ISDi7STRIAL A N D E,VGINEERI,VG CHEMISTRY
October, 1930
1091
of by-product gas a1 sources of cheap power, the problem of conserving the solid on long rail journeys to market was serioudy attacked. While it is practice t o ship sinall amounts by mail or express in paper cartons, large-scale demand required the development of more economical shipping methods. Shipping cases have been designed which in large sizes allow a loss in transit of as little as 1 per cent a day. ,4n efficient railroad transport car has been devised and now a fleet of forty such cars is devoted solely to the transportation of Dry-Ice to remote points. The transit loss in these cars el-en 011 a journey of several days is much less than that in loading and unloading them. By utilizing this low-loss method of rail transportation it has been easily possible to supply peak demands in Chicage, Baltimore, and Washington from Siagara Falls and to equalize supply and demand throughout the entire United States. Obviously, to be prufitable sur11 shipments must get the product to market cheaper than it can be had from competitive sourles. These things sound simple in the telling, but as short a time as two years ago they were far away in the realm of impossibilities even in an industry based on doing the impossible.
prevents injury. A few cases of "burns" have occurred, but their prevention is so simple and so effective and their occurrence so rare that each one attracts unwarranted attention. I n our own plants, where new employdes have had to be broken in in groups to care for rapidly expanding production, in four and a half years of operation only two cases of frost bite have occurred that were considered serious enough to require a physician. S o time was lost on account of either. The treatment of frost bite of this kind is identical with that for burns. Unguentine, picric acid gauze, carron oil, bicarbonate of soda, and other burn treatments are quite effective. I n the early days it was freely prophesied that many workmen would be overcome by the gas itself when it was used in refrigerating large spaces. Practice has demonstrated the inconsequence of this possible hazard. Human lungs are so delicately balanced to carbon dioxide that even the slightest variation in concentration of the gas above a tolerated minimum brings about an immediate reaction and any who have been exposed to carbon dioxide realize that a person will not permit himself to be exposed to dangerous concentrations. N o case of collapse or near collapse from this came has occurred in the wide general use of Dry-Ice.
Freedom from Hazard
Literature Cited
Especial interest attaches to the fact that the introduction on so wide a scale of so totally novel a material has brought with it no serious indust,rial hazard. The extremely low temperature of solid carbon dioxide can cause serious frost bite, but the 1136: Of eve11 thin gloves to protect the hands effectively
(1) Howe, IN,,. E N G . cHE3%,, 20, 1091 (1928). (2) Jones, Chem. h f e t . E n g . , 37,416 (1930).
(3)
IKD.E N G . "1 lg2 (4) Ki!leffer, I b i d . , 22, 140 (1930). ( 5 ) Thornton, J , B o l a n y , 17, 614 (1930), (6) Thornton, IKD. E K G . CHEM.,t o be printed i n the November, 1930,i s u e .
Studies in Diffusion I-Estimation of Diff usivities in Gaseous Systems' J . Howard Arnold DEPARTMEST OF CHEMICAL EXGINEERING, MASSACHUSETTS
I N S T I T U T E OF TECHXOLOCY, CA?rIBRIDGE, M A S S .
