Chemical Reactions on Solid Surfaces - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 424

Table E9-3.2 shows the results of fitting the Langmuir model, Eqn (E9-3.1) to the experi-
mental data. To show the visual appearance of the fit, Fig. E9-3.1 show the experimental
data (as circles) and the Langmuir model fit (as solid line). One can observe that the fit is
reasonably well. However, there is noticeable deviation at high surface coverage.
We next examine the quality fit for the bilayer isotherm as it was developed to accommo-
date high coverage cases. Eqn (9.55) can be rearranged to give

cap A =p A ð 2ap A =p A Þ

1 þ

C As ¼ C As1 N (E9-3.2)

þ cap A =p A ð þ ap A =p A Þ

1 1

Table E9-3.3 shows the results of fitting the Bi-layer isotherm model, Eqn (E9-3.2) to the
experimental data. Fig. E9-3.2 shows the experimental data (as circles) and the Bi-layer model
fit (as solid line). One can observe that the fit is reasonably well. The quality of fit showed
slight improvement over the Langmuir fit as the final variance is smaller and the curve
follows the data better. There is clear improvement in the high coverage area over the Lang-
muir fit as compared with Figs. E9-3.1 and E9-3.2 . However, there is a shift in the low surface
coverage area.
We now examine the quality fit can be achieved from the more general multilayer
isotherm. Eqn (9.72) can be rearranged to give

1 a 0 p A =p A Þ a 0 p A =p A Þ

N

1 þ Nð 1

C As ¼ C As1 N ca 0 p A

h 1

1 i

(E9-3.3)

p A

Nþ

a 0 p A =p A Þ cÞa 0 p A =p A cða 0 p A =p A Þ

ð 1 ð 1

Table E9-3.4 shows the results of fitting the general multilayer isotherm model, Eqn
(E9-3.3) to the experimental data. The parameters obtained are: N ¼ 6.947093;

40

30

20

10

0

0.0 0.2 0.4 0.6 0.8 1.0

Relative Humidity

FIGURE E9-3.1 Langmuir isotherm fit to water vapor adsorption on silica gel at 25 C.