SEPARATION SCIENCE AND ENGINEERING Chinese Journal of Chemical Engineering, 20(5) 823ü830 (2012)
Adsorption and Desorption of Praseodymium (III) from Aqueous Solution Using D72 Resin* XIONG Chunhua (༇ҝ**)ܟ, ZHU Jingfei (ᅋ࠸ᛖ), SHEN Chen (ಋх) and CHEN Qing (ч) Department of Applied Chemistry, Zhejiang Gongshang University, Hangzhou 310012, China Abstract In this work, the feasibility of using a macroporous strong acid ion exchange resin (D72) as an adsorbent for praseodymium (III) was examined. The adsorption behavior and mechanism were investigated with various chemical methods and IR spectrometry. The results showed that the loading of Pr (III) ions was strongly dependent on pH of the medium and the optimal adsorption condition is in HAc-NaAc medium with pH value of 3.0. Adsorption kinetics of Pr (III) ions onto D72 resin could be best described by pseudo-second-order model. The maximum adsorption capacity of D72 for Pr (III) was evaluated to be 294 mg·g1 for the Langmuir model at 298K. The apparent activation energy, Ea, was 14.71 kJ·mol1. The calculated data of thermodynamic parameters, S value of 100 J·mol1·K1 and H value of 8.89 kJ·mol1, indicate the endothermic nature of the adsorption process, while a decrease of G with increasing temperature indicates the spontaneous nature of the adsorption process. Finally, Pr (III) can be eluted by using 1.00 mol·L1 HCl-0.50 mol·L1 NaCl solution and the D72 resin can be regenerated and reused. Thomas model was successfully applied to experimental data to predict the breakthrough curves and to determine the characteristic parameters of the column useful for process design. The characterization before and after adsorption of Pr (III) ions on D72 resin was conformed by IR. Keywords D72 resin, ion exchange, praseodymium (III), adsorption, kinetics, thermodynamics
1
INTRODUCTION
During the past decades, lanthanide elements have received great attention owing to their unique properties and wide applications. Praseodymium and its compounds have numerous industrial applications and they are currently used in ceramic industry, atomic batteries, photo catalytically active material and metallurgy [13]. The consumption of the materials is increasing with the rapid development of the modern industry in the world. Praseodymium may enter the environment in large quantities and accumulate in the human body via the food chain [4]. A number of methods including co-precipitation, solvent extraction, ion exchange and solid phase extraction have been employed for the removal of lanthanide elements from industrial effluents [5, 6]. Solvent extraction and ion exchange are the two most common methodologies for the preconcentration and separation of trace elements. However, the main drawback of solvent extraction process is the loss of extractant into the aqueous solution, which may cause environmental hazards and economic limitations. Compared with solvent extraction, ion exchange is simpler to operate and easier to separate. Various adsorbents including chelate resins and ion exchange resins are used in extraction of praseodymium ions [7, 8]. Chelate resins present good features of easy-functional and chemical stability, and shortcomings of poor hydrophilicity, slow adsorption rate and bad elution. Ion exchange resins are solid and suitably insolubilized high molecular weight polyelectrolytes. The resulting ion exchange is reversible
and stoichiometric with the displacement of one ionic species by another on the exchanger [9, 10]. El-Dessouky et al. [11] studied the sorption of praseodymium (III) from nitrate medium using TVEXPHOR resin. However, the literature data concerning the adsorption process of praseodymium (III) onto strong acid ion exchange resin are limited. In this study, a strong acid ion exchange resin (D72) is used, which is a polymeric material containing a functional group ( SO3H). It presents remarkable chemical and physical stability for temperatures of interest in treating aqueous solutions, and the functional groups ensure a large pH domain of work. Its principal characteristics are high exchange capacity and good ability of regeneration. Moreover, it is cheaper than imported resins. In this work, the adsorption behavior and mechanism of Pr (III) on D72 resin are investigated with various chemical methods and IR spectrometry. Some factors affecting the adsorption, such as initial pH of solution, contact time and temperature, are examined. Adsorption experiments for kinetics and isotherm are carried out. Thermodynamic parameters of adsorption for Pr (III) are calculated. The experimental results may provide a path for the preconcentration and recovery of Pr (III) from aqueous solutions in the environmental protection and hydrometallurgical systems. 2 2.1
MATERIALS AND METHOD Apparatus Pr (III) was determined with Shimadzu UV-2550