Methods are presented for the calculation of difof this expression throughout the film gives therate of transfusion constants in gaseous systems at any temperamechanism of the industure, using as a basis the Stefan-Maxwell-Sutherland fer through the film as a t r i a l l y important procexpression from the kinetic theory of gases. It is shown whole; this integration has esses of absorption, extraction, that the molecular diameters required for the evaluabeen carried out by Lewis and and distillation, the two-film tion of this expression are calculable in terms of the theory proposed by Rhitman Chang ( I O ) and by Mcildams liquid molecular volume at the boiling point, found by and Hanks (13). The appli(23) has proved of great value Kopp's law. A method of calculating the Sutherland in the evaluation of the rate cation of the integrated exof material interchange bepressions so obtained to probconstant for diffusion from the boiling points and molecular volumes of the constituent substances is tween a gaseous and a liquid lems of engineering design redescribed. The basic equation is applied to the existing phase. This theory postulates quires a knowledge of the diffusivity, or diffusion coeffidgta on the diffusion of gases and vapors, and found to that the principal resistance be in good agreement. The methods of estimation are to material transfer is due to cient, D. Experimental valthe existence of relatively believed valid for all gaseous systems, and are of esues of D are available for a q u i e t a n d convectionless pecial value for engineering purposes in that they renumber of systems composed layers of gas and liquid on quire a knowledge of only the molecular formulas and of the ordinary fixed gases, as either side of the interface, the boiling temperatures of the substances involved. well as for the diffusion of through which films material some vapors through air, hytransfer occurs by the slow process of diffusion. At any point drogen, and carbon dioxide. However, for the interdiffusion of vapors, highly important in distillation, no experimental within the film the diffusion rate is given by Fick's law, results whatever have been published; conseqiently, the d N / d 8 = DAdc/dx engineer is handicapped in any effort effectively to utilize This equation is valid for both gaseous and liquid films, the theoretical just outlined. It is accordingly the being the number of mols transferred and c the concentration purpose of this paper to the existing theories and in mols per cubic centimeter; if is desired in grams, c must data on diffusion in gaseous systems in order to develop be expressed in grams per cubic centimeter. The integration therefrom a reliable method for the estimation of D from a 1 Received July 31. 1930. knodedge of the nature of the substances involved.
I
S T H E s t u d y of t h e
IiVD USTRIAL AND ENGINEERING CHEMISTRY
1092
Theories of Diffusion Based on Kinetic Theory of Gases
The kinetic theory of gases has provided two basically different theories of diffusion-that of Stefan, also put forward by Maxwell, and that of Meyer, as modified by Jeans (6). These differ principally in the predicted variation of D with the composition of the gas mixture, the Stefan-Maxwell formula predicting no variation, and the Meyer-Jeans expression allowing a maximum variation of 33 per cent. The recent more rigorous theory of Chapman and Enskog predicts a variation of only a few per cent, which is supported by the experimental data of Schmidt, Jackmann, Deutsch, and Lonius. The formula given by Enskog (Jeans, p. 319) indicates a maximum variation in D (from 0 per cent of one component to 100 per cent of that component in the diffusion mixture) of 8.33 per cent when the mass ratio of the diffusing molecules is infinite, 8.2 per cent for an 80:l ratio, and 6.1 per cent for a 5:l ratio. From these facts we conclude (1) that the Stefan-Maxwell formula gives a more nearly accurate representation of the facts; and (2) that the influence of composition of the value of D is small enough to be disregarded for engineering purposes, especially in view of the fact that the experimental errors are of the same order of magnitude. I n addition, the Stefan-Maxwell formula is simpler and better adapted to rapid computations. With the exception of minor variations in the value of B , the same formula has been deduced by Stefan, Maxwell, Langevin, and Chapman, and modified by Sutherland to allow for the effect of intermolecular forces in increasing the resistance to diffusion :
D =
+
B
d&+
1
T5I2
+
SYT
C)
The factor T / ( T C) is due to Sutherland ( I @ , who has developed the theory of diffusion along the same lines as his well-known theory of viscosity; in view of the marked success of his viscosity theory, we may suppose with confidence that the similar diffusion theory is valid. Of the quantities in the formula, T and M are known; B is given by kinetic theory, or may be obtained empirically from known values of D. For the estimation of D we must obtain suitable values of S and C, S representing the distance between centers of two molecules of different sorts at contact, while C is the Sutherland constant for the system. Calculation of Sutherland Constant
Sutherland has given an expression for the value of C in terms of the corresponding constants for the viscosity of the individual gases composing the system :
The factor F is generally quite close to unity, decreasing slowly from unity as the molecular volumes differ more and more. For several values of the volume ratio, F has the values: VdV1 F
1 2 3 4 5 6 8 1 0 1.00 0.980 0.953 0.920 0.894 0.875 0.838 0.805
The constants C1and Czare to be obtained from experimental measurement of the variation of viscosity with temperature, using the Sutherland equation
It will be noted that this equation contains the constant C in such a manner that its value is extremely sensitive to small errors in either T or 2; when C is zero, 2 varies as the square root of T, while for C infinite, the variation follows a
Vol. 22, No. 10
power law. Thus, while the exponent of T changes by unity, C varies from zero to infinity; accordingly, several accurately determined values of 2 are necessary to give a reliable value of Unfortunately, for most gases values of 2 are available at only two temperatures, and an error of 0.5 per cent in one of these values is reflected to C as an error of about 10 per cent. The calculation of Sutherland constants from theory in a rigorously accurate manner has not yet been accomplished; Enskog (4) has given a relation between C and the law of force of intermolecular attraction; Debye (3) and Keyes ( 7 ) have related C to the dielectric constant. The most generally useful relation for the present purpose is one originally due to Sutherland (18), later put forward more clearly by Vogel (22); Vogel’s equation is
c.
