Sorption behavior of some lanthanides on polyacrylamide stannic molybdophosphate as organic–inorganic composite

Abstract

Sorption behavior of some lanthanide ions such as lanthanum and samarium ions on polyacrylamide stannic molybdophosphate {PASnMoP} as organic–inorganic composite has been investigated. The distribution coefficients of La³⁺ and Sm³⁺ ions in different pH media on PASnMoP were determined with the selectivity order La³⁺ > Sm³⁺. Capacity of PASnMoP for La³⁺ and Sm³⁺ ions was determined and found 24.66 and 15.38 mg g⁻¹ for La³⁺ and Sm³⁺ ions, respectively. The resin dosage dependence for the sorption behavior for La³⁺ and Sm³⁺ ions on polyacrylamide stannic molybdophosphate was conducted. The adsorption isotherms were described by means of Langmuir and Freundlich isotherms for La³⁺ and Sm³⁺ ions. The Langmuir model represented the adsorption process better than the Freundlich model. The kinetic data were tested using Logergren-first-order and Pseudo-second-order kinetic models. The data correlated well with the Pseudo-second-order kinetic model, indicating that the chemical adsorption was the rate limiting step. Thermodynamic parameters ΔG°, ΔH° and ΔS° were also calculated and the data showed that the ion exchange of La³⁺ and Sm³⁺ ions on PASnMoP was spontaneous and endothermic in nature.

Introduction

Rare earth elements (REE) have been increasingly used in the field of chemical engineering, nuclear energy, optical, magnetic, luminescence and laser materials, high-temperature superconductors, secondary batteries and catalysis [1–6]. Lanthanum, one of the most abundant of the lanthanides, is an important element of mischmetal and hydrogen-absorbing alloy [3], Neodymium is the raw material used in high-strength permanent magnets (Nd-B-Fe), making it less expensive than samarium-cobalt permanent magnets [7]. Yttrium is an important element and in great demand in astronavigation, luminescence, nuclear energy and metallurgical industries [8]. Organic polymers as ion exchangers are well known for their uniformity, chemical stability and control of their ion-exchange properties through synthetic methods. The inorganic ion-exchange materials besides other advantages are important in being more stable to high temperature and radiation field than the organic ones [9]. To obtain a combination of these advantages associated with polymeric and inorganic materials as ion exchangers, attempts have been made to develop polymeric–inorganic composite ion exchangers by incorporation of organic monomers in the inorganic matrix [10]; few such excellent ion-exchange materials have been developed and are successfully being used in chromatographic techniques [11–13].

In the present work, polyacrylamide stannic molybdophosphate was synthesized as reported earlier [14]. Distribution coefficient and separation factors (∝) of La³⁺ and Sm³⁺ on polyacrylamide stannic molybdophosphate were determined. Capacity, sorption isotherms and thermodynamic parameters have been calculated for the sorption of La³⁺ and Sm³⁺ ions on polyacrylamide stannic molybdophosphate.

Materials and methods

All reagents and chemicals were of analytical grade purity and used without further purification. pH measurements were performed using pH meter of the bench, model 601A, USA. The concentration of La³⁺ and Sm³⁺ ions in solutions was measured by UV spectrophotometer UV-1700.

Polyacrylamide stannic molybdophosphate {PASnMoP} as organic–inorganic composite was prepared as described earlier by Abdel-Galil [14]. Polyacrylamide was prepared by mixing equal volume of acrylamide and potassium persulfate. A viscous solution was obtained by heating the mixture gently at 70 °C with continuous stirring. Inorganic precipitate of Sn(IV) molybdophosphate was prepared at 25 °C by mixing equal volumes of the solutions of stannic chloride (0.1 M), ammonium molybdate (0.1 M) and orthophosphoric acid (1 M). The yellow precipitate was obtained when the pH of the mixture was adjusted to 1.05 by adding aqueous ammonia (NH₄OH). The viscous solution of polyacrylamide was added to the yellow inorganic precipitate of Sn(IV) molybdophosphate and mixed thoroughly with continuous stirring. The resultant yellow colored slurry was refluxed for 3 h at a temperature of 70 ± 5 °C and the color of the slurry changed from yellow to greenish color. The resultant greenish colored slurry was kept for 24 h at room temperature for digestion. The supernatant liquid was decanted and gel was filtered using a centrifuge (about 10⁴ rpm) and dried at 50 ± 1 °C. The product was crashed to obtain small granules and converted to H⁺-form by treating with 1 M HNO₃ for 24 h with occasional shaking intermittently replacing the supernatant liquid with fresh acid and the color of the product became yellow. The excess acid was removed after several washing with DMW, dried at 50 °C and sieved to obtain particles of particular size range (0.115–0.375 mm). The percentage of yield and physical appearance of beads were selected for further studies.

