International Journal of Mineral Processing 169 (2017) 1–6 Contents lists available at ScienceDirect International Journal of Mineral Processing journal homepage: www.elsevier.com/locate/ijminpro Competitive adsorption characteristics of rhenium in single and binary (Re-Mo) systems using Purolite A170 Mohammad Bagher Fathi, Bahram Rezai ⁎, Eskandar Keshavarz Alamdari Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Tehran 158754413, Iran a r t i c l e i n f o Article history: Received 6 November 2016 Received in revised form 30 September 2017 Accepted 9 October 2017 Available online 10 October 2017 Keywords: Rhenium Purolite A170 Single and binary systems Mechanism a b s t r a c t In this study adsorption of rhenium ions from single and bi-component solutions (Re-Mo) by Purolite A170 was studied experimentally and described by isotherm, kinetic and thermodynamic modeling. Considering coefﬁcient of determination (R2) and values of root mean squared error (RMSE) for the multicomponent isotherms, the extended model of Freundlich isotherm was found to be successful. Moreover, ﬁtting the time-dependent data into different mechanisms showed that the data comply well with the pseudo-second order model. Results from the binary systems demonstrated that the presence of the secondary metal ions in the system causes a decrease in the adsorption capacity of rhenium, which is mainly due to the competitive effects of metals for adsorption sites. Furthermore, evaluation of thermodynamic parameters showed that the reaction mechanisms are different for both systems; however, due to negative values of ΔH, in competitive condition the adsorption of rhenium becomes more feasible with increasing the temperature. © 2017 Published by Elsevier B.V. 1. Introduction Rhenium with abundance concentration of 1 ppb on the Earth's (the Clarke of rhenium being 7 ∗ 10−8%), is one of the rarest elements. Its unique properties have been made it to be demanded in wide industries metallurgy, petrochemical industry, aviation, medicine, defense and chemical (Chekmarev et al., 2004; Nebeker and Hiskey, 2012). Limited world-wide supply of this metal and its critical role in various ﬁelds of modern industry has caused that the price of Re has been in ﬂuctuating in high level and is currently 2500 $/kg (Metalpages[WWWDocument], 2016). Separation of rhenium from the solution could be achieved through different methods such as precipitation, ion-exchange, and solvent extraction. But currently due to high afﬁnity of perrhenate anions (ReO− 4 ) to functionalized resins, preferred recovery technology is selective sorption by ion exchange method (Dąbrowska and Jermakowicz-Bartkowiak, 2008; Mal'tseva et al., 2012a; Zakhar'yan and Gedgagov, 2013). Previous studies have shown that in multicomponent systems, amongst all the various involved metal ions (ferrous and nonferrous), just molybdenum due having very similar chemical behavior with rhenium (the ionic radius of Re4+ and Mo4+ are 0.72 Å and 0.70 Å respectively), can be readily absorbed with the resin and may essentially decrease rhenium loading. Hence, in the processing of bearing solutions, separation of rhenium and molybdenum is the main problem (Blokhin et al., 2011). In a binary Re-Mo system, at pH range of 1–10, perrhenate ions have a stable form of monomeric anion while the structure of Mo ions depends on pH values in the contacting solution tending to form anionic and cationic species. Therefore, it seems that by selecting a proper adsorbent type and grain size and also pH range, these two elements can be separated efﬁciently (Mal'tseva et al., 2012b; Kholmogorov et al., 1999; Mikhaylenko and Blokhin, 2012). Literature survey shows that thus far there is no investigation about detection and description of governing phenomena on the processes of Re-Mo joint presence systems processing using ion exchange method. So, it could be of a great importance to study of a such system to discover the selective or successive adsorption and also mutual effect of metal ion on the sorption of other metal ions, since the presence of other metal ions can lead to synergism, antagonism or non-interaction mechanisms (Chen et al., 2015; Nebeker and Hiskey, 2012). The present study is undertaken to investigate the rhenium ions competitive uptake behavior from the single (Re) and the binary (ReMo) metal ions solutions onto Purolite A170 (weak base/macroporous resin) by the equilibrium, kinetics and thermodynamic relationships. 