Received 2011-02-18, accepted 2011-09-05. * Supported by the National Key Technologies Research and Development Program of China (2008BAD94B09), the Key Laboratory of Advanced Textile Materials and Manufacturing Technology (Zhejiang Sci-Tech University), the Ministry of Education (2011007), and the Zhejiang Provincial Scientific Research Project (Y201223624). ** To whom correspondence should be addressed. E-mail:
[email protected]
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UV-visible spectrophotometer. The resin dosage was measured by electronic balance of Sartorius BS 224S. Mettler Toledo delta 320 pH meter was used for pH measurement. The sample was shaken in the DSHZ300 A temperature constant shaking machine. The water used in the present work was purified using Molresearch analysis-type ultra-pure water machine. The sample for IR spectroscopy was described by Nicolet 380 FT-IR. 2.2
Materials
D72 resin was supplied by Nankai University and its properties are shown in Table 1. Standard solutions of Pr(III) were prepared from Pr2O3 (AR). HAc-NaAc with pH 3.006.00 and triethanolamine-nitric acid with pH 7.20 buffer solutions were prepared from the NaAc, HAc, N(C2H4OH)3 and HNO3 solutions. The chromophoric reagent of 0.1% arsenazo-I solution was obtained by dissolving 0.1000 g arsenazo-I powder into 100 ml deionized water. All other chemicals were of analytical grade and purified water was used throughout. Table 1
General description and properties of D72 Items
Properties macroporous strong acid ion exchange resin
resin functional group
SO3H
structure
macroporous
granularity (70100 nm)/%
ı95
capacity/mmol·g1
ı4.0
glass columns (4.5 mm×235 mm) wet-packed with 300.0 mg (dry mass) D72 resin. The aqueous solution with known concentrations of Pr (III) was then fed to the top of the bed at 0.152 ml·min1 until the breakthrough curve was completed. The samples in the outlet were taken at the preset time intervals and the concentrations of Pr (III) were determined. In addition, dynamic desorption procedures were also carried out. With respect to the stripping of Pr (III) from the resin, eluent of 1.00 mol·L1 HCl-0.50 mol·L1 NaCl solution was employed. 2.3.4 Analytical method A solution containing Pr (III) was accurately added into a 25 ml colorimetric tube, and then 1 ml chromophoric reagent of 0.1% arsenazo-I solution and 10 ml pH 7.2 C6H15O3N-HNO3 buffer solution were added. After the addition of purified water to the mark of colorimetric tube, the absorbency was determined in a 1 cm colorimetric vessel at 580 nm and compared with the blank test. The adsorption capacity (Q), distribution coefficient (D) and desorption ratio (E) were calculated with the following formulas [12]: C0 Ce V Q (1) m C0 Ce V D u (2) Ce m
E
ground pellet ratio/%
ı90
wet superficial density/g·ml1
0.750.80
3
1.201.30
3.1
true wet density/g·ml
1
particle size range/mm
2.3
C0 Ce u 100% C0
(3)
RESULTS AND DISCUSSION Effect of pH on the adsorption for Pr (III)
0.2120.300
Adsorption experiments
2.3.1 Batch studies A desired amount of treated D72 resin was weighed and added into a conical flask, in which a desired volume of buffer solution with pH 3.00 was added. After 24 h, a required amount of standard solution of Pr (III) was added. The flask was shaken in a shaker at the constant temperature. Aliquot samples were taken from the flask at appropriate time intervals as necessary. The residual concentration of Pr (III) in the aqueous phases was measured at 580 nm. 2.3.2 Desorption studies Desorption of Pr (III) was performed by mixing D72-Pr (III) complexes and HCl-NaCl eluent solution of different concentrations, and shaken at 100 r·min1 for 24 h at 298K. The final Pr (III) concentrations in the aqueous phase were analyzed. 2.3.3 Column studies The fixed-bed experiments were carried out in
The adsorption of Pr (III) from aqueous solutions onto D72 resin is primarily effected by the surface charge of the adsorbent [13]. The effect of pH on the adsorption behavior of D72 resin was tested with Pr (III) in the range of pH 2.65.0 for an initial concentration of Pr (III) 0.286 mg·ml1 at 298 K, 100 r·min1. Fig. 1 shows that the adsorption capacity of D72 resin decreases evidently as the pH of solution increases and the maximum adsorption (1.64 mmol·g1) is obtained at pH value of 3.0. Therefore, subsequent experiments were carried out at pH 3.0 in the HAc-NaAc system. 3.2
Effect of contact time
The equilibrium adsorption time of Pr (III) on D72 resin was investigated. As shown in Fig. 2, a high initial slope for the adsorption curves is observed. It indicates that the initial uptake is rapid, since at the beginning of the adsorption process all the reaction sites are vacant and the extent of adsorption is high. After a rapid initial uptake, there is a transitional phase, in which the rate of uptake is slow with uptake
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with equilibrium between the solution and solid phase. For the pseudo-first-order model, the following relation was used for the variation of adsorbed concentration with respect to time [17].