Sorption studies

The distribution coefficients (k _d) of La³⁺ and Sm³⁺ ions on polyacrylamide Sn(IV) molybdophosphate were determined by batch equilibration technique, as a function of different pH values. 0.1 g of {PASnMoP} was shaken with 10 ml of 50 ppm of La³⁺ and Sm³⁺ ions solution at V/m ratio of 100 ml/g. The mixture was placed overnight (sufficient to attain the equilibrium) in a shaker thermostat adjusted at 25, 45 or 65 ± 1 °C. After equilibrium, the solutions were separated by centrifugation and the concentration of La³⁺ and Sm³⁺ ions in the solution was determined using UV spectrophotometer. The pH values of the solutions were measured before and after equilibrium using pH meter. The distribution coefficient (k _d) and separation factor (∝) were evaluated by;

$$ k_{\text{d}} = \frac{{A_{\text{o}} - A_{\text{f}} }}{{A_{\text{f}} }} \times \frac{V}{m} \left( {\text{ml}/\text{g}} \right)\varvec{ } $$

(1)

$$ \propto \varvec{ } = \frac{{\left( {k_{\text{d}} } \right)A}}{{\left( {k_{\text{d}} } \right)B}} $$

(2)

where A _o is the concentration of the ions in solution before equilibrium, A _f is the concentration of the ions in solution after equilibrium, V is the volume of the solution (ml), m is the weight of the exchanger (g), and ∝ is the separation factor between two neighboring ions A and B.

Capacity measurements

The capacity of polyacrylamide stannic(IV) molybdophosphate for La³⁺ and Sm³⁺ ions was determined by the repeated batch technique, by equilibrating 0.05 g of PASnMoP ion exchanger with 5 ml of 100, 200, 400, 600, 800 and/or 1000 ppm of La³⁺ and/or Sm³⁺ ion solutions on a shaker thermostat adjusted at 25 ± 1 °C. After equilibrium, the solution was separated and repeated until no further sorption occurs. The capacity was calculated using the following equation:

$$ {\text{Capacity = Uptake }} \times \frac{V}{m} \times C_{\text{o}} \;{\text{mg/g}} $$

(3)

where C _o is the initial ion concentration in solution, V is the solution volume (ml) and m is the weight of the exchanger (g).

Adsorption isotherm

The adsorption isotherms were done, as it is well known, by a gradual increase in the concentration of sorbate ion in solution and measuring the amount sorbed at each equilibrium concentration. The degree of sorption showed therefore is a function of the concentration of sorbate ions only. The adsorption isotherms were carried out with different initial concentrations varying from 100 to 1000 ppm at different reaction temperatures 25, 45 and/or 65 ± 1 °C and at constant V/m value of 100 ml/g and pH 3. After equilibrium, the respective mixture was filtered and then the concentration of La³⁺ and Sm³⁺ was measured.

Kinetic measurements

The kinetic analysis of the adsorption process for La³⁺ and Sm³⁺ ions on polyacrylamide stannic(IV) molybdophosphate was carried out by mixing the exchanger with metal ions solution at 50 ppm with a V/m ratio of 100 ml/g in a shaker thermostat at 25 ± 1 °C. The solution was separated at different time intervals and analyzed to determine the metal ion concentration in solution using UV spectrophotometer for La³⁺ and Sm³⁺. The extent of sorption was determined from the equation.

$$ {\text{Sorption }}\% \, = \, \left\{ {\left( {A_{\text{i}} {-} \, A_{\text{f}} } \right)/A_{\text{i}} } \right\} \, \times { 1}00 $$

(4)

where A _i and A _f are the initial and final concentrations of metal ions in solution.

