October 1952
INDUSTRIAL AND ENGINEERING CHEMISTRY
2397
LITERATURE CITED
SUMMARY
This work has shown that homogeneous products may be obtained from the styrenation of the dehydrated castor oil fatty acid esters of Epon resins 1001 and 1004. The solvent method was used, but it is necessary t o use approximately equal parts of solvent and total charge t o prevent gelation when the solvent is Solvesso 150. The high viscosity of the ester of Epon 1004 necessitates the use of a mixture of styrene and a-methylstyrene for control of the reaction. With the ester of Epon 1001 straight styrene may be used when low percentages of combined styrene are desired. However, the mixture of styrene and a-methylstyrene is necessary when high percentages of styrene are desired in the final product. Using the technique of adding the styrene-catalyst mixture portionwise t o the heated ester solution, no difficulties were encountered in obtaining homogeneous styrenated products throughout this investigation. When the styrenes were placed in the reactor a t the start of the reaction the products were incompatible. As may be expected from results obtained with other materials, a catalyst is necessary t o produce homogeneous styrenated Epon esters. A comparison of benzoyl peroxide and di-tert-butyl peroxide showed the latter t o be superior in respect t o the efficiency of the reaction under the conditions used. The products o b tained with di-tert-butyl peroxide were decidedly superior in color t o those obtained when benzoyl peroxide was used. Preliminary evaluations of these copolymers indicate improved resistance to water and alkali, while maintaining the excellent adhesion and flexibility characteristics of the Epon resin esters.
Bhow, N., and Payne, H. F., IND. ENG.CHEM., 42,700 (1950). Bradley, T. F., Oficial Digest Federation Paint (e: Varnish Praduction Clubs, No. 310 (1950). Detroit Paint and Varnish Club, Ibid. No. 286, (1948). Dow Chemical Co.,“Styrenated Drying Oils,” Midland, Mich., 1948.
Dunlap, L. H., U. S. Patent 2,382,213(1945). Flint and Rothrock, Ibid., 2,225,534(1940). Greenlee, S. O.,Ibid., 2,456,408(1948). Griess, G. A., and Teot, A. S., Ibid., 2,468,748(1949). Hewitt, D. H.,and Armitage, D., J . Oil & Colour Chemists’ ASSOC., 29,109-128 (1946). Hewitt, D. H., and Wakeford L. E., U. S. Patent 2,392,710(1940). Hoogsteen, H.M.,Young, A. E., and Smith, M. K., IND.ENQ. CHEM.,42,1587 (1950). Lawson, W. E., and Sandborn, U. S. Patent, 1,975,959(1934). Long, J. S.,J . Oil & Colour Chemists’ Assoc., 32,No.350 (1949). Petersen, N. R.,Oficial Digest Federation Paint & Varnish Production Clubs, No. 283 (1948). Powers, P. O., IND. ENG.CHEM.,42,2096 (1950). Sohroeder, A. M.,and Terrill, R. L., J . Am. Oil Chemists’ Sac., 26,153 (1949).
Shell Chemical Co., Tech. Bull. SC:50-40 (1950). Tess, R. E.,and M a y , C. A,, Oficial Digest Federation Paint & Varnish Production Clubs, No.311 (1950).
Wakeford, L. E., and Hewitt, D. H., Brit. Patent 573,809 (1945). Wakeford, L. E.,Hewitt, D. H., and Armitage, F., Ibid., 573, 835 (1945). Ibid.. 580.912 (1946). Wakeford, L. E., Hewitt, D. H., and Davidson, R. R., Ibid., 580,913 (1945). Young, A. E., Oficial Digest Federation Paint & v a r n i s h Production Clubs, No.296 (1949). R E C ~ I V Efor D review January 22, 1952. ACCEPTED June 3, 1952. Presented before the Division of Paint, Varnish, and Plastics Chemistry at the 121st Meeting of the AMERICAN CHEMICAL SOCI~TY Milwaukee, , Wia., March 30-April 3. 1962.
Effect of Temperature on Azeotropy in 1,LDif luoroethane and Dichlorodifluoromethane W. A. PENNINGTON Carrier Corp., Syracuse, N .
