3.2.3. Kinetics and Thermodynamics Studies
Kinetics information regarding Pt (IV) adsorption on XAD7-DB30 C10 were obtained by modeling obtained experimental data obtained for Pt (IV) adsorption from a solution with initial concentration of 25 mg L−1 and pH 4 with Lagergren pseudo-first-order model and Ho and McKay pseudo-second-order model.
Integrated form of the pseudo-first-order kinetic model is expressed by Equation (2) [
1,
2,
4].
where q
t and q
e represent the adsorption capacities at time t and at equilibrium time (120 min), respectively (mg g
−1) and k
1 is the specific adsorption rate constant (min
−1).
From linear dependence of ln(q
e − q
t) versus time (graph presented in
Figure 8a) were evaluated the values of adsorption rate constant (k
1) and maximum adsorption capacity (q
e), associated with the pseudo-first-order model.
Linear form of the pseudo-second-order rate expression is given by Equation (3) [
1,
2,
4]:
where k
2 is the pseudo-second-order constant (g mg
−1·min
−1).
Linear dependence of t/q
t versus t, which represent the linear form of pseudo-second-order model is depicted in
Figure 8b. Values of pseudo-second-order rate constant (k
2) and equilibrium adsorption capacity (q
e) associated with pseudo-second-order model are obtained from the intercept and from the slope of the linear dependence depicted in
Figure 8b.
Also, for both used kinetic models were evaluated the values of the regression coefficients (R
2). All obtained kinetics parameters are summarized in
Table 1.
Based on the data presented in
Table 1, we can observe that the correlation coefficient obtained when the experimental data were modeled with pseudo-first-order model have a lower value than the value obtained when data were modeled using pseudo-second-order model. Also, when the experimental data were modeled using the pseudo-first-order model, can be observed a huge difference between the calculated maximum adsorption capacity and the experimental determined one. When the experimental data were modeled using the pseudo-second-order model, the theoretically predicted adsorption capacity had a value really close to the experimentally determined one, at all used temperatures. Also, the increase of the adsorption rate constant (k
2) with the increase of temperature indicate that the adsorption of Pt (IV) on XAD7-DB30C10 is an endothermic process [
29].
The correlation coefficient (R
2) closer to unity indicates that the kinetics of Pt (IV) adsorption on XAD7-DB30C10 is well described by pseudo-second-order kinetic model [
32,
34].
Further, the value of the activation energy associated with the adsorption process by using the Arrhenius equation was evaluated. Activation energy was determined from linear dependence of lnk
2 versus 1/T (dependence presented in
Figure 9). Speed rate constant was determined by modelling obtained experimental data with pseudo–second–order model.
For studied adsorption process the activation energy have a value of 22.14 kJ mol
−1. Because the activation energy value obtained for studied adsorption process is bigger than 8 kJ mol
−1, we can conclude that the Pt (IV) adsorption on XAD7-DB30C10 is a chemical adsorption [
35,
36,
37].
Also, for confirming the studied process is spontaneous, thermodynamic studies were conducted in temperature range 298 to 318 K. Based on obtained experimental data were evaluated the values of thermodynamic parameters: free Gibbs energy (ΔG
0), free enthalpy (ΔH
0) and free entropy (ΔS
0) were calculated by using relations [
37,
38]:
where:
and
where: R is the gas constant, K
d is the equilibrium constant, T is the temperature (K), C
Ae is the equilibrium concentration Pt (IV) on adsorbent (mg L
−1), and C
e is the equilibrium concentration of Pt (IV) in the solution (mg L
−1).
Free Gibbs energy, enthalpy and entropy changes represent critical design variables used to estimate material adsorptive performance and to predict the adsorption mechanism. These parameters are the basic requirements for characterization and optimization of adsorptive processes.
Changes of enthalpy and entropy associated with the studied adsorption process are evaluated from the slope and from the intercept of linear dependence of lnK
d vs. 1/T (
Figure 10). Based on these values can calculate the value of free Gibbs energy. Values of thermodynamic parameters obtained for Pt (IV) adsorption on XAD7-DB30C10 are presented in
Table 2.
