-
5/26/2018 + Estimation of Diffusion Coefficients for Gases an
Vopors
http:///reader/full/-estimation-of-diffusion-coefficients-for-gases-an-vopo
June 1955 I N D U S T R I A L A N D E N G I N E E R I N G C H E
M I S T R Yprogram of fundamental research sponsored both b y
industrialcontributions and by the U. S.Army, Corps of Engineers
Researchand Development Laboratories. The authors gratefully
acknowl-edge the financial and technical assistance given by the
manysponsoring organizations, and t he advice and criticism offered
b ymembers of th e staff of th e Soil Stabilization Laboratory.
a H =
e =K =K* =L =jy =u =u* =uom =
gn =
A p =e =
NOMENCLATUREactivity of hydrogen ion, gram-mole per
literactivity of sodium ion, gram-mole per literstreaming
potential, stat-voltsvoid ratio, cc. of void per cc. of d ry
solidpermeability coefficient in presence of
counterelectro-permeability coefficient in absence of
counterelectro-thickness of porous bed, om.actual length of flow pa
th in porous bed, cm.superficial linear flow velocity in presence
of counter-superficial linear flow velocity in t he absence of
counter-linear electro-osmosis flow velocity in pores, cm.
perpressure drop across porous bed, gram/cm.( sec.)dielectric
constant
osmosis, sq. cm.osmosis, sq. cm.
electro-osmosis, cm. per secondelectro-osmosis, cm. per
secondsecond
X
= zeta potential, stat-volts= specific conductance of liquid an
d surface of pmedium, stat-mhos per cm.= viscosity of liquid,
gram/(cm.)(sec .)
LITERATURE CITED(1) Booth, F., Proc. Rou. Soc. London), 03A, 533
(1950).2) Carman, P. C., rans. Inst. Chem. Engrs. London), 5(3)
Cornel1 University, Final Report, Soil Solidification Res(4) Elton,
G. A. H., Proc. Roy. SOC. London), 94A, 259(5) Fuerstenau, D. W.,
So. D. thesis, Massachusetts Instit(6) Grace, H. P., Chem.
Eng.Prop. , 49, 303, 367 (1953).(7) Henniker, J. C., Reus. Mod.
Phys., 21, 322 (1949).(8) Kruyt, H. R. , Colloid Science,Vol. I,
Elsevier PublishinNew York, 1952.(9) Michaels, A. S., and Lin, C.
S., ~ N D .ENG. CHEM., 6,(1954).(10) Muskat, M., Flow of
Homogeneous Fluids through Pfifedia, McGraw-Hill, New York,
1937.(11) Prutton, C. F., and Maron, S. H., Fundamental
PrincipPhysical Chemistry, p. 469, Macmillan, New York, 19(12)
Ruth, B. E., ~ N D . NG.CHEM.,8, 564 (1946).
R E C ~ I V ~ Dor review June 26, 1954.
(1937).Vol. 11, 1951.(1948); 197A, 568 (1949).Technology,
1953.
ACCEPTED ecember 23
Estimation of Diffusion Coefficientsfor Gases and Vaporsc.R . WI
LKE AND C . Y . L E E
Division of Chem ical Engineering, University of California,
Berkeley, Calif.
S T H E theory and engineering applications of diffusionalA
perations are advanced, increasing need arises for dif-fusion
coefficients of gases and vapors. I n view of the scarci ty
ofreliable experimental data , methods of predicting such
informa-tion assume a useful role. Th e general objective of this
paper isto review critically the existing methods for estimation of
diffu-sivities. An effort has been made to establish
therelativeaccuracyof various procedures by comparison of
calculated results with abody of selected experimental data .
