Journal of Surface Engineered Materials and Advanced Technology, 2011, 1, 30-34
doi:10.4236/jsemat.2011.12005 Published Online July 2011 (http://www.SciRP.org/journal/jsemat)
Modeling of Adsorptio n of Bi(III) from Nitrate
Medium by Impregnated Resin
D2EHPA/XAD-1180
Nasr-Eddine Belkhouche*, Nacera Benyahia
Laboratory of Separation and Purification Technologies, Department of Chemistry-Facult y of Sciences, Tlemcen University, Algeria.
Received April 6th, 2011; revised May 17th, 2011; accepted May 25th, 2011.
ABSTRACT
Di(2-ethylhexyl)phosphoric acid (D2EHPA) in acetone was supported on the Amberlite XAD-1180 polystyrene divinyl-
benzene copolymer resin. The use of XAD-1180 impregnated with D2EHPA for the extraction of bismuth(III) from ni-
trate medium was carried out using batch technique. Various parameters affecting the uptake of this metal ion were
described in the previous paper Reference [1] and the capacity of the impregnated resin for bismuth(III) was found to
be 490.7 mg/g of resin. Effect of temperature on the values of distribution equilibrium was studied to evaluate the
changes in standard thermodynamic quantities. A comparison of Langmuir forms I, II and Freundlich sorption iso-
therms was realized and the kinetic models applied to the adsorption rate data were evaluated for Lagergren first or-
der, the pseudo second order and Morris–Weber models. From the results, the adsorption of Bi(III) onto
D2EHPA/XAD-1180 resin shown the exothermic character and followed the Langmuir form II isotherm. Thus, the ca-
pacity of monolayer adsorption of Bi(III) was equal to 769.23 mg/g of resin. Both the Lagergren pseudo first order and
film-diffusion models were found to best describe the experimental rate data.
Keywords: Bismuth , XAD-1180 Resin, D2EHPA, Sorption Isotherms, Kinetic Models
1. Introduction
The previous paper [1] was devoted to study the kinetics
of bismuth(III) extraction from nitrate medium by sol-
vent impregnated resin technique (SIR) using the Am-
berlite XAD-1180 resin as support for di(2-ethylhexyl)
phosphoric acid (D2EHPA) as organophosphorus ex-
tractant, in order to know the best operating conditions of
later selective extraction from other metals such as lead,
copper and tin. The bismuth(III) was fixed at 490.7 mg/g
of XAD-1180 resin, at 295 K. The extractant impreg-
nated resin (EIR) of bismuth(III) was studied in function
of the experimental parameters such as: Amberlite XAD-
1180 impregnation, D2EHPA/XAD-1180 ratio, Contact
time and stirring speed, pH of Bi(III) solution, Concen-
tration of Bi(III), Aqueous phase volume, NaCl electro-
lyte and elution of Bi(III) from loaded EIR. The results
were used to determine the constants of polynomial
model which described the experimental data of bismuth
(III) extraction process.
In this present paper we are interested to study the
thermodynamic parameters of the distribution equili-
brium of Bi(III) sorption process for evaluated the
chan ges in sta ndard ther modyna mic quantities. The sor p-
tion isotherms such as: Langmuir forms I, II and Freun-
dlich were tested for exp eri mental data o f Bi(III ) sorptio n
onto D2EHPA/XAD-1180 resin. Also, the kinetics mod-
els as the Lagergren first order, the pseudo second order
and Morris–Weber were applied for modeling the ad-
sorptio n ra te data.
2. Results and Discussion
2.1. Effect of the Temperat ure
The study of the temperature effect on the bismuth(III)
sorptio n from nitrate mediu m onto 15 mmol of D2HPA/g
of X AD-1180 resin was carried out by using 250 ppm of
the concentration of metal ion at pH 3.6 with v/m ratio
equal to 50 ml/g.
