**1. Introduction**

20 Will-be-set-by-IN-TECH

736 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

u*<sup>N</sup>* potential energy of N particles

X measurable thermodynamic quantity

Feynman, R. P.; Leghton, R. B. & Sands, M. (2006). *The Feynman lectures on physics*,Vol. 1,

Lucas K. (1991). *Applied Statistical Thermodynamics*, Springer-Verlag, ISBN 0-387-52007-4, New

Aziz, R.A. (1984). Interatomic Potentials for Rare-Gases: Pure and Mixed Interactions, In:

Slaviˇcek, P.; Kalus, R.; Paška, P.; Odvárková, I.; Hobza, P. & Malijevský, A. (2003).

Malijevský, Alexandr; Karlický, F.; Kalus, R. & Malijevský, A. (2007). Third Viral Coeffcients

Malijevský, A. & Kolafa, J. (2008). Introduction to the thermodynamics of Hard Spheres and

Hansen, J.-P. & McDonald, I. R. (2006). *Theory of Simple Fluids*, Elsevier, ISBN:

Martynov, G. A. (1992). *Fundamental Theory of Liquids*, Adam Hilger, ISBN: 0-7503-0069-8,

Malijevský, A. & Kolafa, J. (2008). Structure of Hard Spheres and Related Systems In: *Theory*

Kolafa, J.; Labík & Malijevský, A. (2002). The bridge function of hard spheres by direct

Baus, M.& Tejero, C., F. (2008). *Equilibrium Statistical Physics: Phases of Matter and Phase*

Ben-Naim, A. (2010). *Statistical Thermodynamics Based on Information: A Farewell to Entropy*,

Plischke, M. & Bergsen, B. (2006). *Equilibrium Statistical Physics*, University of British

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*Transitions*, Springer, ISBN: 978-3-540-74631-7, Heidelberg.

Columbia, Canada, ISBN: 978-981-256-048-3.

*and Simulation of Hard-Sphere Fluids and Related Systems* A. Mulero (Ed.) 1 - 26,

inversion of computer simulation data. *Molecular Physics*, 100, 16, 2629 - 2640, ISSN:

*Inert Gases* M. L. Klein (Ed.), 5 - 86, Springer-Verlag, ISBN 3-540-13128-0, Berlin,

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Related Systems In: *Theory and Simulation of Hard-Sphere Fluids and Related Systems* A. Mulero (Ed.) 27 - 36, Springer-Verlag, ISBN 978-3-540-78766-2, Berlin, Heidelberg. Labík, S.; Kolafa, J. & Malijevský, A. (2005). Virial coefficients of hard spheres and hard disks up to the ninth. *Physical Review E*, 71, 2-1, 021105/1-021105/8, ISSN:1539-3755. Allen, M. P. & Tildesley, D. J. (1987). *Computer Simulation of Liquids*, Claredon Press, ISBN:

W number of accessible states

*τ* time

W work

**11. References**

U internal energy

u pair potential

x mole fraction

Pearson, ISBN 0-8053-9046-4, San Francisco.

York, Berlin, Heidelberg.

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Adsorption is the term that used to describe the metallic or organic materials attaching to an solid adsorbent in low, medium and high coverage as shown in Figure 1. Wherein, the solid is called adsorbent, the metal ions to being adsorbed called adsorptive, and while bounded to the solid surfaces called adsorbate. In principle adsorption can occur at any solid fluid interface, for examples: (i) gas-solid interface (as in the adsorption of a CO2 on activated carbon); and (ii) liquid-solid interface (as in the adsorption of an organic or heavy metal ions pollutant on activated carbon).

Fig. 1. a) Low coverage (no attraction between adsorbate metal ion/ molecules, high mobility, disordered). b) Medium coverage (attraction between adsorbate metal ion / molecules, reduced mobility, disordered). c) High coverage (strong attraction between adsorbate atoms/ molecules, no mobility, highly ordered).

we talk about *Chemisorption* and/ or *Physisorption* processes. However, *the chemisorption* is a *chemical adsorption* in which the adsorption caused by the formation of chemical bonds between the surface of solids (adsorbent) and heavy metals (adsorbate). Therefore, the energy of chemisorption is considered like chemical reactions. It may be exothermic or endothermic processes ranging from very small to very large energy magnitudes. The elementary step in chemisorption often involves large activation energy (*activated adsorption*). This means that the true equilibrium may be achieved slowly. In addition, high

