**2. Methods**

#### **2.1 Reactives and experimental procedure**

The multi-walled carbon nanotubes were obtained from Fluka and were used without further purification; the main characteristics of the adsorbent are given in **Table 1**, with further characteristics (i.e., Raman data) of them published elsewhere [15]. The characteristics of other adsorbent-ion exchangers used in this investigation were described elsewhere: Dowex 1x8 resin [16], oxidized MWCNTs [12] and activated carbon [17].

Stock Cr(VI) solutions were prepared by dissolving K2Cr2O7 (Merck) in distilled water. All other chemicals were of AR grade.

*Removal of Cr(VI) from Waters by Multi-Walled Carbon Nanotubes: Optimization and Kinetic… DOI: http://dx.doi.org/10.5772/intechopen.84225* 


#### **Table 1.**

*Characteristics of the multi-walled carbon nanotubes.* 

Metal adsorption (and elution) studies were carried out in a glass reactor provided for mechanical shaking. Metal adsorption (or elution) was determined by monitoring concentration by AAS in the aqueous solution as a function of time, whereas the metal concentration in the adsorbent was calculated by mass balance.

#### **2.2 Modeling of kinetic adsorption**

#### *2.2.1 Pseudo-first-order model*

The pseudo-first-order equation [18] used in this work can be expressed accordingly with the next equation:

$$\ln\left(\left[\text{Cr}\right]\_{\text{c.c.}} - \left[\text{Cr}\right]\_{\text{c.t}}\right) = \ln\left[\text{Cr}\right]\_{\text{c.c.}} - \text{k}\_1\text{t} \tag{1}$$

where [Cr]c,t and [Cr]c,e are the chromium concentrations in the nanotubes at equilibrium and at an elapsed time, respectively, t is the time and k1 is the constant related to this model.

#### *2.2.2 Pseudo-second-order model*

In this model, the equation used is

$$\frac{\text{t}}{\text{[Cr]}\_{c,t}} = \frac{\text{1}}{\text{k}\_2 \text{[Cr]}\_{c,a}^2} + \frac{\text{t}}{\text{[Cr]}\_{c,a}} \tag{2}$$

In this case, k2 is the constant related to this model.

#### **2.3 Modeling the rate law**

Three possible adsorption mechanisms had been evaluated if the adsorption of chromium(VI) into the MWCNTs must be considered as a liquid-solid phase reaction which includes diffusion of chromium species from the aqueous phase to the adsorbent surface, the diffusion of ions within the nanotubes and the chemical reaction between ions and any functional group in the carbon nanotubes [19]. The rate equations for the above three cases are:

i. film-diffusion controlled process, in which the rate equation is

$$\ln\left(\mathbf{1} - \mathbf{F}\right) = -\mathbf{k}\mathbf{t} \tag{3}$$

ii. particle-diffusion controlled process, with the equation as

$$\ln\left\{\mathbf{1} - \mathbf{F}^{2}\right\} = -\mathbf{k}\mathbf{t} \tag{4}$$

iii. Shrinking core model

$$\text{2 - 3 (1 - F)}^{2/3} - 2\text{F} = \text{kt} \tag{5}$$

In all the above equations, F is the fractional approach to equilibrium, which is defined as

$$\mathbf{F} = \frac{\left[\mathbf{Cr}\right]\_{c,t}}{\left[\mathbf{Cr}\right]\_{c,a}} \tag{6}$$

whereas k is the corresponding rate constant.

#### **2.4 Modeling of adsorption isotherms**

Both the Langmuir and Freundlich approaches had been used to model the experimental data, being both widely used in the modeling of adsorption or ion exchange processes [20].

The Langmuir model is valid for monolayer adsorption onto a surface containing a limited number of identical sites. The equation in its linear form describing this model is

$$\frac{1}{\left[\left[\text{Cr}\right]\_{\text{c,e}}\right]} = \frac{1}{\left[\left[\text{Cr}\right]\_{\text{c,m}}\right]} + \frac{1}{\left[\text{b}\left[\text{Cr}\right]\_{\text{c,m}}\right]} \frac{1}{\left[\left[\text{Cr}\right]\_{\text{c,e}}\right]} \tag{7}$$

where b is a constant related to the model, [Cr]c,m is the maximum metal uptake in the carbon nanotubes and [Cr]s,e is the equilibrium chromium(VI) concentration in the solution.