C = 1.47T~
where T B is the absolute boiling temperature. Since C is a measure of the intermolecular potential energy, which in turn determines the ease of vaporization, such a relation appears quite logical. Table I contains values of C calculated from the Vogel relation, together with observed values taken from the Landolt-Bornstein Tabellen, the International Critical Tables, and Jeans’ “Dynamical Theory of Gases” (p. 285). The recently determined values of Titani (21) for a number of organic vapors, mainly hydrocarbons, are also given. The values 123.6 for air and 533 for bromine are due to Braune, Basch, and Wentzel ( 1 ) ;the 650 for water is from Smith (16), and is of doubtful accuracy. A study of this table indicates that the agreement is as good as may be expected, considering the difficulty of obtaining accurate values of C experimentally. For the common fixed gases for which several values of C are available, the calculated C appears to be accurate to within the experimental error; hydrogen and helium are anomalous, obeying the Sutherland equation a t high temperatures only and having a C larger than calculated. The fairly large deviations shown in some instances are not to be considered serious in view of the large experimental errors to which the vapor-viscosity determinations are subject, especially for high-boiling vapors. We shall therefore make use of calculated values of C in the remainder of this paper; as will be shown, this procedure does not reduce the accuracy of the formulas presented. For hydrogen and helium we retain the experimental values of 72 and 78. Calculation of S
The most logical method of calculating values of S for use in the diffusion equation is the use of molecular diameters calculated from the closely related phenomenon of viscosity. This procedure requires a knowledge of both the Sutherland constant and the viscosity of the gas or vapor. As noted above, C is not easily found from experiment with accuracy, and in the case of organic vapors accurate values of 2 are usually not available. It is therefore necessary to develop and test an alternative method for finding S. This is provided by the equation
s
=
+
v11/3
v2j41/3
where V is the volume of one mol of liquid a t the boiling point. To avoid the necessity for experimental data we make use of Kopp’s law of additive volumes, which states that the value of V is an additive function of the atomic volumes. In doing this, the boiling points are assumed to be van der Waal’s corresponding temperatures, the actual volume of the molecules in any liquid then being proportional to the space occupied, so that the cube root of Vis a measure of the molecular
I-YDGSTRIA L A S D ENGINEERIiYG CHEMISTRY
October, 1930
diameter. We shall use the system of computation developed by Le Bas (5, 8 ) , assigning values to the several elements as follows: carbon 14.8, hydrogen 3.7, chlorine 24.6, bromine 27.0, iodine 37.0, sulfur 25.6, nitrogen 15.6; in primary amines, 10.5; in secondary amines 12.0. Oxygen, 7.4; in methyl esters, 9.1; in higher esters, 11.0; in acids, 12.0; in methyl ethers, 9.9; in higher ethers, 11.0. For benzene-ring formation deduct 15; for naphthalene, 30. (Numerous minor constitutive effects are noted, for the evaluation of which Le Bas' book should be consulted, if accuracy is desired.) T a b l e I-Sutherland
GAS
Ib
Hydrogen Nitrogen Air Oxygen Carbon monoxide Carbon dioxide +Methane Ethane Propane n-Butane Isobutane Isopentane Ethylene Propylene Butylene (1:2) Butylene (2:3) Isobutylene lsoamylene Cyclopropane Acetylene Allylene Carbonyl sulfide S i t r i c oxide S i t r o u s oxide Sulfur dioxide Ammonia Water Hydrogen sulfide Chlorine Bromine Iodine
