Sesbania sesban L. biomass as a novel adsorbent for removal of Pb(II) ions from aqueous solution: non-linear and error analysis

2.1.1 Adsorbent:

Sesbanias sesban L. is a desert plant obtained from Sabha in Libya. The residues of its fruity part were ground and passed through 50–150 μm sieves, washed with distilled water until the filtrate was colorless, washed with acetone, and then finally dried in an electric oven at 60°C for 3 h.

2.1.2 Reagents:

Lead(II) acetate, cadmium(II) acetate, nickel(II) acetate, mercury(II) acetate, zinc(II) acetate, EDTA, sodium carbonate, acetic acid, and acetone were all used as laboratory grade chemicals (Merck, Germany).

2.2.1 Adsorption studies:

A known volume (100 ml) of a Pb(II) ion solution with a concentration in the range 100–1000 mg/l was placed in a 125 ml Erlenmeyer flask. An accurately weighed sample of S. sesban L. adsorbent (0.05 g) with a particle size in the range 50–150 μm was then added to the solution. A series of such flasks was prepared; the pH values of the contents adjusted by the addition of 0.1 m HNO₃ or 0.1 m Na₂CO₃ and then shaken at a constant speed of 150 rpm in a shaking water bath at 30°C for a known time length. At the end of the agitation time, the metal ion solutions were separated by filtration. Blank experiments were carried out simultaneously without the addition of the S. sesban L. adsorbent. The extent of metal ion adsorption onto the adsorbent was calculated mathematically by measuring the metal ion concentration before and after the adsorption through direct titration against the standard EDTA solution. The amount of Pb(II) adsorbed on S. sesban L. at equilibrium, q (mg/g), and percent removal of lead were calculated according to the following relationships:

where C_o and C_e are the initial and final concentrations of Pb(II), respectively, V is the volume of Pb(II) (l), and W is the weight of S. sesban L. adsorbent (g). The extent of Hg(II), Cd(II), Ni(II), and Zn(II) ion adsorption onto adsorbent was also measured by calculating the metal ion concentration before and after the adsorption through direct titration against the standard EDTA solution. All experiments were carried out in duplicate and the mean values of q_e were reported. Microsoft Office Excel and Excel solver softwares were used for kinetic and modeling calculations.

2.3.1 ARE:

2.3.2 APE:

2.3.3 ERRSQ:

2.3.4 HYBRID:

2.3.5 MPSD:

2.3.6 EABS

3.2.1 Effect of pH

The pH of the aqueous solution is an important controlling parameter in the adsorption process [12]. In the present work, the adsorption of Pb(II) onto the S. sesbanL. adsorbent was studied over the pH range of 2–4.5 for a constant adsorbent dose and constant concentration of adsorbate at 30°C. As the pH of the adsorption medium decreases, the extent of adsorption capacity, q_e, decreases (Figure 1). At high acidity, the S. sesban L. particle surface will be completely covered with H₃O⁺ ions, and Pb(II) ions would be able to compete with them for adsorption sites. With the increase in pH, the competing effect of hydronium ion decreases and the positively charged Pb(II) ions would adsorb on the free binding sites of the adsorbents. This is a common observation for all cases of adsorption of metal cations on the solid surface in media of different acidity and basicity [13]. It is also significant that the active sites on the S. sesban L. are weakly acidic in nature and with increasing pH, they are gradually deprotonated making available more and more sites for metal ion uptake [14]. At a pH value that is more than 4.5, the adsorption studied could not be carried out because metal ion will precipitate as lead hydroxide in this range.

Figure 1:

Effect of pH on the adsorption capacity of Pb(II) onto S. sesban L. at 30°C.

[Adsorption conditions employed: Pb(II) ion concentration, 300 mg/l; adsorbent concentration, 0.3 g/l; agitation time, 2 h; adsorption temperature, 30°C; particle size, 50–150 μm.]

3.2.2 Effect of adsorbent concentration (adsorbent dose)

The effect of adsorbent dose on both the adsorption capacity and the percentage removal of Pb(II)ions onto S. sesban L. were studied at pH 4.5 employing adsorbent doses within the range of 0.3–10 g/l and at a fixed initial metal ion concentration of 200 mg/l (Figure 2). It is clear from this figure that the percent removal of Pb(II) increases from 15.3% to 99.2% by increasing the concentration of adsorbent from 0.3 to 10 g/l. On the one hand, the increase in percent removal of Pb(II) with increasing adsorbent concentration could be attributed to the greater availability of the exchangeable sites of the adsorbent. On the other hand, the adsorption capacity (q_e), or the amount of Pb(II) adsorbed per unit mass of adsorbent (mg/g), decreases by increasing the concentration of adsorbent (Figure 2). The decrease in adsorption capacity with increasing adsorbent concentration is mainly due to the fact that the sorbent has high maximal adsorption capacity; furthermore, at tested Pb(II) concentration, when almost total and constant amount of Pb(II) is adsorbed, the adsorption capacity (q_e) decreases.

