Skip to main content

Ion Exchange Equilibria and Kinetics

  • Chapter
  • First Online:
Ion Exchange Technology I

Abstract

The accurate modelling of equilibrium and kinetics of ion exchange is fundamental for economic and safe design of industrial units, particularly to carry out the delicate scale-up studies and simulations.

With regard to equilibrium, this chapter covers the following topics: (1) ion association phenomena; (2) activity coefficients in solution and exchanger phases; (3) the milestones works of Gaines and Thomas, Argersinger et al., and Ioannidis et al. to the thermodynamic treatment of ion exchange; and (4) a deep discussion of the three most important theories in the literature (homogeneous mass action models, ion adsorption and related models, and heterogeneous mass action models).

Concerning ion exchange kinetics and mass transport processes, the chapter reviews semiempirical models, Fick’s law and derived expressions, Nernst–Planck equations, and the Maxwell–Stefan formulation.

The chapter ends with the general modelling approaches to the omnipresent batch and fixed bed applications.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Smith JM, Ness HCV, Abbott MM (2000) Introduction to chemical engineering thermodynamics, 6th edn. McGraw-Hill, Singapore

    Google Scholar 

  2. Zemaitis JF, Clark DM, Rafal M, Scrivner NC (1986) Handbook of aqueous electrolyte thermodynamics. ed. A.I.o.C. Engineers, New York, pp 64–66

    Google Scholar 

  3. Dranoff J, Lapidus L (1957) Equilibrium in ternary ion exchange systems. Ind Eng Chem 49(8):1297–1302

    CAS  Google Scholar 

  4. Pieroni LJ, Dranoff JS (1963) Ion exchange equilibria in a ternary system. Aiche J 9(1):42–45

    CAS  Google Scholar 

  5. Prausnitz JM, Lichtenthaler RN, Azevedo EG (1999) Molecular thermodynamics of fluid-phase equilibria. Prentice Hall, New Jersey

    Google Scholar 

  6. Pitzer KS, Peiper JC, Busey RH (1984) Thermodynamic properties of aqueous sodium chloride solutions. J Phys Chem Ref Data 13(1):1–102

    CAS  Google Scholar 

  7. Robinson RA, Stokes RH (1923) Electrolyte solutions. Butterworths, London

    Google Scholar 

  8. Bromley LA (1973) Thermodynamic properties of strong electrolytes in aqueous solutions. Aiche J 19(2):313–320

    CAS  Google Scholar 

  9. Pitzer KS (1973) Thermodynamics of electrolytes. I. Theoretical basis and general equations. J Phys Chem 77(2):268–277

    CAS  Google Scholar 

  10. Meissner HP, Kusik CL (1972) Activity coefficients of strong electrolytes in multicomponent aqueous solutions. Aiche J 18(2):294–298

    CAS  Google Scholar 

  11. Kusik CL, Meissner HP (1978) Electrolyte activity coefficients in inorganic processing. AIChE Symp Ser 74(173):14–20

    CAS  Google Scholar 

  12. Poling BE, Prausnitz JM, O’Connel JP (2000) The properties of gases and liquids, 5th edn. McGraw-Hill, Singapore

    Google Scholar 

  13. Wohl K (1946) Thermodynamic evaluation of binary and ternary liquid systems. Trans Am Inst Chem Eng 42(2):215–249

    CAS  Google Scholar 

  14. Kester DR, Pytkowicz RM (1975) Theoretical model for the formation of ion-pairs in seawater. Mar Chem 3(4):365–374

    CAS  Google Scholar 

  15. Vo BS, Shallcross DC (2005) Ion exchange equilibria data for systems involving H+, Na+, K+, Mg2+, and Ca2+ ions. J Chem Eng Data 50(3):1018–1029

    CAS  Google Scholar 

  16. Majer V, Stulík K (1982) A study of the stability of alkaline-earth metal complexes with fluoride and chloride ions at various temperatures by potentiometry with ion-selective electrodes. Talanta 29(2):145–148

    CAS  Google Scholar 

  17. Perrin DD, Högfeldt E, Sillen LG, Martell AE (1971) Stability constants of metal-ion complexes. Pergamon, Oxford, Supplement

    Google Scholar 

  18. Johnson KS, Pytkowicz RM (1979) Ion association of chloride and sulphate with sodium, potassium, magnesium and calcium in seawater at 25°C. Mar Chem 8(1):87–93

    CAS  Google Scholar 

  19. Atlas E, Culberson C, Pytkowicz RM (1976) Phosphate association with Na+, Ca2+ and Mg2+ in seawater. Mar Chem 4(3):243–254

    CAS  Google Scholar 

  20. De Robertis A, Rigano C, Sammartano S, Zerbinati O (1987) Ion association of Cl with Na+, K+, Mg2+ and Ca2+ in aqueous solution at 10 ≤ T ≤ 45°C and 0 ≤ I ≤ 1 mol L−1: a literature data analysis. Thermochimica Acta 115:241–248