Results and discussion

Polyacrylamide stannic molybdophosphate as organic–inorganic cation exchange material was prepared as described earlier by Abdel-Gelil [14].

The influence of adsorbent dosage on the adsorption of La³⁺ and Sm³⁺ was studied and the data are shown in Fig. 1. The adsorption of the metals increased with increasing the dosage of the exchanger. This increasing may be related to the increase in the surface area of the exchanger by increasing the adsorbent dosage, so more available active sides on the adsorbent and thus making easier penetration of metal ions to the sorption sides [15]. The data also indicate that the adsorption was almost constant at higher dosage than 0.1 g and the optimum dosage used in all investigation was 0.1 g with batch factor 100 ml/g.

Fig. 1

Effect of ion exchanger dosage on sorption of Sm³⁺ and La³⁺ on {PASnMoP}

The cation exchange process between H⁺ (solid phase) and H⁺ in solution can be represented by the following reaction:

$$ nH^{ + } + \, M^{{n{ + }}} = = = = \overline{{M^{{n{ + }}} }} + {\text{ n}}H^{ + } $$

(5)

where a bar over a character denotes the concentration of M ⁿ⁺ on the solid and unbar denotes the concentration of M ⁿ⁺ in the solution phase.

The distribution coefficient (k _d) values are defined by the following relation:

$$ k_{\text{d}} = \frac{{\left[ {\overline{{M^{n + } }} } \right]}}{{\left[ {M^{n + } } \right]}}\varvec{ } $$

(6)

The selectivity $K_{H}^{M}$ can be defined by the following equation:

$$ K_{H}^{M} \; = \;\frac{{[M^{n + } ][H^{ + } ]^{n} }}{{[H^{ + } ][M^{n + } ]}} $$

(7)

From Eqs. (6 and 7), the distribution coefficient (k _d) can be written in the simple form as follows:

$$ k_{\text{d}} = K_{H}^{M} \times \varvec{ }\frac{{[\overline{{H^{ + } }} ]^{n} }}{{[H^{ + } ]^{n} }} $$

(8)

(or)

$$ { \log }k_{\text{d}} = \log K_{\text{H}}^{\text{M}} \times [\overline{{H^{ + } }} ]^{n} - n\log [H^{ + } ] $$

(9)

From very dilute solutions, the activity coefficient in solution is very small and can be neglected, then

$$ [\overline{{M^{n + } }} ] < < [\overline{{H^{ + } }} ]\quad \text{and}\quad [M^{n + } ] < < [H^{ + } ] $$

Then, the term log $K_{H}^{M} \times [\overline{{H^{ + } }} ]$ is considered as constant and, thus, Eq. (9) can be reduced in the following form:

$$ {\text{Log }}k_{\text{d}} = \, - n{ \log }\left[ {H^{ + } } \right] \, = \, n{\text{ pH}} $$

(10)

When log k _d values are plotted against log pH, a straight line with slope n obtained, where n is refer to the valance of the sorbed ions. Figure 2 and Table 1 show the dependency of k_d values of La³⁺ and Sm³⁺ ions onto PASnMoP on the pH of the ion medium. The linear relationships between log k_d and pH values were observed for La³⁺ and Sm³⁺ ions with slopes 0.246 and 0.182, respectively. These slopes did not equal to the valence of the metal ions sorbed which prove the non-ideality of the exchange reaction between La³⁺ and Sm³⁺ ions and PASnMoP. These findings cannot be explained only in terms of electrostatic interaction between the hydrated cations and the anionic sites in the exchanger. It may, therefore, be considered that the dependence of k_d for cations cannot be understood by a purely columbic interaction with the anionic sites, but also may be due to the formation of a covalent bond similar to a weakly acidic resin; such interaction would be closely related to the ionic potential of the cations [14].

