**3.3 Isosteric heat of the adsorption**

The equilibrium concentration [Cr III]eql of the adsorptive in the solution at a constant [Cr III]uptake was obtained from the adsorption data at different temperatures (Fig. 1 - 4). Then isosteric heat of the adsorption *(ΔHx*) a was obtained from the slope of the plots of ln[Cr III]eql versus 1/T (Fig. 11, 12) and was plotted against the adsorbate concentration at the adsorbent surface [Cr III]eql, as shown in Fig. 13.

Comparison of the Thermodynamic Parameters Estimation for

the Adsorption Process of the Metals from Liquid Phase on Activated Carbons 115

Fig. 9. Plot of Gibb's free energy change (ΔG0) vs temperature, calculated on Langmuir (I); Freundlich (II), BET (III) and thermodynamic equilibrium (IV) constants for Cr(III)

adsorption on parent Norit () and Merck () activated carbons

Fig. 8. Plots of Langmuir (*K*F); Freundlich (*K*F), BET (*K*BET) and thermodynamic equilibrium constants (*K*d) *vs* temperature for the adsorption of Cr(III) on parent Norit () and Merck () and modified by 1M HNO3 Norit (▲) and Merck () activated carbons.

Fig. 8. Plots of Langmuir (*K*F); Freundlich (*K*F), BET (*K*BET) and thermodynamic equilibrium constants (*K*d) *vs* temperature for the adsorption of Cr(III) on parent Norit () and Merck

() and modified by 1M HNO3 Norit (▲) and Merck () activated carbons.

Fig. 9. Plot of Gibb's free energy change (ΔG0) vs temperature, calculated on Langmuir (I); Freundlich (II), BET (III) and thermodynamic equilibrium (IV) constants for Cr(III) adsorption on parent Norit () and Merck () activated carbons

Comparison of the Thermodynamic Parameters Estimation for

the combined chemical-physical adsorption processes.

() –0.22 mmol/g.

1M HNO3 Merck() forms.

the Adsorption Process of the Metals from Liquid Phase on Activated Carbons 117

Fig. 12. Plot of ln[Cr III]eql) vs 1/T, K-1, calculated for the parent Norit : at [Cr III]uptake () – 0.5; () – 0.4; (▲) – 0.26 mmol/g; and parent Merck: at [Cr III]eql () – 0.3; () –0. 26 and

The plots revealed that *(ΔHx*) is dependent on the loading of the sorbate, indicating that the adsorption sites are energetically heterogeneous towards Cr III adsorption. For oxidized by 1M HNO3 Norit and 1M HNO3 Merck activated carbons (Fig. 13), the isosteric heat of adsorption steadily increased with an increase in the surface coverage, suggesting the occurrence of positive lateral interactions between adsorbate molecules on the carbon surface (Do 1998). In contrary, for the parent Norit and Merck activated carbons (Fig. 13), the (*ΔHx*) is very high at low coverage and decreases sharply with an increase in [Cr III]uptake. It has been suggested that the high *(ΔHx*) values at low surface coverage are due to the existence of highly active sites on the carbon surface. The adsorbent–adsorbate interaction takes place initially at lower surface coverage resulting in high heats of adsorption. Then, increasing in the surface coverage gives rise to lower heats of the adsorption (Christmann, 2010). The magnitude of the (*ΔHx*) values ranged in 10-140 kJ mol-1 revealed that the adsorption mechanism for the studied activated carbons is complex and can be attributed to

Fig. 13. Plot of isosteric heating (*ΔHx*) as a function of the amount adsorbed of the parent Norit () and Merck () activated carbons and their oxidized by1M HNO3 Norit (▲) and

Fig. 10. Plot of Gibb's free energy change (ΔG0) vs temperature, calculated on Langmuir (I); Freundlich (II), BET (III) and thermodynamic equilibrium(IV) constants for Cr(III) adsorption on modified by by 1M HNO3 Norit (▲) and Merck () activated carbons

Fig. 11. Plot of ln[Cr III]eql) vs 1/T, K-1, calculated for the modified activated carbons 1M HNO3 Norit : at [Cr III]uptake () – 0.4; () – 0.3; (▲) – 0.2 mmol/g; and 1M HNO3 Merck: at [Cr III]eql () – 0.6; () –0. 4 and () –0.3 mmol/g.

