Coeficientes de difusividad

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Applications of holdup da ta to

explain th e effect of diffusivity on

th e vaporization of liquids in pack-

ings and t o estimate effective inte r-

facial areas for mass transfer have

been outlined.

ACKNOWLEDGMENT

The auth ors wish t o acknowledge

support of thi s work ( Pa rt s

I,

11,

and 111) under Grant G-200 of the

National Science Foundation and

Contract No. AT(30-1 ) -1463 of the

Atomic Energy Commission.

N O T A T I O N

a

= effective interfacial area, sq.

c = constant in Equation (5)

D

= diffusivity of solute in gas,

sq. ft./hr.

D,

=

diameter of sphere possessing

the same surface area a s

a

piece

of

packing, ft.

f t I cu.ft.

G

=

superficia l ga s ra te, 1b.I (hr.)

h, =

operating holdup, cu.ft./cu.ft.

li, = static holdup, cu.ft.1cu.ft.

ht

=

otal holdup, cu.ft./cu.ft.

k

=

gas-phase mass transfer co-

efficient, lb. moles/ (hr. ) (sq.

ft.) (atm.)

k,a

=

gas-phase mass transfer co-

efficient, lb. moles/ (hr .) (cu.

ft.) (atrn.)

L

= superficial liquid rate, 1b.l

(hr.) (sq.ft.)

m = constant in Equation (5)

M M= mean molecular weight

of

(sq.ft.)

gas, 1b.llb. mole

n

=

constant in Equation

(5)

P,, = mean partial pressure of

inert gas in the gas phase,

atm.

Greek Letters

p = liquid viscosity, centipoises

=

gas viscosity, 1b.l (h r. ) (ft.)

p

= liquid density, g./ml.

=

gas

density, 1b.lcu.ft.

o = surface tension, dyneslcm.

o

= void fraction, cu. ft./cu.ft.

Subscripts

w =

f o r water systems

abs = for absorption work without

vap = for vaporization work

LITERATURE CITED

a

chemical reaction

1. Jesser,

B.

W., and

J. C.

Elgin,

Trans

Am. I n s t

Chem. Engrs.,

39, 277 1943).

2. Leva, M., “Tower Packings and

Packed Tower Design,” 2nd ed.,

The United States Stoneware

Company, Akron, Ohio 1953).

3. Mehta, J.

J.,

and

R. H.

Parekh,

S.M. thesis, Mass. Inst. Technol.

1939).

4.

Surosky, A. E., and B.

F.

Dodge,

Znd Eng. Chem. 42, 1112 1950).

arts I and

II

presented

at

t h e

A .

I . Ch. E .

Sf i r ing f i e ld

m c e t i n y

Pa r t

III

a t the

N e w

Y-orn

?nPet ing.

CORRELATION OF DIFFUSION

COEFFICIENTS IN DILUTE

SOLUTIONS

C. R.

WILKE and

PIN CHANG

University of California, Berkeley, California

The diffusion coefficient is nor-

mally defined and assumed in this

study to be the proportionality

constant in the ra te equation writ-

ten for undirectional mass trans-

fer as follows :

Equation i 1) is strict ly applicable

in ideal dilute solutions in which

convective transport due to volume

changes on mixing is negligible,

and in which other possible modes

of mass transfer ar e not opera-

tive. This paper represents an at-

tempi- to generalize the relation of

P to conveniently available proper-

ties

of

dilute solutions

so

as

to per-

mi t est imation of diffusion coeffi-

cients for engineering purposes.

PREVIO US COlRRELATION

In the earlier paper by Wilke

10)

a method of correlating dif-

fusion coefficients was proposed on

the ba sis of qualitative conclusions

of the Eyring theory(3) and the

Stokes-Einstein relation. It was

shown that the group TID-q desig-

nated as the diffusion factor

F

was essentially independent of tem-

perature for available systems.

Furthermore

F

could be repre-

sented as a smooth function of

molal volume fo r diffusion of vari-

ou s

solutes in a given solvent. In

general it was assumed that this

function extrapolated into the

Stokes-Einstein equation at very

large solute molal volumes.