Fig. 2

Log k_d of La³⁺ and Sm³⁺ ions versus pH on {PASnMoP}

Table 1 K_d and separation factor values for La³⁺ and Sm³⁺ ions on PASnMoP

The k _d values and separation factors of La³⁺ and Sm³⁺ ions in different pH on PASnMoP are summarized in Table 1. From the data in Table 1, we found that the selectivity order of the investigated cations on PASnMoP in the same conditions has the following sequence; La³⁺ > Sm³⁺. This selectivity sequence is in accordance with the ionic radii; the ions with smaller ionic radii easily exchanged and move faster than the ions with greater ionic radii [14]. Also from Table 1, the separation factors between La³⁺ and Sm³⁺ metal ions on PASnMoP are relatively high and predict some selective separation of these ions which were available on PASnMoP.

Figures 3 and 4 show the k _d values for La³⁺ and Sm³⁺ ions, respectively, in different media at different reaction temperatures. The effect of reaction temperature on the adsorption was carried out in the temperature range 25–65 ± 1 °C. From these figures, we found that the K_d values are increased for La³⁺ and Sm³⁺ ions on PASnMoP with increasing the reaction temperature from 25 to 65 ± 1 °C. This behavior may be due to the endothermic nature of the system for the reaction of La³⁺ and Sm³⁺ ions on PASnMoP. Also, the increasing k _d with increasing the reaction temperatures may be attributed to the increasing mobility of La³⁺ and Sm³⁺ ions with increasing the reaction temperature [16]. Similar results were obtained by Abou-Mesalam et al. for the distribution coefficients of ²²Na, ⁶⁰Co and ^152,154Eu ions on titanium antimonate [17–19].

Fig. 3

Log k_d of La³⁺ ion as a function of pH on PASnMoP at different reaction temperatures

Fig. 4

Log k_d of Sm³⁺ ion as a function of pH on PASnMoP at different

Figure 5 shows the linear relation between in k_d of La³⁺ and Sm³⁺ ions on PASnMoP and 1/T according to the Van’t Hoff relation [17];

Fig. 5

Van’t Hoff plot of the adsorption of La³⁺ and Sm³⁺ ions on PASnMoP

$$ { \ln }k_{\text{d}} { = }\frac{{\Delta S^{\text{o}} }}{T} - \frac{{\Delta H^{\text{o}} }}{\text{RT}} $$

(11)

where ΔS° is the entropy change of adsorption, ΔH° is the enthalpy change of adsorption, R is the gas constant, and T is the absolute temperature.

It was found that the distribution coefficient of La³⁺ and Sm³⁺ ions increased with increasing temperature from 298 to 338°K (i.e., the distribution coefficient decreased with increasing 1/T) as shown in Fig. 5. This increase in the extent of adsorption with the increase in temperature was attributed to acceleration of some originally slow adsorption steps and creation of some new active sites on the adsorbent surfaces [20, 21]. From the slopes and intercepts of these straight lines represented in Fig. 5, the enthalpy change of adsorption (ΔH°) and entropy change of adsorption (ΔS°) were evaluated and represented in Table 2.

Table 2 Thermodynamic parameters for adsorption of La³⁺ and Sm³⁺ ions on PASnMoP

As shown in Table 2, the positive values of (ΔH°) indicate the endothermic nature of the adsorption process [14]. The positive values of ΔS° indicate that the increased randomness of solid solution interface during the adsorption of these cations on PASnMoP [16]. The data in Table 2 indicate that the values of ΔH° for La³⁺ and Sm³⁺ ions on PASnMoP are greater than 12.6 KJmol⁻¹ which indicated the presence of other mechanism for the adsorption of La³⁺ and Sm³⁺ ions on PASnMoP beside ion-exchange mechanism [22, 23]. These results are supported also from the data of K_d where the slope of the linear relationship between K_d and pH is not equal to the valence of La³⁺ and Sm³⁺ ions.

The free energy change of specific adsorption ΔG° was calculated using the relation:

$$ \Delta G^{\text{o}} = \, \Delta H^{\text{o}} - {\text{ T}}\Delta S^{\text{o}} $$

(12)

and

$$ \Delta G^{\text{o}} = {\text{ RT ln k}}_{\text{d}} $$

(13)

The negative values of free energy change ΔG° represented in Table 2 indicate that the adsorption process is spontaneous and indicates the preferable adsorption of these cations on PASnMoP compared with H⁺ ion [14, 16].