I
N RECENT years use has been made of a solution of 1,ldifluoroethane (Genetron 100) and dichlorodifluoromethane (Freon 12) as a refrigerant, the specified composition being that of the azeotrope a t 0” C. (The new azeotropic refrigerant is Carrene-7.) It has been employed primarily in air-conditioning equipment where the evaporator temperature is usually held between 5 ” and 6 ” C. For azeotropic systems in general, the azeotropic composition changes with temperature, the solution becoming richer with respect to the substance having the higher molar latent heat as the temperature increases. Since this nen refrigerant may be used where the evaporator temperature is low, information is needed concerning the change of azeotropic composition with temperature. GENERAL EFFECT OF TEMPERATURE ON AZEOTROPY
Even though there are a great many data in the literature on azeotropic systems a t some single pressure, there are not many to be found with changing pressures. Since there is a boiling
Y,
temperature for each pressure and composition, this means there is also a dearth of data on azeotropic systems a t varying temperatures. In refrigeration, attention should be focused on the temperature rather than the pressure. Swietoslawski (7) gives a graphical representation of the effect of change of temperature on a system characterized as the maximum-pressure type of azeotrope. Recently, Skolnik (6) discussed the effect of pressure on azeotropy. He arrived a t the conclusion that two sets of accurately determined data-pressure, boiling point, and composition-data completely define an azeotropic system. He gives the equation, log z = a
+ bT
(1)
where 2 is the mole per cent of one substance and T is degrees Kelvin. Obviously, this relation is not compatible with that shown graphically by Swietoslawski because z could not be zero at any real value of T. For this reason, it seems advisable t o search for another type of equation which would be more suitable, particularly for extrapolation purposes. Skolnik showed,
INDUSTRIAL AND ENGINEERING CHEMISTRY
2398
Vol. 44, No. 10
however, that this type of equation does represent the data in the methanol-benzene system fairly me11 from 55.7 to 80.7 mole % methahol.
used at 0" C., and a water bath, heated by an infrared lamp, a t the tn-o highest levels. The variation was not more than a few hundredths of a degree.
PREPARATION O F MATERIALS
COMPOSITIOS AS A FUNCTION OF DENSITY
The 1,l-difluoroethane used in this investigation was first dried by being passed through phosphorus pentoxide under pres8ure and then freed of noncondensables by a method previously described (4). Vapor pressure measurements at 0" C. were used as a criterion of purity with respect to noncondensables. A11 samples tested gave a pressure n-ithin 0.002 of 2.609 atmospheres which gives assurance that there wrre not more than 5 p.p.m, of ail in the liquid. It was not necessary to dry the dichlorodifluoromethane with phosphorus pentoxide for tJ\o reasons. In the first place, the water content of the supply was not more than 5 p.p.m. and, secondly, the purification treatment t o take out noncondensables will remove a very high percentageof the initial water anyway. The vapor pressure a t 0 C. never differed from 3.046 atinospheres by more than 0.002. I n one case, a mixture was made from ingredients treated as described above, was then distilled, and the middle third was selected. This mixture gave precisely the same vapor pressure as another mixture of the same composition whose ingredients uTere not subjected to distillation. The vapor density of the stock materials was the same as the middle cut of the distilled product. O
The folloa-ing general equation has been given ( 3 ) to express the percentage composition as a function of apparent molecular TTeight:
nhere X1, M Z ,and M,,, are the apparent molecular weights of the pure components and the mixture, and y is the percentage of the Eubstance having M I as the apparent molecular weight. (Unless specified as "mole per cent" this, and related terms, means per cent by TT eight throughout this paper.) For the binary system under consideration, it was found that
Y=
121 07 (123.49
- JI,,&)
(3)
JI,
y being the percentage of 1,l-difluoroethanc 2 9 a ,
1
,
1
EXPERIMENTAL TECHNIQUE
A given mixture was prepared by charging desired weights (accuracy bO.01 gram) of the substances into separate cylinders and then connecting the two and pouring the ingredients back and forth four or five times. Dry ice-acetone was finally used to draw the material into one of the cylinders. The cylinder (about 125-ml. capacity) has been described (2).
284
I
263 -12
-IO
-8
-$
-k
RDER OF 54MPLING
-2
0
2
4
6
8
10
I2
Figure 2. Azeotropic Composition a t 24.90' C. i n the Binary System, Dichlorodifluorometharte and Difluoroethane
254 -lL
lb
-L -d _a
d B B
ORQER OF S ~ U P L I ~ ~ C -2 0 2
IO
I?
