CHEMICAL ENGINEERING

MASS TRANSFER 249

whenBis not undergoing mass transfer, oruBD0, then:

RTdCA/dy

DFABCBN^0 A

N^0 AD

RT

FABCB

dCA

dy

D

RT

FABCT

CT

CB

dCA

dy

By comparison with Stefan’s Law:

N^0 ADDAB

CT

CB

dCA

dy

(equation 10.29)

Then: DABDRT/FABCT

or: FABD

RT

DABCT

Applying toAin a mixture ofBandC:

dPA/dyDFABCACBuAuB CFACCACCuAuC

For the case whereuBDuCD0:

RT

dCA

dy

D

RT

DABCT

CBN^0 AC

RT

DACCT

CCN^0 A

or: N^0 AD

dCA/dy

CT

CB/DAB CCC/DAC

i

From Stefan’s Law: N^0 ADD^0

CT

CTCA

dCA

dy

D

dCA/dy

CT

CTCA

/D^0

ii

whereD^0 is the effective diffusivity ofAin the mixture

Comparing equations (i) and (ii):

1

D^0

D

1

DAB

CB

CTCA

C

1

DAC

CC

CTCA

For CO 2 in N 2 : N^0 ADD

CT

CN 2

 lm

CCO 2

L

DDð

1

yN 2

 lm

ð

CTyCO 2

L

(equation 10.33)

DD 1. 6 ð 10 ^5 m^2 /syN 2

1 D 1. 0 ,yN 2

2 D 0 .75,

∴ yN 2
lmD[ 1  0. 75
/ln 1 / 0. 75
]D 0. 87

yCO 2 D 0. 25 ,CTandLare unknown

Hence: N^0 AD

1. 6 ð 10 ^5

0. 87

ð 0. 25

CT

L

D 4. 6 ð 10 ^6 CT/Lkmol/m^2 s

For CO 2 in a mixture of H 2 and N 2 , the effective diffusivity, derived in the first part
of the problem, is used to giveD^0 :

1

D^0

D

1

3. 5 ð 10 ^5

ð

0. 4

1  0. 35

C

1

1. 6 ð 10 ^5

ð

0. 25

1  0. 35

D 2. 4 ð 10 ^5 m^2 /s