    Google Scholar 

  21. Mehablia MA, Shallcross DC, Stevens GW (1994) Prediction of multicomponent ion exchange equilibria. Chem Eng Sci 49(14):2277–2286

    CAS  Google Scholar 

  22. Mumford KA, Shallcross DC, Snape I, Stevens GW (2008) Application of a temperature-dependent semiempirical thermodynamic ion-exchange model to a multicomponent natural zeolite system. Ind Eng Chem Res 47(21):8347–8354

    CAS  Google Scholar 

  23. Velayudhan A, Horváth C (1994) Adsorption and ion-exchange isotherms in preparative chromatography. J Chromatogr A 663(1):1–10

    CAS  Google Scholar 

  24. Shallcross DC (2003) Modelling multicomponent ion exchange equilibrium behaviour. J Ion Exch 14(Supp):5–8

    Google Scholar 

  25. Melis S, Cao G, Morbidelli M (1995) A new model for the simulation of ion exchange equilibria. Ind Eng Chem Res 34(11):3916–3924

    CAS  Google Scholar 

  26. Klein G, Tondeur D, Vermeulen T (1967) Multicomponent ion exchange in fixed beds. General properties of equilibrium systems. Ind Eng Chem Fundam 6(3):339–351

    CAS  Google Scholar 

  27. Smith RP, Woodburn ET (1978) Prediction of multicomponent ion exchange equilibria for the ternary system SO 2−4 - NO 3 - Cl from data of binary systems. Aiche J 24(4):577–587

    CAS  Google Scholar 

  28. Sengupta M, Paul TB (1985) Multicomponent ion exchange equilibria. I. Zn2+−Cd2+−H+ and Cu2+−Ag+−H+ on Amberlite IR 120. React Polym Ion Exch Sorb 3(3):217–229

    CAS  Google Scholar 

  29. Shallcross DC, Herrmann CC, McCoy BJ (1988) An improved model for the prediction of multicomponent ion exchange equilibria. Chem Eng Sci 43(2):279–288

    CAS  Google Scholar 

  30. De Martínez AL, Cañizares P, Díaz JZ (1993) Binary ion exchange equilibrium for Ca2+, Mg2+, K+, Na+ and H+ ions on amberlite IR-120. Chem Eng Technol 16(1):35–39

    Google Scholar 

  31. Ioannidis S, Anderko A, Sanders SJ (2000) Internally consistent representation of binary ion exchange equilibria. Chem Eng Sci 55(14):2687–2698

    CAS  Google Scholar 

  32. Borba CE, Silva EA, Spohr S, Santos GHF, Guirardello R (2010) Ion exchange equilibrium prediction for the system Cu2+−Zn2+−Na+. J Chem Eng Data 55(3):1333–1341

    CAS  Google Scholar 

  33. Helfferich F (1995) Ion exchange. Dover, New York

    Google Scholar 

  34. Kataoka T, Yoshida H (1980) Ion exchange equilibria in ternary systems. J Chem Eng Japan 13(4):328–330

    CAS  Google Scholar 

  35. Elprince AM, Babcock KL (1975) Prediction of ion-exchange equilibria in aqueous systems with more than two counter-ions. Soil Sci 120(5):332–338

    CAS  Google Scholar 

  36. Shehata FA, El-Kamash AM, El-Sorougy MR, Aly HF (2000) Prediction of multicomponent ion-exchange equilibria for a ternary system from data of binary systems. Sep Sci Technol 35(12):1887–1900

    CAS  Google Scholar 

  37. de Lucas A, Valverde JL, Romero MC, Gómez J, Rodríguez JF (2002) The ion exchange equilibria of Na+/K+ in nonaqueous and mixed solvents on a strong acid cation exchanger. Chem Eng Sci 57(11):1943–1954

    Google Scholar 

  38. Vamos RJ, Haas CN (1994) Reduction of ion-exchange equilibria data using an error in variables approach. Aiche J 40(3):556–569

    CAS  Google Scholar 

  39. Pabalan RT, Bertetti FP (1999) Experimental and modeling study of ion exchange between aqueous solutions and the zeolite mineral clinoptilolite. J Sol Chem 28(4):367–393

    CAS  Google Scholar 

  40. Mumford KA, Northcott KA, Shallcross DC, Snape I, Stevens GW (2008) Comparison of amberlite IRC-748 resin and zeolite for copper and ammonium ion exchange. J Chem Eng Data 53(9):2012–2017

    CAS  Google Scholar 

  41. Carmona M, Warchoł J, Ad L, Rodriguez JF (2008) Ion-exchange equilibria of Pb2+, Ni2+, and Cr3+ ions for H+ on amberlite IR-120 resin. J Chem Eng Data 53(6):1325–1331

