CHEMICAL ENGINEERING

MASS TRANSFER 277

Solution

For a binary system, Maxwell’s Law gives:



dCA

dy

DFCACBuAuB (equation 10.77)

For an ideal gas mixture:

RT

dCA

dy

DFCACB

(

N^0 A

CA



N^0 B

CB

)

For a gas absorption process:N^0 BD0ifBis insoluble

or: 

dCA

dy

D

FCB

RT

N^0 A i

from Stefan’s law (equation 10.30):

N^0 ADD

CT

CB

dCA

dy

or: 

dCA

dy

DN^0 A

1

D

CB

CT

ii

DN^0 A

1

D

CTCA

CT

iii

Comparing equations (i) and (ii):

F

RT

D

1

DCT

or: FD

RT

DCT

orDD

RT

FCT

Applying Maxwell’s law to a multicomponent system gives:



dCA

dy

DFABCACBuAuB CFACCACCuAuC CÐÐÐ

ForB,C...insolubleN^0 B,N^0 C...D 0

Writing: FABD

RT

DABCT

, andFACD

RT

DACCT

then: RT

dCA

dy

D

RT

DACCT

N^0 ACBC

RT

DACCT

N^0 ACCCÐÐÐ.

∴ 

dCA

dy

D

N^0 A

CT

(

CB

DAB

C

CC

DAC

CÐÐÐ

)

From equation (iii), using an effective diffusivityD^0 for a multicomponent system gives:



dCA

dy

DN^0 A

1

D^0

CTCA

CT

iv