio of reactants on k. Hence instead of plotting ( k a ) / C against M I L , where a is the value of k corresponding to 0% catalyst, a plot was made of k against M / L (Figure 9). In plotting this curve an average of the values of k for 0,0.1,0.15, and 0.25% catalyst was plotted for the M I L = 4 point as it was believed this would give greater accuracy. Examination of the points for this curve shows that the value of k for M I L = 7.87 does not line up well with the rest. This is the same experiment which was reported as behaving peculiarly when Figure 4 was discussed. Because of the unusual behavior of this run the point corresponding to M I L = 7.87 was not considered in arriving a t the best straight line through the points on a
-
M / L 7.87 (Run B)
o.5
Up to 0.41770 HzSO,, k = 0.001283 Above 0.417% HzS04, k = 0.01588C
-
M / L 7.87 (Run -4) 0.5 1.0 2.0 3.0 4.0 8.0
6.000 800 c. 0.0975 0.1914 0.2699 0.3417 0.4776 0.5912
Ratio of Reactants Series Time, X hours ( A b - X)
i': '7
1 - 4
8
1.0
C,WEIGUT PER CENT +SO4
Figure 8. Variation of Specific Reaction Rate Constant, k, with Catalyst Concentration, C Temperature, 100' C.; m o l e ratio, approximately 4
Below 0 . 4 1 7 7 0 s u l f u r i c acid the catalytic activity is constant, and no term for catalyst concentration is required in the equation. To provide a means for obtaining the effect of mole ratio and catalyst concentration a t values of C above o.41i70, another equation was d e r i v e d by transposing the data as follows:
INDUSTRIAL AND ENGINEERING CHEMISTRY
1408
TABLE IV.
COMPARISON O F +kCTUALAh-D CALCULATED VALUES O F
k
Temp., ’ C.
C,Wt. % Catalyst
M/L
Calculateda
Actualb
25 40 GO 80 100 100 100 100 100 100 100 100
0.0978 0.1194 0.0973 0,0955 0.0968 0.0943 0.101 0.1022 0,098 0 . coo 0.145 0.234
4.02 3.80 4.03 3.78 3.95 1.005 2.05 7.87 7.87 4.00 4.00 4.00
0.00001093 0.C0003304 0.0001323 0.0004255 0.001274 0.0007571 0 .OO09405 0.001962 0.001962 0.001282 0,001282 0.001282
0.00001125 0.0000357 O.QO01328 0.00044 0.001375 0.000672 0.000995 0.00163 0.001585 0.001180 0.001206 0,001372
-0.00000032 -0.00000166 -0,0000005 --F.0000145 -0.000101 0.000085 -0.0000545 +0.000332 +0.000377 +0.000102 +O ,000076 - 0.00009
-2.84 -4.65 -0.38 -3.30 -7.35 +12.65 -5.48 4-20.37 +23.78 +8.64 4-6.30 -6.55
100 100
0.476 1.038
3.90 4.05
0.00220; c 0.01114
0.002225 0.01115
- 0,000024
-1.08 -0.09
a
b 0
k, Liters/(Mole) (Min.)
Deviation,
Difference
+
-0.00001
From Equation 9. From Equation 2. From Equation 10.
A. From Eauation 4 the theoretical value of k a t 0% . - catalvst is -0.005334. B. It is known from previous work t h a t ( k - a ) / C plotted against M I L gives a straight line. Hence the line sought will follow the general curve ( k - a ) / C = m(iM/L) b (6)
+
where m and b are the slope and intercept, respectively, of the line. C. Since a is the value of k at 0% catalyst concentration, the value of -0.005334 is substituted for it. Since the catalyst concentration which will give a value of k of 0.001283 is 0.4170j~,this value must be substituted for C in the equation. This is because all runs in which i V / L was varied were run a t 0.1% catalyst, which was in the region where the apparent effect of catalyst concentration was negligible. D. Values of k and M I L from Figure 9 were substituted into Equation 6 , and values for m and b were obtained. The equation thus obtained, for values of C of 0.417% and above, is k = O.O00422(M/L)(C) 0.014175C - 0.005334 (7)
+
Figure 10 shows that the variation of k with temperature is according to theory, This plot of log k against the reciprocal of the absolute temperature follows a straight line with little variation for temperatures from 25‘ t o 100” C., a mole ratio of reactants of approximately 4, and a catalyst concentration of approximately 0.1% sulfuric acid. These data may be expressed by the equation
- 3069.3/2’
log 105k = 10.3640
%
Vol. 42, No. 7
empirical equations involving all the variables. Two of these equations are necessary. For catalyst concentrations up t o 0.417y0 sulfuric acid k = [O.O001755(M/L) 0.0005807]
+[10(10.36~~60~J8!l.3
/T)
And for catalyst concentrations above 0.417% sulfuric acid k = [0.000422(M/L)(C) f 10(10.38400 - 3183.3 /T) 0.014175C - 0.005334][ 136,5
where k is the reaction rate constant in liters per (mole)(minute); X / L is the ratio of moles of methanol to moles of lactic acid; C is the weight per cent sulfuric acid catalyst; and T is the temperature in O K. The effectiveness of Equation 9 in representing the experimental data, where the catalyst concentration is below 0.417y0, is shown in Table IV, which gives a comparison of the values of k obtained from the experimental data and Equation 2 with the values of k obtained fr6m Equation 9. The average percentage deviation of the twelve runs below o.41770 catalyst is 8.5270. Similarly the comparison of experimental values of k with those calculated from Equation 10 for the two runs in the region above O.417y0 catalyst is shown in Table IV. The average deviation is 0.58%. More runs are needed in this latter region t o make the results more conclusive. EQUILIBRIUM COXSTANTS
It might be more appropriate t o label the equilibrium constants for the 44% technical grade acid as “apparent” equilibrium constants, for no account has been taken of the solid phase present, the impurities in solution, or partial decomposition which occurs under some conditions. (methyl lactate) (water) K = (lactic acid) (methanol) These equilibrium constants were obtained by keeping samples of the reaction mixture in the bath until the composition became constant. I
(8)
where 2’ is the temperature in ’ K. The different variables studied here may be combined into
0,000
/
I 2
4
6
Figure 9. Variation of Specific Reaction Rate Constant, k, with Mole Ratio of Reactants, M I L Temperature, 100’ C.4
!4
0
MA
catalyst concentration, below 0.417%
1A
Figure 10. Relation between Log of Reaction Rate Constant, k, and Reciprocal of Absolute Temperature, 1/T
INDUSTRIAL AND ENGINEERING CHEMISTRY
July 1950
1409
CONCLUSIONS
TABLE V.
