Environmental Engineering Reference
In-Depth Information
where
C
e
and
q
e
are equilibrium concentration of metal (mg/L) and
amount of solute adsorbed at equilibrium conditions (mg/g), respectively;
K
F
and
n
are the characteristic constant related to the adsorption capacity
(L/mg) and adsorption intensity or degree of favorability of adsorption,
respectively.
h e plot of log
q
e
versus log
C
e
has a slope with the value of 1/
n
and an
intercept magnitude of log
K
F
. Log
K
F
is equivalent to log
q
e
when
C
e
equals
unity. h ough, in other case when 1/
n ≠
1, the
K
F
value depends on the
units upon which
q
e
and
C
e
are expressed.
On average, a favorable adsorp-
tion tends to have Freundlich constant
n
between 1 and 10. A larger value
of
n
(smaller value of 1/
n
)
implies stronger interaction between adsorbent
and heavy metal,
while 1/
n
equal to 1 indicates linear adsorption leading
to identical
adsorption energies for all sites [104].
11.7.2.2 Langmuir Isotherm
h e Langmuir isotherm is a well-known model used for describing heavy
metal sorption onto magnetic nanoparticles. h e Langmuir equation
relates the coverage of molecules on a solid surface to concentration of
a medium above the solid surface at a i xed temperature. h is isotherm
is based on three assumptions, namely, adsorption is limited to mono-
layer coverage, all surface sites are alike and only can accommodate one
adsorbed atom, and the ability of a molecule to be adsorbed on a given site
is independent of its neighboring sites occupancy [104, 118]. By applying
these assumptions and a kinetic principle (rate of adsorption and desorp-
tion from the surface is equal), the Langmuir equation can be written in
the following form [119]:
KC
qq
KC
Le
=
(11.16)
e ax
1
+
Le
h e linear form of this equation is ot en written as [117]:
1
C
C
qq Kq
1
e
=
+
(11.17)
e
e ax
L ax
where
C
e
is equilibrium concentration of metal (mg/L) and
q
e
is the amount
of metal adsorbed at equilibrium conditions (mg/g),
q
max
is maximum
monolayer adsorption capacity (mg/g), and
K
L
is sorption equilibrium
constant (L/mg), which is related to the energy of adsorption. Within the
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