REVIEW OF PREVIOUS CORRELATIONSGilliland 7) developed an
empirical formula based on t he h ard
sphere model of the classical kinetic theory 25). Collision
di-ameters were assumed proportional to the cube roots of the
molarvolumes at the normal boiling point as in the earlier method
ofArnold. Examination of available dat a led to the relation:
As used in this paper, the diffusion coefficient is the
proportion-ality constant in the rate equation for mass transfer in
absenceof convection or other modes of transfer, defined as follows
forunidirectional diffusion
where N t = ra te of diffusion of component 1of a binary
mixture,D12 = diffusion coefficient, sq. cm. per secondA =
cross-sectional area perpendicular to direction o fpl
gram-moles per seconddiffusion, sq. cm.
= partial pressure of component 1, atm.
RT = temperature, K.= gas constant, cc.-atm./gram-mole-o K.=
distance in direction of diffusion
In using Equation 1,values of V should be obtained in t heway as
were those used by Gilliland-namely, using Koppof additive volumes,
with the rules and values for each elegiven by LeBas (18). Values
of a tomic volumes have beenmarized in several other sources 1 ,
b3,sO .Arnold Method. Arnold ( 2 ) adopted the general equform
proposed by Sutherland 25)containing an additionalinvolving the
Sutherland constant, Clz, to account for deviafrom the hard sphere
model. Upon examination of avadata to determine the best numerical
constant, Arnold remended the equation:
As outlined by Arnold, the Sutherland constant, C12,mcalculated
from th e expression:
The constants, Cl and CZ,are to be obtained from the absboiling
temperature,
ci = 1 .47T~ ,From Equations 3 and 4 it can readily be seen th
at
ci = 1.47F(TB,TB,)~
-
5/26/2018 + Estimation of Diffusion Coefficients for Gases an
Vopors
http:///reader/full/-estimation-of-diffusion-coefficients-for-gases-an-vopo
1254 I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S
T R Y Vol.47, N
Oo5004
L I N E S O F CONSTANT0 03
V A L UE S O F A F O R XI.OA002
001
001 002003 005 01 02 03 0 5 I O 2 0 3 0 5 0M O L E C U L A R W E
I G H T R A T I O , MIM 2Figure 1, Values of A asmole fraction of
one componentapproaches zero
In absence of experimental dat a V is obtained by using
Kopp'slaw of addit ive volumes, or calculated from viscosity data
.
Hirschfelder, Bird, and Spotz Method. If the proper functionfor
potential energy of interact ion between any two molecules isknown,
the more rigorous kinetic theory as developed by Chap-man and
Cowling 6 )may be employed t o give improved expres-sions for D and
their temperature properties. Hirschfelder,Bird, and Spotz 8-11)
have carried out such calculations fornonpolar gases which have an
energy of attraction varying withthe inverse sixth power of th e
distance between centers of adja-cent molecules and a repulsive
energy varying with the inversetwelfth power. For pairs of nonpolar
gases the first approxi-mation for the diffusion coefficient is
expressed as follows
The numerical constant, B , is equal to 9.2916 Xtheory.felder,
Bird, and Spotz as a function of k T / .values are listed in Table
I.
according toThe collision integral, W(I)(I), as been calculated
by Hirsch-
Representative
Table I. Collision Integrals for Viscosity and DiffusionkT/ v /
w 2 ) 2 ;T / r ) w ) ( l ;k T / m )
0.35960.44320.54320.63010.70230.76130.85230.91720.96571.0361.0851.2221.5501.7142.095
1.3311 . 0 3
30.83350.71970.64790.69910.53730.49980.47450.44180.42110.37120.28780.25850.2085
For mixtures of two nonpolar gasee
and12 = d Z ( 8 )
For collisions between a polar and a nonpolar molecule,
modi-fied forms of equations are suggested 1 4 ) . With these
modifica-tions Equation 6 applies to systems containing a polar and
a non-polar component. However, the energy of interaction
amongpolar molecules, valence-unsaturated molecules, and
cigar-shaped molecules is very different from that between
nonpolarmolecules. Before Equation 6 may be considered stric tly
appli-cable to systems containing such molecules, the collision
integral
should be evaluated according to their respective potential
futions. The labor involved is formidable and as yet this hasbeen
accomplished.