DEVELOPMENT OF N E W

CORRELATION

Sources of Data. At the t ime of the

previous work so few data were

available for diffusion of single

solutes in a varie ty of solvents th at

th e effect of solvent properties,

could not be brought into

a

gen-

eral correlation. I n

a

special effort

to

obtain suitable data of th is kind

a companion experimental study

2 ) was conducted involving the

diffusion of iodine and toluene in

a wide variety of hydrocarbon

Page

264

A.1.Ch.E. Journal

June,

1955



o m

G

10

20

40 GO

80100 200

400

600

1003 2000

S O L U T E MOL

A L

V O L U M E , CU. Cm / q m msl

u ; v 8

6

x v 4

I U

polvents ran ging from hexane

through tetradecane. Data were

also obtained for diffusion of

or-

ganic acids in several solvents.

These new dat a were supplemented

by certain other data from the

literature, including all the data

reported in t he previous paper l o ) ,

to provide

a

basis

f o r

the present

development. All data which sup-

plement those presented in Tables

2 through

5

of referenceil0) are

presented in Table

1.

V

I

5:

FIG.

1.

DIFFUSIONN WATEP..

c I . 2

g v

v s

6 -

Effect of Solute

Molal

Volume.

Fig-

ure 1 shows the diffusion as a

funct ion of molal volume fo r vari-

03 ous solutes in water based on data

fro m Table 2 of reference 10. Molal

volumes used throughout this

work

ar e values a t t he normal boi i?g

point estimated for complex mole-

cules by the atomic contributions

of

LeBas ( I ,6) as summarized in

Table 2 .

As indicated in Figure

1,

F is a

having a log-log slope of about 0.7

400

6oo at low molal volumes and apparent-

V, c c /gm mol ly merging smoothly with the

4

_ _ ____

0

x

0

B E N Z E N E

3 - - -

B R O M O B E

Z

E NE

I I smooth function of molal volume

v

CARBO N TETRACHL O RIDE]

Q

I O D I N E

O T U L U E

N E

I

2 0 40

60

80

100 200

SLOPE

= 0.6

A C E T I C

A B E N Z O I C

0

C l N N A M l C -

0

F O R M I C

v

20 40

60 80 100 200 400

20

40 60 80

100

200 408

v, c.c./gm. mol V, c.c./qm. mol

CARBONTETRACHLORIDE.

FIG.

3. DIFFUSION O F ORGAPI'IC ACIDS N

TOLUENE.

FIG . DIFFUSION

F

ORGANIC

ACIDS N

Vol.

1,

No.

2

A.1.Ch.E.

Journal

Page

263



TABLENAL DIFFUSION DATAFOR VARIOUS SYSTEMS

(Supplementary to Tables

2

to

5

of reference 10)

DXlW DX106

Solute Solvent ture, "C. (obs.) (calc.)

Tempera- sq.cm./sec. sq. cm./sec.

M O L E C U L A R W E I G H T

OF S OLV E N TS

FIG.

5. EFFECT

F

SOLVENT

MOLECULARWEIGHT.

Stokes-Einstein equation which re-

quires a slope of 113 a t high molal

volumes. On the assumption that

molecules are spherical with a

radius equal to ( 3 V / 4 n N ) 1 I 3 the

Stokes-Einstein equation may be

written

as

follows:

= 1.004X 10'

d 3

2)

DS

Equation (2)

is

shown as

a

dotted

line on Figure

1.

The general be-

havior of the curve

of

Figure

1

relative to the Stokes-Einstein

equation constitutes reasonable evi-

dence in favor

of

the proposed

method

of

correlation.

Over th e middle ran ge of molal

volumes th e curve of Fi gu re

1

may

be satisfactorily represented

by

a

line

of

slope 0.6. Bearing in mind

the theoretical limitations of the

assumption it is convenient to

as-

sume that the diffusion factor

is

proportional to P ver the mid-

dle range. The proportionality of

D y to V0.6 was used by Thakar and

Othmer

(8)

in their representation

of the correlation for diffusion of

substances in water.