EQUILIBRIUM CONSTANTS FOR REACTION OF CRUDE 44% LACTICACIDWITH METHANOL M / L . Approximately 4; Catalyst, Approximately 0.1% HzSOr
Temperature Series: Temp.,
O
C.
25 40 60 80 100 Catalyst Series:
Equilibrium Constant, K
3.40 3.40 3.28 3.38 3.26 Average 3.34 M / L , Approximately 4; Temperature, 100” C.
H1SOr. % 0.0 0.0968 0.145 0.260 0.476 1.038
Equilibrium Constant, K
3.10 3.26 3.24 3.31 3.27 3.23 Average 3.24
Production Series:
Temperature, 100’ C.: Catalyst, Approximately 0.1% Ha904 Equilibrium M/L Constant, K
~
1.005 2.05 3.95 7.87
4.42 3.98 3.26 2.65
The data and results presented here show that an excess of sulfuric acid, over that needed t o react with the impurities in the commercial lactic acid, must be present in the reaction mixture to ensure catalytic activity. High ratios of methanol to lactic acid and short contact times a t high temperatures favor high yields and low decomposition. NOMENCLATURE
-
A b = original titratable acidity, moles per liter a = constant, corresponds to the theoretical value of k for 0% catalyst C = weight % catalyst based on total weight of mixture K = equilibrium constant k = specific reaction rate constant, liters per (mole)(minute) L = moles lactic acid per 100 grams of solution M = moles methanzl per 100 grams of solution T = temperature, K. t = temperature, C. X = moles lactic acid, converted a t time 8, per 100 grams solution e = time, minutes or hours as specified LITERATURE CITED
(1) Glasstone, S., “Textbook of Physical Chemistry,” New York,
Table V shows that temperature and catalyst concentration have no appreciable effect on the equilibrium constant in the ranges studied. However, a definite trend can be seen when the ratio of reactants is varied. This is similar to that found when the 85% lactic acid was used (3).
D. Van Nostrand Co.,1946. Troupe, R. A . , and Kobe, K. A., Anal. Chem., 22,545 (1950). (3) Troupe, R.A., and Kobe, K. A., IND. ENG.CHEM.,42,801 (1950). (4)Watson, P.,Ibid., 32,399-401 (1940). (2)
RECEIVEDMarch 13, 1950.
Diglycol Bis(Carbonates) of Lactic Esters LACTIC ACID DERIVATIVES AS PLASTICIZERS C. E. REHBERG, MARION B. DIXON, T. J. DIETZ, AND C. H. FISHER Eastern Regional Research Laboratory, Philadelphia, Pa. Plasticizers made by acylating twenty-three lactic esters with diethylene glycol bis(chloroformate)[O(CH&Hp OCOC1)2] are described. As a class, these plasticizers were high boiling and compatible with a vinyl chloridevinyl acetate copolymer, ethylcellulose, and cellulose ace-
tate. The esters prepared from the n-butyl, n-hexyl, 2ethylhexyl, 2-butoxyethyl, and 2-(2-butoxyethoxy)ethyl esters of lactic acid were relatively fluid and more efficient than many of the commercial plasticizers in plasticizing the vinyl chloride-vinyl acetate copolymer.
B
Considerable work has been done in this laboratory on the preparation and evaluation of high boiling lactic acid derivatives as plasticizers. The present paper describes diglycol bis(carbonates) [diethylene glycol bis( 1-carbalkoxyethyl carbonates) ] made (15, 16) by acylating certain lactic esters with diglycol bis(chloroformate),
ECAUSE the production of plasticizers in the United States has increased tremendously in the last decade-from 30,000,000 pounds in 1939 to about 190,000,000 pounds in 1949 ( 1 ) much effort has been expended to find improved plasticizers and new raw materials for their manufacture. Lactic acid, commercially available as such and as the methyl, ethyl, and butyl esters, is of interest as a starting material for plasticizers because it can be made easily and efficiently (6, 10) from inexpensive materials such as corn sugar, whey, molasses, and sulfite waste liquor (9); its manufacture is not necessarily associated with or limited by other commercial operations; and having two functional groups, it can be transformed into many high boiling derivatives (6,14-16) having ester and other compatibilizing groups. Although the preparation of plasticizers from lactic acid has been described (2-6, 16), appreciable quantities have not been used for this purpose.
+
O(CH2CH20COCI)z 2HOCH(CHa)COOR + Diglycol bis( chloroformate) 0 [CHzCHzOCOOCH(CHa)COOR 12 Diglycol bis( carbonate) Compatibilities of these bis(carbonates) with cellulose acetate and ethylcellulose and the properties of vinyl chloride copolymer plasticized with the bis(carbonates) are given also. The chemicals required to make most of the bis(carbonates) discussed here are available commercially.