    CAS  Google Scholar 

  42. de Lucas A, Rodriguez L, Sanchez P, Lobato J (2003) Retention capacity of the builder δ-Na2Si2O5. Modeling the Ca2+/Mg2+/Na+ equilibrium. Ind Eng Chem Res 42(14):3257–3262

    CAS  Google Scholar 

  43. Robinson C, Gilliland E (1950) Elements of fractional distillation. McGraw-Hill, New York

    Google Scholar 

  44. De Lucas A, Zarca J, Cañizares P (1992) Ion-exchange equilibrium of Ca2+, Mg2+, K+, Na+, and H+ ions on amberlite IR-120: experimental determination and theoretical prediction of the ternary and quaternary equilibrium data. Sep Sci Technol 27(6):823–841

    Google Scholar 

  45. Vo BS, Shallcross DC (2005) Modeling solution phase behavior in multicomponent ion exchange equilibria involving H+, Na+, K+, Mg2+, and Ca2+ ions. J Chem Eng Data 50(6):1995–2002

    CAS  Google Scholar 

  46. Allen RM, Addison PA, Dechapunya AH (1989) The characterization of binary and ternary ion exchange equilibria. Chem Eng J 40(3):151–158

    CAS  Google Scholar 

  47. Allen RM, Addison PA (1990) Ion exchange equilibria for ternary systems from binary exchange data. Chem Eng J 44(3):113–118

    Google Scholar 

  48. Stewart WE, Liou CT, Lim HC, Weigand WA, Berger AJ, HÃla E (1972) Letters to the editor. AIChE J 18(4):875–876

    Google Scholar 

  49. Hála E (1972) Liquid–vapor equilibrium. LII. On boundary conditions between constants of Wilson and NRTL equations in three- and more component systems. Collect Czechoslovak Chem Commun 37:2817–2819

    Google Scholar 

  50. Bajpai RK, Gupta AK, Rao MG (1973) Binary and ternary ion-exchange equilibriums. Sodium-cesium-manganese-Dowex 50W-X8 and cesium-manganese-strontium-Dowex 50W-X8 systems. J Phys Chem 77(10):1288–1293

    CAS  Google Scholar 

  51. Argersinger WJ, Davidson AW, Bonner OD (1950) Thermodynamics and ion exchange phenomena. Kansas Acad Trans 53:404–410

    CAS  Google Scholar 

  52. Gaines JGL, Thomas HC (1953) Adsorption studies on clay minerals. II. A formulation of the thermodynamics of exchange adsorption. J Chem Phys 21(4):714–718

    CAS  Google Scholar 

  53. Provis JL, Lukey GC, Shallcross DC (2005) Modeling multicomponent ion exchange: application of the single-parameter binary system model. Ind Eng Chem Res 44(7):2250–2257

    CAS  Google Scholar 

  54. Ioannidis S, Anderko A (2001) Equilibrium modeling of combined ion-exchange and molecular adsorption phenomena. Ind Eng Chem Res 40(2):714–720

    CAS  Google Scholar 

  55. Fletcher P, Townsend RP (1981) Ternary ion exchange in Zeolites. Part 1. – problem of predicting equilibrium compositions. J Chem Soc Faraday Trans 2:77

    Google Scholar 

  56. Soldatov VS, Bychkova VA (1971) Calculation of activity coefficients of components of the ion exchanger phase in multicomponent systems. Russ J Phys Chem 45(5):707–709

    Google Scholar 

  57. Ioannidis S, Anderko A (2000) Equilibrium modeling of combined ion-exchange and molecular adsorption phenomena. Ind Eng Chem Res 40(2):714–720

    Google Scholar 

  58. Mehablia MA, Shallcross DC, Stevens GW (1996) Ternary and quaternary ion exchange equilibria. Sol Extract Ion Exch 14(2):309–322

    CAS  Google Scholar 

  59. Pabalan RT (1994) Thermodynamics of ion exchange between clinoptilolite and aqueous solutions of Na+/k+ and Na+/Ca2+. Geochim Cosmochim Acta 58(21):4573–4590

    CAS  Google Scholar 

  60. Barreira LD, Lito PF, Antunes BM, Otero M, Lin Z, Rocha J, Pereira E, Duarte AC, Silva CM (2009) Effect of pH on cadmium (II) removal from aqueous solution using titanosilicate ETS-4. Chem Eng J 155(3):728–735

    CAS  Google Scholar 

  61. Camarinha ED, Lito PF, Antunes BM, Otero M, Lin Z, Rocha J, Pereira E, Duarte AC, Silva CM (2009) Cadmium(II) removal from aqueous solution using microporous titanosilicate ETS-10. Chem Eng J 155(1–2):108–114

