**3.2 Adsorption thermodynamics**

108 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

probably due to less developed porous structure of this carbon. Large values of the Langmuir constant (*KL)* of ca. 75-140 (which are relative to the adsorption energy) implied a strong bonding on a finite number of binding sites. Langmuir constants (Table 4) slightly increased with temperature increase indicating an endothermic process of the Cr (III) adsorption on studied activated carbons. This observation could be attributed to the increasing an interaction between adsorbent and adsorbate at higher temperatures for the endothermic reactions (Kapoor & Viraraghavan, 1997). There were unfavourable data correlations (the negative values of *qmax* and *KL*) for the Langmure model application (Tabl. 4). It can be seen that the Langmuir model did not fit the adsorption run for the Norit oxidized sample, while it fitted it for the Merck oxidized carbon. Although the Langmuir isotherm model does not correspond to the ion-exchange phenomena, in the present study it was used for oxidized forms of carbon to evaluate their sorption capacity (*qmax*). According to the obtained results the oxidized Merck

A more general BET (Brunauer, Emmett and Teller) multi-layer model was also used to establish an appropriate correlation of the equilibrium data for the studied carbons. The model assumes the application of the Langmuir isotherm to each layer and no transmigration between layers. It also assumes equal adsorption energy for each layer except the first. It was shown, that in all cases, when Langmuir model failed, the BET model fitted the adsorption runs with better correlations, and an opposite, when Langmure model better correlated the equilibrium data, BET model was less applicable (c.f. the related parameters for the fitting of Langmuir and BET equations for parent Merck and oxidized Norit, Tabl. 4). Still, in some cases, BET isotherm could not fit the experimental data well (as pointed by the low correlation values) or not even suitable for the adsorption equilibrium expression (for instance, negative values of *KBET* Tabl. 4). From the obtained data, three limiting cases are distinguished: (i) when *Ceql* << *Cinit* and *KBET* >> 1, BET isotherm approaches Langmuir isotherm (*KL* = *KBET*/*Cinit*), it was the case of the parent Norit carbon; and (ii) when the constant *KBET* >> 1, the heat of adsorption of the very first monolayer is large compared to the condensation enthalpy and adsorption into the second layer only occurs once the first layer is completely filled, these were the cases of the Cr (III) adsorption by oxidized Merck and Norit carbons; (iii) when *KBET* is small, which was the case of the parent Merck carbon, then a multilayer adsorption already occurs while the first layer is still incomplete. In the last case that is most probably connected to the less developed porous

Based on the obtained results (Tabl. 4), the Freundlich model appeared to be the most "universal" to describe the equilibrium conditions in all studied adsorption systems over the entire range of temperatures. The linear relationships (*R2*~0.95-0.99) were observed among the plotted parameters at different temperatures for oxidized samples indicating the applicability of the Freundlich equation. The Cr (III) isotherms showed Freundlich characteristics with a slope of ~1 in a log–log representation for the oxidized Merck and Norit activated carbons. These values were in the range of ~0.2 for the parent Merck and Norit carbons; and 1*/n* was found to be more than 2.6 in the case of oxidized Norit carbon. Larger value of *n* (smaller value of 1/*n*) implies stronger interaction between adsorbent and adsorbate [39]. It is known that the values of 0.1<(1/*n*)<1.0 shows that adsorption of Cr (III) is favorable (Mckay et al., 1982) and the magnitude of (1/*n)* of to 1 indicates linear adsorption leading to identical adsorption energies for all (Weber & Morris, 1963). Freundlich constants (*K*F) related to adsorption capacity. In average, these values were in a

range of (2-9) and decreased by rising the temperature for all studied carbons.

carbon possessed the highest adsorbate uptake (c.f. *qmax* data, Tabl. 4).

structure of the parent Merck.

The adsorption process involves a solid phase (adsorbent) and a liquid phase containing a dissolved species (adsorptive) to be adsorbed (adsorbate). The affinity of the adsorbent for the adsorbate determines its distribution between the solid and liquid phases. When the sorption equilibrium is established, the adsorbate immobilized in the solid sorbent is in equilibrium with the residual concentration of adsorptive remaining in the liquid phase.

Fig. 5. Plots of ln [Cr III]uptake/[Cr III]eql) vs. [Cr III]uptake for the Cr(III) adsorption on modified by 1M HNO3 Merck activated carbon at () – 22; () – 30; () – 40 and () – 50 0C.