The term A in Equation 6 is a correction factor, a small qutity
usually less than 0.03, which varies with gas compositDetailed
equations for A have been given (8, 9). A is a cplicated function
of mole fraction, molecular weights, viscosithe first approximation
to the diffusion coefficient, and additifunctions of kT / e I 2 .
However, these equations are so lengtha t their use may not be
justified for many engineering calctions, particularly when the
force constants have been estimaAs a first approximation to A for a
given gas system it is suggethat A values for mole fractions of
each component equal to be obtained and an average value
calculated, assuming A tlinear in mole fraction. Values of A a t
zero mole fraction are Rented in Figure 1. This procedure is not
completely safactory, as A may deviate considerably from a linear
function,it should accomplish a major part of the correction.
Thiscedure was adopted in subsequent applications of Equat ion
6
ESTIMATION OF FORCE CONSTANTS FOR SIMILARMOLECULESBoth ~ / knd r
, may be calculated from knowledge of gas
cosity at two temperatures by solving the equation for
visco9).
x 107 =where ?I = viscosity, grams per cm. second, and
V/W2(2)function of k T / e which has been evaluated by
HirschfelBird, and Spotz. Representative values are given in
TabEquation 9 has been well substantiated by experimental evidand
provides the most satisfactory basis for obtaining the
foconstants.
In absence of viscosity dat a Hirschfelder, Curtiss, and
Birdrecommend the following equations, which supersede those
ofearlier work (8).
e l k = 0.77TC= 1.15Tb = 1.92Tm
Prior t o publication of the above equations, in the course
ofpresent work examination of force constant data to checkearlier
suggestions of Hirschfelder, Bird, and Spotz (8) indicthe following
equations to be satis factory:
/ I C = 0.75Tc / k = 1.21Tb
Because the collision integrals a re relatively insensitive to
serrors in e l k , Equations 10 and 11are considered to be equivato
13 and 14 within the limits of precision of subsequent compsons
(Table IV). The relationships developed between T,Tb y Meissner (2
') ndicate tha t the value 1.21 in Equatioshould be preferable to
the value 1.39 8) , assuming that Eqtion 13 is valid, Unavailable
critical and boiling data mayestimated with the equations of
Meissner.
The collision diameter may be calculated from a single
valuviscosity in Equation 6 using / k from Equations 13
andAlternatively Hirschfelder, Bird, and Spotz recommend:
y o = 0.833V: awhere ro = A., and V, = critical volume, cc. per
gram-mole
Bromley and Wilke 4 )have tested the general form of etion
proposed by Licht and Stechert ( 0 ) and obtained a rewhich in
terms of y o becomes
-
5/26/2018 + Estimation of Diffusion Coefficients for Gases an
Vopors
http:///reader/full/-estimation-of-diffusion-coefficients-for-gases-an-vopo
June 1955 I N D U S T R I A L A N D E N G I N E E R I N G C H E
M I S T R Y
Table 11. Selected Diffusion Data for Test of Methods
SystemAir-benzeneAir-ethyl alcoholAir-ethyl
etherAir-diphenylAir-I2Air-nitrobenzeneAir-n-heptadecaneAir-n-hexadecaneAir-n-octadecaneAir-n-octaneAir-materCOz-ethyl
alcoholCOa-ethyl etherC0z-HzC02-
CH4C02-NzCOz-NZOCOz-CsHsco2-I120CO-CZHICO-HiCO-Nzco-01Freon
12-benzeneFreon 12-ethanolFreon 12-materHe-AHe-benzeneHe-ethyl
alcoholHe-NeHe-nitrobenzeneHe-HzHe-HzOH2-NHaHn-AHz-benzeneHa-CClrHi-CzHaHz-ethyl
alcoholHz-CZHIHg-ethyl
etherHI-HC1H2-CHIH2-h-iHz-h-20Hz-02Ha-CaHEH2-SO2H r H z
0h-2-NH1Kz-CzHaNz-HsN2-I*N2-NON2-02NzO-CsHeOs
NHzOz-CCh02-C2H4NHs-C1H4A-NeCsHs-CzHeCzHs-CHI
02-benzene
Exp tl. DiffusionCoefficient SqCm./Sec. (at iTemp., O K.
