CHEMICAL ENGINEERING

272 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

LD^82 D4mmor0.004 m

fD 500 ð 0. 004

 D 2

Thus the effectiveness factor,;D

tanhf

f

D

tanh 2

2

D

0. 96

2

D 0. 48 (equation 10.202)

For a spherical particle:

Thiele ModulusDfD9R

RD

Vo l u m e

Surface

D

4

3 r

3

o

4 ro^2

D

ro

3

RD

5 ð 10 ^3

3

m

fD



^500 ð

5 ð 10 ^3

3

9

 R



D 0. 833

Thus the effectiveness factor, ;D

1

f

coth 3f

1

3 f^2

(equation 10.215)

D

1

0. 833

coth 2. 5 

1

3 ð 0. 8332

D 1. 217  0. 480

 D 0. 736

PROBLEM 10.41

Obtain an expression for the effective diffusivity of componentAin a gaseous mixture
ofA,BandCin terms of the binary diffusion coefficientsDABforAinB,andDACfor
AinC.
The gas-phase mass transfer coefficient for the absorption of ammonia into water from
a mixture of composition NH 3 20%, N 2 73%. H 2 7% is found experimentally to be
0.030 m/s. What would you expect the transfer coefficient to be for a mixture of compo-
sition NH 3 5%, N 2 60%, H 2 35%? All compositions are given on a molar basis. The total
pressure and temperature are the same in both cases. The transfer coefficients are based
on a steady-state film model and the effective film thickness may be assumed constant.
Neglect the solubility of N 2 and H 2 in water.

Diffusivity of NH 3 in N 2 D 23 ð 10 ^6 m^2 /s.

Diffusivity of NH 3 in H 2 D 52 ð 10 ^6 m^2 /s.

Solution

For case1:

The effective diffusivityD^0 is given by:

1

D^0

D

(

73 / 80

23 ð 10 ^6

)

C

(

7 / 80

52 ð 10 ^6

)

(from equation 10.90)