lg Qe Qt lg Q1
Figure 1 Effect of pH on the distribution coefficient (mass of resin 15.0 mg, C0 0.286 mg·ml1, T 298 K, r 100 r·min1)
reaching almost a constant value. Consequently, the adsorption is carried out in two distinct stages, a relatively rapid one followed by a slower one. The results also indicate that an increase of temperature enchances the capacity of praseodymium adsorption [14]. 3.3
Adsorption kinetics study
The study of adsorption kinetics describes the solute uptake rate and evidently the rate controls the residence time of metal ion uptake at the solid-solution interface including the diffusion process. The mechanism of adsorption depends on the physical and chemical characteristics of the adsorbent as well as on the mass transfer process [15]. The experimental results were used to study the kinetics of metal ion adsorption. The kinetics of Pr (III) adsorption on D72 resin was analyzed using pseudo-first-order and pseudo-second-order models [16]. The conformity between experimental data and the model predicted values was expressed by correlation coefficient (R2). The adsorption of Pr (III) from a liquid phase to solid phase can be considered as a reversible process
(4)
where k1 (h1) is the rate constant of pseudo-first-order adsorption, Qe (mg·g1) and Qt (mg·g1) denote the amounts of adsorption at equilibrium and at time t, respectively, and Q1 (mg·g1) is the calculated adsorption capacity. The slopes and intercepts of plots of lg(Qe Qt) versus t were used to determine the pseudo first-order rate constant k1 and Q1. In addition, a pseudo-second-order equation based on sorption equilibrium capacity may be expressed in the form of [18] t Qt
Figure 2 Effect of contact time for the adsorption (mass of resin 15.0 mg, C0 0.286 mg·ml1, pH 3.00, r 100 r·min1) ƽ288 K;ƻ298 K;Ʒ308 K
k1t 2.303
1 t 2 k2 Q2 Q2
(5)
The constants (k2 and Q2) can be experimentally determined by plotting t/Qt versus t from the intercept and slope, respectively, and there is no need to know any parameter beforehand. According to the parameters (Table 2), the experimental results obtained are found to obey the pseudo-second-order model. The theoretical Q1 values estimated from the pseudo-first-order model give significantly different values compared to experimental values, and the correlation coefficients are also found to be lower. These results show that the first-order kinetic model does not describe these adsorption systems. The theoretical Q2 values for the resin are very close to the experimental Qe values in the case of second-order kinetics. The correlation coefficients for the pseudo-second-order equation are greater than 0.989. The pseudo-second-order equation at different temperatures fits well with the experimental data. The pseudo-second-order model is based on the assumption that the rate-determining step may be a chemical sorption involving valence forces through sharing or exchange of electrons between adsorbent and adsorbate [19]. Thus, successful fitting of this model suggests that chemisorption is the rate-controlling step. From Table 2, it is seen that the adsorption capacity increases with temperature, showing an endothermic adsorption process. The activation energy is determined according to the pseudo-second order rate constant, expressed as a function of temperature by the Arrhenius equation [20]. lg k
Ea lg A 2.303RT
(6)
Value of the activation energy, Ea, can be determined from the slope of lgk versus 1/T, and the value is 14.71 kJ·mol1, which can be considered as a low energy barrier in this study. It can be deduced that the adsorption rate accelerates as temperature increases in the scope of experimental temperature.