 The Freundlich model is an empirical expression describing adsorption onto heterogeneous surfaces, having the adsorbent surface sites with a variation of binding energies. In this case, the equation also in its linear form is

$$\ln\left[\text{Cr}\right]\_{\text{c,e}} = \ln\text{k}\_{\text{f}} + \frac{1}{\text{n}}\ln\left[\text{Cr}\right]\_{\text{c,e}}\tag{8}$$

where kf and n are parameters related to the Freundlich model.

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

#### **3.1 Effect of stirring speed**

Adsorption of chromium(VI) from aqueous solution to MWCNTs as a function of the stirring speed at pH 1 ± 0.1 is shown in **Figure 1**. The adsorption of chromium(VI) increases with increasing stirring speed, though from 1000 min<sup>−</sup><sup>1</sup> no significant

*Removal of Cr(VI) from Waters by Multi-Walled Carbon Nanotubes: Optimization and Kinetic… DOI: http://dx.doi.org/10.5772/intechopen.84225* 

#### **Figure 1.**

*Influence of stirring speed on the percentage of chromium(VI) adsorption at the equilibrium. Aqueous solution: 0.01 g/L Cr(VI). MWCNTs dosage: 1 g/L. Temperature: 20°C. Time: 2 h.* 

changes are encountered in metal adsorption specially at the longer contact times. These results shown that from 1000 min<sup>−</sup><sup>1</sup> , the thickness of the aqueous diffusion layer and the aqueous resistance to mass transfer were minimized, and the diffusion contribution of the aqueous species to the adsorption process is assumed to be constant.

#### **3.2 Effect of temperature**

The relationship between chromium(VI) adsorption and the temperature is also studied using aqueous solutions containing 0.01 g/L Cr(VI) at pH 4 ± 0.1 and adsorbent dosage of 1 g/L. **Table 2** shows the variation of log DCr vs. T, over the range of temperatures used, where D (the distribution coefficient) was calculated as

$$\mathbf{D} = \frac{[\mathbf{Cr}]\_{\text{c,e}}}{[\mathbf{Cr}]\_{\text{s,e}}} \tag{9}$$

where [Cr]c,e and [Cr]s,e being the chromium concentrations in the nanotubes and in the aqueous solution at equilibrium. There is a decrease of chromium adsorption with the increase of temperature. One explanation of these results is to consider the nature of the species with the temperature as predicted by the Bjerrum equation. Accordingly, the estimated change of enthalpy is −14 kJ/mol, and the adsorption process is therefore exothermic.


#### **Table 2.**  *Influence of temperature on chromium(VI) adsorption onto the MWCNTs.*

The kinetic adsorption data were simulated with the two models shown in Eqs. (1) and (2), representing the pseudo-first- and pseudo-second-order models, respectively. The results are listed in **Table 3**. From the values of r2, the kinetic adsorption of chromium(VI) at the temperatures of 20 and 60°C can be fitted by the pseudo-second-order model.

### **3.3 Effect of pH**

The pH of the aqueous solution may be one of the most decisive parameters controlling the adsorption process. The influence of pH on the adsorption of chromium(VI) is investigated at pH values ranging from 1 to 13. **Figure 2** shows that the maximum adsorption of the metal occurs at pH 4, and decreases either at more acidic and at alkaline pH values, these mean that HCrO4 <sup>−</sup> species (which is predominant at this range of initial chromium(VI) concentration and pH values below 6) is adsorbed onto the MWCNTs better than CrO4 <sup>2</sup><sup>−</sup> species, which is predominant at alkaline pH values. Furthermore, **Table 4** presented data about the adsorption of 0.005 g/L chromium(VI) at pH values of 1 and 4; it is also observed how the percentage of metal adsorption is greatly dependent on the pH of the aqueous solution, decreasing as the pH shifts to more acidic values.