Comparison of the Thermodynamic Parameters Estimation for

(see Fig. 9 (IV) and 10 (IV)).

the Adsorption Process of the Metals from Liquid Phase on Activated Carbons 111

negative and decreased with the rise in temperature (Fig. 9 (II) and 10 (II)), which indicates that the process is spontaneous in nature is more favourable at higher temperatures. The entropy change (*ΔS0*) values were positive, that indicates a high randomness at the solid/liquid phase with some structural changes in the adsorbate and the adsorbent (Saha, 2011). This could be possible because the mobility of adsorbate ions/molecules in the solution increase with increase in temperature and that the affinity of adsorbate on the

the endothermic nature of the adsorption process, which fact was evidenced by the increase

an idea about the type of sorption. As far as physical adsorption is usually exothermic process and the heat evolved is of 2.1–20.9 kJ mol-1 (Saha 2011); while the heats of chemisorption is in a range of 80–200 kJ mol-1 (Saha 2011), and the enthalpy changes for ionexchange reactions are usually smaller than 8.4 kJ/mol (Nakajima & Sakaguchi, 1993), it is appears that sorption of Cr(III) on studied activated carbons is rather complex reaction. It has to be pointed out, that owing to different operating mechanisms for the Cr (III) adsorption on studied samples, given the *Kd* values are not vary linear with the temperature (see Fig. 8 (IV) and the regression coefficients in Tabl. 5) and hence applying of the van't Hoff type equation for the computation of the thermodynamic parameters for the adsorption on the studied carbons is not fully correct, especially in a case of parent carbons

Fig. 7. Plots of ln [Cr III]uptake/[Cr III]eql) vs. [Cr III]uptake for the Cr(III) adsorption by parent

On the other hand, Langmuir, Freundlich and BET constants showed similar variation with temperature (Fig. 8 (I), (II) and (III)), and hence were also used to calculate the

Merck activated carbon at () – 22; () – 30; () – 40 and () – 50 0C.

thermodynamic parameters (compare the *R2* for different calculations, Table 5).

*H*0 indicate

*H*0 may also give

adsorbent is higher at high temperatures (Saha, 2011). The positive values of

in the adsorption capacity with temperature (Tabl. 5). The magnitude of

The value for the apparent equilibrium constant (*Kd*) of the adsorption process of the Cr (III) in aqueous solution on studied activated carbons were calculated with respect to temperature using the method of [Khan and Singh] by plotting ln (*qeql/Ceql*) vs. *qeql* and extrapolating to zero *qeql* (Fig. 5, 6) and presented in Table. 4. In general, *Kd* values increased with temperature in the following range of the studied activated carbons: Merck\_initial < Norit\_initial < Norit\_ treated by 1M HNO3 < Merck\_treated by 1M HNO3 (Tabl. 4.). However, it should to be noted that in the case of the parent Norit and Merck activated carbons, the experimental data did not serve well for the apparent equilibrium constants calculation (as pointed by the low correlation values (*R2*) on Fig. 7).

Fig. 6. Plots of ln [Cr III]uptake/[Cr III]eql) vs. [Cr III]uptake for the Cr(III) adsorption on modified by 1M HNO3 Norit activated carbon at () – 22; () – 30; () – 40 and () – 50 0C.

As-depicted irregular pattern of linearised forms of [ln (*qeql/Ceql*) vs. *qeql*], (Fig. 7) are likely to be caused by less developed porous structure of the parent materials and their poor surface functionality, thus low adsorption and, consequently, by the pseudo-equilibrium conditions in the systems with parent activated Norit and Merck carbons.

Thermodynamic parameters for the adsorption were calculated from the variations of the thermodynamic equilibrium constant (*Kd*) by plotting of ln *Kd* vs. 1/*T*. Then the slope and intercept of the lines are used to determine the values of *H*0 and the equations (13) and (14) were applied to calculate the standard free energy change *G*0 and entropy change *S*0 with the temperature (Table 5).

Based on the results obtained using the thermodynamic equilibrium constant (*Kd*) some tentative conclusions can be given. The free energy of the process at all temperatures was

The value for the apparent equilibrium constant (*Kd*) of the adsorption process of the Cr (III) in aqueous solution on studied activated carbons were calculated with respect to temperature using the method of [Khan and Singh] by plotting ln (*qeql/Ceql*) vs. *qeql* and extrapolating to zero *qeql* (Fig. 5, 6) and presented in Table. 4. In general, *Kd* values increased with temperature in the following range of the studied activated carbons: Merck\_initial < Norit\_initial < Norit\_ treated by 1M HNO3 < Merck\_treated by 1M HNO3 (Tabl. 4.). However, it should to be noted that in the case of the parent Norit and Merck activated carbons, the experimental data did not serve well for the apparent equilibrium constants

calculation (as pointed by the low correlation values (*R2*) on Fig. 7).