Fig. 10. Plot of Gibb's free energy change (ΔG0) vs temperature, calculated on Langmuir (I); Freundlich (II), BET (III) and thermodynamic equilibrium(IV) constants for Cr(III)

adsorption on modified by by 1M HNO3 Norit (▲) and Merck () activated carbons

Fig. 11. Plot of ln[Cr III]eql) vs 1/T, K-1, calculated for the modified activated carbons 1M HNO3 Norit : at [Cr III]uptake () – 0.4; () – 0.3; (▲) – 0.2 mmol/g; and 1M HNO3 Merck: at

[Cr III]eql () – 0.6; () –0. 4 and () –0.3 mmol/g.

Fig. 12. Plot of ln[Cr III]eql) vs 1/T, K-1, calculated for the parent Norit : at [Cr III]uptake () – 0.5; () – 0.4; (▲) – 0.26 mmol/g; and parent Merck: at [Cr III]eql () – 0.3; () –0. 26 and () –0.22 mmol/g.

The plots revealed that *(ΔHx*) is dependent on the loading of the sorbate, indicating that the adsorption sites are energetically heterogeneous towards Cr III adsorption. For oxidized by 1M HNO3 Norit and 1M HNO3 Merck activated carbons (Fig. 13), the isosteric heat of adsorption steadily increased with an increase in the surface coverage, suggesting the occurrence of positive lateral interactions between adsorbate molecules on the carbon surface (Do 1998). In contrary, for the parent Norit and Merck activated carbons (Fig. 13), the (*ΔHx*) is very high at low coverage and decreases sharply with an increase in [Cr III]uptake. It has been suggested that the high *(ΔHx*) values at low surface coverage are due to the existence of highly active sites on the carbon surface. The adsorbent–adsorbate interaction takes place initially at lower surface coverage resulting in high heats of adsorption. Then, increasing in the surface coverage gives rise to lower heats of the adsorption (Christmann, 2010). The magnitude of the (*ΔHx*) values ranged in 10-140 kJ mol-1 revealed that the adsorption mechanism for the studied activated carbons is complex and can be attributed to the combined chemical-physical adsorption processes.

Fig. 13. Plot of isosteric heating (*ΔHx*) as a function of the amount adsorbed of the parent Norit () and Merck () activated carbons and their oxidized by1M HNO3 Norit (▲) and 1M HNO3 Merck() forms.

Comparison of the Thermodynamic Parameters Estimation for

applicable only to completed equilibration.

Vol.15, No1, pp. 39-56

*of Hazardous Materials,* Vol.87, pp. 127-137

*Biodeterioration and Biodegradation* Vol.40, pp. 63-74

*Materials*, Vol.141, pp. 77-85. ISSN: 0304-3894.

0021- 9614.

ISSN: 1385-8947.

Vol.15, pp. 1307-1316

*Carbon*, Vol.35, pp. 403-410

Research, Vol.34, No.10, pp. 3907-3916

**5. References** 

the Adsorption Process of the Metals from Liquid Phase on Activated Carbons 119

The thermodynamics parameters were evaluated using both the thermodynamic equilibrium constants and the Langmuir, Freundlich and BET constants. The obtained data were compared, when it was possible. Based on adsorption in-behind physical meaning general conclusions were drawn. However, it should be stressed, that the interpretation of the results presented here is tentative. The principal drawback of adsorption studies in a liquid phase is associated with the relatively low precision of the measurements and the long equilibration time that is requires. These factors imply that an extensive experimental effort is needed to obtain reliable adsorption data in sufficient quantity to allow evaluated the process thermodynamics. Therefore, the adsorption experiments are carried out either under pseudo-equilibrium condition when the actual time is chosen to accomplish the rapid adsorption step or under equilibrium condition when the contact time is chosen rather arbitrary to ensure that the saturation level of the carbon is reached. While, the adsorption models are all valid only and, therefore,