To explore the mold volume ef-

fect in nonaqueous systems several

solvents were studied

as

shown in

Figures

2

through

4 .

The

group

D q l T may be represented satis-

factorily as proportional to VO 8

It is therefore a fair generaliza-

tion that D y l T is proportional to

Vo.6 in the medium molal volume

Acetic acid Acetone 40.0 4.044 3.49

25.0 3.309 2.85

15.0 2.916 2.51

Benzene 25.0 2.081 1.74

5.9 1.587 1.22

Carbon tetrachloride

6.5 1.151 1.13

14.8 1.267 1.32

Toluene

25.0 1.490

1.58

40.0

1.780 2.04

25.0 2.265 2.00

15.0 1.905

1.72

6.8 1.661 1.48

i-Amy1 alcohol

Ethyl alcohol 20.0 0.78 0.85

Aniliie

Ethyl alcohol 18.5 2.70 2.41

Benzene

Bromobenzene 7.5 1.02 1.20

Chloroform 15.0 3.70 2.54

n-Hexane 15.0 3.70 3.85

Benzoic acid Acetone

Benzene

13.2 2.368

1.66

25.0

2.622 1.89

40.0

3.054 2.19

15.0 1.170 0.95

25.0

1.379 1.13

40.0 1.762 1.44


14.8 0.776 0.87

25.0 0.908 1.04

40.5 1.168 1.36

Toluene 16.0 1.289 1.16

25.0 1.493 1.34

40.0 1.851 1.65

Benzo-trichloride Toluene

7.6 1.32 1.29

Bromobenzene Benzene

7.3 1.41 1.29

Ethyl benzene 7.3 1.44 1.55

Ethl ether 7.3 3.50 3.80

n-Hexane

7.3 2.60 3.02

Transdecalin

7.3 0.47 0.48

m-X ylene

7.3 1.52 1.69

Cyclohexane 7.3 0.90 0.91

m-Cymene

7.3 1.34 1.18

Mesitylene 7.3 1.31 1.54

Bromform Acetone

Benzene

Ethyl alcohol

Ref.

a

a

a

a

a

d

d

d

d

d

d

d

d

d

d

20.0 2.74 3.22

f

20.0 1.77 1.88

20.0 0.97 0.96

i

Bromonaphthalene Ethyl alcohol 20.0 0.76 0.72

b

a-Bromo-

naphthalene

rn-Bromotoluene

Carbon

tetrabromide

Carbn

tetrachloride

Benzene

Cyclohexane

Decalin

Dibenzyl ether

n-Hexane

a-Methyl naphthalene

Tetralin

Toluene

Toluene

Benzene

Benzene


Cyclohexane

Decalin

Dioxane

n-Heptane

n-Hextane

Isooctane

Kerosene

Tetralin

Toluene

7.3 1.04

-

~

7.3 0.85

7.3 0.34

7.3 0.149

7.3 2.15

7.5 0.226

7.5 0.36

7.5 1.24

7.4 1.52

7.3 1.12

25.0 2.00

25.0 1.41

25.0 1.49

25.0 0.776

25.0 1.02

25.0 3.17

25.0 3.70

25.0 2.57

25.0 961

25.0 0.735

25.0 2.19

1.05

d

0.72 d

0.39

d

0.17 d

2.44 d

0.22 d

0.38

1.31

d

1.48

d

1.27 d

1.87 g

1.74 j

1.32 g

0.733 g

1.01 g

3.25 g

3.11

g

2.86 g

1.03 g

.735 g

2.22

g

Cinnamic acid Acetone 25.0 2.41 2.51

Benzene

25.0 1.21 0.99

a

Carbon tetrachloride 25.0 0.755 0.91 a

Toluene 25.0 1.18 1.14

Ethyl benzoate Acetone 20.0 2.47 2.29 h

Benzo trichloride

20.0 0.52 0.58

h

Ethyl acetate

20.0

1.85 2.01 h

Nitrobenzene 20.0 0.60 0.51 h

Page 266 A.1.Ch.E.