The capacity of PASnMoP for La³⁺ and Sm³⁺ ions was studied and the data are tabulated in Table 3. From Table 3, it is clear that the capacity of polyacrylamide Sn(IV) molybdophosphate samples for La³⁺ and Sm³⁺ has the following order: La³⁺ > Sm³⁺. This sequence is in accordance with the hydrated radii of the exchanged ions. The ions with smaller hydrated radii enter the pores of the exchanger, resulting in higher adsorption [24, 25].

Table 3 Capacity of PASnMoP for La³⁺ and Sm³⁺ ions at 25 ± 1 °C

Sorption isotherm

Sorption equilibrium is usually described by an isotherm equation whose parameters express the surface properties and affinity of the sorbent, at a fixed temperature and pH. An adsorption isotherm describes the relationship between the amount of adsorbate on the adsorbent and the concentration of dissolved adsorbate in the liquid at equilibrium [26]. Langmuir and Freundlich isotherms are Komman kinds of several isotherm equations that were tested to fit the obtained sorption data.

The Langmuir adsorption model assumes that molecules are adsorbed at fixed number of well-defined sites, each of which can only hold one molecule and no trans-migration of adsorbate in the plane of the surface. These sites are also assured to be energetically equivalent and distant to each other, so there are no interactions between the molecules adsorbed to adjacent sites. The linear form of the Langmuir isotherms is represented by the following equation [27]:

$$ \frac{{C_{\text{e}} }}{{ q_{\text{e }} }}{ = }\frac{{C_{\text{e}} }}{{q_{\text{m}} }}{ + }\frac{ 1}{{K_{\text{L}} q_{\text{m}} }} $$

(14)

where C _e is the equilibrium concentration of the metal (mg/L) and q _e is the amount of the metal adsorbed (mg) by per unit of the adsorbent (g). q _m and K _L are Langmuir constants relating adsorption capacity (mg/g) and the energy of adsorption (L/g), respectively, and evaluated from slope and intercept of the linear plots of C _e/q _e versus C _e, respectively.

The linearized Langmuir adsorption of La³⁺ and Sm³⁺ is given in Figs. 6 and 7. The Langmuir adsorption constants evaluated from isotherms and their correlation coefficient are presented in Table 4; it is clear that the Langmuir isotherm model provides an excellent fit to the equilibrium adsorption data, giving correlation coefficient of 0.994 for La³⁺ and 0.980 for Sm³⁺, respectively.

Fig. 6

Langmuir isotherm plot for the adsorption of La³⁺ onto {PASnMoP}

Fig. 7

Langmuir isotherm plot for the adsorption of Sm³⁺ onto {PASnMoP}

Table 4 Parameters of Langmuir isotherm for ion exchange of La³⁺ and Sm³⁺ on PASnMoP

Based on the further analysis of Langmuir equation, the dimensionless parameter of the equilibrium or adsorption intensity (R _L) can be expressed by

$$ R_{\text{L}}\, { = }\, \frac{ 1}{{ 1 { + }K_{\text{L}} C_{\text{o}} }} $$

(15)

where C _o (mg L⁻¹) is the initial amount of adsorbate.

The R _L parameter is considered as more reliable indicator of the adsorption. There are four probabilities for the R _L value: (1) for favorable adsorption, 0 < R _L < 1, (2) for unfavorable adsorption, R _L > 1, (3) for linear adsorption, R _L = 1, and (4) for irreversible adsorption, R _L = 0.

The variation of R _L with the initial metal concentration of solution is shown in Fig. 8. R _L values were found to be between 0 and 1 for all concentrations of La³⁺ and Sm³⁺ and, therefore, ion exchange of both La³⁺ and Sm³⁺ is favorable. From Fig. 8, we can also see that the R _L values decreased with the increasing initial concentration. This indicates that ion exchange is more favorable for the higher initial La³⁺ and Sm³⁺ concentration than for the lower one.

