Ion Exchange frederick j. Dechow 1.0 INTRODUCTION In 1850 Thompson reported the first ion exchange applications which used naturally occurring clays. However, ion exchange resins have only been used in biochemical and fermentation product recovery since the 1930s / In these early studies, biochemicals such as adenosine triphos phate, 4 alcohols, 5I alkaloids, 6) amino acids, 7 growth regulators, 3I hor- mones,penicillin[ol and vitamin B12 i were purified using ion exchange resins Ion exchange applications intensified following the work of Moore and Stein, [2 which showed that very complex mixtures of biochemicals, in this case amino acids and amino acid residues could be isolated from each other using the ion exchange resin as a column chromatographic separator. In biotechnology applications today, ion exchangers are important in preparing water of the necessary quality to enhance the desired microorganism activity during fermentation. Downstream of the fermentation, ion exchange resins may be used to convert, isolate, purify or concentrate the desired product or by-products. This chapter discusses ion exchange resins and their use in commercial fermentation and protein purification operations 382
Ion Exchange Frederick J. Dechow 1.0 INTRODUCTION In 1850 Thompson['] reported the first ion exchange applications which used naturally occurring clays. However, ion exchange resins have only been used in biochemical and fermentation product recovery since the 1930'~.[~1[~] In these early studies, biochemicals such as adenosine triphosphate,i4] alcohols,[5] alkaloids,[6] amino acids,['] growth regulators,[*] hormone~,[~] penicillin[10] and vitamin B12["1 were purified using ion exchange resins. Ion exchange applications intensified following the work of Moore and Stein,[12] which showed that very complex mixtures of biochemicals, in this case, amino acids and amino acid residues could be isolated from each other using the ion exchange resin as a column chromatographic separator. In biotechnology applications today, ion exchangers are important in preparing water of the necessary quality to enhance the desired microorganism activity during fermentation. Downstream of the fermentation, ion exchange resins may be used to convert, isolate, purify or concentrate the desired product or by-products. This chapter discusses ion exchange resins and their use in commercial fermentation and protein purification operations. 382
Ton Exchange 383 1.1 lon Exchange processes Processes involving ion exchange resins usually make use of ion interchange with theresin. Examples of these processes are demineralization conversion,purification and concentration. Chromatographic processes with ion exchange resins merely make use of the ionic environment that the resins provide in separating solutes Demineralization is the process in which the salts in the feed stream are removed by passing the stream through a cation exchange column in the hydrogen ion form, followed by an anion exchange column in the hydroxide or"free-base"form. Water is the most common feed stream in demineraliza tion. It may also be necessary to remove the salts from a feed stream before fermentation High metallic ion concentrations and high total salt content in the carbohydrate feed has been found to decrease the yield in citric acid fermentation. 3] These ions can be removed by passing the carbohydrate olution through cation and anion exchange resin beds. The salts required for optimum microorganism activity can be added in the desired concentration prior to fermentation Conversion or metathesis is a process in which salts of acids are converted to the corresponding free acids by reaction with the hydrogen form of a strong acid cation resin. One such example would be the conversion of calcium citrate to citric acid The terms may also be used to describe a process in which the acid salt is converted to a different salt of that acid by interaction with a ion exchang resin regenerated to the desired ionic form Many fermentation products may be purified by adsorbing them on ior exchange resins to separate them from the rest of the fermentation broth Once the resin is loaded, the product is eluted from the column for further purification or crystallization Adsorbing lysine on ion exchange resin is probably the most widely used industrial method of purifying lysine. The fermented broth is adjusted to pH20 with hydrochloric acid and then passed through a column of strong acid cation resin in the NH form. Dilute aqueous ammonia may be used to elute the lysine from the resin, [4 gordienkoll5)has reported that treating the resin with a citrate buffer solution ofpH3 2 and rinsing with distilled water before elution results in an 83-90% yield of lysine, with a purity of 93-96%
