 2.2. Batch equilibrium studies
Activated carbon (0.05 g) was added to the solutions of Pb(NO
_{3}
)
_{2}
with different initial concentrations. The mixture was stirred for 15 min at room temperature (25℃). The amount of remaining metal ions was determined using an atomic absorption spectrophotometer (ShimadzuJapan). The amount of Pb (II) adsorbed on the adsorbent at adsorption equilibrium was calculated according to the following Eq. (1)
where C
_{0}
and C
_{e}
(mg/L) are the initial and equilibrium Pb (II) concentrations, respectively. V is the volume of the solution (L) and W is the mass of adsorbent used (g).
In the order to study the effect of contact time between adsorbent and adsorbate, at first, we put 20 ppm of Pb (II) and 0.05 g of activated carbon in contact for 240 min; with this contact of 0.05 g of activated carbon, a maximum of adsorbtion took place in the first 15 min of contact.
To analyze the effect of initial Pb (II) concentration, at first we changed the concentration of Pb (II), in a range from 5 to 23 ppm. Then, we put the samples in contact with the adsorbent for 15 min; at this stage, maximum absorbtion in 20 ppm concentration of Pb (II) had taken place.
The effect of the pH on the metal adsorption for modified activated carbon was studied for pH 3, 4, 5, 6, 7, 8, 9, and 11, at which the material exhibits chemical stability.
The effect of activated carbon from walnut shells (ACW) dosage on the adsorption process was investigated by varying the sorbent dosage from 0.01 g1 g of Pb (II) solution. The experiment was conducted by measuring 20 ppm of Pb (II) solution. Appropriate dosage of the ACW was measured into the sample and sample was agitated for 15240 min.
 2.3. Isotherm modeling
According to the Langmuir model, adsorption occurs uniformly on the active sites of the adsorbent, and once an adsorbate occupies a site, no further adsorption can take place at this site. Thus, the Langmuir model is given by equation
[6]
.
where q
_{max}
and b, the Langmuir constants, are the saturated monolayer adsorption capacity and the adsorption equilibrium constant, respectively. A plot of C
_{e}
/q
_{e}
versus C
_{e}
would result in a straight line with a slope of (1/q
_{max}
) and intercept of 1/ bq
_{max}
The Langmuir parameters can be used to predict the affinity between the sorbate and the adsorbent using the dimensionless separation factor R
_{L}
:

The RLvalue indicates the shape of the isotherm, as follows[7]:

RL> 1 Unfavorable

RL=1 Linear

0

RL= 0 Irreversible
The Freundlich model stipulates that the ratio of solute adsorbed to the solute concentration is a function of the solution. The empirical model was shown to be consistent with an exponential distribution of active centers, characteristic of heterogeneous surfaces. The amount of Pb (II) adsorbed onto the modified ACW at equilibrium, qe, is related to the concentration of Pb (II) in the solution, C
_{e}
, following
[8]
:
This expression can be linearized to give
where K
_{f}
and n are the Freundlich constants, which represent adsorption capacity and adsorption intensity, respectively. A plot of lnqe versus lnC
_{e}
would result in a straight line with a slope of (1/n) and intercept of lnK
_{f}
.
The DubininRadushkevich (DR) isotherm was employed in the following linear form
[9]
:
The Polanyi potential ε, can be expressed as
The Temkin equation suggests a linear decrease of sorption energy as the degree of completion of the sorptional centers of an adsorbent is increased. The Temkin isotherm has been generally applied in the following form
[10
,
11]
:
where B=RT/b, R is the gas constant, b is the Temkin isotherm constant, T is the absolute temperature (K), and A is the Temkin isotherm constant (L/mg), Therefore, by plotting q
_{e}
versus ln C
_{e}
, one can determine the constants A and B.
3. Results and Discussion
 3.1. Adsorption isotherms
A list of the parameters obtained, together with the R
^{2}
values, is given in
Table 1
. The experimental results were analyzed by using Langmuir, Freundlich, Tempkin, and DR isotherm models. The correlation coefficients for the Langmuir and Tempkin equations fitted better than those of the Freundlich and DR equations for activated carbon modified by H
_{3}
PO
_{4}
; the correlation coefficients for the Langmuir and DR equations fitted better than those of the Freundlich and Tempkin equations for activated carbon modified by K
_{2}
CO
_{3}
. The experimental data indicate that the adsorption isotherms are well described by the
Comparison of the coefficients isotherm parameters for adsorption of Pb (II) onto activated carbon modified by H3PO4and K2CO3
Comparison of the coefficients isotherm parameters for adsorption of Pb (II) onto activated carbon modified by H_{3}PO_{4} and K_{2}CO_{3}
Langmuir isotherm equation and that the calculated adsorption capacity of activated carbon was 14.43 (mg/g) at 25℃ for activated carbon modified by H
_{3}
PO
_{4}
and 58.82 (mg/g) for activated carbon modified by K
_{2}
CO
_{3}
. Based on the data in
Table 1
, it is clear that the correlation coefficient R
^{2}
_{L}
is comparatively higher than R
^{2}
_{F}
, R
^{2}
_{T}
, and R
^{2}
_{(DR)}
. The value of R
_{L}
for the adsorption of Pb (II) with activated carbon modified by H
_{3}
PO
_{4}
was 0.282 and the value of R
_{L}
for the adsorption of Pb (II) with activated carbon modified by K
_{2}
CO
_{3}
was 0.039. These values indicate that the adsorption behavior of activated carbon was favorable.
 3.2. Adsorption kinetics
In order to elucidate the mechanisms and the possible rates of solute adsorption of solutions, different kinetic models have been applied.
The pseudo firstorder equation was presented by Lagergren
[9]
for the sorption of oxalic acid and malonic acid onto charcoal. Afterwards, many researchers reported first order Lagergern kinetics for adsorption of different pollutants on different sorbents
[13]
. The linearized form of the pseudo firstorder equation of Lagergren is generally expressed as follows
[14]
:
where q
_{t}
is the amount of Pb (II) adsorbed (mg/g) at time t, k
_{1}
is the equilibrium rate constant of the pseudofirst order kinetics (min
^{1}
), and t is the constant time (min). According to Eq. (9), the plots of
Ln
(
q_{e}
–
q_{t}
) vs. t for the adsorption of Pb (II) onto ACW were also tested in order to obtain the rate parameters.
The linearized form of the pseudo second order chemisorptions kinetic rate equation is presented below
[15