Journal June,

1955



Ethylene bromide

Formic acid

n-Heptyl bromide

n-Hexyl bromide

Iodine

Iodine

Iodobenzene

Methyl iodide

Nitrobenzene

n-Octyl bromide

Pyridine

1, 2, 4, 5-Tetra-

chlorobenzene

1,2, 4-Trichloro-

toluene

Toluene

Ethylene chloride

Acetone

Benzene


Toluene

Heptane

Hexane


Cyclohexane

Dioxane

Ethyl alcohol

Heptane

Hexane

n-Hexane

Methyl cyclohexane

n-Octane

n-Tetradecane

Benzene

Toluene

Methylene chloride

Acetone

Ethyl benzoate

Ethyl acetate

Octane

Ethyl alcohol

Benzene

Benzene

n-Decane

n-Dodecane

n-Heptane

n-Hexane

n-Tetradecane

7.3

25.0

18.5

6.5

6.2

13.9

25.0

8.5

25.0

15.0

6.2

14.1

25.0

7.4

7.6

25.0

15.0

25.0

40.0

25.0

25.0

25.0

25.0

40.0

30.0

15.0

25.0

7.3

7.4

7.5

20.0

20.0

20.0

75

20.0

7.6

7.6

25.0

25.0

40.0

25.0

6.9

25.0

25.0

1.11

3.768

3.274

3.132

1.991

2.306

2.577

1.612

1.888

1.673

2.285

2.463

2.646

1.52

2.31

1.50

1.54

1.07

1.772

1.316

3.42

4.05

4.24

2.71

2.30

2.43

0.96

1.35

2.23

2.06

2.94

0.73

2.25

1.46

1.12

1.24

1.34

2.09

1.35

4.33

3.72

2.95

4.21

1.02

1.31

3.59

3.12

2.87

1.48

1.76

2.14

1.48

2.01

1.67

1.90

2.32

2.54

1.48

2.54

2.30

1.19

1.31

1.72

1.32

4.60

4.96

4.37

2.74

2.28

3.04

1.14

1.31

2.40

2.54

2.83

0.66

2.48

1.42

1.00

1.03

1.12

1.77

1.19

4.08

3.35

2.56

4.13

0.86

d

a

a

a

a

d

d

i

a

i

a

i

a

2

a

a

d

d

d

h

h

h

d

b

d

d

a

a

a

a

a

a

a

@hang, Pin, and C .

R.

Wilke, "Some Measurements of Diffusion in Liquids,"

bznternat ional Cri t ical Tables 5 63-75 1929).

CMuchin,

G.

E., and G.

P.

Faermann,

2.

physik.

Chem. 121, 180

1926).

dHerzog,

R.

O . et al., 2. physik. Chem.

A )

67, 329 and 343 1933).

C e

Monde, H.,

J .

phys.

radium,

7,

371-8 1936).

fOholm, L.

W.,

Medd. Nobelinst .

2 23 1913).

gHammofid, B.

R.,

and

R.

H. Stokes, personal communication to

J.

H. Hilde-

ILDurnmer, E.,

2.

ak org . u. a l lge m Che m . 109, 49 1919).

%tokes, R. H., P. J. Dunlop, and J . R. Hall.,

T r a n s . F a r a d a y

Soc.

49,

886

jWatts, H. .

J.

Alder, and J . H. Hildebrand, J . Phys.

Chem.

23, 659 1955).

J . Phys.

Che m .

(in press).

brand (Sept. 21, 1954).

1953).

range for both aqueous and non-

aqueous solvents. However, it must

be recognized that special struc-

tur al features of molecules and

other molecular interactions may

be important in certain cases and

that therefore the proposed rela-

tionship is a t best

an

oversimplifi-

cation utilized to obtain a practical

result.

Effect of Solvent Properties. Study

of the effect of solvent properties

in addition to viscosity centered on

the behavior of the group D-qlT

f o r

diffusion of single solutes in

a

variety of solvents. A wide variety

of variables such as molal volume,

heat of vaporization, molecular

weight, etc., were examined. Of

these the solvent molecular weight

appeared to correla te the data most

successfully. Figure

5

shows the

group

D-qlT

as a function of molec-

ular weight

f o r

diffusion of given

solutes in a number of solvents.