-252.7 -195.7 192 183 190 78.5 164 88.3 44.5
--
0.6
10.2 28 -103.9 47 18 1 4 - 6 20 1 35 83 6 - 32 48 -151 5 89 6 10 1 - 33 5 100 61 33.6 58.6 184.4
-
-
-
-
C o n s t a n t s (C)
----
CALCD. 30 72.2, 114 110.6, 119 123.6, 132 138, 122 118, 286 240, 160 144, 272 336 402 386 336 248 332 364 -103 392 430 350 278 354 330 180 270 386 352 548 312 352 487 672
RATIO CALCD./ OBSD.---OBSD. 83 ... 71.7, 79, ... 113, 118 . .. 113, 111.3, ii!3:4 127 ... ... 100 ... 277 2j4' , i . i i , ' 0.81 198 . 287 0.95 0.99 341 377 1.07 336 1.15 0.67 500 0.96 259 1.03 322 1.11 329 1.11 362 1.16 339 1.17 368 0 94 372 1.40 198 1.28 277 330 1.00 195 0.92 260 1 04 0.98 396 0.95 370 0 84 650 0.94 331 1.08 325 1.06. 0.91 460, 533 1:14 690
.. . ..
...
...
. .
Calculation of Molecular Volumes
On adding together the proper values selected from the table, we obtain a value of I' which Le Bas has shown to correspond closely to that measured a t the boiling point; we have now to investigate the relationship between this value of V and the value c:ilculated from gas-viscosity data. Jeans (6, p. 276) gives the relation
The molecular velocity E is to be evaluated from the relations
p
= '/3~(1.086t)~(p. 118)
1093
where V Eis to be shown equal to Vk. Table I1 shows values of Ti, calculated from the data of Titani, with the aid of the equation above, using the calculated values of C from Table I ; the best agreement between T7, and Vis is obtained with A set equal to 1.40 times lo-' (determined graphically). The values of V,/Vk tabulated in the last column are as near unity as may be expected, considering the rather large probable errors in C. It may be noted in passing, however, that the use of the observed values does not decrease the average deviation appreciably, and in some cases,. g., acetylene-gives much greater deviations. T a b l e II- -Molecular V o l u m e s Using D a t a of Titani SUBSTANCE v k VJVk zo V* 51.8 1.028 53.2 863 Ethane 1.000 74.0 74.0 751 Propane 0.916 8 8 . 1 96.2 n-Butane 682 0.953 96.2 91.6 689 Isobutane 1,123 44.4 49.9 907 Ethylene 1.010 66.8 67.5 783 Propylene 1.025 88.8 91.0 708 Butylene (1:2) 0.963 88.8 85.5 694 Butylene ( 2 3 ) 0.907 88.8 80.5 732 Isobutylene 0,907 111.1 100.9 666 lsoamylene 1.094 37.0 40.5 954 Acetylene 0.992 59.2 58.8 808 Allylene 1,020 60.4 807 61.5 Cyclopropane
I n Table I11 a similar comparison is made for a number of gases, using data from the International Critical Tables, together with calculated values of C from Table I and the value of A just found. I n calculating T i e for those gases which contain oxygen or nitrogen, the atomic volumes were used which gave the best agreement. It is of interest to note that the atomic volumes of hydrogen, oxygen, and carbon stand in the ratio 1:2:4-that is, in the same ratio as the valences (Le Bas). I n the case of carbon monoxide the best agreement is obtained by assigning an atomic volume of 4 X 3.7 or 14.8 to the oxygen, assuming it to be fully quadrivalent. V o l u m e s Using D a t a from I n t e r n a t i o n a l Critical Tables Z vz v k VdVk 7.4 14.3 842 1.067 24.0 25.6 1926 31.2 1,000 31.2 1676 1.006 29.7 29.9 1724 29.6 3 0 . 7 1660 1,000 34.0 34.0 1370 0.986 45.4 44.8 1170 0,983 24.0 23.6 1780 1.010 36.0 36.4 1350 0.966 26.7 25.8 918 1.027 18.4 18.9 882 0.996 32.9 33.0 1175 1.002 51.4 61.5 1126 0,984 49.2 48.4 1230 0.985 54.0 53.2 1428 0.965 74.0 71.5 1190
T a b l e 111-Molecular SUBSTAXCE Hydrogen Oxygen Sitrogen Air Carbon monoxide Carbon dioxide Sulfur dioxide Nitric oxide Nitrous oxide Ammonia Water Hydrogen sulfide Carbonyl sulfide Chlorine Bromine Iodime
...
