Biosorption of Organic Dyes: Research Opportunities and Challenges - Green Chemistry for Dyes Removal from Wastewater - page 318

By combining Equations 8.9 and 8.10, the known Equation 8.11 can be
obtained [132-135]:

0 0

H
RT

S
R

(8.11)

ln(K)

The plot of ln K against 1/T (van't Hoff plot) theoretically yields a straight
line that allows calculation of ΔH 0 and ΔS 0 from the respective slope and
interception of Equation 8.11 [132-135].
In biosorption systems, the values of ΔG 0 , ΔH 0 and ΔS 0 are employed
to obtain information about the process. The Gibbs energy change (ΔG 0 )
indicates the degree of spontaneity of a biosorption process, and a higher
negative value reflects a more energetically favorable biosorption [132].
In relation to ΔH 0 , negative values reflect exothermic processes and posi-
tive values reflect endothermic processes [19,23,35,90,135]. From the
magnitude of ΔH 0 it is possible to infer the biosorbent-dye interactions.
Physisorption, such as van der Waals interactions, are usually lower than
20 kJ mol -1 , and electrostatic interaction ranges from 20 to 80 kJ mol -1 .
Chemisorption bond strengths can be from 80-450 kJmol -1 [23]. Regarding
ΔS 0 , the negative valuesshow that the randomness decreases at the solid-
solution interface during the biosorption [9,12,13,43]. Positive values sug-
gest the possibility of some structural changes or readjustments in the
dye-biosorbent complex [136]. Furthermore, by comparing the values of
ΔH 0 and TΔS 0 it can be verified if the biosorption is an enthalpy-controlled
or an entropy-controlled process [69]. Table 8.6 shows typical values for
Gibbs free energy change (ΔG 0 ), enthalpy change (ΔH 0 ) and entropy
change (ΔS 0 ) in some biosorption systems.

8.4.3 Kinetic Models

Kinetic study is fundamental in biosorption systems. From kinetic analy-
sis, the solute uptake rate, which determines the residence time required
for completion of biosorption reaction, may be established [137]. This
study explains how fast the biosorption occurs and also provides informa-
tion on the factors affecting the process [13]. Furthermore, it is possible
to investigate the rate-controlling steps [12]. Several biosorption reaction
models and diffusional models have been used to study the biosorption
of SODs [9-13,23-35,37,44,45,60,67-69]. Among these models, the most
commonly used ones are the pseudo-first-order [138], pseudo-second-
order [139], general order [13], Elovich [140], Avrami [141] and Weber-
Morris [142].