Atm.)29829829349
1298298298298298298298273273273.2273.2288298298297.7273273288273298298298273.2298298293298293298293293.2273296273340293293294273
2293273 2273
2300273293293300288273293273298293296298293293293293293
0.09620.1350.08960.1600.08340.08680.4230.04050.03970.06020.2600.06930
, 0 5 4 10 , 5 5 00.1530.1580.1170.08630.1640.1510.6220 . 2 1
10.1850.03850 , 0 4 7 50.1050.6410 . 3 8 40.4941 . 2 30.3721 . 6
40.9080.8490.7700.3170 . 3 4 50.4390.5780.4830 . 3 5 40.7950.6261 .
2 0 50 . 5 3 50.6970 . 4 5 00.4830 . 8 5 00 2410.1870 , 7 4 30
0700.2320 1810.0860.2530.09390.07310.1820.1770.3290 . 0 8
50.163
Examination of da ta as in the case of e l k suggested an
alter-native method of estimation of ro based on molal volume a t
thenormal boiling point, which may be expressed as:
ro = 1.18V1ia (17)Equation 17 appears to be somewhat more
satisfactory than
Equation 15 or 16. The /3 power on V e has been retained
inEquation 15, as it has a theoretical basis in the
Lennard-Jonesand Devonshire theory of gases and liquids 8 ) ,
lthough the da taseem to correlate better us. V.O.sg. In
application of Equation17 molal volumes may be estimated from
Kopp's law and therules of LeBas as in the methods of Gilliland and
Arnold.
COMPARISON OF EQUATIONS WITH EXPERIMENTALDIFFUSION DATATo serve
as a basis for comparison in determining the relative
accuracy of t he foregoing methods, experimental diffusion da
tawere selected from reliable sources for 64 systems at
atmosphericpressure and near room temperature. (All methods of this
paperpertain to moderate pressure systems where ideal gas
behaviormay be assumed-Le., where th e product DP is independent
of
Table 111. Force Cons tants and Collision Diam eteComponents of
Selected SystemsTO A . from Vias qp&f;
AirAmmoniaArgonBenzeneCOZcoCClrCzHaC2H30HDiphenylEthyl
etherCzHaFreon
12Heliumn-HeptadecaneH2HC1IodineCHINeonNitrobenzeneNONNzOn-Octadecanen-Octane0
2PropaneSO2Water
9 7 . 0315124.0440190110.3327230391600350b205288 b8003 3 .
3360550136.53 5 . 7539 b1199 1 . 52208200320113.2254252363356d
6 . 0 3
3.6172.6243.4185.2703 , 9 9
63.5905.8814.4184.4556.223=5,424'4.2325 l l O
d2.707.92352.9683.3054.9823.8822 . 8 04.9313 . 4
73.6813.8797.963a7.4513.4335.0614 , 2 9 02.6552.649e
All values obtained f rom viscosity are ta ken from
Hirschfelder, BSpotz ( a ) , unless otherwise noted. A mole
complete table is preseHirschfelder, Curtiss, and Bird (IS).Values
estimated from diffusion data.b Values estimated from T c .
C Values estimated from boiling temperature.d 6). e 94) .
3 02 0
w 1.0Im 05
02
i o 1
3
l-a-I D E V I A T I O N 200
005003003005 01 0 2 03 05 10 20 30
Figure 2. Comparison of experimental datawith results calculated
by Gilliland equationO B S E R V E D D , S Q C M / S E C
pressure.) These data are summarized in Table 11. In vthe
uncertainty and lack of precision in many investigatioported in th
e literature, use of this limited number of da tselected sources
covering a wide range of dif fusion coefand related properties was
considered preferable to use of abody of da ta selected a t random.