Fig. 8

Variation of adsorption intensity (R_L) with initial La³⁺ ion concentration (C_o ppm)

Freundlich isotherm is an empirical equation that encompasses the heterogeneity of sites and the exponential distribution of sites and their energies. The sorption data have been analyzed using the logarithmic form of the Freundlich isotherm as shown below:

$$ {\text{Log}}\;q_{\text{e}} {\text{ = log }}K_{\text{f}} { + }\frac{ 1}{n} {\text{log }}C_{\text{e}} $$

(16)

where K _f (mg/g) and n are Feundlich constants incorporating all factors affecting the adsorption process such as adsorption capacity and intensity of adsorption. These constants are determined from the slope and intercept of linear plot of log q _e versus log C _e, respectively.

The constants K _f and n of the Freundlich model are, respectively, obtained from the intercept and the slope of the linear plot of log q _e versus log C _e according to Figs. 9 and 10. The constants K _f can be defined as an adsorption coefficient which represented the quantity of adsorbed metal ion for a unit equilibrium concentration (i.e., C _e = 1). Higher values of K _f indicate higher affinity for La³⁺ and Sm³⁺. The slope 1/n is a measure of the adsorption intensity or surface heterogeneity [28, 29].

Fig. 9

Freundlich isotherm plot for the adsorption of La³⁺ onto PASnMoP

Fig. 10

Freundlich isotherm plot for the adsorption of Sm³⁺ onto PASnMoP

The Freundlich adsorption constants evaluated from isotherms and their correlation coefficient are presented in Table 5. For 1/n = 1, the partition between the two phases is independent of the concentration; the situation 1/n < 1 is the most common and corresponds to a normal L-type Langmuir isotherm, while 1/n > 1 is indicative of a cooperative adsorption which involves strong interaction between the molecules of adsorbate. Values of 1/n < 1 show favorable ion exchange of metals on ion-exchange resin, as shown in Table 5.

Table 5 Parameters of Freundlich isotherm for ion exchange of La³⁺ and Sm³⁺ on {PASnMoP}

Kinetic investigation

The two important physicochemical factors for parameter evaluation of the adsorption process as a unit operation are the kinetics and the equilibrium. Kinetics of adsorption describing the solute uptake rate, which in turn governs the residence time of adsorption reaction, is one of the important characteristics defining the efficiency of adsorption. Hence, in the present study, the kinetics of metal removal has been carried out at 298–338°K to understand the behavior of this exchanger.

In the study, Lagergren-first-order equation and Pseudo-second-order equation were used to test the experimental data. The lagergren-first-order equation is expressed as [30, 31]:

$$ { \ln }\left( {q_{\text{e}} {-} \, q_{\text{t}} } \right) \, = { \ln }q_{\text{e}} {-} \, k_{ 1} t $$

(17)

where k ₁ (min⁻¹) is the rate constant of first-order adsorption, q _e is the amount of metal adsorbed at equilibrium and q_t is the amount adsorbed at time “t”. Plotting ln(q _e − q _t) against “t” at (298–338) °K provided first-order adsorption rate constant (k ₁) and q _e values from the slope and intercept (Table 6).

Table 6 Comparison between adsorption rate constants, estimated q_e and coefficients of correlation associated with the Lagergren-first-order and the Pseudo-second-order kinetic models

The Pseudo-second-order equation [32, 33].

$$ \frac{t}{{q_{\text{e}} }}{ = }\frac{ 1}{{k_{ 2} q_{\text{e}}^{ 2} }}{ + }\frac{ 1}{{q_{\text{e}} }} $$

(18)

The product $k_{2} q_{e}^{2}$ is the initial adsorption rate “h” (mg g⁻¹ min⁻¹):

$$ h \, \;{ = }\;k_{ 2} q_{\text{e}}^{ 2} $$

(19)