2. Experimental 2.1. Materials and reagents ⁎ Corresponding author. E-mail address: email@example.com (B. Rezai). https://doi.org/10.1016/j.minpro.2017.10.003 0301-7516/© 2017 Published by Elsevier B.V. Rhenium and Molybdenum standard stock solutions were prepared by dissolving NH4ReO4 (Aldrich) and (NH4)6Mo7O24.4H2O (Aldrich), 2 M.B. Fathi et al. / International Journal of Mineral Processing 169 (2017) 1–6 respectively, in double-distilled water. In binary joint system the pH of the solutions was kept approximately 2 in the studied temperature range. The ion exchanger Purolite A170 (from Purolite) (in what follows, A170) was examined as sorbent. Physical and chemical properties of the resin are provided in Table 1. All reagents were of analytical grade and used without further puriﬁcation. The pH was measured using pH meter (Metrohm 827). The whole tests were perfumed using the Ds311 incubator shaker. Concentration of metal ions in solutions was determined using ICP-OES (Optima 7300 DV Perkin Elmer). 2.2. Method of the experiment 2.2.1. Resins treatment The A170 anionite preliminary was converted to SO24 − form (Abisheva and Zagorodnyaya, 2011; Mal'tseva et al., 2012a; Joo et al., 2012). Weighed amount of resin was kept with 2 mol/l H2SO4 for 48 h which subsequently led to the swelling of resin. Thereafter, the treated resin was ﬁltered and washed by deionized water till a constant value of pH was achieved and later was dried by an oven at 323 ± 1 K duration next 24 h. Before the resin extraction in aqueous solution for sorption of meal ions, it was subjected to soak in water overnight. 2.2.2. Experimental procedure The adsorption experiments were carried out under static condition with ﬂasks of 150 mL volume. Amount of adsorbed metal on anionites was determined from the difference between its initial and ﬁnal concentration in the solution (Blokhin et al., 2011). Experiments of equilibrium isotherms were conducted at 288 K. For single solutions, speciﬁed amounts of the resins (about 0.1 g) were mixed with each of a series of ﬂasks with 50 mL of the ions solution having concentrations ranging from 50 to 250 ppm. In natural deposits, generally it has been accepted that rhenium is mainly carried by molybdenite through the isomorphous replacement of Mo and it has been known as molybdenum coproduct, accordingly always in this systems the concentration of Mo is higher than Re (Maria-Ondina and Daniel, 2013). Hence, for binary solutions in order to get closer to real conditions, concentration of rhenium was varied over the range of 20 to 100 ppm, with Mo concentration ratio of 5. The ﬂasks were kept in a thermostated shaker and stirred continuously for 24 h at shaking speed of 180 rpm to achieve equilibrium state. Kinetics and thermodynamics investigations were followed by adding 0.1 g of the adsorbent in 50 mL adsorbents solution of 250mgl−1 rhenium and 500mgl−1 molybdenum concentration (in binary system) at different temperatures, e.g. 299, 310 and 321 K. The capacity of adsorbed metal was calculated from the mass balance equation as follows: qe ¼ C 0 −C e V W ð1Þ where C0 and Ce are the concentrations of metal ion (mg/l) at t = 0 and equilibrium, V is the total volume of solution (l) and W is the weight of dry resins (gr) (Nur et al., 2014). Table 1 Physical and chemical properties of A170 ion exchange resin. 