Figure 2:

Effect of sample dose on both adsorption capacity and % removal of Pb(II) onto S. sesban L. at 30°C.

[Adsorption conditions employed: Pb(II) ion concentration, 300 mg/l; pH, 4.5; agitation time, 2 h; adsorption temperature, 30°C; particle size, 50–150 μm.]

3.2.3 Effect of contact time

Figure 3 shows the effect of agitation time at various initial adsorbate concentrations on the adsorption capacity of S. sesban L. towards Pb(II) ions. As can be seen, the adsorption capacity increased with increasing agitation time and initial concentration of the adsorbate, remaining virtually constant after equilibrium had been attained. The time necessary to achieve equilibrium increased with increasing adsorbate concentration, being 30 and 60 min for adsorbate concentrations of 246.6 and 474.2 mg/l, respectively. This contact time, which is one of the parameters for economical wastewater treatment plant operations, is very small.

Figure 3:

Effect of contact time on adsorption capacity of Pb(II) onto S. sesban L. at 30°C.

[Adsorption conditions employed: Pb(II) ion concentrations, 247, 474 mg/l; pH, 4.5; adsorbent concentration, 0.3 g/l; adsorption temperature, 30°C; particle size, 50–150 μm.]

3.2.4 Effect of adsorbate concentration

3.2.4.1 Adsorption isotherm

Adsorption isotherm describes how adsorbates interact with adsorbents are critical in optimizing the use of adsorbents. The amount of adsorbate per unit mass of adsorbent at equilibrium, q_e (mg/g), and the adsorbate equilibrium concentration, C_e (mg/l), allows plotting the adsorption isotherm, q_e vs. C_e (Figure 4) at 30°C; here, mathematical models can be used to describe and characterize the adsorption process. The most common isotherms for describing solid-liquid sorption systems are two-parameter isotherms (Langmuir, Freundlich, Temkin, and Dubinin) and three-parameter isotherms (Redlich-Peterson isotherms, Toth, Sips, Khan, and Hill). Therefore, in order to investigate the adsorption capacity of Pb(II) onto S. sesban L., the experimental data were fitted to these equilibrium models.

Figure 4:

Equilibrium adsorption isotherm of Pb(II) onto S. sesban L. at 30°C.

[Adsorption conditions employed: pH, 4.5; adsorbent concentration, 0.3 g/l; adsorption temperature, 30°C; agitation time, 2h; particle size, 50–150 μm.]

3.2.4.1.1 Two parameter isotherms

The Langmuir model: Langmuir equation [15] was applied for adsorption equilibrium of Pb(II) by S. sesban L. This model is based on the assumption that the maximum adsorption corresponds to a saturated monolayer of adsorbate molecules on the adsorbent surface, and that the energy of adsorption is constant because there is no transmigration of adsorbate in the plane surface. The nonlinear form of Langmuir isotherm is given by the following equation:

(9)qe=KL.Ce1+aL.Ce, (9)

where a_L is Langmuir isotherm constant (l/mg), K_L is the Langmuir constant (l/g), and k_l/a_L represents the adsorption capacity, q_max (mg/g).

The Freundlich model: The Freundlich model [16] is a special case applied to non-ideal adsorption on heterogeneous surfaces and to multilayer adsorption, suggesting that binding sites are not equivalent and/or independent. This model is described by Eq. 10 as follows:

(10)qe=KF.Ce1/n, (10)

where q_e is the equilibrium concentration of Pb(II) on S. sesban L. adsorbent (mg/g), C_e is the equilibrium concentration of Pb(II)ions (mg/l), and K_F (mg/g) and n are the Freundlich constant characteristic of the system, which are the indicators of adsorption capacity and adsorption intensity, respectively.

The Temkin model: The Temkin isotherm [17] has been used in the following form:

(11)qe=RTbTln(ATCe), (11)

where R is the universal gas constant (8.31441 J^-1.mol^-1.K^-1), T is the absolute temperature (K), A_T is the Temkin isotherm constant (g/mg), and b_T is the Temkin constant.