Figure 1. Azeotropic Composition a t 0" C. i n the Binary System, Dichlorodifluoromethane and Difluoroethane
In general, about 100 grams of mixture were prepared for a single run. The cylinder containing the mixture M-as placed in a thermostat and successive samples were withdrawn from the gas port, using equipment and technique also described (5) previously, until all liquid was exhausted. I n general, every fourth purge m w taken for analysis by the gas density method, the density being expressed as apparent molecular weight. Runs were made a t four temperatures: -30.5", O.O", 24.90°, and 40.08" C. At the lowest level, the temperature n-as controlled by a bath of liquid dichlorodifluoromethane in a Dewar flask open to the air. The control was poorest by far at this level, there being a variation of about 0.2" C. An ice bath was
I t was discovered that there were at least two errors involved in the derivation of Equations 2 and 3. I t was assumed that the apparent molecular weight of each constituent is the same in the mixture as in the pure stat'e. Actually, it is somewhat lower. Were this not true there would be no azeotrope. This error, however, is probably not very large. There is another error which has t o do m-ith the absorption of the gases in the stopcock grease. This second error may be larger than the first, depending upon the type of grease used. A correction factor can be determined for use Jyith any particular setup by analyzing the gas from a single liquid to exhausttion. The true average vapor analysis must be identical with the composition of t8heoriginal liquid. Therefore, if substitutions in Equation 3 give values m-ith a higher average than the original liquid, the difference, depending on the sign, can be added to or subtracted from the right-hand side of the equation to give another equation accurate for the special set of conditions which actually exist. If the stopcock grease is changed or the Dumas bulb cleaned, then another equation should be determined. In reality, this method becomes one of comparative measurements. It has been found that silicone grease gives the best results \Titi1 apparently very little absorption. Where it was used with a tTell-cleaned bulb, the following equation was established:
2399
INDUSTRIAL AND ENGINEERING CHEMISTRY
October 1952
Y =
120.70 (122.96
- Mm)
M,
(4)
Since the same equation was found with a stainless steel bulb, provided with an angle valve, where there was no grease a t all, it is accepted as the true equation. It can be used for any bulb where there is no appreciable error due t o absorption of gases in a film of grease. It is not necessary or desirable always t o have the conditions which will permit the use of a single accurate equation. It is much simpler and just as accurate t o find for each setup its correct equation 01, better, use Equation 4 and, if the average for the gas samples is not the same as that for the original liquid, adjust the values so as t o make the average identical with the composition of the liquid. The technique involving the adjustment was used throughout this work. AZEOTROPIC COMPOSITION AT 0 ' C.
After several preliminary runs a t 0" C., three runs were made with liquid samples, XL, XLIX, and XLI, containing 25.90, 26.20, and 26.40% difluoroethane, respectively. The results are shown in Figure 1, the curves being fitted by the law of least squares. Inasmuch as the difluoroethane content increases with successive sampling for sample XLI, it is obvious that the azeotrope contains less than 26.40% difluoroethane. Likewise, it contains more than 25.90% because X L definitely gives less difluoroethane with successive sampling. The azeotrope then lies between 25.90 and 26.40%. Point A represents the vapor in equilibrium with the original liquid for XLI; B represents a similar point for XL. It is obvious that the azeotrope lies between these two compositions: 26.317 and 26.035. If a value (26.176) midway between A and B be taken, i t cannot be more than 0.14 from the true value based upon the premise that the azeotrope must lie between A and B. A further refinement can be made in the interpretation by extending the lines t o their intersections or by solving pairs of the following equations simultaneously:
- 0.022562
XL
y = 26.035
XLIX
y = 26.185
(6)
XLI
y =
(7)
+ 0.002972 26.317 + 0.014672
AZEOTROPLC COMPOSITION AT 24.90' C.
Three mixtures, XLVII, XLVIII, and XLV, containing 28.50, 28.745, and 29.04y0 difluoroethane were run a t 24.90" C. The data are shown in Figure 2, giving the three mathematical solutions D', E', and F'. The equations, by the law of least squares, are:
+ 0.00158s = 28.935 + 0.019332
XLVIII y = 28.737 XLV
y
- 0.022422
AZEOTROPIC COMPOSITION AT -40.06" C.
Two mixtures, L I and LII, containing 30.00 and 31.00% difluoroethane gave results a t 40.08' C. which can be represented by y = 30.329
- 0.058302
(11)
L I I y = 30.854
+ 0.027672
(12)
LI
The data are shown in Figure 3, the algebraic solution represented b y G' being 30.69%. AZEOTROPlC COiMPOSITION AT -30.5' C.