18]
:
where k
_{2}
(g/mg min) is the rate constant for the pseudo second order adsorption. The intercept and slope of
vs. t (
Figs. 1
and
2
) were used to calculate the pseudo second order rate constants k
_{2}
and q
_{e}
, respectively.
Fitting of pseudo second order model for Pb (II) on activated carbon modified by K_{2}CO_{3}.
Fitting of pseudo second order model for Pb (II) on activated carbon modified by H_{3}PO_{4}.
Effect of pH on the adsorption of Pb (II) on activated carbon modified by K_{2}CO_{3}.
The results obtained from these studies were analyzed by using pseudo first order and pseudo second order kinetic models. The calculated qe values agree very well with the experimental data; also, the correlation coefficients for the secondorder kinetic model are higher than 0.99 in all cases for activated carbon modified by K
_{2}
CO
_{3}
and H
_{3}
PO
_{4}
. These results indicate that the adsorption of acid dyes from wastewater onto activated carbon obeys the pseudo second order kinetic model.
 3.3. Effect of pH
The pH level of the aqueous solution is an important variable for the adsorption of metals onto the adsorbent. The effect of the pH on Pb (II) adsorption by activated carbon modified was studied for pH 3, 4, 5, 6, 7, 8, 9, and 11, at which the material exhibits chemical stability. The efficiency of Pb (II) sorption depends on the pH level of the aqueous solutions. The various influences of pH on the adsorption of Pb (II) onto modified activated carbon are shown in
Figs. 3
and
4
. It is apparent that using the solution at pH>1 gives the highest removal of Pb (II) on activated carbon modified by K
_{2}
CO
_{3}
. We can see that the adsorption capacity is low at pH<1 and that Pb (II) adsorption decreases with the pH decrease from 4 to 8
Effect of pH on the adsorption of Pb (II) on activated carbon modified by H_{3}PO_{4}.
The effect of the initial Pb (II)concentration.
Pb (II) on activated carbon modified by K
_{2}
CO
_{3}
. The amount of adsorbed Pb (II) is at its minimum rate at pH > 6 on activated carbon modified by H
_{3}
PO
_{4}
; the maximum adsorption capacities were calculated at pH = 5.
 3.4. Effect of contact time
The effect of contact time on the amount of Pb (II) adsorbed per gram of ACW by H
_{3}
PO
_{4}
and K
_{2}
CO
_{3}
was investigated. Equilibrium is reached after 15 min of immersion; the adsorption process is a relatively fast one.
The maximum adsorption, mentioned above, is due to the following factors:

1) Reduction of the weight of activated carbon

2) Reduction in the speed of pore development

3) Filling of pores during the activation time
 3.5. Effect of initial Pb (II) concentration
The effect of initial dye concentration has been studied and results are presented in
Fig. 5
. These results show the effect of the Pb (II) concentration on the adsorption of the different levels of Pb (II) at pH 5. The figure shows that the amount of Pb
Effect of adsorption dosage on adsorption Pb (II).
(II) adsorbed increases with increasing concentration and then tends to level off. The maximum milligrams per gram of Pb (II) adsorption is 8.23.
 3.6. Effect of sorbent dosage
Fig. 6
shows the effect of ACW according to H
_{3}
PO
_{4}
and K
_{2}
CO
_{3}
dose on the removal percentage of Pb (II). The effect of ACW dosage on the adsorption process was investigated by varying the sorbent dosage from 0.011 g of Pb (II) solution. The experiment was conducted by measuring 20 ppm of Pb (II) solution. The appropriate dosage of ACW was measured in and sample was agitated for 15240 min. Samples were withdrawn at fixed intervals and analyzed for residual Pb (II); the amount of sorbate sorbed per unit mass of the ACW was calculated by using the mass balance procedure.
4. Conclusions
Activated carbon adsorption of metallic ions (mainly Pb (II)), at levels similar to or even better than those obtained using commercial products, was performed by chemical activation of walnut shells.
The results show that as the amount of the adsorbent increased, the percentage of Pb (II) removal increased accordingly.
The optimum pH value for lead adsorption was determined to be 5. The maximum removal of Pb (II) was obtained at pH 5, at a level of 98.84% for activated carbon modified by H
_{3}
PO
_{4}
and 99.03% for activated carbon modified by K
_{2}
CO
_{3}
; the adsorbent dose was 0.05 g and the initial Pb (II) concentration at room temperature was 20 mg/L .
The experimental results were analyzed using Langmuir, Freundlich, Tempkin and DR isotherm models. The correlation coefficients for the Langmuir and Tempkin equations fitted better than those of the Freundlich and DR equations for the activated carbon modified by H
_{3}
PO
_{4}
and the correlation coefficients for Langmuir and DR equations fitted better than Freundlich and Tempkin equations for the activated carbon modified by K
_{2}
CO
_{3}
.
The results of this investigation show that activated carbon modified by H
_{3}
PO
_{4}
and K
_{2}
CO
_{3}
has a suitable adsorption capacity for the removal of Pb (II) from aqueous solutions.
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