The distribution coefficient (Kd) of metal ion between
the aqueous bulk phase and the resin phase was calcu-
lated from the Equation (1):

Modeling of Adsorption of Bi(III) from Nitrate Medium by Impregnated Resin D2EHPA/XAD-1180
31
0e
de
CCV
Kx
CM
−
=
(1)
Figure 1 shows the variation of the distribution coef-
ficient (Kd) of bismuth(III) sorption in function of dif-
ferent temperatures. From where, an increasing of the
temper ature from 22 to 60˚C decreased the adsorption of
the bismuth(III). The van’t Hoff relation [2] given by
Equation (2) can be used to calculate the enthalpy
changes associated with the adsorption process of the
bismuth(III).
0
1
log 2.303
d
H
KC
RT
∆
=− ×+
(2)
From the plots of Kd vs.
1T
(Figure 1), a straight
line was observed, from which ∆H0 (the enthalpy varia-
tion) can be deduced according to the Equation (3):
02,303HR Slope∆=−× (3)
The free energy variation, ∆G0 was also calculated
based on the logarithmic value of the distribution ratio
d
LogK
at 22˚C according to the Equation (4):
0
2.303
d
G RTLogK∆=−
(4)
Also, the entropy variation, ∆S 0 was obtained from
∆G0 and ∆H0 with the Equation (5 ):
HG
ST
∆°−∆ °
∆ °=
(5)
The thermodynamic parameters of the sorption of
bismuth (III) were given in Table 1 . The nega t ive sig n o f
the enthalpy variation value showed the exothermic cha-
racter of the liquid-solid extraction and sorption process.
This result is similar to the p revious pa per [3]. W hile the
negative sign of the free energy variation value
3.0 3.1 3.2 3.3 3.4
-1.5
-1.0
-0.5
0.0
0.5
logK
d
1/Tx10
3
, K
-1
Slope=4.75
R
2
=0.98
Figure 1. Variat ion of log Kd with 1/T for the sorption of B i
(III) ion from nitrate medium by D2EHPA/XAD-1180 resin.
Table 1. Thermodynamic parameters for the adsorption of
bismuth (III) from nitrate medium by D2EHPA/XAD-1180
resin.
Metal ion ΔH0 (kJ/mol) ΔG0 ( k J/ m ol ) ΔS0 ( J/ m ol ·K)
Values (KJ/mol) −91.01 −2.91 −298.64
indicated the spontaneous phenomenon of bismuth(III)
sorption and the value sign of the entropy variation sug-
gested that the system exhibit a disorde r .
As reported in literature [4], the p roc ess o f so lve nt i m-
pregnated resin (SIR) can be evaluated as film-diffusion
contr olled when Ea < 16.7 kJ/mol, particle d iffusion con-
trolled when Ea > 42 kJ/mol and reaction controlled
when Ea = 50.2 kJ/mol. The activation energy (Ea) of
sorption reaction of bismuth(III) by the XAD-1180 resin
i mpre gnated with D2EHPA was calculated by applying
the Arrhenius relation where Ea was be found to 1.14
kJ/mol which confirmed that the sorption was governed
by the film-diffusion.
2.2. Sorption Isotherm
The experimental results obtained for the adsorption of
bismuth(III) by D2EHPA impregnated onto XAD-4 resin
at temperature equal to 295 K under the optimum condi-
tions [1] were tested for Langmuir form I, II and Freun-
dlich adsorption isotherms. The Langmuir isotherm can
be written under the Eq uation (6) and Equation (7), form
I and II respectively as:
00
1
ee
e
CC
qbQ Q
= +
(Form I) (6)
00
111
ee
qbQ CQ
= +
(Form II) (7)
where
( )
0ee
V
qC Cx
M
= −
(8)
The Langmuir isotherms Form I and II for sorption of
bismuth (III) ions on the impregnated resin were pre-
sented in Figure 2 and Figure 3 respectively.
