Mathematical modeling of adsorption of Co2+ ions on sugarcane bagasse

6162 | P a g e DOI : 10.24297/jac.v%vi%i.6277 S e p t e m b e r 2 0 1 7 h t t p : / / c i r w o r l d . c o m Mathematical modeling of adsorption of Co2+ ions on sugarcane bagasse S.Elanza, H.Taouil, A. Amine, M. Doubi, A. Lebkiri, El. Rifi 1 Laboratory of Organic Synthesis and Process of Extraction, Faculty of Sciences, University Ibn Tofail, Kentia, Morocco. 2 Laboratory of Materials, Electrochemistry and Environment.Faculty of Sciences University Ibn Tofail kénitra Morocco 3 Laboratory of Analytical Chemistry and Physical Chemistry of Materials. Hassan II University of Casablanca 4 Laboratory of condensed matter and renewable energy. Faculty of Sciencesand Technology. Hassan II University. E-mail : elanza.said@hotmail.com Abstract

The process of adsorption can be divided into two mechanisms that can occur independently or simultaneously: -Physical adsorption is due to electromagnetic forces between molecules of the adsorbent and the adsorbate, often referred to as van deer Waals forces. These attractions lead to molecular condensation where substances adsorbed remain on the surface or are irreversibly bound [10].
-Chemical adsorption relies on a chemical bond which is stronger than a physical bond between the solid and the adsorbed species. This union leads to the release of heat and the formation on a monomolecular layer of the adsorbate [11]. The strong interaction produced can be irreversible.
In this work, we have modeled the experimental results obtained during the study of the adsorption of the metal ions Co 2+ by the sugarcane bagasse for approximate the nature of the adsorption [12].

2-1-Preparation of the adsorbent
The sugarcane bagasse is the residue which remains after the extraction of sugar contained in sugarcane; it was dried with the air, under the action of the solar rays, then crushed and tamised so as to obtain homogeneous materials for the experimental achievements, and the fraction of granularity of very low diameter.

Preparation of adsorbate
The metal solutions of cobalt are prepared by dissolving of the cobalt chloride salt hydrated (CoCl2, 3H2O) in distilled water. The pH of each solution was adjusted by hydrochloric acid (HCl) and the sodium hydroxide (NaOH).

2-2-1-First order kinetic
The first order kinetic model expressed by the Lagergren equation.

2-2-2-second order kinetic.
The kinetic model of second order is expressed by the equation of HO and MCKAY.
dq dt = k 2 (q e − q t ) 2 After integration between t = 0 and t, qt = 0 and qt we obtain the linear form: The course of the curve t/qt = f (t) gives a straight line with the slope equal 1/q e and intercept equal to 1 K 2 q e 2 k2 (g min-1mg-1): speed constant of the adsorption process of the second order.

2-2-2-3 Elovich model
The kinetic model of Elovich was also applied to the experimental results. This model is one of the most used models to verify and describe the adsorption of chemisorption.
The kinetic model of Elovich is expressed by the following equation.
The Elovich model is expressed by the equation.

= ( )
After integration this equation we obtain the linear form: The course of the curve qt = f (lnt) gives a straight line with the slope equal 1 and intercept equal to 1 ln .
The constant α (mg g -1 min -1 ) is the initial rate of adsorption and β (g mg -1 ) is the desorption constant related to the extent of surface coverage and activation energy for chemisorption.

2-3-1-Model of Freundlich.
The Freundlich model is based on the hypothesis of a heterogeneous surface of the adsorbent with an exponential distribution of the active sites as a function of the adsorption energies.
The Freundlich model is expressed by the following equation: The linear form of this model is given by the following equation:

lnqe  lnKF 1/n lnCe
The plot of the linear form lnqe = f (Ce) gives a line of slope 1 / n and the ordinate at the origin equal à lnKF.   qm is the quantity needed to cover the entire surface with a monolayer of adsorbed substance, and KL is the constant of Langmuir isotherm . RL is the Langmuir separation factor or the equilibrium parameter was used to give an indication on adsorption. 0 <RL <1, the adsorption is favorable, RL> 1 the adsorption is unfavorable, RL = 0 the adsorption is irreversible and RL = 1 the adsorption is linear.

2-3-2-Model of Langmuir
RL is terminated by the following relation: With Co (mg/g) is the initial concentration, and KL is the constant of Langmuir.

2-3-3-Model of Temkin.
The Temkin isotherm assumes that the decrease in heat of adsorption is linear and that the adsorption is characterized by a uniform distribution of binding energies. The Temkin model is expressed by the following equation:

Kinetic models of first and second order
The results of the study of the kinetic model of first and second order during the adsorption of the Co 2+ ions on the SCB are presented in fig 1 and fig 2. The results in this table show that the correlation coefficient R 2 given by the second order kinetic model is greater than the first order, also the binding capacity calculated at equilibrium (qcal) for the second order kinetic model is very close to the experimental binding capacity at equilibrium (qexp), therefore we can deduce that the extraction kinetics of Co 2+ by SCB is expressed by the second order kinetic.

Kinetic model of Elovich
The results of the study of the kinetic model of Elovich during the adsorption of the Co 2+ ions on the SCB are presented in fig 3.

Fig 3: Curve of the linear form of the kinetic model of Elovich
The table 2 gathers the correlation and the parameters kinetics of Elovich model.    Table 3 summarizes the parameters of the Freundlich model during the adsorption of the Co 2+ ions on the SCB. According to these results, it can be seen that the correlation coefficients R 2 are close to the unity, and 1/n < 1. Therefore the adsorption process is favorable and the surface of the SCB material is heterogeneous.

Model of Langmuir
The results of the study of the linear shape of the Langmuir model during the adsorption of the Co 2+ ions on the SCB are shown in fig 5.  The results obtained show that all the correlation coefficients R 2 are close to the unity, 0 < RL <1 and the calculated maximal fixing capacities (qm cal) are very close to the maximum experimental capacities (qm exp). Therefore, the adsorption process is favorable and the surface of the SCB material is heterogeneous.  The results of this table show that all the correlation coefficients R 2 are close to unity. Therefore, it can be concluded that the adsorption is monolayer and the distribution of the binding energies is uniform.

Thermodynamic study of the adsorption of Co 2+ on the SCB
The results of the thermodynamic study of the adsorption of Co   The results of the thermodynamic study of the adsorption of metal ions Co

Conclusion
The mathematical modeling of the adsorption of Co 2+ ions on sugarcane bagasse (SCB) was studied. The results obtained give the following conclusions:  The study of kinetic models shows that, the adsorption process is expressed by the second order kinetic law.  The study of the adsorption isotherm models show that, the adsorption process is favorable, chemisorption, monolayer, the surface of the SCB material is heterogeneous and the distribution of the binding energies is uniform.