    CAS  Google Scholar 

  62. Ferreira TR, Lopes CB, Lito PF, Otero M, Lin Z, Rocha J, Pereira E, Silva CM, Duarte A (2009) Cadmium(II) removal from aqueous solution using microporous titanosilicate ETS-4. Chem Eng J 147(2–3):173–179

    CAS  Google Scholar 

  63. Lopes CB, Lito PF, Otero M, Lin Z, Rocha J, Silva CM, Pereira E, Duarte AC (2008) Mercury removal with titanosilicate ETS-4: batch experiments and modelling. Micropor Mesopor Mater 115(1–2):98–105

    CAS  Google Scholar 

  64. Lopes CB, Otero M, Coimbra J, Pereira E, Rocha J, Lin Z, Duarte A (2007) Removal of low concentration Hg2+ from natural waters by microporous and layered titanosilicates. Micropor Mesopor Mater 103(1–3):325–332

    CAS  Google Scholar 

  65. Lopes CB, Otero M, Lin Z, Silva CM, Pereira E, Rocha J, Duarte AC (2010) Effect of pH and temperature on Hg2+ water decontamination using ETS-4 titanosilicate. J Hazard Mater 175(1–3):439–444

    CAS  Google Scholar 

  66. Lopes CB, Otero M, Lin Z, Silva CM, Rocha J, Pereira E, Duarte AC (2009) Removal of Hg2+ ions from aqueous solution by ETS-4 microporous titanosilicate – kinetic and equilibrium studies. Chem Eng J 151(1–3):247–254

    CAS  Google Scholar 

  67. Otero M, Lopes CB, Coimbra J, Ferreira TR, Silva CM, Lin Z, Rocha J, Pereira E, Duarte AC (2009) Priority pollutants (Hg2+ and Cd2+) removal from water by ETS-4 titanosilicate. Desalination 249(2):742–747

    CAS  Google Scholar 

  68. Altin O, Özbelge HÖ, Dogu T (1998) Use of general purpose adsorption isotherms for heavy metal-clay mineral interactions. J Colloid Interface Sci 198(1):130–140

    Google Scholar 

  69. Petrus R, Warchol JK (2005) Heavy metal removal by clinoptilolite. An equilibrium study in multi-component systems. Water Res 39(5):819–830

    CAS  Google Scholar 

  70. Ku Y, Lee K-C, Wang W (2005) Removal of phenols from aqueous solutions by purolite A-510 resin. Sep Sci Technol 39(4):911–923

    Google Scholar 

  71. Carmona M, Lucas AD, Valverde JL, Velasco B, Rodríguez JF (2006) Combined adsorption and ion exchange equilibrium of phenol on Amberlite IRA-420. Chem Eng J 117(2):155–160

    CAS  Google Scholar 

  72. Caetano M, Valderrama C, Farran A, Cortina JL (2009) Phenol removal from aqueous solution by adsorption and ion exchange mechanisms onto polymeric resins. J Colloid Interface Sci 338(2):402–409

    CAS  Google Scholar 

  73. Myers AL, Byington S (1986) Thermodynamics of ion exchange: prediction of multicomponent equilibria from binary data. In: Rodrigues AE (ed) Ion exchange: science and technology. Martinus Nijhoff, Dordrecht, pp 119–145

    Google Scholar 

  74. Novosad J, Myers AL (1982) Thermodynamics of ion exchange as an adsorption process. Can J Chem Eng 60(4):500–503

    CAS  Google Scholar 

  75. Sircar S, Myers AL (1971) A thermodynamic consistency test for adsorption from binary liquid mixtures on solids. AIChE J 17(1):186–190

    CAS  Google Scholar 

  76. Harned HS, Owen BB (1958) The physical chemistry of electrolytic solutions, 3rd edn. Reinhold, New York

    Google Scholar 

  77. Saunders MS, Vierow JB, Carta G (1989) Uptake of phenylalanine and tyrosine by a strong-acid cation exchanger. AIChE J 35(1):53–68

    CAS  Google Scholar 

  78. Dye SR, Decarli JP, Carta G (1990) Equilibrium sorption of amino-acids by a cation-exchange resin. Ind Eng Chem Res 29(5):849–857

    CAS  Google Scholar 

  79. Zammouri A, Chanel S, Muhr L, Grevillot G (2000) Ion-exchange equilibria of amino acids on strong anionic resins. Ind Eng Chem Res 39(5):1397–1408

    CAS  Google Scholar 

  80. Jones IL, Carta G (1993) Ion exchange of amino acids and dipeptides on cation resins with varying degree of crosslinking. 1. Equilibrium. Ind Eng Chem Res 32(1):107–117