Although there is considerable

scat ter of the points a line

of

slope

112 on the log-log plots correlates

each system moderately well. As in

th e case of the molal-volume effect

there are obviously other factors

involved so that use of solvent

molecular weight

is

satisfactory

only as a first approximation. The

data of Trevoy and Drickamer(9)

are for 0.50 mole fraction of phenol

in various hydrocarbons so that the

solvent molecular weight

is

used

primarily to show the trend.

General Correlation for Unassociated

Liquids. From th e results of th e pre-

ceding section it was concluded

th at an equation of the frllowing

form would express the effects of

solute and solvent:

(3)

TM /

r VoP6

D = const. ___

Figure

ti

shows a log-log plot

of

D I T vs. the group T V O . ~ / M ~ / ~or a

wide varie ty of unassociated solv-

ents embracing the dat a of Table

2 of t hi s paper and Table

5

of

reference

10.

The method of plot-

ting was selected to spread the

data and best illustrate the scope

of the correlation. The line through

the data has slope -1 as required

in the assumptions of t he correla-

tion and may be expressed by the

equation

Data f o r

155

points among 123 dif-

ferent solute-solvent systems are

expressed by the correlation with

an average deviation of 12% be-

tween calculated and observed re-

sults.

Correlationof Associated Liquids. AS-

sociated liquids such as water and

other hydrogen-bonding solvents

might be expected t o show devia-

tion from the correlation of Figu re

6.

Figure shows the plot of

DIT

vs. -qVO.6/M1/2 for diffusion in

water. The best line through the

data falls clearly above the dotted

line representing Figure ti. This

deviation

is

in the direction corre-

sponding to association of the

solvent. By assigning a molecular

weightt to the solvent equal to 2.6

times the nominal molecular weight

of wate r one can bring the data of

Vol.

1,

No. 2

A.1.Ch.E. Journal

Page

267



TABLE

-ATOhllC VOLU MES FOR COMPLEX MOLECULES,

MOLECULAR

VOLUMES FOR SIMPLE SUBSTANCES

Atomic Volumes

Bromine

27.0 Nitrogen, in secondary amines 12.0

Carbon

14.8 Oxygen (except as noted below) 7.4

Chlorine

24.6 Oxygen, in methyl esters 9.1

Iodine

37.0 Oxygen, in higher ethers and esters 11.0

Nitrogen, in primary amines 10.5 Sulfur 25.6

Hydrogen

3.7 Oxygen, in methyl ethers 9.9

Nitrogen, doub e bonded. 15.6 Oxygen, in acids 12.0

For

For

For

three-membered ring, as in ethylene oxide, deduct

four-membered ring, as in cyclobutane, deduct

five-membered ring, as

in

furan, thiophene, deduct

0.6

8.5

11.5

For pyridine, deduct

15

For benzene ring, deduct 15

For naphthalene ring, deduct 30

For anthracme ring, deduct 47.5

Molecular Volumes

H,

0,

N

Air

co

coz

so2

NO

D,O *

*Estimated value.

14.3 N

2 0

25.6 NH,

31.2 H,O

29.9 H&

3c1.7

cos

34.0

Clz

44.8

Br

2

23.6

2

20.0

36.4

25.8

18.9

32.9

7 v0 6

M 12

FIG.6.

DIFFUSION

N

UNASSOCIATED LIQUIDS.

Figure 7 squarely onto the curve

of Figure 6.

Thus t he correlation f or diffusion

in water and also in nonassociated

solvents may be expressed by the

general equation

The association parameter is in-

troduced to define the effective

molecular weight of the solvent

with respect t o th e diffusion proc-

ess. For nonassociated solvents

z = 1 and for water = 2.6.