Ion Exchange 383 1.1 Ion Exchange Processes Processes involving ion exchange resins usually make use of ion interchange with the resin. Examples ofthese processes are demineralization, conversion, purification and concentration. Chromatographic processes with ion exchange resins merely make use of the ionic environment that the resins provide in separating solutes. Demineralization is the process in which the salts in the feed stream are removed by passing the stream through a cation exchange column in the hydrogen ion form, followed by an anion exchange column in the hydroxide or “free-base” form. Water is the most common feed stream in demineralization. It may also be necessary to remove the salts from a feed stream before fermentation. High metallic ion concentrations and high total salt content in the carbohydrate feed has been found to decrease the yield in citric acid fermentati~n.[’~] These ions can be removed by passing the carbohydrate solution through cation and anion exchange resin beds. The salts required for optimum microorganism activity can be added in the desired concentration prior to fermentation. Conversion or metathesis is a process in which salts of acids are converted to the corresponding free acids by reaction with the hydrogen form of a strong acid cation resin. One such example would be the conversion of calcium citrate to citric acid. The terms may also be used to describe a process in which the acid salt is converted to a different salt of that acid by interaction with a ion exchange resin regenerated to the desired ionic form. Many fermentation products may be purified by adsorbing them on ion exchange resins to separate them from the rest of the fermentation broth. Once the resin is loaded, the product is eluted from the column for further purification or crystallization. Adsorbing lysine on ion exchange resin is probably the most widely used industrial method of purifying lysine. The fermented broth is adjusted to pH 2.0 with hydrochloric acid and then passed through a column of strong acid cation resin in the NH; form. Dilute aqueous ammonia may be used to elute the lysine from the resin.[14] Gordienko[151 has reported that treating the resin with a citrate buffer solution ofpH 3.2 and rinsing with distilled water before elution results in an 83-90% yield of lysine, with a purity of 93-96%
384 Fermentation and Biochemical Engineering Handbook lon exchange can be used to concentrate valuable or toxic products of fermentation reactions in a manner similar to purification, the difference between the two processes is in the lower concentration of the desired product in the feed solution of concentration processes Shiratoll6] reported the concentration process for the antibiotic tubercidan produced from fermented rice grain using the microorganism, Streptomyces tubercidicus. Macroporous strong acid cation resin was used to concentrate the antibiotic from 700 ug/ml in the fermentation broth to 13 mg/ml when eluted with 0.25 N HCl. The yield of the antibiotic was about 1.2 Chromatographic Separation In most ion exchange operations, an ion in solution is replaced with an ion from the resin and the former solution ion remains with the resin, In contrast, ion exchange chromatography uses the ion exchange resin as an adsorption or separation media, which provides an ionic environment, allowing two or more solutes in the feed stream to be separated. The feed solution is added to the chromatographic column filled with the separation beads and is eluted with solvent, often water in the case of fermentation products. The resin beads selectively slow some solutes while others are eluted down the column(Fig. 1). As the solutes move down the column, they separate and their individual purity increases. Eventually, the solutes appear at different times at the column outlet where each can be drawn off separately Chromatographic separations can be classed according to four types depending on the type of materials being separated: affinity difference, exclusion, size exclusion and ion retardation chromatography. These