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5 Recovery of Metals from Electronic Waste
Langmuir isotherm was originally derived from the adsorption of gas on activated
carbon. For a single-component metal adsorption system, the Langmuir isotherm is
as following [20]:
Q e =
Q max bC e
1 + bC e
(5.10)
where Q e is the equilibrium metal sorption capacity, Q max is the maximum sorption
capacity, C e is the equilibrium concentration of adsorbate in solution, and b is the
Langmuir adsorption equilibrium constant. For a multi-component metal adsorption
system containing k solutes, the equation is [20]:
Q i =
Q maxi b i C i
1 +
k
j=1 b j C j
(5.11)
In which Q i is the equilibrium metal sorption capacity of solute i, C i is the equilibrium concentration of adsorbate i in the solution, b i is the Langmuir adsorption
equilibrium constant for solute i (adsorbate) and Q maxi is the maximum sorption
capacity of solute i.
The Freundlich isotherm describes the adsorption on heterogeneous surfaces with
different affinities and is modeled as follows [20]:
Q e = KC
n
e
(5.12)
where K and n (0 < n < 1) are Freundlich constants representing the sorption capacity
and intensity, respectively. For multi-component metal adsorption system containing
k solutes, the equation can be modified to [20, 29]:
Q ei = K i C ei
⎛
⎝
k
j=1
a ij C j
⎞
⎠
n i−1
(5.13)
In which a ij is the competition coefficient (a ii = 1). For the multi-component
systems, there is also a general equation proposed by Fritz and Schluender to calculate
the adsorption equilibria of organic solutes in aqueous solutions [20, 30]:
Q ei =
b i0 C
ki0
i
D i +
k
j=1 b ij C
k ij
j
(5.14)
In a special case when k i0 = k ij = D i = 1, the equation is the same as the
Langmuir model for multi-component systems (Eq. 5.11).
5 Recovery of Metals from Electronic Waste
Langmuir isotherm was originally derived from the adsorption of gas on activated
carbon. For a single-component metal adsorption system, the Langmuir isotherm is
as following [20]:
Q e =
Q max bC e
1 + bC e
(5.10)
where Q e is the equilibrium metal sorption capacity, Q max is the maximum sorption
capacity, C e is the equilibrium concentration of adsorbate in solution, and b is the
Langmuir adsorption equilibrium constant. For a multi-component metal adsorption
system containing k solutes, the equation is [20]:
Q i =
Q maxi b i C i
1 +
k
j=1 b j C j
(5.11)
In which Q i is the equilibrium metal sorption capacity of solute i, C i is the equilibrium concentration of adsorbate i in the solution, b i is the Langmuir adsorption
equilibrium constant for solute i (adsorbate) and Q maxi is the maximum sorption
capacity of solute i.
The Freundlich isotherm describes the adsorption on heterogeneous surfaces with
different affinities and is modeled as follows [20]:
Q e = KC
n
e
(5.12)
where K and n (0 < n < 1) are Freundlich constants representing the sorption capacity
and intensity, respectively. For multi-component metal adsorption system containing
k solutes, the equation can be modified to [20, 29]:
Q ei = K i C ei
⎛
⎝
k
j=1
a ij C j
⎞
⎠
n i−1
(5.13)
In which a ij is the competition coefficient (a ii = 1). For the multi-component
systems, there is also a general equation proposed by Fritz and Schluender to calculate
the adsorption equilibria of organic solutes in aqueous solutions [20, 30]:
Q ei =
b i0 C
ki0
i
D i +
k
j=1 b ij C
k ij
j
(5.14)
In a special case when k i0 = k ij = D i = 1, the equation is the same as the
Langmuir model for multi-component systems (Eq. 5.11).