Dubinin-Radushkevich model: This isotherm [18] is generally expressed as follows:

(12)qe=qD.exp(-BD[RT  ln(1+1Ce)]2) (12)

Dubinin-Radushkevich have reported that the characteristic sorption curve is related to the porous structure of the sorbent. The constant, B_D is, related to the mean free energy of sorption per mole of the sorbate as it is transferred to the surface of the solid from infinite distance in the solution. This energy can be computed using the following relationship by Hasany and Chaudhary [19]:

(13)E=12BD. (13)

3.2.4.1.2 Three-parameter isotherms

Redlich-Peterson model: The Redlich-Peterson model is used as a compromise between the Langmuir and Freundlich models, and is written as follows [20]:

(14)qe=A⋅Ce1+B⋅Ceg, (14)

where q_e is the amount of lead adsorbed (mg/g) at equilibrium, C_e(mg/l) is the concentration of adsorbate at equilibrium, and A (L/g) and B are the Redlich constants and gis exponent, respectively, which lie between 1 and 0.

Toth model: The Toth isotherm model [21] is useful in describing heterogeneous adsorption systems, which satisfy both the low and high-end boundaries of the concentration [22]. It can be represented by the following equation:

(15)qe=KtCe(at+Ce)1/t, (15)

where K_t, a_t, and t are the Toth isotherm constants.

Sips model: Sips isotherm [23] is a combined form of Langmuir and Freundlich expressions deduced for predicting the heterogeneous adsorption systems [24], and circumventing the limitation of the rising adsorbate concentration associated with the Freundlich isotherm model. The Sips model can be represented by the following equation:

(16)qe=KsCeBs1+as⋅CeBs, (16)

where K_s is the Sips model isotherm constant (L/g), a_s is the Sips model constant (L/mg), and B_s is the Sips model exponent. At low sorbate concentrations, it effectively reduces to the Freundlich isotherm and does not obey Henry’s law.

Khan model: Khan isotherm [25] is a generalized model suggested for the pure solutions, in which b_K and a_K are devoted to the model constant and model exponent, respectively. The Khan isotherm model can be represented as follows:

(17)qe=qk.bK.Ce(1+bK.Ce)aK, (17)

where b_k is the Khan model constant, a_k is the Khan model exponent, and q_k is the maximum uptake (mg/g). The maximum adsorption capacity, q_max, is considered to be the most important parameter for the comparison of adsorbents. The adsorption capacity values for Pb(II) obtained from the Langmuir isotherm model was found to be 303.03 mg/g. In comparison with other adsorbents reported in the literature for adsorption of Pb(II), the S. sesban L. biomass had a better affinity for removal of Pb(II) ions [2].

3.4.1 Pseudo-first-order model

The pseudo-first-order equation [26] is given by the following:

where q_t is the amount of adsorbate adsorbed at time t (mg/g), q_e is the adsorption capacity at equilibrium (mg/g), k is the pseudo-first-order rate constant (min^-1), and t is the contact time (min). By integrating Eq. (18) with the initial condition, q_t=0 at t=0, the following equation is obtained:

In order to obtain the rate constants, the straight line plot of log(q_e-q_t) against t for Pb(II) onto Sesbania sesban L. was tested. The intercept of this plot should give logq_e. However, if the intercept is not equal to q_e, the reaction is not likely to be first order even if this plot has high correlation coefficient (R²) with the experimental data [27]. For the data obtained in the present study, the plots of log(q_e-q_t) vs. t as required by Eq. 19 for the adsorption of Pb(II) at initial concentrations of 246.6 and 474.2 mg/l by S. sesban L. (figure not shown) give correlation coefficients, R², with low values. This indicates that the adsorption of Pb(II) onto S. sesban L. is not acceptable for this model.

3.4.2 Bhattacharya-Venkobachar model

The Bhattacharya-Venkobachar [28] equation is expressed as

where C_o, C_t, and C_e are the concentrations of Pb(II) (mg/l) at time zero, time t and at equilibrium time, and k is the first order rate constant (min^-1) for adsorption of Pb(II) onto S. sesban L. The R² values for the concentrations of 246.6 and 474.2 mg/l (figure not shown) are very low, indicating that the adsorption of Pb(II) onto S. sesban L. is not acceptable for this model.

3.4.3 Pseudo-second-order model

The pseudo-second-order model [27] is represented as follows:

where k₂ is the pseudo-second-order rate constant (g/mg.min). By integrating Eq. (21) with the initial condition, q_t=0 at t=0, the following equation is obtained:

where k₂ is the pseudo-second-order adsorption rate constant. This equation predicts that if the system follows pseudo-second-order kinetics, the plot of t/q_e vs. t should be linear. Plotting the experimental data obtained for the adsorption of Pb(II)at initial concentrations of 246.6 and 474.2 mg/l onto S. sesban L. according to the relationship given in Eq. (22) gives linear plots. The correlation coefficient values, R², are 0.977 and 0.999 for the initial concentrations of 246.6 and 474.2 mg/l, respectively (Figure 7 and Table 4), indicating the applicability of the pseudo-second-order kinetic equation to the experimental data. Given that the first-order and pseudo-second-order models cannot identify the diffusion mechanism, the kinetic results were then subjected to analysis using the intra-particle diffusion model.

