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BINARY DIFFUSION

COEFFICIENTSGases

yMagnitude 1 210 /cm s} yTemperaturedependence: yWeakdependence onconcentrationyPressuredependence: 1p}

Experimentaldetermination ofdiffusivities

methoddeveloped by

Winkelmann - liquidis

allowedto evaporateina

verticalglasstube over

thetop of whichastream

ofvapour-freegasis

passed,ataratesuchthat

thevapourpressureis

maintainedalmostat zero.

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apparatusismaintainedatasteady temperature -

no eddy currentsintheverticaltubeandmass

transfertakesplace fromthesurface by molecular

diffusionalone.

evaporation ratedetermined by fall ofliquid

surface concknown - diffusivity calculated.

calculatethediffusivity ofcarbontetrachloride

vapourinairat 321 Kandatmosphericpressure

Time from

commencement

ofexperiment

Liquid

level

Time from

commencement

ofexperiment

Liquid

level

h min ks mm h min ks mm0 0 0.0 0.0 32 38 117.5 54.7

0 26 1.6 2.5 46 50 168.6 67.0

3 5 11.1 12.9 55 25 199.7 73.8

7 38 27.4 23.2 80 22 289.3 90.3

22 16 80.2 43.9 106 25 383.1 104.8Thevapourpressure ofcarbontetrachlorideat

321 Kis 37.6 kN/m2andthedensity oftheliquid

is 1540 kg/m3. Thekilogrammolecularvolume

may betakenas 22.4 m3.

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Diffusion Coefficient forGases

Prediction

two approaches:

1.Thekinetictheory ofgases2.Use ofmolecularinteractions

Simple Kinetic Theory

dilutegasmixturesatlow pressuresmoleculesarerigid,non-attracting,andspherical.

rigidsphericalparticlesandelasticcollisions

= averagevelocity ofmolecules = mean freepath

Lennard-Jones

Accounting forintermolecularforcesand

differentsizes ofthetwo componentmolecules

317 2 22

2

,

1.8583 10 1 1( )

AB

AB D AB A B

TcmD

s P M M

!

;+

W

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,

,

,

,

,

int

AB

D AB

T Temperature

kgM Molecular weight

kgmol

p absolute pressure at m

collision diameter m

collison egral

!

; !

=

=

=W .

Fullersemi-empiricalmethod

3

,

,

,

,

T Te

mperature

kgM Molecular weight

kgmol

mv Diffusion volumekgmol

p total pressure at m

!

!

!

!

.

fromtheseeqns

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Liquids

yOrderofmagnitude:

2510 cm

s

yGenerally increasing function oftemperatureyPressureinsensitiveyOftenastrong function ofconcentrationdensity andresistanceto diffusionhigherthanin

gases - intermolecularforcesmoreimportant

difficultto characterizetheoretically - correlation

ofdataandpredictiondifficult.

Stokes-Einstein hydrodynamic model

very largesphericalmolecule (A) diffusingina

liquidsolvent (B) ofsmallmolecules

viscosity inPas

VAsolutemolarvolumeat b.p. m3/(kgmol)

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usefuleqn forthecalculationin ofdilutesolutions

ofnon-electrolytes

Wilke and Chang

semi-theoretical

dilutesolution

DABdiffusivity ofsolute A insolvent B (m2/s),

association factorforthesolvent (2.26 for

water, 1.9 formethanol, 1.5 forethanoland 1.0

forunassociatedsolventssuchashydrocarbons

andethers),

MB molecularweight ofthesolvent,Bviscosity of B (N s/m

2)

Ttemperature (K),and

VAmolarvolume ofthesolute (m3/kmol) - Values

forsimplemoleculesgivenin Table. Formore

complex molecules, VAcalculated by summation

oftheatomicvolumeand othercontributions for

water0.0756 m3/kmolshould beused.

1 216

0.61.173 10

AB B

B A

TD M

V

! v J

Q

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Solids

mechanismincrystallinesolids - movement of

atomsinto vacancies orby interstitialmovement.

Orderofmagnitude:quitevariable2

510 cms

Strongtemperaturedependence exp( )BRT

}

Porous Solids

Diffusionthroughsolidscan be by three

mechanisms:

Ordinary diffusion

Knudsendiffusion

Surfacediffusion

Whentheporediameterislargeincomparisonto

themean freepaththen ordinary diffusion occurs

andinthecontrary case Knudsendiffusion

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occurs. Ineithercaseitcan beaccompanied by

surfacediffusionthat occurs whenmolecules

adsorbed onthesurfacemovealongthesurface

usually inthedirection ofdecreasingconcentration (actually,ingeneral,decreasing

chemicalpotential). Surfacediffusionisthemost

difficultto characterize.

In Knudsendiffusionthemoleculescollide

more often withthepore wallthan with other

moleculesanditcan bepredicted fromkinetic

theory:0

( )3

A K

udD ! .

Hereu isthevelocity ofthemoleculesand disthe

diameterofthepore. Forstraight,roundpore:

1

0 2( ) 97 ( )A K

A

TD r

M! .

Here

r = poreradius,m 0( )A KD = Knudsendiffusioncoefficient,

2m

s

T = temperature, K

Themeanporeradiuscan beestimated by

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22 p

B

Vr

S S

I

V! ! .

HereS = surfacearea ofporoussolid, 2m

kg

BV = bulkdensity ofsolid, 3kg

m

pV = specificporevolume,3

mkg

I = porosity ofsolid

In orderto account forthetortuousity ofthepores

oncanuse:

0 0

( ) ( ) ( )A K A K D D

I

X! .

HereX isthetortuousity factor,ameasure ofthedeviation fromstraightcylindricalpores.

Example

T(K) r(m)

X I

1. Silica-alumina 298 91.6 10

0.725 0.40

catalyst