...
M = 22,400~= mN = 6.06 X 1OZ3m Evaluation of B
with the result that mZ = 3.96 X 10-19
dz
since p , the atmospheric pressure, is 1,013,230 dynes per sq. cm. Insertion of this result in the equation for Z givw, after the introduction of the Sutherland temperature factor,
Returning to the original formula for D, we shall now evaluate the constant B , both from theory and from experiment. Chapman ( 2 ) found a relation which in our notation is
where
p
= 1,013,230 dynes per sq. cm.
N = 6.06 To = 273
x
1023
V, and
Solving this equation for the cube of the molecular diameter,
From the comparison of
Since the molecular volume V k found from Kopp's law is to be shown proportional to u3, we have to test the validity of the equation
showing that the molecular diameter in Angstrom units is numerically equal to the cube root of the molecular volume of the liquid a t the boiling point, as noted by Titani. On making the substitutions indicated and solving for B , we have
03/v
= 1.40
x
Vk
we find the relation
10-31/1.40 x 10-7 =
10-24
INDUSTRIAL AND EYGIIL-EERING CHEMISTRY
1091
Vol. 22, s o . 10
B = 0.00740 (Chapman)
Application of Diffusivity Equation to Existing Data
Jeans and Maxwell have given slightly different values for the numerical multiplier, leading to
The diffusion of vapors through fixed gases has been iiivestigated by a number of workers, all employing the evaporative method devised by Stefan ( 1 7 ) . The most extensive research mas that of Winkelmann (84), who determined the diffusivities of about forty substances, mainly aliphatic acids, alcohols, and esters, through hydrogen, air, and carbon dioxide. His work was continued and extended by Pochettiiio (Is),who worked only with air, and found results in good agreement with those of Winkelmann, with an exactly similar apparatus. Le Blanc and Wuppermann (Q), however, have shown Winkelmann's technic t o be faulty in that it took no account of evaporative cooling of the liquid surface, which a t times amounted to nearly 2 degrees, and caused considerable error in the diffusivities obtained. Mack (12) has recently used a modification of the Stefan method for the diffusion of several vapors through air; his experiments with iodine vapor were repeated by Topley and Gray (do), who found hi5 result too high and the method difficult of application.
B = 0.00740 ( 3 2 / 9 ~ )= 0.00837 (Jeans, p . 316) B = 0.00740 (4/3) = 0.00985 (Maxwell) Calculation of Diffusivities
As a matter of interest, we may calculate the fraction of the liquid volume at the boiling point actually occupied by the molecules; this is, agreeing with Titani's value, 7~/6N d / V = 7r/6 (6.06 X loz3)
=
0.318
Table I V contains values of D / B T 3 I 2calculated from the equation for D; S has been found from the values of V , in Tables I1 and 111, while C is obtained from the C's for the individual gases given in Table I as C calculated, using the relation given above, C = F d m
As B and T are the same for all systems, these values should be proportional to the observed diffusivities. Figure 1 shows DobFdplotted against Doelcd /BT3 j 2 , The values of DubJ*.