types of separations may be described in terms of the distribution of the material to be separated between the phases involved Figure 2 shows a representation ofthe resin-solvent-solute components of a column chromatographic system. The column is filled with resin beads of the solid stationary phase packed together with the voids between the beads filled with solvent. The phases of interest are(i)the liquid phase between the resin beads, (ii)the liquid phase held within the resin beads and (iii)the solid phase of the polymeric matrix of the resin beads. When the feed solution is placed in contact with the hydrated resin in the chromatographic column, the solutes distribute themselves between the liquid inside the resin and that between the resin beads. The distribution for component i is defined by the distribution coefficient, K
384 Fermentation and Biochemical Engineering Handbook Ion exchange can be used to concentrate valuable or toxic products of fermentation reactions in a manner similar to purification. The difference between the two processes is in the lower concentration ofthe desired product in the feed solution of concentration processes. Shirato[l6] reported the concentration process for the antibiotic tubercidan produced from fermented rice grain using the microorganism, Streptomyces tubercidicus. Macroporous strong acid cation resin was used to concentrate the antibiotic from 700 pg/d in the fermentation broth to 13 mg/d when eluted with 0.25 N HCl. The yield of the antibiotic was about 83%. 1.2 Chromatographic Separation In most ion exchange operations, an ion in solution is replaced with an ion from the resin and the former solution ion remains with the resin. In contrast, ion exchange chromatography uses the ion exchange resin as an adsorption or separation media, which provides an ionic environment, allowing two or more solutes in the feed stream to be separated. The feed solution is added to the chromatographic column filled with the separation beads and is eluted with solvent, often water in the case of fermentation products. The resin beads selectively slow some solutes while others are eluted down the column (Fig. 1). As the solutes move down the column, they separate and their individual purity increases. Eventually, the solutes appear at different times at the column outlet where each can be drawn off separately. Chromatographic separations can be classed according to four types depending on the type of materials being separated: affinity difference, ion exclusion, size exclusion and ion retardation chromatography. These types of separations may be described in terms of the distribution of the materials to be separated between the phases involved. Figure 2 shows a representation ofthe resin-solvent-solute components of a column chromatographic system. The column is filled with resin beads ofthe solid stationary phase packed together with the voids between the beads filled with solvent. The phases of interest are (i) the liquid phase between the resin beads, (ii) the liquid phase held within the resin beads and (iii) the solid phase of the polymeric matrix of the resin beads. When the feed solution is placed in contact with the hydrated resin in the chromatographic column, the solutes distribute themselves between the liquid inside the resin and that between the resin beads. The distribution for component i is defined by the distribution coefficient, Kd,:
where Cr is the concentration of component i in the liquid within the resin bead and Cai is the concentration of component i in the interstitial liquid. The distribution coefficient for a given ion or molecule will depend upon that component's structure and concentration, the type and ionic form of the resin and the other components in the feed solution. The distribution coefficients for several organic compounds are given in Table 1. 7 Desorbent Added Added Solute Mixture 幽隙 c s Occurs Fast omen Component Removed Removed From Colun Figure 1. The steps of chromatographic separation are: addition of the mixed solutes to the column, elution to effect separations, and removal of the separated solute