3. Results and discussion 3.1. Adsorption isotherms Equilibrium studies and development of appropriate isotherm models are basic requirements to analysis and optimize of an adsorption system (Srivastava et al., 2006). Generally, in multicomponent systems due to complicated relations between metal ions and adsorbent, no single component isotherms can demonstrate nature of such interactions at equilibrium state (Senthilkumar and Murugappan, 2015a). In the present research, in order to assess the effects of the most serious adsorption competitor e.g. Mo, on Re uptake from the pregnant natural solutions, two systems namely single and binary Re-Mo, were examined. 3.1.1. Adsorption isotherms for single-component systems Equilibrium data obtained from both Re and Mo single component systems were analyzed separately, using linear forms of four the most frequently applied isotherm models, namely, Langmuir, Freundlich, Temkin and Dubinin–Radushkevich (Eqs.(2)–(5) respectively) (Lou et al., 2013). Langmuir : Ce Ce 1 ¼ þ qe qmax qmax KL Freundlich : logqe ¼ logk f þ Temkin : qe ¼ ð2Þ 1 logCe n ð3Þ RT RT lnA þ logC e b b ð4Þ Dubinin‐Radushkevich ðD‐RÞ : ln qe 1 2 1 ¼ lnqm −β RT ln 1 þ ; E ¼ pﬃﬃﬃﬃﬃﬃ Ce 2β ð5Þ where qe is the equilibrium amount of metal adsorbed on resin (mg·g−1), Ce is the equilibrium metal ions concentration in solution (mg·l− 1), qmax is the monolayer maximum loading capacity of the resin, KL is the Langmuir constant related to the energy of adsorption (l·mg−1), KF is the Freundlich constant related to the adsorption capacity (l·mg−1), 1/n is the heterogeneity factor, A and b are the Temkin constants, qm is the Dubinin-Radushkevich monolayer capacity (mg·g−1) and β (mol2·kJ−2) is a constant with dimensions of energy, and E is the mean free energy of adsorption per mole of the adsorbate (kJ·mol−1). The calculated isotherm parameters are listed in Table 2. As shown from the results, adsorption data of perrhenate ions lie well on isotherm's model as R2 values for these plots are higher than 0.97; however, Freundlich and D-R isotherm models show the selectivity Table 2 Isotherm constants for different models for Re and Mo adsorption on A170 from single component system. Resin type Constants Re Mo Langmuir qmax (mg/g) Kl(L mg−1) R2 Kf((mg/g)/(mg/l)1/n) n R2 A(L mg−1) b(J mol−1) R2 qm(mg/g) β(mo 2 kJ−2) E(kJ/mol) R2 166.67 0.67 0.985 53.83 2.09 0.993 8.76 83.86 0.978 0.006 3.37 ∗ 10−9 12.18 0.998 166.67 0.46 0.962 46.77 1.81 0.818 4.40 68.34 0.941 0.016 4.32 ∗ 10−9 10.755 0.846 Property Description Basic information Structure Matrix Functional group Ionic form Macroporous Polystryrene/divinylbenzene Complex amine OH (free base) Freundlich Physical/chemical Bead size Speciﬁc gravity Moisture retention Total capacity 0.6–1.2 mm 1.05 42–47% (in Cl− form) 1.3 meq/mL Dubinin – Radushkevich (D-R) Temkin M.B. Fathi et al. / International Journal of Mineral Processing 169 (2017) 1–6 coefﬁcient N 0.99. While for Mo, the Langmuir isotherm shows a better ﬁt to the adsorption data than the others. The Langmuir model is the best-known isotherm for describing adsorption from aqueous solution. This model assumes that there is no interaction between the adsorbate molecules and due to homogenous distribution of active sites on the adsorbent surface the adsorption is localized in amonolayer (Xiong et al., 2012; Xiong et al., 2013). In Table 2, the maximum Langmuir monolayer capacities (Qm) for Re and Mo are the same (166.67 mg/g), in contrast, for constant Kl, Re has higher value (0.67) than Mo (0.46), which suggests that perrhenate ions have highest afﬁnity to bind to the A170 functional groups rather than molybdenum. The adsorption intensity of the metal ions on adsorbents also can be determined by A constant in Temkin model. The obtained values of A parameter in Table 2 revealing a higher A170-metal ion potential for Re compared to the Mo ion (Shahmohammadi-Kalalagh, 2011). Another empirical equation is the Freundlich model with KF and 1/n constants that incorporate all factors affecting the adsorption capacity and an indication of the favorability of metal ion adsorption, respectively (Kadirvelu et al., 2008). For classiﬁcation as favorable adsorption the value of n should be within 1 b n b 10 also smaller the value of the 1/n, the higher will be the afﬁnity and the heterogeneity