Also, for a large majori tysystems force constants based on
viscosity (see Table 111known for the indiv idual components.
Diffusivities calculated by Equations 1 and 2 and by Eq6 with
force constants from viscosity are presented in Figurand 4.
Comparison between calculated and observed from Table I1 are
illustrated for these three methodsmethods of Arnold and of
Hirschfelder, Bird , and Spotznearly comparable results, with the
latter somewhat bettermethod of Gilliland gives poor agreement for
these systems.ious equations for estimating force constants were
emploconnection with Equation 6 to obtain additional compari
-
5/26/2018 + Estimation of Diffusion Coefficients for Gases an
Vopors
http:///reader/full/-estimation-of-diffusion-coefficients-for-gases-an-vopo
1256 I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S
T R Y Vol. 47, N. .v2.0
vn 1.0i7 0.5
.3Q 0.25g 0.1
W
rn
W
a 0.050.03003 005 01 0.2 0.3 0.5 I O 20 3.0O B S E R V E D D ,
SQ GM/SEC .
Figure 3. Comparison of experimental datawith results calculated
by Arnold equation
2 0c H . B . S . M E T H O D
DEVIATION 7.0
0.03 .05 0.1 0.2 0.3 0.5 1.0 2.0 3.0O B S E R V E D 0 SQ.CM. / S
E C .Figure 4. Comparison of experimental datawith results
calculated by Hirschfelder,Bird, and Spotz equation
e/k and o from viscosity
Table IV. Deviations Between Experimental Data andCalculated
Values for 64 SystemsAy. % Max. ,Deviation Deviationtem Method
1 Gilliland2 Arnold3 Hirschfelder, Bird and Spotz,4 T O from T c
/ p ? , (Eq. le , e l k5 TO from V ( E a . 17 , / k from
e / k and r o from viscosityfrom viscosity
6 r o7 TO8 M9 r o10 T O11 ro12 T O13 TO1 4 TO15 TO
viscosityfrom V (Eq. 151, a/k fromviscosityfrom V (Eq. 17 , e /
k = 1.21Tb (Eq. 14)[odified Hirschfelder Bird ,Spotz, ,Eq. ,18, e l
k 'and rofrom viscosityfrom T c / p c (Eq. 16), c / kfrom
viscosityfrom V (Eq. 17 , /k fromviscosityfrom V e (Eq. 15), r / k
fromviscosityfrom viscosity, c / k = 0.75Tc (Eq. 13from viscosity,
r / k = 1.39Tb 9)from viscosity, a / k = 1.21from V ( E q . 17 , /
k =1.21Tb Eq. 14Ta (Eq. 14
Equat ion12
181818181.8181818
20.08.47.010.110.311.812.03.99.47.01o.a5.47.25.17.7
46.820.521.431.324.932.731.016.032.721.937.626.024.920.524.5
0.1 0 2 0.3 0.4 0 5 0 6 0 7 0.8
Figure 5. Variation of constant in Hirschfelder, Birand Spotz
equationcalculations with observed dat a. Average and maximum
devtions between calculation and experiment are summarizedTable I V
for all methods.
It is of interest to compare the three methods with respectthe
effect of temperature on the diffusion coefficient. Th e eqtion of
Gilliland is theoretically at variance with the Arnold athe
Hirschfelder, Bird, and Spotz equations. The two latmethods
consider possible molecular interaction upon collisand therefore in
principle should give more satisfactory resulThis conclusion is
borne out by the relatively meager experimtal evidence available.
Table V shows the temperature behavof the carbon dioxide-air system
over a range of 293 O to 1500 Kas observed by Kilbanova,
Pomerantsev, and Frank-Kamenets16). Results calculated by each
method, assuming the value293 K. to be correct, are also given. The
Arnold and t
Hirschfelder, Bird, and Spotz methods agree closely,
probabwithin the limits of experimental error, while the Gilliland
eqtion gives low values a t higher temperatures.