From the data presented in
Table 2 can observe that the ΔH
0 has a positive value, suggesting that the adsorption process is an endothermic one, so any increase of temperature has a beneficial effect onto the Pt (IV) adsorption. Negative value of free Gibbs energy (ΔG
0) suggests that the Pt (IV) adsorption on XAD7-DB30C10 is spontaneous and favourable process. Also, can observe that the increase of temperature leads at more negative values of free Gibbs energy meaning that Pt(IV) adsorption speed increases when temperature rises. Positive value of ΔSº suggests that the adsorption speed increase at adsorbent material/solution interface, and the degree of particles clutter increases when the temperature increases [
32,
33].
3.2.4. Effect of Initial Concentration and Equilibrium Study
Also was studied the effect of initial concentration on the adsorption process, obtained data are presented in
Figure 11.
Based on data presented in
Figure 11 can observe that the adsorption capacity increases when the initial concentration of Pt (IV) increases, until a maximum adsorption capacity is reached. This adsorption capacity represents the experimentally determined maximum adsorption capacity of XAD7-DB30C10, having a value of 12.3 mg g
−1. When adsorption was performed using unfunctionalized material, was obtained a maximum adsorption capacity of 0.03 mg of Pt (IV) per g of used adsorbent material. Maximum adsorption capacity represents another important parameter for designing of adsorptive systems.
Adsorption mechanism can be established by modeling obtained experimental data with different adsorption isotherms. In order to evaluate the adsorption mechanism and to determine the maximum adsorption capacity of Pt (IV) ions onto XAD7-DB30C10 experimental data were modeled using Freundlich, Langmuir and Sips isotherms [
35,
36,
39,
40,
41].
Linear form of the Freundlich isotherm is expressed by Equation (7) [
39]:
and of the Langmuir isotherm as the following equation:
Sips isotherm represent a combination between Freundlich and Langmuir isotherms, which at limits can describe the Langmuir or Freundlich isotherms (Equation (9)) [
41]:
where: q
e is the amount of platinum adsorbed per gram of sorbent at equilibrium (mg g
−1); C
e is the equilibrium concentration of platinum (mg L
−1); K
F and 1/n are characteristic constants that can be related to the relative adsorption capacity of the adsorbent and the intensity of adsorption; q
m (maximum adsorption capacity) (mg g
−1) and K
L is a constant related to the free energy of adsorption; q
S is the maximum absorption capacity (mg g
−1); K
S is the constant related to the adsorption capacity of the adsorbent and n
S is the heterogeneity factor.
Results obtained when experimental data were modeled using Freundlich, Langmuir and Sips adsorption isotherms are presented in
Figure 12. Based on Freundlich, Langmuir and Sips isotherms presented in
Figure 12 were determined the parameters associated with Pt (IV) adsorption, parameters depicted in
Table 3.
Analyzing the data presented in
Table 3, we can observe that the correlation coefficients obtained for Freundlich and Langmuir isotherms have a lower values compared with the value obtained when experimental data are modeled using Sips isotherm. Lower value of correlation coefficients suggests a restriction in use of Langmuir and Freundlich isotherms to describe the studied adsorption process.
Correlation coefficient of 0.9884 suggests that the Pt (IV) adsorption on XAD7-DB30C10 is better described by the Sips isotherm, which follows the adsorption process for entire concentration range. The value of the maximum adsorption capacity calculated from Sips isotherm have value of 12.53 mg g
−1, which is very close to the experimental obtained value of 12.3 mg g
−1. Closer value of maximum adsorption capacity represents a strong confirmation that Sips isotherm describes the adsorption process of Pt (IV) ions onto the studied adsorbent material. Because the calculated value for the coefficient ns is higher than 1 can conclude that the studied adsorption process is a heterogeneous one [
29].
To see if the new obtained adsorbent material can be used in real application was compared the maximum adsorption capacity with the one obtained for different adsorbents (data are presented in
Table 4).