#### **3.4 Effect of carbon nanotubes dosage**

 It is apparent that the amount of adsorbent used in the removal of a given solute from aqueous solutions is critical for the practical application of such system. Thus, adsorption of chromium(VI) as a function of MWCNT dosages at pH 4 ± 0.1 is shown in **Figure 3**. The percentage of metal adsorption increases with the MWCNT dosage increasing, i.e. near 90% chromium(VI) is adsorbed at the adsorbent dosage of 10 g/L and this value down until 44% when the adsorbent dose is 1 g/L. These results are consistent with the fact that the increase of the adsorbent dosage results in the increase of the active sites in which the metal can be adsorbed, thus increasing the percentage of metal adsorbed or eliminated from the aqueous solution.

The data of the amount of chromium(VI) adsorbed on the MWCNTs (mg/g) and the metal concentration remaining in solution (mg/L) are fitted to the Langmuir and Freundlich models represented by Eqs. (7) and (8), respectively. The relative parameters obtained from the fit are listed in **Table 5**. The experimental data are well described by both models, indicating that the chromium(VI) uptake onto the MWCNTs is homogeneous and multilayer in nature. However, a singular fact of the Langmuir model can be described by the dimensionless separation factor, defined as

$$\mathbf{R} = \frac{1}{\mathbf{1} + \mathbf{b} \left[ \mathbf{C} \mathbf{r} \right]\_{s,0}} \tag{10}$$


**Table 3.** 

*Constants for the kinetic adsorption of chromium(VI) to MWCNTs using different adsorption models.* 

*Removal of Cr(VI) from Waters by Multi-Walled Carbon Nanotubes: Optimization and Kinetic… DOI: http://dx.doi.org/10.5772/intechopen.84225* 

**Figure 2.**  *Influence of the pH on chromium(VI) adsorption. Experimental conditions as in* **Figure 1***.* 


#### **Table 4.**

*Influence of pH on chromium(VI) adsorption onto the MWCNTs.* 

 where [Cr]s,0 is the initial metal concentration in the solution and b is the Langmuir constant. The value of R indicates if the adsorption is unfavorable (R > 1), linear (R = 1), favorable (0 < R < 1) or irreversible (R = 0). The value of R in this investigation was found to be 0.82, indicating that the adsorption of chromium(VI) is favorable.

#### **3.5 Effect of metal concentration**

The various adsorptions of chromium(VI) on MWCNTs as a function of initial metal concentration at pH 4 ± 0.1 are shown in **Figure 4**. The adsorption percentage of chromium(VI) decreases with initial metal concentration increasing.

The rate law governing the metal adsorption was investigated using the three models depicted in Eqs. (3)–(5), and the results from these fits were summarized in **Table 6**. It can be seen that within the particle-diffusion controlled model, the chromium(VI) adsorption onto the MWCNTs was better explained.

#### **3.6 Comparison with other adsorbent-anion exchangers**

The adsorption capacity, in terms of percentage of adsorption, found in this investigation was compared with the results obtained using other potential adsorbent-anion exchangers for Cr(VI). The results obtained from this set of

#### **Figure 3.**

*Influence of MWCNTs dosage on chromium(VI) adsorption. Aqueous solution: 0.01 g/L Cr(VI) at pH 4. Temperature: 20°C. Time: 2 h.* 


#### **Table 5.**

*Langmuir and Freundlich constants.* 

#### **Figure 4.**

*Influence of initial chromium(VI) concentration on metal adsorption. MWCNTs dosage: 10 g/L. Temperature: 20°C.* 

*Removal of Cr(VI) from Waters by Multi-Walled Carbon Nanotubes: Optimization and Kinetic… DOI: http://dx.doi.org/10.5772/intechopen.84225* 


**Table 6.** 

*The rate law governing the adsorption of chromium(VI) onto the MWCNTs.* 

experiments together with the experimental conditions used in the investigation were summarized in **Table 7**.