of the adsorbent sites (Shahmohammadi-Kalalagh, 2011; Srivastava et al., 2006). From Table 2, the ﬁrst: n value changes are indicating the favorable adsorption of ions from aqueous medium, and the second: the A170 shows intensive afﬁnity as well as heterogeneity for Re than that for Mo ions. Meanwhile, the KF values indicate the higher uptake of rhenium than that of molybdenum ions. The value of E in D-R model is usually applied to distinguish the physical and chemical adsorption of metal ions. When the value is below 8 kJ/mol, the adsorption process can be considered as the physical adsorption while if it is located in the range of 8–16 kJ/mol, it is the chemical adsorption and indicating ion-exchange mechanism (Liu and Wang, 2013; Singha and Das, 2013). As shown in Table 2, its value for both metals is above 8 kJ/mol that is conﬁrming ion exchange mechanism and also chemical adsorption type in the process. 3.1.2. Adsorption isotherms for multi-component systems In multicomponent solutions the interactions and competitions between different adsorbates to reach the adsorbent, complicate the process. To evaluate such systems, several methodologies have been derived and developed from those of the single-component systems. In the present work, since the adsorption behavior of the investigated metals species in the single-component systems obeyed the Langmuir and Freundlich models, their developed forms for multi component adsorption isotherms namely Extended Langmuir, Modiﬁed Langmuir, Extended Freundlich and Langmuir-Freundlich models (Eqs. (6)–(9)) were used to describe the nature of process. Extended Langmuir : qe;i ¼ Modified Langmuir : qe;i ¼ q max;i KL;i Ce;i 1þ q max;i KL;i 1þ Extended Freundlich : qe;i ¼ C ei ηi N ∑ j¼1 KL; j Cej η j K F;i Cne;ii þxi N ∑ j¼1 Cxe;ii þ yi Cze;i j 1 Langmuir‐Freundlich : qe;i ¼ ð6Þ N ∑ j¼1 KL; j Ce; j aC ð7Þ sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 n ð∑i¼1 Xobs;i −Xmodel;i RMSE ¼ n one metal ion in binary and single systems respectively. Three possible types of behavior may be stated: qe;mix =qe N1, synergism (sorption of target species will be promoted by the presence of other metal ions); qe;mix =qe ¼ 1, no net interaction effect is observed and qe;mix =qe b1, antagonism (the effect of the mixture is less than that of each individual adsorbates in the mixture)(Mahamadi and Nharingo, 2010; Srivastava et al., 2006; Zhu et al., 2012). Under the investigated conditions, the qe;mix =qe values of Re in Re-Mo binary system were ≈ about 0.85which is implying inhibitory effect of molybdenum ions on binding of the perrhenate ions due to their competition for occupying vacant sites on adsorbent with rhenium ions and accordingly perrhenate ions adsorption is suppressed. 3.2. Adsorption Kinetic Analysis of ion exchange kinetics and thermodynamic parameters, such as diffusion coefﬁcient, energy and entropy of activation, or free energy change are of importance as they provide valuable insight into the reaction pathways and into the mechanism of the reaction. In the present work the evaluation of essential parameters for rhenium uptake from both single and binary systems have been done with variation of Re and Mo sorption as a result of temperature changing. Modeling of Table 3 Multi-component isotherm parameter values for the simultaneous adsorption of Re and Mo adsorption on A170. Extended Langmuir Re Mo Modiﬁed Langmuir RMSE R2 ηi RMSE R2 8.72 75.89 Negative Negative 58.23 185.7 1.307 26.13 0.9876 0.2903 Extended Freundlich Re Mo ð9Þ where, qe,i is the equilibrium amount of component i adsorbed in the system, Ce,i is the equilibrium concentration of component i, Ce,j ð10Þ where Xobs,i are the observed values and Xmodel,i are the modeled values (Fouladgar et al., 2015). Fitting parameters, correlation coefﬁcients (R2) and RMSE are given in Table 3. It is evident from the data that the Extended Freundlich model with higher coefﬁcients of determination R2 and lower values of RMSE is the most convenient model to predict the isotherm of Re-Mo binary