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Table 2
The first-order and second-order kinetics parameters Pseudo-first-order kinetics
Qe(exp) /mg·g1
k1/h1
Q1/mg·g1
R2
k2/g·mg1·h1
Q2/mg·g1
R2
288
201
0.085
181
0.9889
5.27×103
244
0.9987
298
221
0.112
195
0.9828
6.56×103
256
0.9993
263
0.9995
308
233
0.121
Figure 3 Langmuir isotherm (mass of resin C0 0.286 mg·ml1, pH 3.00, r 100 r·min1) ƽ 288 K;ƻ298 K;Ʒ308 K
3.4
Pseudo-second-order kinetics
T/K
197
0.9949
15.0 mg,
Equilibrium adsorption isotherms
Equilibrium data, commonly known as adsorption isotherms, are the basic requirements for the design of adsorption systems. Equilibrium data for a specific adsorbate/adsorbent system can be obtained experimentally, with a time-consuming procedure that is incompatible with the growing need for sorption system design. Analysis of equilibrium data is important for developing an equation that can be used to compare different sorbents under different operational conditions and to design and optimize an operating procedure [21, 22]. Langmuir [23, 24] and Freundlich [25] equations are used to reveal the linearity fitting and to describe how solutes interact with the resins. The linear forms of the Langmuir and Freundlich isotherms are represented as follows. Langmuir isotherm: Ce Qe
Ce 1 Qmax bQmax
(7)
where Qe is the adsorption capacity in equilibrium state, Ce is the equilibrium Pr (III) concentration in solution, Qmax is the maximum capacity of the adsorbent and b is the Langmuir constant which reflects quantitatively the affinity between the D72 resin and Pr (III). Freundlich isotherm: lg Qe
1 lg K f lg Ce n
(8)
7.85×10
3
Figure 4 Freundlich isotherm (mass of resin 15.0 mg, C0 0.286 mg·ml1, pH 3.00, r 100 r·min1) ƽ 288 K;ƻ298 K;Ʒ308 K
The Freundlich isotherm constants Kf and n are constants incorporating all factors affecting the adsorption process such as adsorption capacity and intensity of adsorption. The Langmuir and Freundlich isotherms are shown in Figs. 3 and 4, and the parameters are listed in Table 3. It is evident that the adsorption of Pr (III) onto D72 resin fits the Langmuir isotherm model better than the Freundlich isotherm model, as indicated by the R2 values and the adsorption capacity values in Table 3. Since the Langmuir isotherm assumes a monolayer coverage and uniform activity distribution on the adsorbent surface, this is an expected result. The maximum adsorption capacity of the D72 for Pr (III) is evaluated to be 294 mg·g1 (2.09 mmol·g1) for the Langmuir model at 298 K and the adsorption molar ratio (metal/functional group) of D72 resin for Pr (III) is 0.523. It means that the complex ratio of the functional group ( SO3H) to Pr (III) is about 2Ή1. The essential features of a Langmuir isotherm can be expressed in terms of a dimensionless constant, separation factor or equilibrium parameter RL, which is used to predict that an adsorption system is “favorable” or “unfavorable” [26]. RL
1 1 bC0
(9)
The RL values for the adsorption on clarified sludge at initial concentration of 0.3 mg·ml1 are listed in Table 3. The results reveal that the adsorption of Pr (III) on D72 resin is a favorable adsorption.
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Table 3
Freundlich model T/K n
3.6
Langmuir and Freundlich parameters
Kf/mg·g
1
Langmuir model
2
R
b/ml·mg
1
Qmax/mg·g1
R2
RL
288 8.10
336
0.9895
61
293
0.9987 0.052
298 8.42
338
0.9805
75
294
0.9984 0.043
308 8.17
356
0.9806
96
303
0.9993 0.034
3.5
Desorption studies
Thermodynamic parameters
In order to evaluate the feasibility and the effect of temperature better, thermodynamic parameters such as standard free energy change (G), standard enthalpy change (H) and standard entropy change (S) are also evaluated [27]: (10) (11) From the slope and intercept of the plot (Fig. 5), the values of H and S are computed, while G is calculated using Eq. (11). The values of these parameters thus calculated are recorded in Table 4. It may be concluded from the positive values of H that the sorption process is endothermic while the positive value of S is an indicative of increased randomness at the adsorbent-absorbate interface during the adsorption. The negative value of G confirms the feasibility and spontaneous nature of the adsorption process [28].