POSSIBLE MODIFICATION OF HIRSCHFELDER,BIRD, AND SPOTZ EQUATIONAs
a means of studying deviations of Equation 6 from expe
menta l results, values of the constant B were computed for
easystem given in Table I11 which would make the equation agwith
experiment. Force constants were based on viscosiVarious attempts
were made t o relate these values of B to proerties of the systems.
As shown in Figure 5 , there appears tosome correlation of the
constant with the molecular weight gro[ M h k y ]. Assuming a
linear relationship, the data Figure 5 may be approximated by the
equation:
B = 10.7 2.46 [ L;Mfz] l IResults obtained employing Equation 18
in connection w
Equation 6 for the systems are shown in Figure 5 and Table IThe
average and maximum deviations between calculated aexperimental
values are significantlylese than those obtained wEquation 6, using
the theoretical value of 9.2916 X lod4 or
Table V. Variation of D with Temperature for CarbDiffusion
Coefficient, 9s. Cm./Sec.
Dioxide-Air SystemExptl. dat a Arnold H.B.S. GillilandT K.
(smoothed) method method method
293400600800100013001500
0.1510.2730.5550.9151.321.972.45
0 :2670.5430.9051.281.972.49
0 :2660.5230.8831.972.521.28
0:iiz0.4480.6900.9701.421.77
-
5/26/2018 + Estimation of Diffusion Coefficients for Gases an
Vopors
http:///reader/full/-estimation-of-diffusion-coefficients-for-gases-an-vopo
June 1955 I N D U S T R I A L A N D E N G I N E E R I N G C H E
M I S T R Y3.O2.0 MODIF IED H.B.S. ME T H O D
O B S E R V E D D , SQ. GM. / SECFigure 6 . Comparison of
experimental datawith results calculated by modified Hirsch-felder,
Bird, and Spotz equation
3.02.0
: .0ic; 0.5Vvo- .3
.2W-I5iY .1aV0.050.030.03 0.05 0 1 0.20.3 0 5 1.0 20 3.0
O B S E R V E D D, SQ.CM. /SECFigure 7 . Results of modified
Hirschfelder,Bird, and Spotz equation using estimatedforce
constants
Further results using estimated force constants are summarizedin
Table IV, items 9 to 15. Figure 7 shows results obtained
withEquation 18 using force constants estimated from boiling
pointand molar volume. This procedure seems comparable in ac-curacy
to t he Arnold method for these systems.
W ) I) = collision integral for diffusion, function of kT/eA =
small correction term seldom exceeding 0.03E = maximum energy of
attraction7 = viscosity, gram/cm.-sec.
Subscripts 1 and 2 denote components 1 and 2, respectiv
DISCUSSIONOne of t he reasons for using Equat ion 18was to
obtain a bestpossible correlation of t he da ta using force
constants based onviscosity, and then to use this relation as a
basis for comparingthe various procedures for estimating the force
constants.Methods of obtaining r oare compared in Tab le IV, items
8 to 11.Estimation of r o from molar volume (Equation 17) appears
mostsatis factory. Use of T J P , yields slightly better results
than useof critical volume. However, experimental uncertain ty in
meas-uremen t of critical properties m ay con tribute to th e
apparen t in-accuracy. Methods of estimating ~ / kre compared in
Table
IV, items 12 to 14. Equation 13 / I C = 0.755 T,) and Equation1
4 e l k = 1.21 T i ) show essentially equivalent behavior. Asnoted
reviously, Equat ions 10 and 11 should be essentiallyequivagnt to
13 and 14.It is recognized th at Equation 18 is highly empirical
and th at i tsuse can be justified only on th e basis of th e
improved corre-lation obtained for the present systems. It is
believed that thedeviations of B from the theoretical value as
shown in Figure 5represent some failure in t he theory, which
should ultimately beimproved by a more fundamental approach. T o
seek modifiedrelations for obtaining t he force constants for
dissimilar moleculesfrom th e values for the pure components would
seem moreromising ultimately th an t he more simple expedient of
modi-rying the numerical constant in t he diffusion
equation.NOMENCLATURE
B = numerical constant equal to 9.2916 X accordingC =
Sutherlands constant for diffusion, O K.D = diffusion coefficient,
sq. cm. per secondk = gas constant/molecule, Boltzmanns
constant
= molecular weightP = total pressure, atm.r = molecular
diameterr 2or ro = collision diameter, A .7 = absolute temperature,
O K.Ta = normal boiling point, O K.T , = critical temperature, O
K.T , = melting point, O K.