The half adsorption time is the time required to uptake half of the maximal amount of adsorbate at equilibrium. It characterizes the adsorption rate as well. In case of Pseudo-second-order process, its value is given by the following relationship:

$$ t_{1/2} \; = \;\frac{1}{{k_{2} q_{\text{e}} }} $$

(20)

where k ₂ (mg g⁻¹ min⁻¹) is the Pseudo-second-order rate constant, q _e is the amount adsorbed at equilibrium, t _1/2 is the half adsorption time and q _t is the amount of metal adsorbed at time “t”. Plotting t/q _t against “t” at (298–338 °K) (Figs. 11, 12) provided second-order adsorption rate constant (k ₂) and q _e values from the slope and intercept (Table 6). The values of correlation coefficient indicate a better fit of Pseudo-second-order model with the experimental data compared to the Lagergren-first-order model at all studied temperatures. The same type results were also given in same works.

Fig. 11

Test of Pseudo-second-order equation for adsorption of La³⁺ from {PASnMoP} at different reaction temperatures

Fig. 12

Test of Pseudo-second-order equation for adsorption of Sm³⁺ from {PASnMoP} at different reaction temperatures

Thermodynamic parameters evaluation

Temperature dependence of the adsorption process is associated with several thermodynamic parameters. Thermodynamic considerations of an ion-exchange process are necessary to conclude whether the process is spontaneous or not. Thermodynamic parameters such as Gibbs free energy (ΔG°), enthalpy change (ΔH°) and entropy change (ΔS°) can be estimated using equilibrium constants changing with temperature. The Gibbs free energy change of the adsorption reaction is given by the following Eq. (23):

$$ \overline{{\Delta G^{ \circ } }} = \varvec{ } - {\text{RT lnK}} $$

(21)

where R is universal gas constant (8.314 mol⁻¹ k⁻¹), T is the absolute temperature (K) and K(q _e/C _e) is the distribution coefficient [15, 34].

Relation between ΔG°, ΔH° (enthalpy change) and ΔS° (entropy change) can be expressed by the following equation [35, 36]:

$$ \Delta G^{\text{o}} = \, \Delta H^{\text{o}} {-} \, T\Delta S^{\text{o}} $$

(22)

Equation (22) can be written as:

$$ {\text{lnK = }}\frac{{\Delta S^{\text{o}} }}{\text{R}} - \frac{{\Delta H^{\text{o}} }}{\text{RT}} $$

(23)

where values of ΔH ^o and ΔS ^o can be determined from the slope and the intercept of the plot between ln K versus 1/T (Fig. 13).

Fig. 13

Plots of Ln K vs. 1/T for adsorption of La³⁺ and Sm³⁺ ions onto PASnMoP

The values ΔG ^o, ΔH ^o and ΔS ^o along with relation coefficient are given in Table 7. The magnitude of ΔG ^o decreased with rising the temperature; from Table 7, the values of ΔH ^o were positive, indicating that the ion-exchange reaction is endothermic. This is also supported by the increase in value of uptake capacity of the adsorbent with rising the temperature.

Table 7 Thermodynamic parameters of La³⁺ and Sm³⁺ adsorption onto {PASnMoP}

The positive values of ΔS show the increasing randomness at the solid/liquid interface during the adsorption of La³⁺ and Sm³⁺ on PASnMoP. Obviously, it is shown from the results reported in Table 7 that the temperature affects the adsorption process of metal ion adsorption onto the resin in which the higher temperature provided more energy to enhance the adsorption rate.

Conclusion

The distribution coefficients of the prepared polyacrylamide Sn(IV) molybdophosphate (PASnMoP) have been investigated for La³⁺ and Sm³⁺ ions and the values of thermodynamic parameters were determined and the overall adsorption processes were found to be spontaneous and endothermic. The linear Langmuir and Freundlich isotherm models were used to represent the experimental data, and the experimental data could be relatively well intercept by the Langmuir isotherm. R _L values between 0 and 1.0 further indicate a favorable adsorption of La³⁺ and Sm³⁺. By applying the kinetic models to the experimental data, it was found that the adsorption of La³⁺ and Sm³⁺ onto PASnMoP followed the Pseudo-second-order rate kinetics. The negative ΔG ^o values showed that the ion exchange of La³⁺ and Sm³⁺ was spontaneous. The positive values of ΔS ^o revealed the increased randomness at the solid solution interface.