Anirudhan, T. & Radhakrishnan, P. (2011). Adsorptive Removal and Recovery of U(VI),

Anirudhan, T. & Radhakrishnan, P. (2008). Thermodynamics and Kinetics of Adsorption of

Ajmal, M.; Rao, R.; Ahmad, R.; Ahmad, J. & Rao, L. (2001). Removal and Recovery of Heavy

Araújo, M. & Teixeira, J. (1997). Trivalent Chromium Sorption on Alginate Beads. *Int.* 

Argun, M.; Dursun, S.; Ozdemir, C. & Karatas, M. (2007). Heavy Metal Adsorption by

Aydin, Y.A. & Aksoy, N.D. (2009). Adsorption of Chromium on Chitosan: Optimization,

Bailey, S.; Olin, T.; Bricka R. & Adrian D. (1999). A Review of Potentially Low-cost Sorbents

Brigatti, M.; Franchini, G.; Lugli, C.; Medici, L.; Poppi L. & Turci, E. (2000). Interaction

Brown, P.; Gill, S. & Allen, S. (2000). Metal Removal from Wastewater using Peat. Water

Carrott, P.; Ribeiro Carrott, M,; Nabais, J. & Prates Ramalho, J. (1997). Influence of Surface

for Heavy Metals. Water Research, Vol.33, No.11, pp. 2469-2479

Cu(II), Zn(II), and Co(II) from Water and Industry Effluents. *Bioremediation Journal*,

Cu(II) from Aqueous Solutions onto a New Cation Exchanger Derived from Tamarind Fruit Shell. *Journal of Chemical Thermodynamics*, Vol.40, pp. 702-709. ISSN:

Metals from Electroplating Wastewater by using Kyanite as an Adsorbent. *Journal* 

Modified Oak Sawdust: Thermodynamics and Kinetics. *Journal of Hazardous* 

Kinetics and Thermodynamics. *Chemical Engineering Journal*, Vol. 151, pp. 188-194.

between Aqueous Chromium Solutions and Layer Silicates. *Applied Geochemistry*,

Ionization on the Adsorption of Aqueous Zinc Species by Activated Carbons,

## **3.4 General remarks**

It should be stressed, however, that the interpretation of the results presented here is tentative. According to our previous investigation on the equilibrium for the studied systems at different pHs and at a room temperature there are both slow and fast Cr(III) uptakes by Norit and Merck carbons (Lyubchyk, 2005). The actual time to reach equilibrium is strongly depended on the initial and equilibrium pH of the solution, as well as on the surface functionality and material texture, and was varied between 0.5 and 3 months for different carbons at different pHs. The process did not appear to achieve equilibrium over the time interval used for the batch experiment of ca. 0.5-1 month, especially for the carbons reached by surface functionality (i.e. those modified by nitric acid), as well as for the all systems at moderated acidic pH values, i.e. pH 2 and 3.2. Thus, for the Norit and Merck carbons treated by 1 M HNO3 the chromium removal increased from 40–50 % to 55–65 % as the contact time is increased from 0.5 to 3 months at pH 3.2. At pH 3.2 the carbon's surface might have different affinities to the different species of chromium existing in the solution. Under real equilibrium conditions our results showed that studied Merck activated carbons adsorb Cr (III) from the aqueous solution more effective then corresponded Norit samples. It is related to the microporous texture of Norit carbons that could be inaccessible for large enough Cr (III) cations (due to their surrounded layers of adsorbed water).

This finding points out that the chosen current conditions for batch experiment at different temperatures could be out of the equilibrium conditions for the studied systems. Therefore current analysis of the thermodynamic parameters should be corrected taking into account the behaviors of the systems in complete equilibrium state.
