Biosorption of Organic Dyes: Research Opportunities and Challenges - Green Chemistry for Dyes Removal from Wastewater - page 317

The Tóth model was found from a modification of the Langmuir model
and suggests that the biosorption occurs via multilayer formation. This
model is given by Equation 8.8 [125]:

qC

(8.8)

mT e

q e

mT

1
k

mT

C

e

T

where q mT is the maximum biosorption capacity from the Tóth model
(mg g -1 ), k T is the Tóth constant (mg L -1 ) mT and m T is Tóth exponent. This
model was adequate to describe the biosorption of Methylene Blue and
Eriochrome Black onto Scolymus hispanicus L. [130].
The fit of these mathematical models on the biosorption isotherm curves
and the consequent determination of the adjustable isotherm parameters
are fundamental to know a biosorption process, since these can furnish
the following information: i) a equilibrium relation which can be used in
kinetic studies; ii) an idea about the biosorbent-dye interactions; iii) the
affinity between biosorbent and dye; iv) the maximum biosorption capacity
of the biosorbent in a specific condition; v) the amount of biosorbent which
should be used for the removal of a certain quantity of dye from an effluent;
vi) the influence of the experimental conditions on the equilibrium.

8.4.2 Thermodynamic Parameters

In the biosorption field, the thermodynamic is generally studied thought
the estimation of Gibbs free energy change (ΔG 0 , kJ mol -1 ), enthalpy change
(ΔH 0 , kJ mol -1 ) and entropy change (ΔS 0 , kJ mol -1 K -1 ) [6,16,19,43,44]. From
a thermodynamic viewpoint, the biosorption is considered as a uniphasic
reaction [12,13], and so the Gibbs free energy change can be estimated by
Equation 8.9 [131]:

0

(8.9)

G RTln(K)

where R is the universal gas constant (8.314 J mol −1 K −1 ), T the tem-
perature (K) and K thermodynamic equilibrium constant (dimension-
less) [132]. The K values are obtained in different ways in the literature
[23,35,43,90,92,102,113,132-135]. Detailed and consistent forms to obtain K
can be found in the works of Liu [132], Milonjic [133] and Zhou et al. [134].
The relationship of ΔG 0 to enthalpy change (ΔH 0 ) and entropy change
(ΔS 0 ) of biosorption is expressed in the form of Equation 8.10 [131]:

0 0 0

(8.10)

GHTS