Environmental Engineering Reference
In-Depth Information
h e pseudo-i rst-order and pseudo-second-order kinetic models are the
most well-liked models to study the adsorption kinetics of heavy metals
and quantify the extent of uptake in adsorption kinetics.
11.7.1.1
Pseudo-First-Order Kinetic Model
Lagergren's i rst-order rate expression based on solid capacity is generally
expressed as follows [99]:
dq
=
kq q
1
(
−
)
(11.5)
e
dt
where
q
and
q
e
are amounts of adsorbate adsorbed (mg/g) at time, t (min)
and at equilibrium, respectively,
k
1
is the rate constant of adsorption (l/
min). Integration of the above equation with the boundary conditions: t=0,
q=0, and t=t, q=q, gives
In (
qq qkt
−=
)
In
−
1
e
e
(11.6)
h is equation can be written in the linear form:
qq pkt
=−−
1
(1
(
) )
e
(11.7)
Kinetic adsorptions by numerous magnetic nanomaterials have been
studied using the pseudo-i rst-order kinetic model.
11.7.1.2 Pseudo-Second-Order Kinetic Model
Predicting the rate of adsorption for a given system is among the most
important factors in adsorption system design, as the system's kinetics
determine adsorbate residence time and the reactor dimensions [104]. As
previously noted, various factors govern the adsorption capacity, i.e., ini-
tial heavy metals concentration, temperature, pH of solution, nanoparticle
size, heavy metals nature; a kinetic model is only concerned with the ef ect
of observable parameters on the overall rate. h e pseudo-second-order
model is derived on the basis of the sorption capacity of the solid phase,
expressed as [105, 106, 107, 108]:
dq
kq q
dt
2
=
2
(
−
)
e
(11.8)
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