    CAS  Google Scholar 

  81. Moreira MJA, Ferreira LMGA (2005) Equilibrium studies of phenylalanine and tyrosine on ion-exchange resins. Chem Eng Sci 60(18):5022–5034

    CAS  Google Scholar 

  82. de Kock FP, van Deventer JSJ (1995) Statistical thermodynamic model for competitive ion exchange. Chem Eng Commun 135(1):21–45

    Google Scholar 

  83. Lukey GC, Van Deventer JSJ, Shallcross DC (2000) Equilibrium model for the selective sorption of gold cyanide on different ion-exchange functional groups. Minerals Eng 13(12):1243–1261

    CAS  Google Scholar 

  84. Lukey GC, Van Deventer JSJ, Shallcross DC (2001) Equilibrium model for the sorption of gold cyanide and copper cyanide on trimethylamine ion exchange resin in saline solutions. Hydrometallurgy 59(1):101–113

    CAS  Google Scholar 

  85. Provis JL, Lukey GC, Shallcross DC (2004) Single-parameter model for binary ion-exchange equilibria. Ind Eng Chem Res 43(24):7870–7879

    CAS  Google Scholar 

  86. Barrer RM, Meier WM (1959) Exchange equilibria in a synthetic crystalline exchanger. Trans Faraday Soc 55:130–141

    CAS  Google Scholar 

  87. Melis S, Markos J, Cao G, Morbidelli M (1996) Multicomponent equilibria on ion-exchange resins. Fluid Phase Equilibria 117(1–2):281–288

    CAS  Google Scholar 

  88. Valverde JL, de Lucas A, Rodriguez JF (1998) Comparison between heterogeneous and homogeneous MASS action models in the prediction of ternary ion exchange equilibria. Ind Eng Chem Res 38(1):251–259

    Google Scholar 

  89. Namasivayam C, Senthilkumar S (1998) Removal of arsenic(V) from aqueous solution using industrial solid waste: adsorption rates and equilibrium studies. Ind Eng Chem Res 37(12):4816–4822

    CAS  Google Scholar 

  90. Ho YS, McKay G (1999) Pseudo-second order model for sorption processes. Process Biochem 34(5):451–465

    CAS  Google Scholar 

  91. Ho YS, McKay G (1999) The sorption of lead(II) ions on peat. Water Res 33(2):578–584

    CAS  Google Scholar 

  92. Reddad Z, Gerente C, Andres Y, Le Cloirec P (2002) Adsorption of several metal ions onto a low-cost biosorbent: kinetic and equilibrium studies. Environ Sci Technol 36(9):2067–2073

    CAS  Google Scholar 

  93. Yardim MF, Budinova T, Ekinci E, Petrov N, Razvigorova M, Minkova V (2003) Removal of mercury (II) from aqueous solution by activated carbon obtained from furfural. Chemosphere 52(5):835–841

    CAS  Google Scholar 

  94. Chiron N, Guilet R, Deydier E (2003) Adsorption of Cu(II) and Pb(II) onto a grafted silica: isotherms and kinetic models. Water Res 37(13):3079–3086

    CAS  Google Scholar 

  95. Aksu Z (2005) Application of biosorption for the removal of organic pollutants: a review. Process Biochem 40(3–4):997–1026

    CAS  Google Scholar 

  96. Zhang F-S, Nriagu JO, Itoh H (2005) Mercury removal from water using activated carbons derived from organic sewage sludge. Water Res 39:389–395

    CAS  Google Scholar 

  97. Chen S, Yue Q, Gao B, Xu X (2010) Equilibrium and kinetic adsorption study of the adsorptive removal of Cr(VI) using modified wheat residue. J Colloid Interface Sci 349(1):256–264

    CAS  Google Scholar 

  98. Edebali S, Pehlivan E (2010) Evaluation of amberlite IRA96 and Dowex 1x8 ion-exchange resins for the removal of Cr(VI) from aqueous solution. Chem Eng J 161(1–2):161–166

    CAS  Google Scholar 

  99. Faghihian H, Kabiri-Tadi M (2010) Removal of zirconium from aqueous solution by modified clinoptilolite. J Hazard Mater 178(1–3):66–73

    CAS  Google Scholar 

  100. Ofomaja AE, Naidoo EB, Modise SJ (2010) Biosorption of copper(II) and lead(II) onto potassium hydroxide treated pine cone powder. J Environ Manage 91(8):1674–1685

    CAS  Google Scholar 

  101. Wahab MA, Jellali S, Jedidi N (2010) Effect of temperature and pH on the biosorption of ammonium onto Posidonia oceanica fibers: equilibrium, and kinetic modeling studies. Bioresour Technol 101(22):8606–8615

    CAS  Google Scholar 

  102. Wang L, Zhang J, Zhao R, Li Y, Li C, Zhang C (2010) Adsorption of Pb(II) on activated carbon prepared from Polygonum orientale Linn.: kinetics, isotherms, pH, and ionic strength studies. Bioresour Technol 101(15):5808–5814