Ion Exchange 385 where Cri is the concentration of component i in the liquid within the resin bead and C,, is the concentration of component i in the interstitial liquid. The distribution coefficient for a given ion or molecule will depend upon that component’s structure and concentration, the type and ionic form of the resin and the other components in the feed solution. The distribution coefficients for several organic compounds are given in Table 1 .[171 Solutes Addad 4 Solute { Mixture - Desorbent Added 4 4- sol Utes Added To col URll Separation s1 ow Occurs Fast Colrponent Component Removed FlWl col uan Removed Fron COluSn Figure 1. The steps ofchromatographic separation are: addition ofthe mixed solutes to the column, elution to effect separations, and removal of the separated solutes
386 Fermentation and Biochemical Engineering Handbook Resin Bead Interstitial Liquid Liquid in Rest r Figure 2. Representation of the three phases involved in chromatographic separatic The ratio of individual distribution coefficients is often used as a measure of the possibility of separating two solutes and is called the separation factor, a, or relative retention factor Kdy/k From Table l, the separation factors for acetone-formaldehyde separabil- ity are 0. 49, 0.98 and 1.54 for Dowex 50WX8(H"), Dowex 1X8(CI)and Dowex 1X8(So4)resins, respectively. For comparison purposes, it may be necessary to use the inverse of a, so that the values would be 2.03 and 1.02 for Dowex 50wX8(H)and Dowex 1X8(CI), respectively. When a is less han l, the solute in the numerator will exit the columnfirst. Whenais greater than l, the solute in the denominator will exit the column first
386 Fermentation and Biochemical Engineering Handbook -Resin Bead -Interstitial Llquld /iquid In @sin (v,, (Vq) Figure 2. Representation of the three phases involved in chromatographic separation. The ratio of individual distribution coefficients is often used as a measure of the possibility of separating two solutes and is called the separation factor, a, or relative retention factor. From Table 1 , the separation Mors for acetone-formaldehyde separability are 0.49, 0.98 and 1.54 for Dowex 50WX8 (H'), Dowex 1X8(C1-) and Dowex 1X8(SOi2) resins, respectively. For comparison purposes, it may be necessary to use the inverse of a, so that the values would be 2.03 and 1.02 for Dowex SOWX8(H') and Dowex 1X8(Cl-), respectively. When a is less than 1 , the solute in the numerator will exit the column first. When a is greater than 1, the solute in the denominator will exit the column first
Ton Exchange 387 Table 1 Distribution Coefficients[17l Resin Ethylene Glycol Dowex 50-X8.H Dowex 50-X8.H' d-Glucose Dowex 50-X8.H 22 Glycerine Dowex 50-X8, H Triethylene glycol Dowex 50-X8.H+ Dowex 50-X8.H 3.08 Acetic Acid Dowex 50-X8.H Acetone Formaldehyde Dowex 50-X8.H Methanol Dowex 50-X8.H Dowex 1-X75 CI Dowex 1-X75 cI. Glycerine Dowex 1-X7,5. CI 12 Methanol Dowex 1-X7,5. CI Phenol Dowex 1-X75 CI Formaldehyde Dowex I-8,SO4=,50-1001.02 Acetone Dowex 1-X8, SO4=, 50-100 Xylose Dowex 50-X8 Na Glycerine Dowex 50-X8 Na+ Pentaerythritol Dowex 50-X8 Na+ Ethylene Glycol Dowex 50-X8 Na Diethylene glycol Dowex 50-X8. Nat Triethylene Glycol Dowex 50-X8, Na Ethylene Diamine Dowex 50-X8 Na+ Dowex 50-X8, Na Triethylene Tetramine Dowex 50-X8, Na Tetraethylene Pentamine Dowex 50-X8, Na 66 The acetone-formaldehyde separation would be an example of affinity difference chromatography in which molecules of similar molecular weight or isomers of compounds are separated on the basis of differing attractions or distribution coefficients for the resin. The largest industrial chromatogra- phy application of this type is the separation of fructose from glucose to produce 55% or 90% fructose corm sweetener
Ion Exchange 387 Table 1 Distribution Coefficients["1 Solute Resin Kd Ethylene Glycol Sucrose d-Glucose Glycerine Triethylene Glycol Phenol Acetic Acid Acetone Formaldehyde Methanol Formaldehyde Acetone Glycerine Methanol Phenol Formaldehyde Acetone Xylose Glycerine Pentaerythntol Ethylene Glycol Diethylene Glycol Triethylene Glycol Ethylene Diamine Diethylene Triamine Triethylene Tetramine Dowex 50-X8, H' .67 Dowex 50-X8, H' .24 Dowex 50-X8, H' .22 Dowex 50-X8, H' .49 Dowex 50-X8, H' .74 Dowex 50-X8, H' 1.20 Dowex 50-X8, H' .59 Dowex 50-X8, H' 3.08 Dowex 50-X8, H' .71 Dowex 50-X8, H' .6 1 Dowex 1-X7.5, C1- 1.06 Dowex 1-X7.5, C1- 1.08 Dowex 1-X7.5, C1- 1.12 Dowex 1-X7.5, C1- .61 Dowex 1-X7.5, Cl- 17.70 Dowex 1-X8, SO4=, 50-100 .66 Dowex 50-X8, Na' -56 Dowex 50-X8, Na' .63 Dowex 50-X8, Na' .67 Dowex 50-X8, Na' .61 Dowex 1-X8, SO,=, 50-100 1.02 Dowex 50-X8, Na' .45 Dowex 50-X8, Na' .39 Dowex 50-X8, Na' .57 Dowex 50-X8, Na' .57 Dowex 50-X8, Na' .64 Tetraethylene Pentamine Dowex 50-X8, Na' .66 The acetone-formaldehyde separation would be an example of affinity difference chromatography in which molecules of similar molecular weight or isomers of compounds are separated on the basis of differing attractions or distribution coefficients for the resin. The largest industrial chromatography application of this type is the separation of fructose from glucose to produce 55% or 90% fructose corn sweetener