The representation of Langmuir isotherm form II for
experimental data of bismuth(III) sorption by D2EHPA
impregnated in XAD-1180 resin (Figure 3) showed a
good linear fitting (R2 = 0.99) compared with that given
in Figure 2. From where the fit of experimental data us-
ing Langmuir isotherm form I was equal to 0.92. Thus,
the sorption of Bi(III) onto D2EHPA impregnated in
XAD-1180 was expected as a monolayer adsorption and
that all active sites are similar and have the same energy
[5]. Parameters of Langmuir model form II are given in
Table 2.

Modeling of Adsorption of Bi(III) from Nitrate Medium by Impregnated Resin D2EHPA/XAD-1180
32
05001000 1500 2000 2500
1.0
1.2
1.4
1.6
1.8
2.0
2.2
R
2
=0.92
C
e
/q
e
, g /L
C e , mg /L
Figure 2. Langmuir isotherm (Form I) for sorption of
Bi(III) onto impregnated D2EHPA/XAD-1180 resin.
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0. 0
0. 1
0. 2
0. 3
1/ q
e
x10
2
, mg/g
1/ C
e
x10
2
, L /mg
Slope=0.11
R
2
=0.99
Figure 3. Langmuir isotherm (Form II) for sorption of
Bi(III) onto impregnated D2EHPA/XAD-1180 resin.
Table 2. Parameters of Langmuir isotherm for sorption of
Bismuth(III) by D2EHPA/XAD-1180 resin.
Metal ion Parameters of Langmu ir model form II
Q0 (mg/g) b( L/g)
Bi(III) 769.23 0.011
In fact, the f it of data usi ng the equation o f Freundlic h
isotherm was carried out. From the fitting factor (R2 =
0.97) which was lower than that the Langmuir isotherm,
we suggests that, the sorption process was restricted to
one specific class of sites and assumes surface homo-
geneity.
2.3. Kinetic Modeling
Several kinetic models were tested to select the model
that describes our exp e rimental da ta for establis hed to the
appropriate mechanism of sorption of Bi3+ by D2EHPA
impregnated onto XAD-1180 resin. The batch sorption
process of bismuth(III) was analyzed using Lagergren
first order and the pseudo second order kinetics model
[6,7]. T he equat ion of La gergre n was wide ly used in liq-
uid-solid extraction for sorption of solute from aqueous
or organic solution [3]. The Legergren first order model
was given by the Equation (9):
( )
1
loglog 2.303
et e
k
qq qt−= −
(9)
Fro m the results shown in Figure 4, linear fit was ob-
served for the metal ion, during t he first 30 min of sha k-
ing time, the first o rder rate constant ( k1) was fou nd to be
approximately 0.10 min−1. In fact, the experimental data
were analyzed using the Legergren pseudo second order
model but the data fitting was not better than the Le-
gergren pseudo first order which confirm that it’s appro-
priate to use this last mod el to predic t the sorption kinet-
ics of bismuth(III) ions onto D2EHPA impregnated in
XAD-1180 resin.
The diffusion of the particles from the bulk solution
into the sorbent po res can constitute a li miting step in the
process of bismuth(III) sorption by D2EHPA impreg-
nated in XAD -1180 resin. For this, the e xperimental data
were used to study intraparticle diffusion. The equation
of Morris–Weber model is given as Equation (10):
t ad
qKt=
(10)
As shown in Fig ure 5, multi-linearity correlation of
experimental data was obtained by plotting a graph of qt
vs. t0.5. From theory [8,9], the preliminary conclusions
indicated that the intraparticule diffusion cannot be in-
volved in the sorption process (linear plot, R2 = 0.95) and
was not the rate controlling step because the fit line no
pass through the origin.
In the way to verify the conclusions brought on the
rate controlling step of bismuth(III) sorption, the graphs:
[–Ln(1 – F)] = kt and [3-3(1 – F)2/3– 2F] = kt plotted in
04812 1620 2428
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
log(q
e
-q
t
)
t, min
Slope=4.33x10
-2
R
2
= 0.99
Figure 4. Legerg ren pseudo first order plot for the removal
of Bi(III) ion from nitrate solution by D2EHPA/XAD-1180.

