**2.4.2 Thermodynamic parameters**

102 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

To determine which model (Scheme 2) to use to describe the adsorption isotherms for particular adsorbate/adsorbent systems, the experimental data were analyzed using

Scheme 2. Models presentation of the adsorption process (after Christmann 2010), where

The results of Cr (III) adsorbed on activated carbons were quantified by mass balance. To test the system at equilibrium, the following parameters were used: adsorption capacity of the carbon (*qeql*) expressed in terms of metal amount adsorbed on the unitary sorbent mass (mmol/g), i.e. ([*Cr III*]*uptake*); and sorption efficiency of the system (*R%*) indicated from the percentage of removed metal ions relative to the initial amount, i.e. [*CrRem*], %. These

( ) *init eql*

(6)

(7)

(9)

*m*

*C C*

( ) % <sup>100</sup> *init eql eql*

*C C*

*C*

where *Cinit* and *Ceql* are, respectively, the initial and equilibrium concentrations of metal ions

The data for the uptake of Cr (III) at different temperatures has been processed in accordance with the linearised form of the Freundlich [8], Langmuir [9] and BET [10]

 log *qeql* = log *K*F+1/*n* log *Ceql* (8) The Langmuir model linearization (a plot of *1/qeql* vs *1/Ceql* ) was expected to give a straight

> 1 11 1 *eql L eql q Kq C q*

max max

*eql*

*q*

*R*

symbol (*θ*) is the fraction of the surface sites occupied.

parameters have been calculated as indicated below [6, 7]:

in solution (mmol/l) and *m* is the carbon dosage (g/l).

For the Freundlich isotherm the log-log version was used [8]:

**2.4 Theoretical calculations 2.4.1 Isotherms analysis** 

isotherm equations.

line with intercept of *1/qmax* [9]:

model's linearization.

Thermodynamic parameters such as change in Gibb's free energy *G*0, enthalpy *H*0 and entropy *S*0 were determined using the following equation [11]:

$$K\_d = \frac{q\_{eql}}{\mathcal{C}\_{eql}} \tag{11}$$

where *Kd* is the apparent equilibrium constant, *qeql* (or [*Cr III*]*uptake*); is the amount of metal adsorbed on the unitary sorbent mass (mmol/g) at equilibrium and *Ceql* (or [*Cr III*]*eql*) equilibrium concentrations of metal ions in solution (mmol/l), when amount adsorbed is equals *qeql*;

*eql eql q <sup>C</sup>* - relationship depends on the type of the adsorption that occurs, i.e. multi-layer,

chemical, physical adsorption, etc.

The thermodynamic equilibrium constants (*Kd*) of the Cr III adsorption on studied activated carbons were calculated by the method suggested by (Khan and Singh, 1987) from the intercept of the plots of ln (*qeql/Ceql*) vs*. qeql*

Then, the standard free energy change *G*0, enthalpy change *H*0 and entropy change *S*<sup>0</sup> were calculated from the Van't-Hoff equation [12].

$$
\Delta G^{0=-RT} \ln K\_{d\_1} \tag{12}
$$

where *Kd* is the apparent equilibrium constant; *T* is the temperature in Kelvin and R is the gas constant (8.314 Jmol-1K-1):

The slope and intercept of the Van't-Hoff plot [13] of ln *Kd* vs. *1/T* were used to determine the values of *H*0 and *S*0,

$$
\ln K\_d = \left(\frac{-\Delta H^\circ}{R}\right)\frac{1}{T} + \frac{\Delta S^\circ}{R} \tag{13}
$$

Then, the influence of the temperature on the system entropy was evaluated using the equations [14]

$$
\Delta \mathbf{G} \mathbf{0} = \Delta \mathbf{H} \mathbf{0} \text{--} T \Delta \mathbf{S} \mathbf{0} \tag{14}
$$

The thermodynamic parameters of the adsorption were also calculated by using the Langmuir constant *(KL*), Freundlich constants (*KF*) and the BET constant (*KBET*) for the

Comparison of the Thermodynamic Parameters Estimation for

or another of the adsorption systems only.

the Adsorption Process of the Metals from Liquid Phase on Activated Carbons 105

entire range of temperatures, when the Langmuir and BET models were appropriate for one

Fig. 1. Isotherms of the Cr (III) adsorption on modified by 1M HNO3 Norit activated carbon

Fig. 2. Isotherms of the Cr (III) adsorption on modified by 1M HNO3 Merck activated carbon

at different temperatures: () – 22; () – 30; () – 40 and () – 50 0C.

at different temperatures: () – 22; () – 30; () – 40 and () – 50 0C.

equations [12–14] instead of (*Kd*). The obtained data on thermodynamic parameters were compared, when it was possible.