SYSTEM
Hz-0%
Table .IV-Calculation of Diffusivities 1 D X 104,' S? + c BT3/2 D c a l d . D o b s d . 29 0 0,730 96 186 0.700 0 67
d$i
Hz- air HI-CO Hz-CC2 H?-N,O Hg-SC2 Hz-CHa H?-CzHd Hz-CzHa H?NZ coz- 02 COz-air
30 5 31 0 32 1 33 0 35 8 32 8 37 4 38 3 31 1 38 2 40 1 coz-co 40 5 CO2-X20 43 0 COz-CHa 42 6 C 02-Cz H4 48 0 co-02 37 0 CO-C~HI 46 5 Orair 36 5 Oz-h7z 37 2 ,%-He 24 3 SHa-air 36 S
c
0
0
0 730 0 731 0 723 0 703 0 718 0 750 0 731 0 730 0 731 0 232 0 239 0 242 0 213 0 292 0 242 0 258 0 267 0 256 0 258 0 525 0 305
90
180
177 139 149 135 146 158 127 103 166 127 134 130 130 88 178 194 3 5 . 5 184 35.6 187 35.4 278 24.5 214 38.4 266 25.5 127 47.5 174 36.7 125 48.1 123 47.8 92 162 204 47.4 91
Table V-Diffusion VAPOR
V
1
0 679 0 667
0 561
0 550 0 479 0 625 0 505 0 490 0 670 0 134 0 134 0 133 0 093 0 145 0 096 0 179 0 132 0 181 0 180 0 610 0 179
C M . ? SEC.
0 722 0.690
n
706
ii93 0.64 O'k42 0 65 0.53 0.5.56 0:i33 ... 0.53
...
0:i36 0.135 0.131 0.092 0.147 0.101 0 187
0.117
... .. .
O'ii3
..
0.63 0.48 0.46
...
...
...
0'6kl
0' i A i 0.142 0.141 0 098 0 139
0 : i36
...
...
...
...
0 : ixo
0.178 0.179
... ...
of Vapors in Air C Dcnlcd.
...
... 0' is6
0.634 0.198
nuhsd.
MACK
74
Iodine Toluene Xapthalene Anthracene Octane Aniline Diphenyl Benzidine
0
118 2
147.7 199 185 110.2 184.6 213
0 0826 0 0797 0 0675 0 0850 0 0655 0 0785 0 0600 0 0810
0 0 0 0 0 0 0 0
234 230 244 242 230
0,0994 0 OS60 0 0863 0 1285 0.238
0 102 0 092
232 2338 244
0 0793 0.0698 0,0630 0.0576 0 0526 0 0733 0,0876 0 0740 0.180
272 337 261 284 228 260 263 291
108 0844 0611 078.2 0602
0726 0727 0555
L E BLAXC AND W U P P E R M A N N
Benzene Propyl acetate Chlorobenzene Ethyl alcohol Water
42
4% 42 42
96 129.4 116.9 59.2 18.4
43
1
0 094 0
0
145 288
UINKELMANN
Ethyl formate acetate .