system. Mutual interference effects of metal ions on adsorption capacity can be probe using qe;mix =qe , where qe, mix and qeare the sorption capacity for ð8Þ =mi i e;i 1= m N ∑ j¼1 b j Ce; j j (j = 1, 2, …, N; N is the number of the components) is the equilibrium concentration of each component, KL(i,j) and (KF(i,j),ni) are the Langmuir and Freundlich constants for component i and j, respectively and qmax,i is the maximum adsorption capacity of component i. The parameters qmax,i, ni and KL,F(i,j) are obtained from the single adsorption isotherm. The other parameters (ηi,j, xi, yi,zi, ai,bj, mi,j) can be obtained from the optimized ﬁtting method (Al-Asheh et al., 2000; Senthilkumar and Murugappan, 2015b; Srivastava et al., 2006; Sukpreabprom et al., 2015). This procedure was performed in MATLAB program. RMSE (root of mean square errors) was also used to evaluate quality of the ﬁtting. RMSE is given as: Adsorbate 3 xi yi zi RMSE R2 −0.4815 −7.774 0.8481 1.74E-06 1.155 −5.727 0.8794 5.078 0.9944 0.9732 Langmuir-Freundlich Re Mo ai mi mj bi bj RMSE R2 54 47 0.5287 4.302 0.7497 4.438 0.3447 12.61 0.6756 −19.96 1.288 15 0.9879 0.7661 4 M.B. Fathi et al. / International Journal of Mineral Processing 169 (2017) 1–6 batch kinetic adsorption performed using linear form of pseudo-ﬁrstorder, pseudo-second-order, Elovich and intra-particle diffusion equations (Eqs.(11)–(14)).(Lou et al., 2013): k1 t Pseudo first‐order equation : log qq ‐qt ¼ logqe − 2:303 Pseudo second‐order equation : Elovich equation : qt ¼ t 1 1 ¼ þ t qt k2 q2e qe ð11Þ ð12Þ 1 1 ln ðαβÞ þ ln t β β ð13Þ Intra‐particle diffusion equation : qt ¼ ki t0:5 ð14Þ where in Eqs. (11) and (12), qt and qe are the amount of adsorbate (mg g−1) at any time (t) and at equilibrium, respectively, and k1 is the rate constant of pseudo ﬁrst-order model (h− 1). k2 (mgg− 1 h−1) is the rate constant for pseudo-second-order. In Eq. (13), α (mg g−1 h−1) is the initial sorption rate constant, and β (mg g−1) is related to the extent of surface coverage and chemisorptions energy of activation and in Eq. (14), ki (mg g−1 h-0.5) is the intra-particle diffusion rate constant. 3.2.1. Kinetics of single and binary component adsorption The kinetic models parameters and selectivity coefﬁcient (R2) are summarized in Table 4. As seen from the R2 values, in all studied conditions the second order kinetic equation is more applicable than others. Moreover, in both systems based on comparison of adsorption capacities for experimental and calculated values, it can be deduced that there are not any signiﬁcant differences between them. The pseudosecond order model demonstrates that the adsorption reaction is the rate determining step. Comparing of the qe and k2 values for the pseudo-second order, in both systems, approves the competitive inhibition in the mixture of ion solutions. Identifying the ion exchange process rate limiting step and involved likely mechanism is commonly performed through the intra-particle diffusion model (Wu et al., 2009). The rate constants for rhenium uptake from both systems corresponding to this model are shown in Figs. 1 and 2, in which the slope of each portion determines its rate. As seen from Fig. 1, in single system, there are 3 stages in adsorption of rhenium on A170 including: (1) diffusion of the ions from the bulk solution to the ﬁlm surrounding the adsorbent, (2) their diffusion from the ﬁlm to the adsorbent surface and (3) diffusion from the surface to the internal sites (Igwe and Abia, 2006; Lou et al., 2013; Qiu et al., 2009). Comparison of slopes show that the sharper portion is belong to arriving of adsorbates ions to adsorbents surrounding ﬁlm by shaking (180 rpm). However, in Fig. 2, it is clear that in binary system, perrhenate ions adsorption is limited just in two stages and third portion has been omitted that is attributed most likely to shield-shaped inhibitions of multicharged molybdenum anions that adsorbed on the resin surface and prevent the rhenium ions penetration into the bead (Mikhaylenko and Blokhin, 2012). Behavior of rhenium ions sorption/desorption Fig. 1. Intra-particle diffusion equation for the adsorption of Re from single system on the A170 resin at the different temperature. Initial concentration of metal ions = 250 mg L−1, resin dosage = 0.1 mg, pH = 2. within grains of A170 was demonstrated by Mal'tseva et al. (2012a, 2012b). In their works the kinetics of the process were analyzed by the limited-volume method. The results conﬁrmed that in both cases (sorption/desorption), the rate is limited by internal diffusion (Mal'tseva et al., 2012a, 2012b). 