The differential isosteric heat of adsorption (*Hx*) at constant surface coverage was calculated using the Clausius-Clapeyron equation [15]:

$$\frac{d\ln(\mathcal{C}\_{eq})}{dT} = -\frac{\Delta H\_x}{RT^2} \tag{15}$$

Integration gives the following equation [16]:

$$\ln(\mathbf{C}\_{eq}) = -\left[\frac{\Delta H\_{\text{x}}}{R}\right]\frac{\mathbf{1}}{T} + \mathbf{K} \tag{16}$$

where *K* is a constant.

The differential isosteric heat of adsorption was calculated from the slope of the plot of ln(*Ceql*) vs 1/*T* and was used for an indication of the adsorbent surface heterogeneity. For this purpose, the equilibrium concentration (C*eql*) at constant amount of adsorbate adsorbed was obtained from the adsorption isotherm data at different temperatures according to (Saha & Chowdhury, 2011).

### **3. Results and discussion**

#### **3.1 Adsorption isotherms**

The equilibrium measurements focused on the determination of the adsorption isotherms. Figures 1–4 show the relationship between the amounts of chromium adsorbed per unit mass of carbon, i.e. [Cr(III)uptake] in mmol/g, and its equilibrium concentration in the solution, i.e. [Cr(III)elq] in mmol/l, at the temperatures of 22, 30, 40 and 50 0C. The carbon adsorption capacity improved with temperature and gets the maximum at 40 0C in the case of the oxidized Norit and Merck carbons and slightly improved with temperature in the case of the parent Norit and Merck activated carbons. The isotherms showed two different shapes. There are isotherms of type III (Fig. 1, 2) for the oxidized samples and of type IV (Fig. 3, 4) for the parent Norit and Merck carbons. Therefore in all cases, the adosrption of the polar molecules (like Cr III solution) on unpolar surface (like the studied activated carbons) is characterized by initially rather repulsive interactions leading to a reduced uptake (Fig. 1, 2), while the increasing presence of adsorbate molecules facilitate the ongoing adsorption leading to isotherms of type III. Furthermore, the porous adsorbents are used and additional capillary condensation effects appeared leading to isotherms of type IV (Fig. 3, 4).

Batch adsorption thermodynamics was described by the three classic empirical models of Freundlich (Eq. 8), Langmuir (Eq. 9) and BET (Eq.10). Regression analysis of the linearised isotherms of Freundlich (log *qeql* vs log *Ceql*) and Langmuir (1/*qeql* vs 1/*Ceql*) and

( ( ) *eql eql init eql eql init C C vs C Cq C* ) using the slope and the intercept of the obtained straight line

gave the sorption constants (*K*F ,1*/n* and *K*L, *K*BET*, qma*x). The related parameters for the fitting of Freundlich, Langmuir and BET equations and correlation coefficients (*R*2) at different temperatures are summarized in Tables 4.

Based on the results, we can concluded that the Freundlich model appeared to be the most "universal" to describe the equilibrium conditions for all studied activated carbons over the

equations [12–14] instead of (*Kd*). The obtained data on thermodynamic parameters were

ln( ) *eql <sup>x</sup> d C H dT RT*

<sup>1</sup> ln( ) *<sup>x</sup>*

*<sup>H</sup> C K R T* 

The differential isosteric heat of adsorption was calculated from the slope of the plot of ln(*Ceql*) vs 1/*T* and was used for an indication of the adsorbent surface heterogeneity. For this purpose, the equilibrium concentration (C*eql*) at constant amount of adsorbate adsorbed was obtained from the adsorption isotherm data at different temperatures according to

The equilibrium measurements focused on the determination of the adsorption isotherms. Figures 1–4 show the relationship between the amounts of chromium adsorbed per unit mass of carbon, i.e. [Cr(III)uptake] in mmol/g, and its equilibrium concentration in the solution, i.e. [Cr(III)elq] in mmol/l, at the temperatures of 22, 30, 40 and 50 0C. The carbon adsorption capacity improved with temperature and gets the maximum at 40 0C in the case of the oxidized Norit and Merck carbons and slightly improved with temperature in the case of the parent Norit and Merck activated carbons. The isotherms showed two different shapes. There are isotherms of type III (Fig. 1, 2) for the oxidized samples and of type IV (Fig. 3, 4) for the parent Norit and Merck carbons. Therefore in all cases, the adosrption of the polar molecules (like Cr III solution) on unpolar surface (like the studied activated carbons) is characterized by initially rather repulsive interactions leading to a reduced uptake (Fig. 1, 2), while the increasing presence of adsorbate molecules facilitate the ongoing adsorption leading to isotherms of type III. Furthermore, the porous adsorbents are used and additional capillary

Batch adsorption thermodynamics was described by the three classic empirical models of Freundlich (Eq. 8), Langmuir (Eq. 9) and BET (Eq.10). Regression analysis of the linearised isotherms of Freundlich (log *qeql* vs log *Ceql*) and Langmuir (1/*qeql* vs 1/*Ceql*) and

gave the sorption constants (*K*F ,1*/n* and *K*L, *K*BET*, qma*x). The related parameters for the fitting of Freundlich, Langmuir and BET equations and correlation coefficients (*R*2) at different

Based on the results, we can concluded that the Freundlich model appeared to be the most "universal" to describe the equilibrium conditions for all studied activated carbons over the

) using the slope and the intercept of the obtained straight line

*eql*

condensation effects appeared leading to isotherms of type IV (Fig. 3, 4).