= function of A T / V = molar volume a t normal boiling point,
cc. per gram-Vc = critical volume, cc. per gram-mole
to theory
W2 2)mole (total molar volume of each component)
REFERENCES(1) Arnold, J. H., IND.NQ.CHEM.,2, 091 (1930).(2)
Boardman, L. E., and Wild, N.E., Proc . Roy. SOC Lo(3) Bradley, R.
S., and Shellard, A.D., Ib id . , A198,239 (19(4) Bromley, L. A, ,
and Wilke, C. R., IND. NQ.CHEM.,(5) Buddenberg,J. W., and Wilke, C.
R., I b i d . , 41,1345 (1946) Chapman, Sydney, and Cowling, T. G.,
Mathematical of Nonuniform Gases, Cambridge University Press
A162, 511 (1937).
(1951).
dington, 1939.(7) Gilliland, E. R., IND.NQ.CHEM.,6, 81
(1934).8)Hirschfelder, J. O., Bird, R. B., and Spota, E. L., Chem.
R205 (1949).(9) Hirschfelder; J. O., Bird, R. E., and Spotz, E. L.,
J . Chem16. 968 (1948).- - -(10) Hirsohfelder, J . O., Bird, R. E.,
and Spotz, E. L., TranSOC.Mech. Enors., 7 1 , 921 (1949).(11)
Hirschfelder, J. O., Curtiss, C. F., and Bird, R. B., MoTheory of
Gases and Liquids, pp. 538-40, WileyYork, 1954.(12) Hirschfelder,
J. O., Curtiss, C. F., and Bird, R. B., TranSOC.Me . Engrs., 71,
45, 8.6-4 (1949).(13) I b i d . , pp. 1110-12.(14) I b i d . , ~
.000, Eq. 8.6-3,8.6-4.(15) Xennard, E. H., Kinetic Theory of Gases,
p. 195, M
(16) Kilbanova, Pomerantsev, and Frank-Kamenetskir, J(17)
Landolt-Bijrnstein, Physikalisoh-chemische Tabellen(18) LeBas, G.,
Chem. News, 99,206 (1909).(19) Lee, C. Y. nd Wilke,C . R.,
IND.NG.CHEM.,6, 381 (20) Licht, W., Jr., and Stechert, D. G., J .
Phys. Chem.,(21) Mack, Edward, Jr., J . Am . Chem. Soc. , 47,2 468
(1925).(22) Meissner, H. P., Chem. Eno. Progr., 45, 49 (1949).(23)
Perry, J. H., Chemical Engineers Handbook, McGr(24) Rowlinson, J.
S., Tran s. Faraday SOC. 7,120 (1951).(25) Sutherland,PhiL Mug.,
36,5 07 (1893).(26) Titani, T.,Bull. Chem. SOC Japan),5,4 1
(1930).(27) Trautr, M., and Mtiller, W., Ann. Phy s i k , 414, 33
(1935(28) Waldmann, L., Naturwissenschaften, 32, 223 (1944).(29)
Wall, F. T., and Kidder, G. A., J.Phys. Chem., 50, 235(30) Wilke,
C. R., Chem. Eng. Progr., 45, 19 (1949).
Hill Book Co., New York, 1938.Phys. U.S.S.R.),12, 4-30
(1942).Springer, Berlin, (1923-35).
(1944).
Book Co., New York.
RECEIVEDor review June 1 , 1954. A C C E P T E December