Diffusion in methyl alcohol is

shown similarly in Figure 8, indi-

cating an association parameter of

1.9,

and for diffusion in ethyl alco-

TABLE 3-COMPARISON OF ASSOCIA-

TION PARAMETERS

WITH

ASSOClAl’ION

NUMBERS

F JACOBSEN

-4ssociation

Solvent

parameter,

Water 2.6

Methyl alcohol 1.9

Ethyl alcohol 1.5

Benzene

1

o

Ether 1

o

Heptane 1.0

Association

number *

3.5

2.7

1.0

1.02

1.0

60

*At 20°C.

hol, illustrated in Figure 9,

is

found to be 1.5.

It is of interest to compare the

values of with th e association

numbers recommended by Jacobsen

4 ) from intermolecular free-

length relationships as given in

Table

3.

Although Jacobsen’s

as-

sociation numbers are larger than

the present association parameters

the agreement in order

of

the

solvents suggests that the general

concept of the association effect

may be valid. The results further

suggest t ha t th e methods of Jacob-

sen might be used to select an as-

sociation parameter which normal-

ly would lie between the values

of

2.6 for water and 1.0 fo r unassoci-

ated solvents.

By

use

of the given association

parameters the

data

€or diffusion

in water ar e correlated by Equakion

(5) with an average deviation of

about

6%.

Data for methyl alcohol

ar e predicted within

11 .

t should

be noted that the experimental

data for methyl alcohol systems

ar e known to be of rather

low

pre-

cision in the original source.

DISCUSSION

General Comment.

The correlation

represented by Equation (5) is

satisfactory for estimation of dif-

fusion coefficients in dilute solu-

tions with sufficient precision

€o r

most engineering purposes, i.e.,

about 1 0 average error.” It must

be emphasized that the diffusion

process is extremely complex and

that any rigorous treatment must

consider solute-solvent interaction

in a more detailed manner than

the present relation could possibly

imply.? Although the present func-

tional rela tionship of diffusion co-

efficient to solute molal volume

rests upon some qualitative theo-

*For

285

points among 251 solute-solvent

s y s t e m s of this

study.

?Diffusion of iodine in

aromatic hydrocarbons,

for

example, bas been

excluded from t h e

present

correlation because of known comples forrna-

t

ion.

Page 268 A.1.Ch.E. Journal

June, 1955



retical foundation, th e relation- tionship or some improved corre- ed here. Study of th e correlation

ship t o solvent molecular weight

and deviations from constancy of

is strict ly empirical. Some theo- Only a tenfold range of viscosity th e group DTIT over more exten-

retical basis for the latter rela-

is

covered by th e solvents present- sive temperature and viscosity

ranges is especially needed. Al-

though deviations in constany of

DTIT

have been observed and

might well be expected for strongly

interacting solute-solvent systems

such as iodine

in

aromatic solvents

and acetic acid in ethylene glycol,

use of the group seems justified

for prediction of the effect of tem-

perature on D in absence of ex-

perimental data.

lation would be highly desirable,

0.4 0.6 2 4

6 8

I0 2

3

V

0 6

M

2

FIG.

7. DIFFUSIONN

W A T E R .

al

X

all

0.4

0.6

I

2

4

6

8

10

20

9 vo.6

M

4

FIG.

8.

DIFFUSION

N METHYLALCOHOL.

Comparison with

Other

Correlations.

Olson and Walton

5 )

have pro-

posed a general form

of

correla-

tion of diffusion coefficients based

on surface-tension lowering of the

solvent by hhe solute. In view of

the special data required no at-

tempt will be made to compare

their method quantitatively with

the present correlation.

Scheibel(7) has fitted the corre-

lation of Wilke to a general equa-

tion involving the molal volumes

of solute and solvent based on the

curves for water, methyl alcohol,

and benzene. In view of th e special

distinction developed above be-

tween water and methyl alcohol as

associated solvents and benzene as

an unassociated solvent the basic

assumptions used by Scheibel are

believed to be in error.

Thakar and Othmer

(8)

have pro-

posed the following general equa-

tion developed through the refer-

ence substance method :

For

diffusion in water only it was

assumed th at the group D ql.1 fitted

the temperature behavior better

than did the Stokes-Einstein group

DqlT.