    CAS  Google Scholar 

  103. Wang XM, Huang JH, Huang KL (2010) Surface chemical modification on hyper-cross-linked resin by hydrophilic carbonyl and hydroxyl groups to be employed as a polymeric adsorbent for adsorption of p-aminobenzoic acid from aqueous solution. Chem Eng J 162(1):158–163

    CAS  Google Scholar 

  104. Chien SH, Clayton WR (1980) Application of Elovich equation to the kinetics of phosphate release and sorption on soils. Soil Sci Amer J 44:265

    CAS  Google Scholar 

  105. Sparks DL (1986) Kinetics of reaction in pure and mixed systems. In: Sparks DL (ed) Soil physical chemistry. CRC press, Boca Raton

    Google Scholar 

  106. Anirudhan TS, Radhakrishnan PG (2010) Uptake and desorption of nickel(II) using polymerised tamarind fruit shell with acidic functional groups in aqueous environments. Chem Ecol 26(2):93–109

    CAS  Google Scholar 

  107. Davila-Rangel JI, Solache-Rios M, Badillo-Almaraz VE (2005) Comparison of three Mexican aluminosilicates for the sorption of cadmium. J Radioanal Nuc Chem 267(1):139–145

    Google Scholar 

  108. Ngah WSW, Hanafiah M (2008) Adsorption of copper on rubber (Hevea brasiliensis) leaf powder: kinetic, equilibrium and thermodynamic studies. Biochem Eng J 39(3):521–530

    Google Scholar 

  109. Sivasankara V, Ramachandramoorthy T, Chandramohan A (2010) Fluoride removal from water using activated and MnO2-coated Tamarind Fruit (Tamarindus indica) shell: batch and column studies. J Hazard Mater 177(1–3):719–729

    Google Scholar 

  110. Ritchie AG (1977) Alternative to the Elovich equation for the kinetics of adsorption of gases on solids. J Chem Soc Faraday Trans 73:1650–1653

    CAS  Google Scholar 

  111. Helfferich F (1962) Ion exchange. McGraw-Hill, New York

    Google Scholar 

  112. Liberti L, Boari G, Passino R (1978) Chloride-sulfate exchange on anion resins – kinetic investigations.2. Particle diffusion rates. Desalination 25(2):123–134

    CAS  Google Scholar 

  113. Trgo M, Peric J, Medvidovic NV (2006) A comparative study of ion exchange kinetics in zinc/lead – modified zeolite-clinoptilolite systems. J Hazard Mater 136(3):938–945

    CAS  Google Scholar 

  114. Trgo M, Peric J, Medvidovic NV (2006) Investigations of different kinetic models for zinc ions uptake by a natural zeolitic tuff. J Environ Manage 79(3):298–304

    CAS  Google Scholar 

  115. Cincotti A, Mameli A, Locci AM, Orru R, Cao G (2006) Heavy metals uptake by Sardinian natural zeolites: experiment and modeling. Ind Eng Chem Res 45(3):1074–1084

    CAS  Google Scholar 

  116. Varshney KG, Gupta PA, Tayal N (2003) Kinetics of ion exchange of alkaline earth metal ions on, acrylamide cerium(IV) phosphate: a fibrous ion exchanger. Colloids Surf B Biointerfaces 28(1):11–16

    CAS  Google Scholar 

  117. Patzay G (1995) A simplified numerical solution method for the Nernst-Planck multicomponent ion exchange kinetics model. React Funct Polym 27(1):83–89

    CAS  Google Scholar 

  118. Smith TG, Dranoff JS (1964) Film diffusion-controlled kinetics in binary ion exchange. Ind Eng Chem Fundam 3(3):195–200

    CAS  Google Scholar 

  119. Chanda M, Rempel GL (1995) Sorption of sulfide on a macroporous, quaternized poly(4-vinyl pyridine) in alkaline medium. React Polym 24(3):203–212

    CAS  Google Scholar 

  120. Dolgonosov AM, Khamizov RK, Krachak AN, Prudkovsky AG (1995) Macroscopic model for multispecies ion-exchange kinetics. React Funct Polym 28(1):13–20

    CAS  Google Scholar 

  121. Rodriguez JF, Valverde JL, Rodrigues AE (1998) Measurements of effective self-diffusion coefficients in a gel-type cation exchanger by the zero-length-column method. Ind Eng Chem Res 37(5):2020–2028

    CAS  Google Scholar 

  122. Samson E, Marchand J (1999) Numerical solution of the extended Nernst-Planck model. J Colloid Interface Sci 215(1):1–8

