Multicomponent Equilibrium Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 93

where K Freun and 1 /n are empirically adjusted parameters. K Freun is an indicator of
the adsorption capacity and 1 /n is an indicator of the adsorption intensity. If n is 1,
there is no distinction between the Freundlich and linear adsorption isotherms.

E XAMPLE 3.18 U SE OF A DSORPTION I SOTHERMS TO A NALYZE E XPERIMENTAL
D ATA

Three important examples are chosen to illustrate the use of adsorption equations to
analyze experimental data in environmental engineering.
The first example is a solid-liquid system and is an important component in the
design of an activated carbon reactor for wastewater treatment. The requisite first step
is to obtain the isotherm data for a compound from aqueous solution onto granular
activated carbon (GAC) in batch shaker flasks. In these experiments, a known amount
of the pollutant is left in contact with a known weight of GAC under stirred conditions
for an extended period of time and the amount of pollutant left in the aqueous phase at
equilibrium is determined using chromatography or other methods. Dobbs and Cohen
(1980) produced extensive isotherm data at 298 K on a number of priority pollutants.
Consider the case of an insecticide (chlordane) on activated carbon.

Amount Adsorbed Equilibrium Aqueous-Phase

(mg/g Carbon) Concentration (mg/L)

87 0.132

79 0.061

64 0.026

53 0.0071

43 0.0032

31 0.0029

22 0.0021

18 0.0016

12 0.0006

11 0.0005

The molecular weight of chlordane is 409. Hence the above data can be divided by the
molecular weight to obtain Γ i in mol/g and C i in mol/L. Since it is not clear as to which
isotherm will best represent these data, we shall try both Langmuir and Freundlich
isotherms.
Figure 3.13a is a Langmuir plot of 1 / Γ I versus 1 /C i . The fit to the data at least in the
mid-region of the isotherm appears good, although at low 1 / Γ I the percent deviation is
considerable. The correlation coefficient ( r 2 ) is 0.944. The slope is 4.03 × 10 − 5 with a
standard error of 3.46 × 10 − 6 , and the intercept is 6655 with a standard error of 2992.
Hence, K Lang = 1.65 × 10 8 L/mol and Γ

i = 1.5 × 10 − 4 mol/g.
Figure 3.13b is a Freundlich plot of log Γ i versus log C i . The correlation coefficient
is ( r 2 ) 0.897. The intercept is − 1.0821 with a standard error of 0.112, and the slope is
0.381 with a standard error of 0.045. Hence K Freun = 0.0827 and 1 /n = 0.381.
Although r 2 appears to be better for the Langmuir plot, the errors involved in the esti-
mated slopes and intercepts are considerably larger. The adsorption isotherms obtained
from these parameters are shown in Figure 3.14. Both the isotherms fit the data rather
continued

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