Fig. 6. Plots of ln [Cr III]uptake/[Cr III]eql) vs. [Cr III]uptake for the Cr(III) adsorption on

in the systems with parent activated Norit and Merck carbons.

intercept of the lines are used to determine the values of

the temperature (Table 5).

were applied to calculate the standard free energy change

modified by 1M HNO3 Norit activated carbon at () – 22; () – 30; () – 40 and () – 50 0C. As-depicted irregular pattern of linearised forms of [ln (*qeql/Ceql*) vs. *qeql*], (Fig. 7) are likely to be caused by less developed porous structure of the parent materials and their poor surface functionality, thus low adsorption and, consequently, by the pseudo-equilibrium conditions

Thermodynamic parameters for the adsorption were calculated from the variations of the thermodynamic equilibrium constant (*Kd*) by plotting of ln *Kd* vs. 1/*T*. Then the slope and

Based on the results obtained using the thermodynamic equilibrium constant (*Kd*) some tentative conclusions can be given. The free energy of the process at all temperatures was

*H*0 and the equations (13) and (14)

*S*0 with

*G*0 and entropy change

negative and decreased with the rise in temperature (Fig. 9 (II) and 10 (II)), which indicates that the process is spontaneous in nature is more favourable at higher temperatures. The entropy change (*ΔS0*) values were positive, that indicates a high randomness at the solid/liquid phase with some structural changes in the adsorbate and the adsorbent (Saha, 2011). This could be possible because the mobility of adsorbate ions/molecules in the solution increase with increase in temperature and that the affinity of adsorbate on the adsorbent is higher at high temperatures (Saha, 2011). The positive values of *H*0 indicate the endothermic nature of the adsorption process, which fact was evidenced by the increase in the adsorption capacity with temperature (Tabl. 5). The magnitude of *H*0 may also give an idea about the type of sorption. As far as physical adsorption is usually exothermic process and the heat evolved is of 2.1–20.9 kJ mol-1 (Saha 2011); while the heats of chemisorption is in a range of 80–200 kJ mol-1 (Saha 2011), and the enthalpy changes for ionexchange reactions are usually smaller than 8.4 kJ/mol (Nakajima & Sakaguchi, 1993), it is appears that sorption of Cr(III) on studied activated carbons is rather complex reaction. It has to be pointed out, that owing to different operating mechanisms for the Cr (III) adsorption on studied samples, given the *Kd* values are not vary linear with the temperature (see Fig. 8 (IV) and the regression coefficients in Tabl. 5) and hence applying of the van't Hoff type equation for the computation of the thermodynamic parameters for the adsorption on the studied carbons is not fully correct, especially in a case of parent carbons (see Fig. 9 (IV) and 10 (IV)).

Fig. 7. Plots of ln [Cr III]uptake/[Cr III]eql) vs. [Cr III]uptake for the Cr(III) adsorption by parent Merck activated carbon at () – 22; () – 30; () – 40 and () – 50 0C.

On the other hand, Langmuir, Freundlich and BET constants showed similar variation with temperature (Fig. 8 (I), (II) and (III)), and hence were also used to calculate the thermodynamic parameters (compare the *R2* for different calculations, Table 5).


Table 5. Thermodynamic parameters of the Cr III adsorption on studied activated carbons at different temperatures

Comparison of the Thermodynamic Parameters Estimation for

the available surface sites are both responsible for the Cr (III) uptake.

tendency for physical adsorption mechanism.

The negative

at T > 40°C.

the vital basis.

**3.3 Isosteric heat of the adsorption** 

adsorbent surface [Cr III]eql, as shown in Fig. 13.

the Adsorption Process of the Metals from Liquid Phase on Activated Carbons 113

According to the calculation using (KL), (KF) and (KBET) constants (Tabl. 6), the free energy of the processes at all temperatures was negative and increased with the temperature rise (Fig. 9 (I), (II), (III) and Fig. 10 (I), (II), (III)), which indicates spontaneous in nature adsorption processes. While, an increase in the negative value of ΔG0 with temperature indicates that the adsorption process is more favorable at low temperatures indicating the typical