    CAS  Google Scholar 

  123. Varshney KG, Pandith AH (1999) Forward and reverse ion-exchange kinetics for some alkali and alkaline earth metal ions on amorphous zirconium(IV) aluminophosphate. Langmuir 15(22):7422–7425

    CAS  Google Scholar 

  124. Rodriguez JF, de Lucas A, Leal JR, Valverde JL (2002) Determination of intraparticle diffusivities of Na+/K+ in water and water/alcohol mixed solvents on a strong acid cation exchanger. Ind Eng Chem Res 41(12):3019–3027

    CAS  Google Scholar 

  125. Valverde JL, De Lucas A, Carmona M, Gonzalez M, Rodriguez JF (2004) A generalized model for the measurement of effective diffusion coefficients of heterovalent ions in ion exchangers by the zero-length column method. Chem Eng Sci 59(1):71–79

    CAS  Google Scholar 

  126. Valverde JL, De Lucas A, Carmona M, Gonzalez M, Rodriguez JF (2005) Model for the determination of diffusion coefficients of heterovalent ions in macroporous ion exchange resins by the zero-length column method. Chem Eng Sci 60(21):5836–5844

    CAS  Google Scholar 

  127. Wesselingh JA, Vonk P, Kraaijeveld G (1995) Exploring the Maxwell-Stefan description of ion-exchange. Chem Eng J Biochem Eng J 57(2):75–89

    CAS  Google Scholar 

  128. Lagergren S (1898) About the theory of so-called adsorption of soluble substances Kungliga Svenska Vetenskapsakademiens. Handlingar 24:1–39

    Google Scholar 

  129. Ruthven DM (1984) Principles of adsorption and adsorption processes. Wiley, New York

    Google Scholar 

  130. Crank J (1999) The mathematics of diffusion, 2nd edn. Oxford University Press, Great Britain

    Google Scholar 

  131. Vermeulen T (1953) Theory for irreversible and constant-pattern solid diffusion. Ind Eng Chem 45(8):1664–1670

    CAS  Google Scholar 

  132. Inglezakis VJ, Grigoropoulou HP (2001) Applicability of simplified models for the estimation of ion exchange diffusion coefficients in zeolites. J Colloid Interface Sci 234(2):434–441

    CAS  Google Scholar 

  133. Aharoni C, Sparks DL (1991) Kinetics of soil chemical-reactions – a theoretical treatment. Rates Soil Chem Process 27:1–18

    CAS  Google Scholar 

  134. Aharoni C, Sparks DL, Levinson S, Ravina I (1991) Kinetics of soil chemical-reactions – relationships between empirical equations and diffusion-models. Soil Sci Soc Am J 55(5):1307–1312

    CAS  Google Scholar 

  135. Slater MJ (1991) Principles of ion exchange technology. Butterworth-Heinemann, Great Britain

    Google Scholar 

  136. Patzay G (1995) A simplified numerical solution method for the Nernst-Planck multicomponent ion exchange kinetics model. React Funct Polym 27:83–89

    CAS  Google Scholar 

  137. Krishna R, Wesselingh JA (1997) Review article number 50 – the Maxwell-Stefan approach to mass transfer. Chem Eng Sci 52(6):861–911

    CAS  Google Scholar 

  138. Krishna R (1990) Multicomponent surface-diffusion of adsorbed species – a description based on the generalized Maxwell-Stefan equations. Chem Eng Sci 45(7):1779–1791

    CAS  Google Scholar 

  139. Krishna R (1993) Problems and pitfalls in the use of the Fick formulation for intraparticle diffusion. Chem Eng Sci 48(5):845–861

    CAS  Google Scholar 

  140. Kapteijn F, Moulijn JA, Krishna R (2000) The generalized Maxwell-Stefan model for diffusion in zeolites: sorbate molecules with different saturation loadings. Chem Eng Sci 55(15):2923–2930

    CAS  Google Scholar 

  141. van de Graaf JM, Kapteijn MF, Moulijn JA (1999) Modeling permeation of binary mixtures through zeolite membranes. Aiche J 45(3):497–511

    Google Scholar 

  142. van der Stegen JHG et al (1999) Application of the Maxwell-Stefan theory to the transport in ion-selective membranes used in the chloralkali electrolysis process. Chem Eng Sci 54(13–14):2501–2511

    Google Scholar 

  143. Hogendoorn JA, Veen AJVd, Stegen JHGVd, Kuipers JAM, Versteeg GF (2001) Application of the Maxwell-Stefan theory to the membrane electrolysis process: model development and simulation. Comput Chem Eng 25:1251–1265

    CAS  Google Scholar 

  144. Wesselingh JA, Vonk P, Kraaijeveld G (1995) Exploring the Maxwell-Stefan description of ion-exchange. Chem Eng J Biochem Eng J 57(2):75–89