2

*Hx*) at constant surface coverage was

(15)

(16)

compared, when it was possible.

where *K* is a constant.

( ( )

 

*eql eql init eql eql init C C vs*

temperatures are summarized in Tables 4.

*C Cq C*

(Saha & Chowdhury, 2011).

**3. Results and discussion 3.1 Adsorption isotherms** 

The differential isosteric heat of adsorption (

Integration gives the following equation [16]:

calculated using the Clausius-Clapeyron equation [15]:

entire range of temperatures, when the Langmuir and BET models were appropriate for one or another of the adsorption systems only.

Fig. 1. Isotherms of the Cr (III) adsorption on modified by 1M HNO3 Norit activated carbon at different temperatures: () – 22; () – 30; () – 40 and () – 50 0C.

Fig. 2. Isotherms of the Cr (III) adsorption on modified by 1M HNO3 Merck activated carbon at different temperatures: () – 22; () – 30; () – 40 and () – 50 0C.

Comparison of the Thermodynamic Parameters Estimation for

Langmuir constants Freundlich

mmol/g *<sup>K</sup>*L,l/mmol *R2 <sup>K</sup>*F,

T,

<sup>22</sup>1M HNO3

<sup>30</sup>1M HNO3

<sup>40</sup>1M HNO3

<sup>50</sup>1M HNO3

<sup>22</sup>1M HNO3

<sup>30</sup>1M HNO3

<sup>40</sup>1M HNO3

<sup>50</sup>1M HNO3

<sup>22</sup>1M HNO3

<sup>22</sup>1M HNO3

temperatures

0C *R2 <sup>q</sup>*max,

the Adsorption Process of the Metals from Liquid Phase on Activated Carbons 107

Fixed [Cr III] = 200 ppm, pH3.2 Merck 22 Initial 0.7671 0.1290 75.9837 0.9795 10.6608 0.78360.9641 0.1197 9.1498 0.0945 4.701 30 Initial 0.7921 0.2617 138.7455 0.5253 3.9487 0.05080.9608 0.1092 3.4681 0.1976 6.688 40 Initial 0.7711 0.3332 23.7812 0.6158 3.2485 0.13510.9443 0.1164 -16.8765 0.2040 5.445 50 Initial 0.7730 0.3027 4.2890 0.6773 4.2274 0.17480.8825 0.0997 -9.3369 0.1677 4.754

0.9877 -3.7564 -0.0466 0.9898 5.4386 1.07560.9214 0.3525 3.1462 0,9630 3.9361

0.9606 2.3453 0.1021 0.9595 4.7632 1.22350.6241 0.3164 2.5019 0.9717 4.7063

0.9042 2.1961 0.2201 0.9671 2.5448 1.01750.5632 0.5651 2.6392 0,9636 5.6350

0.9403 2.2412 0.1245 0.9680 4.1034 0.97950.8566 0.2990 3.8750 0,9745 5.2799

0.9728 -1.0185 -0,0954 0.9644 0.1022 1.25500.9641 0.3525 9.5353 0.7945 3.1000

0.9688 -0.1399 -0.2946 0.9701 28.9194 2.62280.3015 0.2937 3.2066 0.9727 4.3925

0.9810 -0.3438 -0.3443 0.9677 9.7227 1.69420.7065 0.2134 2.7445 0.9672 5.0415

0.9827 -0.4389 -0.2106 0.9588 9.4387 1.64540.7735 0.1910 2.7281 0.9860 4.6223

0.9661 1.0690 0.3985 0.9868 3.1705 0.83620.9746 0.4179 2.3340 0.9701 5. 2972

0.9851 0.5617 0.8277 0.9891 0.2496 1.53840.9817 0.1720 8.0431 0.9758 4.7848

Fixed [Carbon] = 4 g/l, pH3.2 Merck 22 Initial 0.9915 0.1159 84.5720 0.9752 1.1620 0.06150.9670 0.0689 10.4093 0.0667 3.1676

Norit 22 Initial 0.9716 0.2756 28.0537 0.9792 3.2751 0.37480.9786 0.1157 9.5029 0.1740 3.2031