The first mixture, LV, run a t this temperature, contained 20,2070 difluoroethane and was far below the azeotropic composition. The first vapor sample contained 20.66% and the last, 18.47% difluoroethane. The data may be represented by LV y
21.360 - 0.231832
(13)
The fit is not nearly so good as those previously shown for other temperatures because the straight line no longer gives a good fit where the original mixture is so far removed from the azeotrope. While the straight line definitely does not fit the data, it may still be used arbitrarily to help arrive a t the azeotropic composition.
(5)
The three values for A', B', and C' are 26.206, 26.168, and 26.151. The mid point of the range is 26,18% and doubtless is very close to the true azeotropic composition. An examination of the graph will reveal that the results for XLIX are not as desirable as for the other two samples, therefore A' is the best individual solution. This value at 26.206 has been rounded off in the downward direction to give some little consideration to the mathematical solutions represented by B' and C'. The azeotropic composition at 0" C. then is accepted as 26.20% difluoroethane and is regarded as being accurate to r t 0 05.
XLVII y = 28.621
single solution; therefore it has been favored in the selection of 28.78 as the azeotropic composition at 24.90' C.
(8) (9)
(10)
Their solutions, in pairs, result in 28.719, 28.790, and 28.729 for D', E', and F'. The nriter is inclined t o favor E'over any other
Figure 3. Azeotropic Composition at 40.08' C. i n the Binary System, Dichlorodifluoromethane and Difluoroethane
The other mixtures, LVII and LVIII, containing 22.50 and 22.20y0 difluoroethane gave y = 22.491
+ 0.002331:
(14)
LVIII y = 22.268
- 0.011641:
(15)
LVII
The solution of these two equations gives 22.45 for the azeotropic composition at -30.5' C. Even though mixture LV was considerably removed from the azeotropic composition, the solutions of its equation with Equations 14 and 15, giving 22.48 and 22.32, are not far different from the preferred value of 22.45. COMPOSITION A S A FUNCTION OF TEMPERATURE
The results for the four temperatures are summarized in Table I. The compositions are given both in weight and in mole per cent. The latter will be used in the mathematical relations which are to follow.
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
2400
Vol. 44, No. 10
Turning attention to the possibility of attaining nonazeotropy 1. AZEOTROPICCOMPOSITIONS I N DICHLORODIFLUORO- toward difluoroethane, one may find that the critical temperaMETHAXE-DIFLUOROETHAXE SYSTEM ture, 381' K., of this compound is lower than the value calculated t , C. T, F. CHaCHFs, Wt. % CHBCHF2, Mol. % by Equations 16, 17, or 19. B maximum occurs in Equation 18 -30.5 242.66 22,45 34.64 at 63.3% difluoroethane. At this point, the temperature is 0.00 273.16 26,20 39.40 298.06 28.78 607' K. 24.90 42.53 30.69 40.08 313.24 44.78 If any of the four equations can be accepted to represent the system over a broad range of concentrations, azeotropy is continuous throughout the entire liquid range. It might be well to Several equations were fitted by the law of least squares t o turn to the literature for more light on which equation may be give the azeotropic composition as a function of temperature. more reliable for azeotropic systems in general. From these, the following have been selected as having the most The z parabola will be eliminated a t this point because it merit: tends to reach a maximum within the realistic range of concentration. log z = 1.16257 0.00156567' (16) TABLE
+
z
= 90.419 log
x
= -16.19
T
7'
-
181.00
+ 0.261922' - 0.00021567T2 = 112.35 + 1.21566~+ 0 . 0 7 3 3 4 0 ~ ~
(17) (18) (19)
For convenience the types of equations are referred to as the log equation, the log T equation, the z parabola, and the T parabola in the order listed. 2
OTHER SYSTEMS
ETHANOL-ETHYL ACETATE. ?.lore coniplete data ( I J are available for this system than any other found, extending from about 22 to 55 m 0 l e 7 ~ethanol. The following equations have been fitted for this system: log N = 0.16897 0.004324897' (20)
+
z = 272.81 log 2' - 625.62 (21) T = 184.41 4.6243.~- 0 . 0 2 4 5 6 ~ ~ (22) The adequacy of the various fits is shown in Table I11 where it may be seen that the T parabola, with an average deviation of 0.24, is better than the log 2: equation with a deviation of 0.44: the log T equation, with an average deviation of 0.98, is not
+
satisfactory .
TABLE 111. DETIATIONS FROM OBSERVEDVALUES I N ETH.4XOLETHYLACETATE SYSTEM
I
t t 230 I
T
INCREASING -4
Figure 4.