Figure 1
are taken from the Landolt-Biirnstein Tabellen, except for the system ammonia-air recently investigated by Wintergerst (25);all values are a t 0" C. and 760 mm. Those in the first column under D o b a d are due to Obermayer, and in the second, to Loschmidt. Figure 1 also contains three lines representing the three values of B due to Maxwell, Jeans, and Chapman; it is seen that the value 0.00837 given by Jeans agrees best with experiment, while those of Maxwell and Chapman represent upper and lower limits, almost all the data falling between these two lines. We may therefore write as the final equation
Ethyl propionate butyrate Ethyl valerate Ethyl ether Carbon disulfide Benzene Water
0 0
0 0
0 0 0
0
85.0 107.2 129.4 151.6 174.8 107 2 66 0 96.0 18.4
250
257 223 229 234 250
0.0852
0.0709
0.0631 0.0574 0.0505
0.0775 0 0883 0.07.51 0.198
Table V shows the data of Mack, Le Blanc, and Kuppermann, and Winkelmann for diffusion through air; only a portion of Winkelmann's data is given. Study oi this table indicates that the agreement in many cases is excellent; in others, much of the error is probably experimental. It is of interest to note that Mack's value of 0.108 for iodiiie is much too high, while Topley and Gray, by a sphere-evaporation method as well as by Mack's method, obtained 0.0824 (graphically smoothed), almost identical with the calculated 0.0828. Table I'I contains additional data by Kinkelmann for diffusion through hydrogen and carbon dioxide; the large deviations in the case of hydrogen are probably due niainly
ISDIISTRIIZL A S D E.YGINEERISG CHEMISTRY
October, 1930
t o the high diffusion rate and consequent large cooling effect a t the liquid surface. It is evident, as Loeb (11) has pointed out, that the evaporative method requires further development of certain correction factors before it may be regarded as t r (1stn-ort h y . The \alidity of the T-ogel rule as a method seems substantiated by the agreement of calculated and observed diffusii.ities; little aceurate work has been done on the variation of diffusivities with temperature. From the data of Obermayer ( I d ) , Sutherland (19) has calculated values of C shown 111 Table T’II for comparison with the estimated values; as these are based on two temperatures only, the probable error i c large, and thcl agreement with the estimated \-alues is as good as may be expected. That the constants for the last two sy*teins should he larger than either C1 or C l is very unlikely, i n Hydrogen and Carbon Dioxide I N CAKROND I O X I D E
T a b l e VI-Diffusion [N
c
\.iPOR
1:thyl formate Ethyl acetate Ethyl propionate E t h y l biityrate Ethvl valerate Ethvl ether i r r h o n dicnlfide \I ater 1 cnzene
HYDKOGEN Dealrd. Dobsd.
0.360 0.327 0.300 0.279 0.261 0.334 0 398 0 633 0 338
163 162 162
161 162 I53 167 198 166
0.336 0.273 0.237 0.224 0.205 0.296 0 364 0 687 0 294
c 360 364 366 370 374
340 359 384
368
Dcitlcd.
Dobsd.
0.0532 0.0470 0.0423 0.0384 0.0357 0 0500 0 0584 0 1270 0 049.5
0.1372 0.0487 0.0430
0.0407
+
J’:1/3
=
2(J711/3,L721 3) 1
and. siiice varies inversely as ( T q u a t i o n for D as
2,
molecular volume = ,P (atomic volumes) C = Fd/C1C2 = 1.47Fv’TBITB? F depends on the ratio I’2/ Vi.
It is believed t’hat the methods of estimation herein preserit.ed are of fundamental soundness, and, in the absence of experimental data, provide t’he best available means of obtaining values of diffusivities a t any given temperature for any system. The agreement obtained with gas-gas and vaporgas systems indicates that the equations may safely be used for extrapolation to vapor-vapor systems of engineering importance. The most serious source of error is in the estimation of C from the boiling temperature. It is hoped in a subsequent communication t o present more accurate methods of calculating this quantity.
The writer is indebted to Professors 11‘. K. Lewis and W.H. hlcXdams for their interest and assistance in the work above described.
’’
+ C)l/
=
Acknowledgment
0 1320
It may be she\\ n that, provided the molecular volumes are calculated from T-iscosity data, errors in C1 and C2 have a negligibly small effert on the estimated D. When TY1 and IT2 are not far different, we may use a geometric mean value of S illstead of the arithmetic, 4
1‘
0 0630
Constants for Gaseous Systems Osso. CALCD. Hydrogen-oxygen 100 96 Hydrogen-carbon dioxide 106 139 Carbon monoxid e-oxvgen 124 127 Sitrogen-oxygen 136 123 i’arbon dioxide-air 250 184 Carbon dioxide-nitrous oxide 380 278
1
For ready reference the equations necessary for estimating D may be summarized:
0 0327
SYSTEN
5’
Conclusion
0.0366 0 0552
T a b l e VII--Suthe:rland
and TT2 is found to agree with the Xopp la\\-, I-A, use of the estimated C and the T’L must produce, good agreement in the equation for D , regardless of the agreement of the estimated and observed C’s; this, in fact, is the basis of the preqent system of correlation.
T a b l e of N o m e n c l a t u r e .4, B-Proportionality
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