    CAS  Google Scholar 

  145. Graham EE, Dranoff JS (1982) Application of the Stefan-Maxwell equations to diffusion in ion-exchangers.1. Theory. Ind Eng Chem Fundam 21(4):360–365

    CAS  Google Scholar 

  146. Graham EE, Dranoff JS (1982) Application of the Stefan-Maxwell equations to diffusion in ion-exchangers.2. Experimental results. Ind Eng Chem Fundam 21(4):365–369

    CAS  Google Scholar 

  147. Pinto NG, Graham EE (1987) Characterization of ionic diffusivities in ion-exchange resins. Ind Eng Chem Res 26(11):2331–2336

    CAS  Google Scholar 

  148. Jackson R (1977) Transport in porous catalysts. Elsevier, Amsterdam

    Google Scholar 

  149. Mason EA, Malinauskas AP (1983) Gas transport in porous media: the dusty gas model. Elsevier, Amsterdam/The Netherlands

    Google Scholar 

  150. Treybal RE (1981) Mass-transfer operations, 3rd edn. McGraw-Hill, Singapore

    Google Scholar 

  151. Misic DM, Sudo Y, Suzuki M, Kawazoe K (1982) Liquid-to-particle mass-transfer in a stirred batch adsorption tank with non-linear isotherm. J Chem Eng Jpn 15(1):67–70

    CAS  Google Scholar 

  152. Kulov NN, Nikolaishvili EK, Barabash VM, Braginski LN, Malyusov VA, Zhavoronkov NM (1983) Dissolution of solid particles suspended in agitated vessels. Chem Eng Commun 21(4–6):259–271

    CAS  Google Scholar 

  153. Miller SA, Amber CM, Bennet RC, Dahlstrom DA, Darji JD, Emmet RC, Gray JB, Gurnham CF, Jacobs LJ, Klepper RP, Michalson AW, Oldshue JY, Silverblatt CE, Smith JC, Todd DB Liquid-solid systems, In: Perry RH, Green D (eds) Perry’s chemical engineers’ handbook. McGrow-Hill, Singapore

    Google Scholar 

  154. Townsend R, Harjula R (2002) Ion exchange in molecular sieves by conventional techniques, in post-synthesis modification I. Springer, Berlin/Heidelberg, pp 1–42

    Google Scholar 

  155. Thomas HC (1944) Heterogeneous ion exchange in a flowing system. J Am Chem Soc 66:1664–1666

    CAS  Google Scholar 

  156. Bohart GS, Adams EQ (1920) Some aspects of the behavior of charcoal with respect to chlorine. J Am Chem Soc 42:523–544

    CAS  Google Scholar 

  157. Clark RM (1987) Evaluating the cost and performance of field-scale antigranulocytes activated carbon systems. Environ Sci Technol 21(6):573–580

    CAS  Google Scholar 

  158. Yoon YH, Nelson JH (1984) Application of gas-adsorption kinetics.1. A theoretical-model for respirator cartridge service life. Am Ind Hyg Assoc J 45(8):509–516

    CAS  Google Scholar 

  159. Wolborska A (1989) Adsorption on activated carbon of p-nitrophenol from aqueous solution. Water Res 23(1):85–91

    CAS  Google Scholar 

  160. Baral SS, Das N, Ramulu TS, Sahoo SK, Das SN, Chaudhury GR (2009) Removal of Cr(VI) by thermally activated weed Salvinia cucullata in a fixed-bed column. J Hazard Mater 161(2–3):1427–1435

    CAS  Google Scholar 

  161. Han R, Wang Y, Zhao X, Wang Y, Xie F, Cheng J, Tang M (2009) Adsorption of methylene blue by phoenix tree leaf powder in a fixed-bed column: experiments and prediction of breakthrough curves. Desalination 245(1–3):284–297

    CAS  Google Scholar 

  162. Pitzer KS (1991) Ion interaction approach: theory and data correlation. In: Pitzer KS (ed) Activity coefficients in electrolyte solutions. CRC Press, Boca Raton, pp 75–153

    Google Scholar 

  163. Aniceto JPS, Cardoso SP, Faria TL, Lito PF, Silva CM (2012) Modeling ion exchange equilibrium: analysis of exchanger phase non-ideality. Desalination 290:43–53

    CAS  Google Scholar 

  164. Aniceto JPS, Lito PF, Silva CM (2012b) Modeling sorbent phase non-ideality for accurate prediction of multicomponent ion exchange equilibrium with homogeneous mass action law. J Chem Eng Data doi:10.1021/je300156H

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Carlos M. Silva .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Lito, P.F., Cardoso, S.P., Loureiro, J.M., Silva, C.M. (2012). Ion Exchange Equilibria and Kinetics. In: Dr., I., Luqman, M. (eds) Ion Exchange Technology I. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1700-8_3

Download citation

Publish with us

Policies and ethics