The overall process on oxidized carbons seems to be endothermic; whereas that on initial Norit and Merck activated carbons is more evident being exothermic, the negative values of H0 in the last case indicate that the product is energetically stable (Tabl. 6). Had the physisorption been the only adsorption process, the enthalpy of the system should have been exothermic. The result suggests that Cr (III) sorption on initial activated carbons is either physical adsorption nor simple ion-exchange reactions, whereas it on oxidized carbons is much more complicated process. Probably, the transport of metal ions through the particle solution interface into the porous carbon texture followed by the adsorption on

activated carbons that could be due to fixation of Cr (III) to the adsorption sites resulting in a decrease in the degree of freedom of the systems. In some cases of oxidized Merck carbon the entropy at all the temperatures positive and is slightly decreases with the temperature with an exception for 40°C. It means that with the temperature the ion-exchange and the replacement reactions have taken place resulted in creation of the steric hindrances (Helfferich, 1962) which is reflected in the increased values for entropy of the system, but at 50°C, these processes are completed and the system has returned to a stable form. Thus it can be concluded that physisorption occurs at a room temperature, ion-exchange and the replacement reactions start with the rise in the temperature and they became less important

Based on adsorption in-behind physical meaning, some general conclusions can be drawn. When the activated carbon is rich by surface oxygen functionality and has well developed porous structure, including mesopores, the evaluation of the thermodynamic parameters can be well presented by all of (*Kd*) (*KL*), (*KF*) and (*KBET*) constants. When similar, but more microporous carbon is used, the thermodynamic parameters is better to present by (*Kd*), (*KF*) and (*KBET*) constants. However, when the carbon has less developed structure and surface functionality, thermodynamic parameters is better to evaluate based on (*KL*) and (*KF*) constants. As a robust equation, Freundlich isotherm fits nearly all experimental adsorption data, and is especially excellent for highly heterogeneous carbons. Therefore (*KF*) constants can be used for the comparison of the calculated thermodynamic parameters for different activated carbons. However, predictive conclusions can be hardly drawn from systems operating at different conditions and proper analysis will require relevant model as one of

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

*S*0 value shows a greater order of reaction during the adsorption on initial

Table 5. Thermodynamic parameters of the Cr III adsorption on studied activated carbons at

different temperatures

According to the calculation using (KL), (KF) and (KBET) constants (Tabl. 6), the free energy of the processes at all temperatures was negative and increased with the temperature rise (Fig. 9 (I), (II), (III) and Fig. 10 (I), (II), (III)), which indicates spontaneous in nature adsorption processes. While, an increase in the negative value of ΔG0 with temperature indicates that the adsorption process is more favorable at low temperatures indicating the typical tendency for physical adsorption mechanism.

The overall process on oxidized carbons seems to be endothermic; whereas that on initial Norit and Merck activated carbons is more evident being exothermic, the negative values of H0 in the last case indicate that the product is energetically stable (Tabl. 6). Had the physisorption been the only adsorption process, the enthalpy of the system should have been exothermic. The result suggests that Cr (III) sorption on initial activated carbons is either physical adsorption nor simple ion-exchange reactions, whereas it on oxidized carbons is much more complicated process. Probably, the transport of metal ions through the particle solution interface into the porous carbon texture followed by the adsorption on the available surface sites are both responsible for the Cr (III) uptake.

The negative *S*0 value shows a greater order of reaction during the adsorption on initial activated carbons that could be due to fixation of Cr (III) to the adsorption sites resulting in a decrease in the degree of freedom of the systems. In some cases of oxidized Merck carbon the entropy at all the temperatures positive and is slightly decreases with the temperature with an exception for 40°C. It means that with the temperature the ion-exchange and the replacement reactions have taken place resulted in creation of the steric hindrances (Helfferich, 1962) which is reflected in the increased values for entropy of the system, but at 50°C, these processes are completed and the system has returned to a stable form. Thus it can be concluded that physisorption occurs at a room temperature, ion-exchange and the replacement reactions start with the rise in the temperature and they became less important at T > 40°C.

Based on adsorption in-behind physical meaning, some general conclusions can be drawn. When the activated carbon is rich by surface oxygen functionality and has well developed porous structure, including mesopores, the evaluation of the thermodynamic parameters can be well presented by all of (*Kd*) (*KL*), (*KF*) and (*KBET*) constants. When similar, but more microporous carbon is used, the thermodynamic parameters is better to present by (*Kd*), (*KF*) and (*KBET*) constants. However, when the carbon has less developed structure and surface functionality, thermodynamic parameters is better to evaluate based on (*KL*) and (*KF*) constants. As a robust equation, Freundlich isotherm fits nearly all experimental adsorption data, and is especially excellent for highly heterogeneous carbons. Therefore (*KF*) constants can be used for the comparison of the calculated thermodynamic parameters for different activated carbons. However, predictive conclusions can be hardly drawn from systems operating at different conditions and proper analysis will require relevant model as one of the vital basis.