Modeling of Adsorption of Bi(III) from Nitrate Medium by Impregnated Resin D2EHPA/XAD-1180
33
the cases of film-diffusion controlled and chemical reac-
tion controlled respectively [10,11].
Fro m the results shown in Figure 6 and Figure 7, the
2 3 4 5
110
115
120
125
qt, mg /g
t0.5, min0. 5
Figure 5. Morris–Weber plot for the adsorption of Bi(III)
ion from nitrate solution by D2EHPA/XA D-1180 resin.
05 10 15 20 25 30
2. 0
2. 5
3. 0
3. 5
4. 0
R
2
=0.99
-Ln(1-F)
t, min
Figure 6. Plot [–Ln(1 – F)] vs. time for the adsorption of
Bi(III) ion from nitrate solution by D2EHPA/XAD-1180
resin.
0510 152025 30
0. 5
0. 6
0. 7
0. 8
0. 9
R
2
=0.96
3-3(1-F)
2/3
-2F
t, min
Figure 7. Plot [3-3(1 − F)2/3 − 2F] vs. t i me f or t he a dso rption
of Bi(III) ion from nitrate solution by D2EHPA/XAD-1180
resin.
linear correlation of experimental data was better (R2 =
0.99) when plotting [–Ln(1 – F)] vs. time where the cor-
relation factor was equal to 0.95 in the case of the plot-
ting [3 – 3(1 – F)2/3 – 2F] vs. time. Thus, the film-diffu-
sion was the rate contro lling step o f bismuth(III) sorption
by impregnated resin D2EHPA/XAD-1180. This result
was similar to that found by the activation energy expla-
nation.
The calculation of the diffusion coefficient (Dr) was
given by the Equation (11) [10]:
2
02
π
r
r
Dk=
(11)
where, the diffusion coefficient was equal to 5.84·10-6
cm2·min−1.
3. Conclusions
The physical impregnation of D2EHPA in Amberlite
XAD-1180 resin for the Bi(III) sorption from aqueous
nitrate medium was carried in batch system. The ther-
modynamics values of extraction reaction of Bi(III)
shown the exothermic process where the activation
energy was be found to 1.14 kJ/mol. The equilibrium
isotherms for sorption of the investigated metal ion were
modeled successfully using the Langmuir isotherm
(Form II) where the sorption capacity of monolayer was
found equal to 769.23 mg/g of impregnated resin.
Also, the experimental data were tested for different
kinetic model expressions and the data were successfully
modeled using the Legergren pseudo first order where
the first order rate constant was found to be approx-
imately 0.1 min−1. Besides, the pushed studies on the
mechanism of the Bi(III) sorption showed that the rate
controlling step was the fim-diffusion and the coefficient
of diffusion was 5.84·10−6 cm2·min−1.
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Symbols
b: Constant related to the free energy of adsorption, b ∞
exp(−∆G/RT)
C: Co ns t ant
C0: Initial concentration of metal ion in solution, mg/L
Ce: Equilibrium concentration of metal ion in solution,
mg/L
F = qt/qe
k: Rate constant, min−1
k1: Pseudo first or der rate constant, min−1
Kad: Rate consta nt o f intraparti c le transport, mg/g min0.5
M: Weight of the adsorbent, g
Q0: Monolayer adsorption capacity, mg/g
qe: Amount of solute sorbed per unit weight of adsorbent
at equilibriu m, mg/g
qt: Conc entrat ion of ion in the adsorbent at time t, mg/g
R: Uni versal gas constant (8.314 J·mol−1·K−1)
r0: radius of particles of resin (0.024 cm)
T: Absolute tempe rature, Kel vin
V: Volume of bulk solution, L