Biosorption of Organic Dyes: Research Opportunities and Challenges - Green Chemistry for Dyes Removal from Wastewater - page 320

The kinetic models of pseudo-first-order [138] and pseudo-second-order
[139] are based on the biosorption capacity. The pseudo-first-order model
(Equation 8.12) is generally applicable over the initial 20-30 min of the
sorption process, while the pseudo-second-order model (Equation 8.13) is
suitable for the whole range of contact time.

q q (1 exp(-k t)) (8.12)

t 1 1

t

(8.13)

q

t 2

(1/k q ) (t/q )

22 2

where k 1 and k 2 are the rate constants of pseudo-first-order and pseudo-
second-order models, respectively, in (min -1 ) and (g mg -1 min -1 ), q 1 and q 2
are the theoretical values for the biosorption capacity (mg g -1 ), and q t is the
biosorption capacity at any time t. The pseudo-first-order model was suit-
able to represent the biosorption of Reactive Black 5 onto chitosan beads
[143] and Reactive Blue 4 onto Bacillus subtilis [53]. he pseudo-second-
order model was suitable to represent the biosorption of basic dyes onto
wood apple shell [26], Methylene Blue onto peanut husk [27] and Congo
red onto cashew nut shell [144].
An alternative to the pseudo-first-order and pseudo-second-order
models is the general order model [13]. For this model, the biosorption
process on the surface of biosorbent is assumed to be a rate-controlling
step. The general order model can be described by Equation 8.14 [13,44]:

q

(8.14)

qq

n

t n

1/ n 1

n1

kq (n )1

nn

where q n is the biosorption capacity at the equilibrium (mg g -1 ), k n the rate
constant (min -1 (g mg -1 ) n-1 ) and n is the biosorption reaction order with
regard to the effective concentration of the biosorption sites available on
the surface of biosorbent. This model was adequate to represent the bio-
sorption of Reactive Red 120 onto Spirulina platensis [44].
When the biosorption processes occur through chemisorption on solid
surface, and the biosorption velocity decreases with time due to covering
of the superficial layer, the Elovich model is most used. The Elovich kinetic
model is described according to Equation 8.15 [140]:

1
a ln(1

(8.15)

q abt)

t