Chemical Reactions on Solid Surfaces - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 403

Solution . This example is typical of adsorption experiments where the concentrations of
adsorbate (phenol in this example) are measured in the bulk fluid phase and in the adsorbent.
This is different from the coverage we have been discussed in Langmuir isotherm and the
nonideal isotherms. However, it is clear that

C As
C As N

q A ¼ (9.28)

where C As N is the concentration of adsorbate on the adsorbent surface when the concentra-

tion of the adsorbate in the bulk fluid phase is infinitely high, i.e. all the active sites on the
adsorbent surface are covered by the adsorbate. This quantity is a property of the adsorbent
and adsorbate pair and is not a function of temperature.
Substitute Eqn (9.27) into Eqn (9.9) , we obtain the Langmuir model

K A C A

C As ¼ q A C As N ¼ C As N (9.29)

1 þ K A C A

Therefore, we can fit the experimental data with Eqn (9.29) to check if the model can reason-
ably describe the experimental data. For this exercise, a spreadsheet program is convenient to
use as illustrated in Table E9-1.2 .
One can observe from Table E9-1.2 that the Langmuir model fit is consistent with the
experimental data: the errors or deviations are consistent with the errors apparent in the
experimental data. However, the fit is better at high coverage than the lower coverage
(concentrations). Fig. E9-1 shows the visual quality of the fit. Visual inspection of the data
shown in Fig. E9-1 agrees with our assessment based on Table E9-1.2. Furthermore, visual
inspection shows the data are scattered around the model (solid line). Therefore, the Lang-
muir model is consistent with experimental data within the experimental accuracy.

TABLE E9-1.2 Least Square Parameter Estimation for the Langmuir Isotherm. The Final Solution Shown
Are for C As N ¼ 178.1 mg-phenol/g-activated carbon and K A ¼ 0.21732 (mg/L) 1 , Which
Were Obtained by Minimizing the Variance between the Langmuir Model and the
Experimental Data, s L , While Changing C As N and K A

Error 2
(

Aqueous solution
C A , mg/L

On activated carbon
C

Eqn (9.29)
C As , mg/g C As LC 0 As ) 2 ' As , mg/g

0 0 0 0

1.5 53.0 43.78934 84.8362

2.0 62.4 53.96358 71.17314

5.1 82.8 93.63607 117.4205

6.6 105.0 104.9492 0.002578

22.9 137.0 148.3163 128.0591

51.6 172.2 163.5351 75.07994

80.2 170.9 168.4535 5.985588

s

P 8
i ¼

ðC As;i C 0 As;i Þ

2

1

s L ¼ ¼ 8 : 302814

8 1