3.3. Selectivity investigation of A170 toward Re & Mo The magnitude of A170 afﬁnity for studied metal ions was determined by separation percentage (rt) Eq. (15). rt ¼ 100 ðC0 −Ct Þ C0 ð15Þ where C0 and Ct are the concentrations of the metal ions at t = 0 and time t, respectively (Rahmani et al., 2010). Comparing rt values for Re and Mo ions in binary system shows that in all studied conditions the rhenium separation percentage values are always higher (≈ 26%) than for molybdenum values. This is in accordance with results of (Virolainen et al., 2015), who concluded that, the complex amine functional group in the A170 resins favor more univalent anions (ReO− 4 ) than larger and multivalent ions (polymeric oxy anions of molybdenum). Differences between average values of rt for the rhenium in the both systems show a decrease of the perrhenate ions uptake in the presence of the Mo ions by a factor of 63.28%. This difference indicates that in spite of the A170 preference for the adsorption of Re ions, in the presence of a competitor ion, adsorption of this ion is affected by competitive inhibition and shield preventing effects. 3.4. Thermodynamics study Temperature variations impact on thermodynamic constants of Re & Mo ions adsorption on the A170, including changes in the enthalpy Table 4 Kinetic parameters of Re adsorption on to the PuroliteA170 from single (Re = 250 ppm) and binary (Re = 250 ppm-Mo = 500 ppm) system. Pseudo ﬁrst-order Pseudo second-order Elovich Intraparticle diffusion T (K) System qe (exp) (mg g−1) qe (mg g−1) K1 (h−1) R2 Model qe (mg g−1) K2 (mg g−1 h−1) R2 α (mg g−1 h−1) β(gmg−1) R2 Ki (mg g−1 h-0.5) R2 299 124 100.67 124 100.67 124 100.67 40.79 2.847 43.28 2.715 56.75 2.587 3.05 2.21 3.07 2.17 2.94 2.15 310 321 Single Binary Single Binary Single Binary 116.5 100 117.4 98.75 119 98.2 55.53 26.78 63.62 26.84 54.76 26.84 0.012 0.006 0.011 0.006 0.01 0.006 0.992 0.996 0.988 0.997 0.987 0.992 0.00035 0.00022 0.00036 0.00021 0.00037 0.00029 0.999 0.987 0.999 0.995 0.999 0.996 0.056 0.135 0.057 0.136 0.06 0.136 0.986 0.985 0.985 0.995 0.984 0.983 0.922 0.962 0.92 0.965 0.917 0.945 M.B. Fathi et al. / International Journal of Mineral Processing 169 (2017) 1–6 5 weakening the randomness of the system due to occurrence of reaction via an arrangement of metal ions at the surface of the sorbent. 4. Conclusions Fig. 2. Intra-particle diffusion equation for the adsorption of Re from binary (Re-Mo) system on the A170 resin at the different temperature. Initial concentration of metal ions Re = 250 mg L−1, Mo = 500 mg L−1 resin dosage = 0.1 mg, pH = 2. (ΔH), entropy (ΔS) and free energy (ΔG) were calculated using the following equations: Kad ¼ Ca Ce ð16Þ ΔG ¼ −RT ln Kad ð17Þ ΔG ¼ ΔH−TΔS ð18Þ The adsorption mechanism of rhenium on Purolite A170 from single and Re - Mo jointed systems was studied by isotherms, kinetics and thermodynamic modeling. In single systems, the Langmuir maximum adsorption capacity of Re and Mo were found the same (166.67 mg/g). For binary system, adsorption of the Re ions were described well by Extended Freundlich isotherm. Investigation of mutual interference effects of Mo ions on Re adsorption capacity indicated that due to trend of molybdenum ions for occupying vacant sites on adsorbent, always the adsorption of perrhenate ions is suppressed. Kinetic studies showed that the adsorption of the discussed metal ions from the both systems follows a second-order kinetic model with R2 N 0.98. The ﬁt of the data to this model denotes that the