Antoine Lines for Various Compositions in an Assumed Binary System
__-
T
Xobsd.
271.77 283.74 296. 88 311.58 320.99 328.08 333.78 338.56 342.73 344.97 346.43 349.79 352.84 355.64 358.23 360.64 362.90 365.02
21.93 24.47 28.10 33.05 36.64 39.40 41.64 43.55 45.25 46.19 46.78 48.18 49.09 50.69 51.86 52.97 54.04 55.08
Av.
Deviations Eq. 21 4-2.48 +0.01 -0.82 -1.60 -1.53 -1.36 -1.16 -0.93 +0.32 -0.52 -0.43 -0.17 -0.31 +O. 38 $0.68 +1.00 4-1.33 +1 68 0.98
____
____-I
Eq. 20 -0.17 -0.43 -0.28 +o. 19 1-0.56 1-0.68 $0.66 4-0.58 +0.46 1-0.38 +0.30
+o.
12 -0.45 -0.25 -0.32 -0.57 -0.72 -0.85 0.44
The adequacy of the fit in each case is revealed in Table 11,the deviations having a positive sign where the calculated value is smaller. The average deviations, disregarding signs, are 0.24, 0.10, 0.11, and 0.11, respectively. The log x equation is the poorest fit and, in addition, can be objected to because it will not permit the system to become nonazeotropic as z approaches zero.
Eq. 22
+0.63 -0.26 -0.60 -0.40 -0.05 +O. 14 +0.22 +0.25 +0.22 $0.26 +0.23 $0.16 -0.29 $0.01 +0.05 -0.12 -0.18 -0.24 0.24
The T parabola gives 184.4 for 1' where z is zero; the log z equation becomes meaningless. Where z i8 100, the former gives 401.1; the latter, 423.4. Because it is a better fit and does not become meaningless as x approaches zero, the T parabola is the best single equation to represent the data for the ethanolethyl acetate system. ETEAXOL-WATER.K a d e and hlerriman (8) have obtained FROM OBSERVED VALUESIN DICHLOROTABLE11. DEVIATIONS data for this system which show that it becomes nonazeotropic DIFLUOROMETHANE-DIFLUORO>~ETHANE SYSTEM around 307' K. as the temperature is lowered. The log z equation Deviations T Xobed. Eq. 16 Eq. 17 Eq. 18 Eq. 19 IS not applicable. The log T equation was again found to be a -0.03 -0.03 -0.23 -0.01 242.66 34.64 poor fit, The T parabola, +O.lO +0.14 +0.13 +0.47 273.16 39.40 -0.19 -0.19 -0.18 -0.05 298.06 42.53 T = 313.99 - 3 9i86x 0.074916x2 (23) fO.09 +0.08 $0.11 44.78 -0.20 313.24 is the most suitable equation. However, it does not fit well a t very low values of x primarily because of a minimum in the curve. Perhaps the experimental data are not sufficiently accurate The other equations permit the system to become nonaeeoSkolnilr (6) suggested thc log 2: equaMETHANOL-BENZENE. tropic at.100", 65", and 112" K., respectively. All values are tion for this system and it fits reasonbly well throughout the below the freezing point, 118' K., of dichlorodifluoromethane, so range of concentrations used in his discussion. that, if any of the three equations is suitable for extrapolation, The following equations have been fitted to the data occurring the system cannot actually become nonazeotropic as the temin Skolnik's paper: perature is lowered.