Figure 5 Relationship between lgD and T1 (mass of resin 15.0 mg, C0 0.286 mg·ml1, pH 3.00, r 100 r·min1)
The economic feasibility of using an adsorbent to absorb metal ions from wastewater relies on its regeneration ability during multiple adsorption/desorption cycles. Adsorption of metal ions on any adsorbent can be by physical, chemical bonding, ion exchange or combination of all. Desorption study can give a clear idea about the mechanism of adsorption and is useful in recycling of the adsorbent and recovery of metals. In this work, desorption of Pr(III) with various concentrations of eluent solution are carried out. The results presented in Table 5 show that the elution ratio is different when the eluent concentration changes. Maximum recovery of Pr(III), at 100%, is achieved with the 1 mol·L1 HCl-0.5 mol·L1 NaCl eluent solution. The results show that the Pr (III) adsorbed by the D72 resin can easily be desorbed, which indicates that the resin can be employed repeatedly in Pr (III) adsorption. Table 5
The elution test of Pr (III)
Composition of HCl-NaCl
Elution percentage/%
0.25 mol·L1 HCl-0.25 mol·L1 NaCl
96.0
1
1
0.5 mol·L HCl-0.5 mol·L NaCl 1
0.75 mol·L HCl-0.25 mol·L NaCl
98.8
1.0 mol·L1 HCl-0.5 mol·L1 NaCl
100
3.7 Dynamic adsorption and desorption 3.7.1 Dynamic adsorption curve The performance of packed beds is described through the concept of the breakthrough curve. The breakthrough curve shows the loading behavior of Pr (III) to be removed from solution in a fixed bed and is usually expressed in terms of adsorbed Pr (III) concentration or normalized concentration defined as the ratio of effluent Pr (III) concentration to inlet Pr (III) concentration (Ce/C0) as a function of time or volume of effluent for a given bed height. The area under the breakthrough curve obtains by integrating the adsorbed concentration versus the throughput volume plot could be used to find the total adsorbed Pr (III) quantity (maximum column capacity). Total adsorbed Pr (III) quantity in the column for a given feed concentration and flow rate is calculated as follows [29] Ve
Q
³ 0
Table 4
Thermodynamic parameters for Pr (III) on D72 resin
H /kJ·mol1
S /J·mol1·K1
8.89
100.38
G/kJ·mol1 T
288K T
37.80
298K T
38.80
308K T
39.80
318K
40.81
96.4
1
C0 Ce m
dVe
(12)
The capacity value Q is obtained by graphical integration as 201 mg·g1. Successful design of a column adsorption process requires prediction of the concentration versus time profile or breakthrough curve for the effluent. The maximum sorption capacity of resin is also needed in design. Traditionally, the Thomas model is used to fulfill the purpose, which is [30]
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Ce C0
1 1 exp ª¬ K T Q0 m C0Ve / T º¼
(13)
The linearized form of the Thomas model is as follows §C · ln ¨ 0 1¸ © Ce ¹
K T Q0 m
T
K T C0
T
Ve
(14)
The kinetic coefficient KT and the adsorption capacity of the bed Q0 can be determined from a plot of ln[(C0/Ce) 1] versus t at a certain flow rate as shown in Fig. 6. The Thomas equation coefficients for Pr (III) adsorption are KT 1.42×102 ml·min1·mg1 and Q0 203 mg·g1. The theoretical predictions based on the model parameters are compared with the experimental data as shown in Fig. 7.
resin in column is essential to ensure the reuse of resin for repeated adsorption/desorption cycles. With respect to the stripping of Pr (III) from D72 resin, 1.0 mol·L1 HCl-0.5 mol·L1 NaCl eluant is employed. Desorption curve is plotted with the effluent concentration (Ce) versus elution volume from the column at a certain flow rate. It can be seen from Fig. 8 that the adsorption flow rate is less so that the volume of elution is less, which helps in easy handling and high concentration for economical recovery of Pr (III). It is observed that the total volume of eluent is 150 ml, after which further desorption is negligible. Therefore, the 1.0 mol·L1 HCl-0.5 mol·L1 NaCl eluant is appropriate.