adsorption reaction is the rate limiting step of the overall adsorption process. The value of thermodynamic parameters also suggested that the adsorption of perrhenate ions from single component system is spontaneous and endothermic in addition the process follows the dissociative mechanism while for binary condition it is spontaneous and exothermic meanwhile it obeys an associative mechanism as revealed by negative values of entropy. Acknowledgments ln Kad ΔS ΔH 1 − : ¼ R R T ð19Þ where R is the gas constant, T is the reaction temperature (K), Kad is adsorption equilibrium constant, Ca and Ce are concentration of Re(VII) on the adsorbent and solution at equilibrium (mg L−1) respectively. Δ H can be calculated by the slope of the linear Van't Hoff plot (lnKad versus (1/T) acc. to Eq. (19)) (Xiong et al., 2013). Table 5 shows thermodynamic constants of studied both systems related to rhenium adsorption. The positive value of ΔH in single system reveals energy is adsorbed as ion exchange proceeds, and the reaction is endothermic but in competitive state, the negative value of enthalpy implies two phenomenon: (1) the adsorption process is exothermic, due to dissociating of the hydrated metal ions into free ions that are then exchanged, and (2) the overcoming of the dehydration energy of rhenium ions during adsorption was exothermic (Liu et al., 2014). The negative variation of Gibbs free energies show that the adsorption of Re from both systems are spontaneous over the temperature range 299–321 K·The value of ΔS is an indication of whether or not the reaction follows an associative or dissociative mechanism. Positive values of ΔS generally imply a dissociative mechanism, whereas negative values indicate an associative mechanism (Khan et al., 2014). Dissociative mechanism can be attributed to the exchange of the metal ions with more mobile ions present on the exchanger, which would cause increase in the entropy (Xiong et al., 2012) as well as it can be raised from the release of water molecule produced by ion exchange reaction (Lee et al., 2007). In the present study, positive value of entropy for nocompetitive condition, shows the increased randomness at the solid/solution interface during the adsorption process and it reconﬁrms the dissociative mechanism whereas for other case negative sing, indicates Table 5 Thermodynamic parameters of Re(VII) adsorption onto the A170 from single (Re = 250 ppm) and binary (Re = 250 ppm - Mo = 500 ppm) system. System ΔH (kJ/mol) ΔS (J mol−1 K−1) ΔG(kJ/mol) Single Binary 3.34 −4.37 27.31 −8.86 T = 299 K −4.94 −1.72 T = 310 K −5.16 −1.63 T = 321 K −5.35 −1.53 The authors gratefully acknowledge ﬁnancial support from the National Iranian Copper Industries Co. (NICICO). 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Xiong, Y., Xu, J., Shan, W., Lou, Z., Fang, D., Zang, S., Han, G., 2013. A new approach for rhenium (VII) recovery by using modiﬁed brown algae Laminaria japonica adsorbent. Bioresour. Technol. 127, 464–472. Zakhar'yan, S., Gedgagov, E., 2013. Anion-exchange separation of rhenium and selenium in schemes for obtaining ammonium perrhenate. Theor. Found. Chem. Eng. 47, 637–643. Zhu, Y., Hu, J., Wang, J., 2012. Competitive adsorption of Pb (II), Cu (II) and Zn (II) onto xanthate-modiﬁed magnetic chitosan. J. Hazard. Mater. 221, 155–161. Mohammad Bagher Fathi is Ph.D. candidate of mineral processing in Department of Mining and Metallurgical Engineering, Amirkabir University of Technology. Bahram Rezai is a Lecturer at the Department of Mining and Metallurgical Engineering Amirkabir University of Technology. His research interest is hydrometallurgical separation & puriﬁcation techniques particularly ion exchange, liquid-liquid extraction (LLX), which includes optimization of the current technology and development of new techniques. Eskandar Keshavarz Alamdari is a Lecturer at the Department of Mining and Metallurgical Engineering Amirkabir University of Technology. His research ﬁelds are Thermodynamics, Kinetics, simulation, Hydrometallurgy and Pyrometallurgy.