Figure 7:

Pseudo-second order reaction of Pb(II) onto S. sesban L. at 30°C.

3.4.4 Bangham model

Bangham’s equation [29] was employed for applicability of adsorption of Pb(II) onto S. sesban L., whether the adsorption process is diffusion controlled. This is expressed as follows:

where C_o is initial concentration of adsorbate (mg/l), V is the volume of metal ion (ml), m is the weight of adsorbent used per liter of solution (g/l), q is the amount of adsorbate retained at time t (mg/g), and α(≺1) and k₀ are constants. The double logarithmic plot, according to Eq. 23, yields satisfactory linear curves for the adsorption of Pb(II) by S. sesban L. The R² values of 246.6 and 474.2 mg/l (figure not shown) are very low, indicating that the adsorption of Pb(II) onto S. sesban L. is not acceptable for this model.

3.4.5 Intra-particle diffusion

The intra-particle diffusion model [30] can be expressed by the following equation:

where k_p is the intra-particle diffusion rate constant (mg. g^-1.min^-1/2), and q_t is the amount of solute adsorbed per unit mass of adsorbent. The data of solid phase metal concentration against time t at the initial concentrations of 246.6 and 474.2 mg/l of Pb(II) were further processed in order to test the rate of diffusion in the adsorption process. Adsorption process incorporates the transport of adsorbate from the bulk solution to the interior surface of the pores in S. sesban L. The rate parameter for intra-particle diffusion, k_p, for the Pb(II)on S. sesban L. is measured according to Eq. 24. The plots of q_t vs. t^1/2for the Pb(II) concentrations of 246.6 and 474.2 mg/l is shown in Figure 8. As can be seen, the plot is curved at the initial portion followed by linear portion and plateau. The initial curved portion is attributed to the bulk diffusion and the linear portion to the intra-particle diffusion, while the plateau corresponds to the equilibrium. The deviation of straight lines from the origin (Figure 9) may be attributed to the difference between the rate of mass transfer in the initial and final stages of adsorption. Further, such deviation of straight line from the origin indicates that the pore diffusion is not the rate-controlling step [31]. The values of k_p (mg. g^-1.min^-1) obtained from the slope of the straight line (Figure 9) are listed in Table 4. The R² value for the initial concentrations of 246.6 and 474.2 mg/l are listed in Table 4. The value of intercept, C (Table 4), gives an idea about the boundary layer thickness, i.e., the larger the intercept, the greater the boundary layer effect [32]. This value indicates that the adsorption of Pb(II) onto S. sesban L. is acceptable for intra-particle diffusion mechanism.

Figure 8:

Intra-particle diffusion of Pb(II) onto S. sesban L. at concentrations of 246.5645 and 474.1625 mg/L.

Figure 9:

Test of intra-particle diffusion of Pb(II) onto Sesbania sesban L at concentrations of 246.5645 and 474.1625 mg/l.

3.4.6 Elovich equation

The Elovich model equation [33] is generally expressed as follows:

where α is the initial adsorption rate (mg/g.min), and β is the adsorption constant (g/mg) during the experiment. To simplify the Elovich equation, Chien and Clayton [33] assumed αβ≻≻1; by applying the boundary conditions q=0 at t=0 and q_t=q_t at t=t, Eq. 25 becomes

If Pb(II) adsorption onto S. sesban L. fits the Elovih model, a plot of q_e vs. ln(t) should yield a linear relationship with a slope of 1/β and an intercept of 1/βln(αβ). Figure 10 shows a plot of the linearization form of Elovich model at the Pb(II) concentrations of 246.6 and 474.2 mg/l. The slope and intercept of the plots of q_t vs. ln(t) were used to determine the constant β and the initial adsorption rate α. The R² values for the concentrations of 246.6 and 474.2 mg/l are listed in Table 4. The correlation coefficient values for the Elovich kinetic model obtained at the Pb(II) concentration of 246.6 and 474.2 mg/l are below 0.87, indicating that the adsorption of Pb(II) onto S. sesban L. is not acceptable for this model.

Figure 10:

Elovich model of Pb(II) onto S. sesban L. at 30°C.