It can be concluded that, under the present experimental conditions, Dowex 1×8 resin is the most effective to remove hazardous chromium(VI) from near neutral or acidic solutions, whereas MWCNTs presented the worse registers. The above is not a bad conclusion about the use of these MWCNTs as adsorbents for Cr(VI), and not delegitimize the investigation presented in this work, only stated that there are other potential adsorbents-ion echangers that remove Cr(VI) from liquid effluents with a better efficiency.

### **3.7 Thermodynamics**

Besides the data of the change of enthalpy (see Section 3.5) derived for the adsorption process of chromium(VI) onto the carbon nanotubes, a further thermodynamic analysis of the adsorption process can be considered taking into account the next equations:

$$
\Delta \mathbf{G}^\* = -\mathbf{R} \mathbf{T} \ln \mathbf{b} \tag{11}
$$

$$
\Delta \mathbf{G}^\* = \Delta \mathbf{H}^\* - \mathbf{T} \Delta \mathbf{S}^\* \tag{12}
$$

 Accordingly with Eq. (11) in which b is the Langmuir constant showed in **Table 5**, it can be obtained that the value of ΔG° is 9 kJ/mol, confirming that the chromium(VI) uptake onto the nanotubes is nonspontaneous.

To calculate ΔS° for the present adsorption system, Eq. (12) is used, obtaining a value of −0.08 kJ/mol K. The negative value for the change of entropy characterizes a decrease disorder of the system when chromium(VI) is adsorbed onto the nanotubes.


*Aqueous solution: 0.01 g/L Cr(VI) at different pH values. Solid dosage: 1 g/L. Temperature: 20°C. Stirring speed: 1000 min<sup>−</sup><sup>1</sup> . Time: 1 h. QAS: quaternary ammonium salt.* 

#### **Table 7.**  *Percentage of Cr(VI) adsorption using various adsorbent-anion exchangers.*

#### **3.8 Chromium(VI) desorption**

In the present investigation, the desorption of chromium(VI) from the metalloaded carbon nanotubes was studied using hydrazine sulfate solutions as desorbent for the metal, at the same time, in the desorption process, Cr(VI) is reduced to the less hazardous Cr(III) oxidation state, accordingly to

$$\mathrm{4HCrO\_4^- + 10H^+ + 3N\_2H\_4 \cdot H\_2SO\_4 \to 4Cr^{3+} + 16H\_2O + 3N\_2 + 3SO\_4^{2-}} \tag{13}$$

Desorption experiments were carried out with aqueous solutions containing 25–50 g/L of hydrazine sulfate and 2 mg/g Cr(VI)-loaded MWCNTs at a 25 mL/g solution volume/weighed MWCNTs relationship and 20°C. The results from these experiments indicated that:


### **4. Conclusions**

The adsorption of chromium(VI) onto the multi-walled carbon nanotubes is dependent on the pH values of the aqueous solution. The adsorption reaches a maximum at pH 4 and decreases at more acidic and alkaline pH values. The adsorption is exothermic (ΔH° = −14 kJ/mol) and nonspontaneous (positive ΔG° valor), whereas at 20–60°C, the adsorption of chromium (VI) onto the nanotubes better fits to the pseudo-second-order model. In the 0.005–0.04 g/L range of chromium(VI) concentrations in the aqueous solution, the metal uptake onto the nanotubes responded well to the particle-diffusion model, and the metal adsorption responded to the Langmuir and Freundlich isotherms, indicating that the adsorption process is homogeneous and multilayer in nature. Chromium(VI) can be desorbed from MWCNTs by the use of hydrazine sulfate solutions, which releases to the aqueous solution chromium in the less hazardous (III) valence state.

#### **Acknowledgements**

This research was funded by the Ministry of Science, Innovation and Universities of the Spanish Government, in the "Challenges collaboration" call for proposals in 2017 (Ref. RTC-2017-6629-5).

### **Conflict of interest**

The authors declare no conflicts of interest.

*Removal of Cr(VI) from Waters by Multi-Walled Carbon Nanotubes: Optimization and Kinetic… DOI: http://dx.doi.org/10.5772/intechopen.84225* 
