Chemical Reactions on Solid Surfaces - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 429

40

30

20

10

0

0.0 0.2 0.4 0.6 0.8 1.0

Relative Humidity

FIGURE E9-3.3 General multilayer isotherm fit to water vapor adsorption on silica gel at 25 C.

For multispecies adsorption on the same sites nonselectively, the coverage of species j on
layer i (among the total of N layers) is given by

i 1 N

cðb b Þ

q ij ¼

1 K j C j

(9.79)

Nþ

1 ð 1 cÞb b

Where K j is the adsorption isotherm constant for species j for all layers above the first one
layer, c is ratio of the adsorption isotherm constant of the first layer to that of layers above

K 1j
K j ;

c ¼ (9.80)

and

X

N S

b ¼ K j C j (9.81)

j¼ 1

The total number of species j molecules adsorbed is given by

i 1 N

n js;N ¼ n s1 P

N

1 q ij ¼ n s1 c P

N

b b

1 K j C j Nþ

1 ð 1 cÞb cb

i¼ i¼ 1

(9.82)

N

1 b

N

b Nb

N

1 ½ 1 þ Nð 1 bÞb

1

¼ n s1 c

1 K j C j ¼ n s1 c

K j C j

Nþ Nþ 1

1 ð 1 cÞb cb ð 1 bÞ½ 1 ð 1 cÞb cb

Therefore, we have the general multispecies multilayer adsorption isotherms.