The Langmuir model was applicable (*R2* ca. 0.96) for the parent Norit carbon, which has low apparent surface area and poor surface oxygen functionality (Tabl. 1, 3), thus indicating strong specific interaction between the surface and the adsorbate and confirmed the monolayer formation on the carbon surface. The lower values of the correlation coefficients (*R2* ca. 0.76) for the parent Merck carbon indicated less strong fitting of the experimental data, most

Table 4. Parameters of the Cr(III) adsorption on studied activated carbons at different

Norit 22 Initial 0.9728 0.3509 22.0336 0.6793 3.7895 0.10170.9436 0.1931 9.7116 0,1412 3.5450 30 Initial 0.9411 0.4684 31.7875 0.8272 3.7895 0.18200.9973 0.4087 176.2481 0.2345 5.0420 40 Initial 0.8679 0.5344 15.4698 0.8058 2.1710 0.23600.9899 0.4127 130.3293 0.1845 3.9250 50 Initial 0.9576 0.5419 12.7623 0.8327 1.9333 0.23200.9854 0.4020 148.4132 0.0945 4.6290

mol/g <sup>1</sup>*/n R2 <sup>q</sup>*max,

constants BET constants Equlibrium

constants

mmol/g *<sup>K</sup>*BET *R2 <sup>K</sup>*<sup>d</sup>

Fig. 3. Isotherms of the Cr (III) adsorption on initial Merck activated carbon at different temperatures: () – 22; () – 30; () – 40 and () – 50 0C.

Fig. 4. Isotherms of the Cr(III) adsorption on initial Norit activated carbon at different temperatures: () – 22; () – 30; () – 40 and () – 50 0C.



Fig. 3. Isotherms of the Cr (III) adsorption on initial Merck activated carbon at different

Fig. 4. Isotherms of the Cr(III) adsorption on initial Norit activated carbon at different

temperatures: () – 22; () – 30; () – 40 and () – 50 0C.

temperatures: () – 22; () – 30; () – 40 and () – 50 0C.

Table 4. Parameters of the Cr(III) adsorption on studied activated carbons at different temperatures

The Langmuir model was applicable (*R2* ca. 0.96) for the parent Norit carbon, which has low apparent surface area and poor surface oxygen functionality (Tabl. 1, 3), thus indicating strong specific interaction between the surface and the adsorbate and confirmed the monolayer formation on the carbon surface. The lower values of the correlation coefficients (*R2* ca. 0.76) for the parent Merck carbon indicated less strong fitting of the experimental data, most

Comparison of the Thermodynamic Parameters Estimation for

exchange is no longer the main mechanism of sorption.

**3.2 Adsorption thermodynamics** 

the Adsorption Process of the Metals from Liquid Phase on Activated Carbons 109

While Langmuir and BET isotherms indicate the homogeneity of the adsorbent surface and uniform energies of the adsorption, the Freundlich type isotherm hints towards transmigration of sorbate in the plane of the surface and its heterogeneity. Therefore, the surface of studied activated carbons could be made up of small heterogeneous adsorption patches which are very much similar to each other in respect of adsorption phenomenon. Since here the Norit and Merck activated carbons were used as supplied and after postchemical oxidative treatment, Cr(III) uptake on initial carbons, i.e. those without surface functionality, taken place mainly due to physisorption and increased with the increase in temperature. For oxidized samples total adsorption increases with the temperature until certain temperature, and further temperature rising led to the reversal adsorption capacity when the total adsorption decreases with the temperature. The cross over appears at 400C. This can be explained by the fact that for carbon reached by surface functionality there is more than one mechanism of chromium sorption: along with the normal physisorption the chemisorption of chromium on the active sites takes place leading to increased adsorption via surface exchange reactions, then with the rise in temperature, i.e. T > 40 0C, the ionic

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.

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

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 structure of the parent Merck.

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.

While Langmuir and BET isotherms indicate the homogeneity of the adsorbent surface and uniform energies of the adsorption, the Freundlich type isotherm hints towards transmigration of sorbate in the plane of the surface and its heterogeneity. Therefore, the surface of studied activated carbons could be made up of small heterogeneous adsorption patches which are very much similar to each other in respect of adsorption phenomenon. Since here the Norit and Merck activated carbons were used as supplied and after postchemical oxidative treatment, Cr(III) uptake on initial carbons, i.e. those without surface functionality, taken place mainly due to physisorption and increased with the increase in temperature. For oxidized samples total adsorption increases with the temperature until

certain temperature, and further temperature rising led to the reversal adsorption capacity when the total adsorption decreases with the temperature. The cross over appears at 400C. This can be explained by the fact that for carbon reached by surface functionality there is more than one mechanism of chromium sorption: along with the normal physisorption the chemisorption of chromium on the active sites takes place leading to increased adsorption via surface exchange reactions, then with the rise in temperature, i.e. T > 40 0C, the ionic exchange is no longer the main mechanism of sorption.
