CHEMICAL ENGINEERING

MASS TRANSFER 265

From Stefan’s Law:

dCA

dy

DN^0 A

1

D

Ð

CB

CT

(equation 10.30)

Thus: DD

RT

FCT

or: FD

RT

DCT

ii

For the three-component system, equation 1 may be written:



dCA

dy

D

N^0 A

RT

FABCBCFACCC

From (2): FABD

RT

DABCT

andFACD

RT

DACCT

.

Substituting: 

dCA

dy

DN^0 A

(

CB

DAB

C

CC

DAC

)

1

CT

iii

Stefan’s law for 3-components system may be written as:

N^0 ADD^0 Ð

CT

CTCA

dCA

dy

whereD^0 is the effective diffusivity

or: 

dCA

dy

DN^0 A

1

D^0

Ð

CTCA

CT

iv

Comparing equations (iii) and (iv):
1
D^0

D

1

DAB

Ð

CB

CTCA

C

1

DAC

Ð

CC

CTCA

D

x^0 B

DAB

C

xC^0
DAC
wherexB^0 andx^0 Care mole fractions ofB,Cin the “stationary” gas. TakingAas NH 3 ,B
as H 2 andCas N 2 , then:
Case 1
xB^0 D 0. 5 x^0 CD 0. 5
1
D^0

D

(

0. 5

52 ð 10 ^6

)

C

(

0. 5

23 ð 10 ^6

)

D 0. 03135 ð 106 s/m^2

and: D^0 D 31. 9 ð 10 ^6 m^2 /s

xBMD

1  0. 95

ln[ 1 / 0. 95

 ]

D

0. 05

ln 0. 95

 ^1

D 0. 975 ,and

xT

xBm

D 1. 026

Mass transfer rate, N^0 AD

D^0

L

CA

xT

xBm

D

1

L

CA

xT

xBm

D^0

D

1

L

CA

xT

xBm

Ð 31. 9

Case 2

x^0 BD 0. 8 x^0 CD 0. 2

1

D^0

D

(

0. 8

52 ð 10 ^6

)

C

(

0. 2

23 ð 10 ^6

)

D 0. 0241 ð 106 s/m^2

and: D^0 D 41. 5 ð 10 ^6 m^2 /s