+
INDUSTRIAL AND ENGINEERING CHEMISTRY
October 1952 log x = 1.3508
x T
=
+ 0.0013152T
(24)
170.039 log T - 366.65
(25)
141.60
(26)
+ 10.08~- 0.038406~~
The average deviations for z are 0.56,0,99, and 0.56, respectively. Again the log T equation is a poor fit. The other two give identical average deviations, but the T parabola again has the advantage of permitting z to be zero. Where z is zero, the T parabola gives a negative value of T indicating that the system cannot become nonaseotropic as the temperature is lowered. The system becomes nonazeotropic, according to the parabola, at 209’ C. as the temperature is raised. This is somewhat lower than the value of 219’ C. given by Skolnik. The Antoine equations (log P = A - B / [ t f 2301) for methanol and the azeotrope have been solved simultaneously by Skolnik t o fix the point of nonazeotropy as the temperature is raised. Such a solution gave 202” C. which is a good check with the other values, Even so, the writer believes a criticism should be offered against the connotation assigned to the word “azeotrope.” The concept of there being a straight line to represent the azeotrope is contradictory simply because the azeotropic composition changes with temperature. It is true that some Antoine equation will represent any one composition, which may be azeotropic a t some temperature, but certainly not all azeotropic compositions a t one time. Figure 4 is presented to depict the uniqueness of an azeotropic point where plotted on an Antoine graph for an assumed binary system of the substances M and N , the latter having the higher molar latent heat of vaporization. Starting a t point yl,the azeotrope contains zl mole yo N and has a pressure PI and temperature Ti. If the temperature is changed a t all, the composition is no longer an azeotrope. This composition has a PT relation represented by the line A B , but the only point on it that is azeotropic is
thermodynamics to azeotropic solutions. It is contended that the lines AD, CD,and EF can be used t o calculate latent heat without any regard for heat of solution. These lines represent definite compositions but not azeotropes. THE T PARABOLA FOR T H E DICHLORODIFLUOROMETHANEDIFLUOROETHANE SYSTEM
This parabola represents the data for the 1,l-difluoroethanedichlorodifluoromethane as well as any other equation considered and, in addition, is superior for all other binary systems considered. Consequently, Equation 19 has been selected to represent the change in composition with temperature. According t o this equation, azeotropy may exist to a point lower than the melting point and higher than the critical temperature for difluoroethane. Therefore, azeotropy is continuous throughout the entire liquid range. If one day there is an interest in using this azeotropic refrigerant for rather low temperatures, there may be an advantage in selecting a composition, with respect to difiuoroethane, lower than 39.40 mole % ’ (26.2% by weight) which is now used, primarily in air-conditioning applications. One low point which might be considered comes a t about -75” C. At this temperature, the azeotrope will contain, according to Equation 19, 26.9 mole % difluoroethane or 16.7% by weight. SUMMARY
The T parabola, T = 112.35
.
+ 1.215662 f 0.073340s*, where
T is degrees Kelvin, has been selected to represent the change of azeotropic composition with temperature in the 1,l-difiuoroethane-dichlorodifluoromethane system. Azeotropy is continuous throughout the liquid range.
z is mole per cent difluoroethane and
Y1.
A t the same temperature, there is a point y2 with a pressure PZ which may be satisfied by two compositions. One contains xz mole yo N and the other z3. The solution containing x2 is represented by the line CD; that containing 2 3 , by EF. Because N has a higher latent heat, x2 is higher and 3 3 lower than 21. At point y4)the lines AB and CD intersect for a common pressure of P,, the compositions being z1 and x2. The azeotropic composition must he higher a t some point y3 where the pressure is P3. Likewise, A B intersects EF, the common point being a t ?J6 where the pressure is Pe and the two compositions are $1 and x3. At some higher pressure Pg, there is a point gs representing the azeotrope, whose composition is between XI and xa. A curved line such as GH may be drawn through all the azeotropic points (yb, yl,9 8 ) etc.) but it cannot be employed as though it were one composition. The slope of this curved line can be used in conjunction with the Clausius-Clapeyron equation to get the molar latent heat of vaporization for the azeotrope as accurately as it can be for a pure compound. This contention is substantiated by Redlich and Schutz ( 5 ) in their application of
240 1
ACKNOWLEDGiMENT
The author appreciates the help of others within the Carrier Corp. in carrying out this work. H e is especially indebted to Michael Kin for his painstaking efforts in the laboratory, to Beverly Woonton for assistance with the statistical work, and to Theodore Kolakowski for help in the presentation. LITERATURE CITED
(1) Merriman, R. W.,J . Chem. Soc., 103, 1801-16 (1913). (2) Pennington, W. A., Anal. Chem., 21, 766-9 (1949). (3) Pennington, W.A., Modern Refrig., 53, 123 (1950). (4) Pennington, W.A,, Refrig. Eng., 58, 261-5 (1950). (5) Redlich, O.,and Sohutz, P. W., J . Am. Chem. Soc., 66, 1007-11 (1944). (6) Skolnik, H.,IND.ENG.CHEM.,43, 172-6 (1951). (7) Swietoslawski, W.,“Ebulliometric Measurements,” p. 116,New York, Reinhold Publishing Corp., 1945. (8) Wade, J., and Merriman, R. W., J . Chem. Soc., 99, 997-1011 (1911). RECEIVED for review June 22, 1951.
_._
._:::s::iiii
- _ -
...
ACCEPTED April 16, 1952.