Thermodynamics Approach in the Adsorption of Heavy Metals 739

1. Transfer of adsorbate from bulk solution to adsorbent surface, which is

From the previous studies, it was shown that the rate-determining step for the adsorption of

Normally, the driving force for the adsorption process is the concentration difference between the adsorbate in the solution at any time and the adsorbate in the solution at equilibrium (C-Ce) [17]. but, there are some important factors affecting adsorption, such as

Larger surface area imply a greater adsorption capacity, for example, carbon and activated

Smaller particle sizes reduce internal diffusion and mass transfer limitation to penetrate of the adsorbate inside the adsorbent (i.e., equilibrium is more easily achieved and nearly full adsorption capability can be attained). Figure 2 represents the removal efficiency Fe3+ ions by natural zeolite through three different particle sizes (45, 125 and 250 m). It can be observed that the maximum adsorption efficiency is achieved with particle size 45 m. This is due to the most of the internal surface of such particles might be utilized for the adsorption. The smaller particle size gives higher adsorption rates, in which the Fe3+ ion has

> 0 50 100 150 200 250 300 **Size of JNZ, mm**

The longer residence time means the more complete the adsorption will be. Therefore, the required contact time for sorption to be completed is important to give insight into a sorption process. This also provides an information on the minimum time required for considerable adsorption to take place, and also the possible diffusion control mechanism

short path to transfer inside zeolite pores structure of the small particle size [19].

Fig. 2. Percent removal of Fe3+ ions (1000 ppm) *vs.* natural zeolite particle size: 1 g

adsorbent/ 50 ml Fe3+ ion solution, initial pH of 1% HNO3, and 300 rpm.

2. Migration of adsorbate (Fe3+ ion, where its ionic radius = 0.064 nm) into pores. 3. Interaction of Fe3+ ion with available sites on the interior surface of pores.

the factors affecting the adsorption of Fe3+ ions in the aqueous solution:

usuallymentioned as diffusion.

**2.1 Surface area of adsorbent** 

**2.2 Particle size of adsorbent** 

0 0.1 0.2 0.3 0.4 0.5 0.6

**2.3 Contact time or residence time** 

**The percent removal of Fe (III), %** 

Fe3+ ion is step (3).

carbon [18].

temperatures is favored for this type of adsorption, it increases with the increase of temperatures. For example, materials that contain silica aluminates or calcium oxide such as silica sand, kaolinite, bauxite, limestone, and aluminum oxide, were used as sorbents to capture heavy metals at high temperatures. The adsorption efficiency of the sorbents are inuenced by operating temperature [2-7]. Usually, the removal of the chemisorbed species from the surface may be possible only under extreme conditions of temperature or high vacuum, or by some suitable chemical treatment of the surface. In deed, the chemisorption process depends on the surface area [8]. It too increases with an increase of surface area because the adsorbed molecules are linked to the surface by valence bonds. Normally, the chemi-adsorbed material forms a layer over the surface, which is only one chemisorbed molecule thick, *i.e.* they will usually occupy certain *adsorption sites* on the surface, and the molecules are not considered free to move from one surface site to another [9]. When the surface is covered by the monomolecular layer (monolayer adsorption), the capacity of the adsorbent is essentially exhausted. In addition, this type of adsorption is irreversible [10], wherein the chemical nature of the adsorbent(s) may be altered by the surface dissociation or reaction in which the original species cannot be recovered *via* desorption process [11]. In general, the adsorption isotherms indicated two distinct types of adsorption—reversible (composed of both physisorption and weak chemisorption) and irreversible (strongly chemisorbed) [10-11].

On the other hand *Physisorption* is a physical adsorption involving intermolecular forces (Van der Waals forces), which do not involve a significant change in the electronic orbital patterns of the species [12]. The energy of interaction between the adsorbate and adsorbent has the same order of magnitude as, but is usually greater than the energy of condensation of the adsorptive. Therefore, no activation energy is needed. In this case, low temperature is favourable for the adsorption. Therefore, the *physisorption* decreases with increase temperatures [13]. In physical adsorption, equilibrium is established between the adsorbate and the fluid phase resulting multilayer adsorption. Physical adsorption is relatively non specic due to the operation of weak forces of attraction between molecules. The adsorbed molecule is not affixed to a particular site on the solid surface, but is free to move about over the surface. Physical adsorption is generally is reversible in nature*;* i.e., with a decrease in concentration the material is desorbed to the same extent that it was originally adsorbed [14]. In this case, the adsorbed species are chemically identical with those in the fluid phase, so that the chemical nature of the fluid is not altered by adsorption and subsequent desorption; as result, it is not specific in nature. In addition, the adsorbed material may condense and form several superimposed layers on the surface of the adsorbent [15].