However since the ratio

[ ql.ll [ q /

TI changes only 10% for

water between

0

and

80°C.

it

is

difficult t o ju st if y a choice between

the two ways of representing th e

temperature dependence on the

basis of th e relatively limited data

presently available.

Contrary to conclusions of the

present study, for diffusion of a

single solute in various solvents at

20°C. Equation 6 ) does not per-

mit variation of Dq,O with solvent

molecular weight. Application

of

Equation (6) to thirty-six repre-

sentative systems involving dif-

fusion of various solutes among

twenty-one unassociated solvents

gave rather unsatisfactory results,

with an average deviation of over

30 between calculated and ex-

perimental diffusion coefficients.

Vol. 1, No.

2

A.1.Ch.E. Journal

Page 269



CONCLUSION caution of course should be ob-

served in extending the method f a r

represents an improvement over beyond th e ran ge of variables and

previous correlations of diffusion types of systems included in th e

coefficients in dilute solutions. Due present development. To facilitate

It

is

believed that Equation

( 5 )

d

0 )

v )

I

Y

0

4

u

€

u

s

use

of

the method

a

revised

dif-

fusion-faotor chart

is

given in Fig-

ure 10 to include the association

parameter and molecular weight of

the solvent.

ACKNOWLEDGMENT

Assistance of Research Corpora-

tion through a grant-in-aid is

gratefully acknowledged.

N W A T ION

C

=

concentration, g. moles/cc.

D

=

diffusion coefficient, sq.cm./

F

= diffusion factor, T J D q

see.

(OK.) (see.)

Q

X

4

0.4

0.6 2 4

6 8

10 20

1 V O . 6

M

‘/2

FIG.

. DIFFUSION

N

ETHYL

LCOHOL.

(sqxm.) (centipoise)

solvent

water

L

=

latent heat of vaporization of

L = atent heat of vaporization of

M

=

molecular weight

of

solvent

N =

Avogadro’s number, mole-

cules per mole

N A

=

diffusion rate

of

component

A, g. moles/ (see.) (sqxm.)

V

=

molal volume

of

solute at nor-

mal boiling point, cc.lg. mole

t =temperature, “ C .

T

=

temperature, OK

= association parameter, multi-

ple

of

nominal molecular

weight of solvent to give ef-

fective value

Z = distance in direction of dif-

fusion

q

=

viscosity of solution, centi-

poise

qw= viscosity of water, centipoise

q S o

=

viscosity of solvent at

20°C .

centipoise

S O L U T E M O L A L V O L U M E CU. cm. /gm.

mol.

FIG.

10.

GENERALIZEDIFFUSION-FACTOR

CHART.

Page 270 A.1.Ch.E. Journal

LITERATURE

ITED

1.

Arnold, J. H., Ind.

Eng.

Chem.

2. Chang, Pin, and C. R. Wilke, J .

3. Eyring,

H.,

J . Chem. Phys . 4

4. Jacobsen, Bertil, “Association

Numbers in Liquid Systems from

Intermolecular Free Length Re-

lationships,” Karolinska Institute,

Stockholm ( in press) .

5. Olson,

R.

L., and J.

S.

Walton,

I n d . Eng. Chem. 43, 701 (1953).

6. Perry, J. H., “Chemical En-

gineers’ Handbook,” McGraw-

Hill Book Company, Inc., New

York (1950).

7. Scheibel, E. G., Ind.

Eng.

Chem.

46 2007 (1954).

8. Thakar, N. S., and D. F. Othmer,

I n d .

Eng.

Chem.

45,

589 (1953).

9.

Trevoy,

D.

J.,

and H.

G.

Dricka-

mer,

J.

Ch em . P h ys .

17, 1117

(1949).

10. Wilke, C.

R.,

Chem. Eng. Progr .

45 219 (1949).

22, 1091 (1930).

Phys. Chem. ( in pre ss) .

283-91 (1936).

Presented at A .

I.

Ch. E. brew Yo rk meetinp

June, 1955

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