Figure 8 Dynamic desorption curve (mass of resin 300 mg, 0.10 ml·min1) Figure 6 Linear plots of ln(C0/Ce 1) versus t by application of Thomas model (mass of resin 300 mg, pH 3.00, C0 0.10 mg·ml1, 0.152 ml·min1)
Figure 7 Dynamic adsorption curve (mass of resin 300 mg, pH 3.00, C0 0.10 mg·ml1, 0.152 ml·min1) ƽ experimental data; Ƹ Thomas model
The Thomas model is found in a relatively good fitness with breakthrough curves for adsorption of Pr (III) on D72 resin with a high R2 value (0.9725), and the theoretical Q0 value is very close to the experimental one. Therefore, the experimental data fits well to the Thomas model. 3.7.2 Dynamic desorption curve Efficient elution of adsorbed solute from D72
3.8
IR spectra
From the results above, it can be deduced that the adsorption of Pr (III) by D72 resin is assigned to a chemical adsorption. Therefore, the functional group of D72 resin, SO3H, and Pr (III) are supposed to form chemical bonds. To identify this possibility, IR spectra are obtained for D72 resin before and after Pr (III) adsorption, as shown in Fig. 9. In general, significant changes are observed. The IR spectra of D72 resin exhibit major band at 3433 cm1 for OH stretching vibration. Medium broad vibrations observed in the IR spectrum in the range 17402786 cm1 are assigned to overtones/combinations of hydrogen bonded OH bending modes from proton tunneling and Fermi resonance interactions [3133]. The SO2 asymmetric vibration is found to be at 1221 cm1 as a medium band in the IR spectrum [34]. The symmetric SO2 stretching vibration appears around 1179 cm1 in both IR and Raman spectra. By comparison with SOH bending frequencies in sulfuric acid and other sulfonic acids, the band at ~1127 cm1 is assigned to SOH bend. A comparison of the spectra for free D72 resin with that of Pr loaded D72 resin reveals characteristic changes of OH, asSO2 and sSO2, which shifts from 3433, 1221 and 1179 cm1 before Pr (III) adsorption to 3409, 1223 and 1156 cm1 Pr (III) after adsorption. These findings may suggest that there are coordination bonds between Pr (III) ion and oxygen atoms in the
Chin. J. Chem. Eng., Vol. 20, No. 5, October 2012
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Figure 9 Infrared spectra 1übefore adsorption; 2üafter Pr (III) adsorption
OH and S O groups in the adsorption. 4
CONCLUSIONS
In this study, the adsorption characteristics are investigated at different pH values, temperatures and contact time by batch and column experiments. We conclude that D72 resin can be used for preconcentration of Pr (III) very effectively. It is observed that Pr (III) adsorption is highly dependent on pH. In addition, D72 resin dosage and initial Pr (III) concentration are effective on Pr (III) adsorption process. Kinetic studies show that the adsorption process obeys pseudo-secondorder kinetics, and the adsorption behavior can be modeled using the Langmuir isotherm. The maximum adsorption capacity of Pr (III) is estimated to be 294 mg·g1 by batch method at 298 K. The apparent activation energy is 14.71 kJ·mol1. The adsorption parameters of thermodynamic are H 8.89 kJ·mol1, G 38.80 kJ·mol1, S 100 J·mol1·K1, which indicates that the adsorption of Pr (III) on the D72 resin is endothermic in nature. Column experiments show that it is possible to adsorb Pr (III) from aqueous solutions dynamically. In summary, D72 resin have many advantages to adsorb Pr (III) in the solution and it has a potential for the treatment of industrial effluents containing rare earth elements. NOMENCLATURE
b Ce C0 D E Ea G H Kf KT k1 k2 m n Q Qe Qmax Q0 Q1 Q2 R RL S T V Ve as s
REFERENCES 1
A
Arrhenius factor
Langmuir isotherm constant, ml·mg1 equilibrium praseodymium concentration, mg·ml1 initial praseodymium concentration, mg·ml1 distribution coefficient desorption ratio Arrhenius activation energy, kJ·mol1 standard free energy change, kJ·mol1 standard enthalpy change, kJ·mol1 Freundlich isotherm constant, mg·g1 Thomas rate constant, ml·min1·mg1 rate constant of pseudo-first-order adsorption, h1 rate constant of pseudo-second-order adsorption, g·mg1·h1 mass of dry D72 resin used, g a constant indicating the Freundlich isotherm curvature adsorption capacity, mg·g1 adsorption capacity in equilibrium state, mg·g1 maximum capacity of adsorbent, mg·g1 theoretical adsorption capacity, mg·g1 theoretical adsorption capacity of pseudo-first-order model theoretical adsorption capacity of pseudo-second-order model gas constant, 8.314 J·mol1·K1 equilibrium parameter standard entropy change, J·mol1·K1 solution temperature, K total volume of solution, ml volume of metal solution passed through the column, ml stretching vibration asymmetric stretching vibration symmetric stretching vibration volumetric flow rate, ml·min1
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