Some times, both physisorption and chemisorption may occur on the surface at the same time, a layer of molecules may be physically adsorbed on a top of an underlying chemisorbed layer [16].

In summary, based on the different reversibility and specic of physical and chemical adsorption processes, thermal desorption of the adsorbed sorbent could provide important information for the study of adsorption mechanism.

### **2. Factors affecting adsorption**

In general, the adsorption reaction is known to proceed through the following three steps [16]:


From the previous studies, it was shown that the rate-determining step for the adsorption of Fe3+ ion is step (3).

Normally, the driving force for the adsorption process is the concentration difference between the adsorbate in the solution at any time and the adsorbate in the solution at equilibrium (C-Ce) [17]. but, there are some important factors affecting adsorption, such as the factors affecting the adsorption of Fe3+ ions in the aqueous solution:

### **2.1 Surface area of adsorbent**

738 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

temperatures is favored for this type of adsorption, it increases with the increase of temperatures. For example, materials that contain silica aluminates or calcium oxide such as silica sand, kaolinite, bauxite, limestone, and aluminum oxide, were used as sorbents to capture heavy metals at high temperatures. The adsorption efficiency of the sorbents are inuenced by operating temperature [2-7]. Usually, the removal of the chemisorbed species from the surface may be possible only under extreme conditions of temperature or high vacuum, or by some suitable chemical treatment of the surface. In deed, the chemisorption process depends on the surface area [8]. It too increases with an increase of surface area because the adsorbed molecules are linked to the surface by valence bonds. Normally, the chemi-adsorbed material forms a layer over the surface, which is only one chemisorbed molecule thick, *i.e.* they will usually occupy certain *adsorption sites* on the surface, and the molecules are not considered free to move from one surface site to another [9]. When the surface is covered by the monomolecular layer (monolayer adsorption), the capacity of the adsorbent is essentially exhausted. In addition, this type of adsorption is irreversible [10], wherein the chemical nature of the adsorbent(s) may be altered by the surface dissociation or reaction in which the original species cannot be recovered *via* desorption process [11]. In general, the adsorption isotherms indicated two distinct types of adsorption—reversible (composed of both physisorption and weak chemisorption) and irreversible (strongly

On the other hand *Physisorption* is a physical adsorption involving intermolecular forces (Van der Waals forces), which do not involve a significant change in the electronic orbital patterns of the species [12]. The energy of interaction between the adsorbate and adsorbent has the same order of magnitude as, but is usually greater than the energy of condensation of the adsorptive. Therefore, no activation energy is needed. In this case, low temperature is favourable for the adsorption. Therefore, the *physisorption* decreases with increase temperatures [13]. In physical adsorption, equilibrium is established between the adsorbate and the fluid phase resulting multilayer adsorption. Physical adsorption is relatively non specic due to the operation of weak forces of attraction between molecules. The adsorbed molecule is not affixed to a particular site on the solid surface, but is free to move about over the surface. Physical adsorption is generally is reversible in nature*;* i.e., with a decrease in concentration the material is desorbed to the same extent that it was originally adsorbed [14]. In this case, the adsorbed species are chemically identical with those in the fluid phase, so that the chemical nature of the fluid is not altered by adsorption and subsequent desorption; as result, it is not specific in nature. In addition, the adsorbed material may

condense and form several superimposed layers on the surface of the adsorbent [15].

Some times, both physisorption and chemisorption may occur on the surface at the same time, a layer of molecules may be physically adsorbed on a top of an underlying

In summary, based on the different reversibility and specic of physical and chemical adsorption processes, thermal desorption of the adsorbed sorbent could provide important

In general, the adsorption reaction is known to proceed through the following three steps

chemisorbed) [10-11].

chemisorbed layer [16].

[16]:

information for the study of adsorption mechanism.

**2. Factors affecting adsorption** 

Larger surface area imply a greater adsorption capacity, for example, carbon and activated carbon [18].