388 Fermentation and Biochemical Engineering Handbook Ion exclusion chromatography involves the separation of an ionic component from a nonionic component. The ionic component is excluded from the resin beads by ionic repulsion, while the nonionic component will be distributed into the liquid phase inside the resin beads. Since the ionic solute travels only in the interstitial volume, it will reach the end of the column before the nonionic solute which must travel a more tortuous path through the ion exchange beads. a major industrial chromatography application of this type is the recovery of sucrose from the ionic components of molasses In size exclusion chromatography, the resin beads act as molecular sieves, allowing the smaller molecules to enter the beads while the larger molecules areexcluded. Figure 3ns shows the effect of molecular size on the elution volume required for a given resin. The ion exclusion technique has been used for the separation of monosodium glutamate from other neutral 9 ETHYLENE GLYCOL IETHYEE GLYCOL AR TETRAETHYLENE GLYCOL 3 POLYETHYLBE GLYCOL M400 7 VoiD VOUME 10020050100 MLECULAR WEIGHT OF SOLUTE Figure 3. Effect of molecular weight on the elution volume required for glycol Ion retardation chromatography involves the separation of two ionic solutes with a common counter ion. Unless a specific complexing resin is used, the resin must be placed in the form of the common counter ion. The other solute ions are separated on the basis of different affinities for the resin Ion retardation chromatography is starting to see use in the recovery of acids from waste salts following the regeneration of ion exchange columns
388 Fermentation and Biochemical Engineering Handbook Ion exclusion chromatography involves the separation of an ionic component from a nonionic component. The ionic component is excluded from the resin beads by ionic repulsion, while the nonionic component will be distributed into the liquid phase inside the resin beads. Since the ionic solute travels only in the interstitial volume, it will reach the end ofthe column before the nonionic solute which must travel a more tortuous path through the ion exchange beads. A major industrial chromatography application of this type is the recovery of sucrose from the ionic components of molasses. In size exclusion chromatography, the resin beads act as molecular sieves, allowing the smaller molecules to enter the beads while the larger molecules are excluded. Figure 31181 shows the effect ofmolecular size on the elution volume required for a given resin. The ion exclusion technique has been used for the separation of monosodium glutamate from other neutral amino acid~.I’~] 1Do 90 ;. 9” Figure 3. compounds. [*I Effect of molecular weight on the elution volume required for glycol Ion retardation chromatography involves the separation of two ionic solutes with a common counter ion. Unless a specific complexing resin is used, the resin must be placed in the form of the common counter ion. The other solute ions are separated on the basis of different affinities for the resin. Ion retardation chromatography is starting to see use in the recovery of acids from waste salts following the regeneration of ion exchange columns
Ton Exchange 389 2.0 THEORY The important features of ion exchange reactions are that they are stoichiometric, reversible and possible with any ionizable compound. The reaction that occurs in a specific length of time depends on the selectivity of he resin for the ions or molecules involved and the kinetics of that reaction he stoichiometric nature of the reaction allows resin requirements to be predicted and equipment to be sized The reversible nature of the reaction, Eq,(3) R-H+NaC动R-Na++HCl allows for the repeated reuse of the resin since there is no substantial change in its structure The equilibrium constant, K, for Eq. (1), is defined for such mono- valent exchange by the equation Eq(4) K R-H+Na+CI In general, if K is a large number, the reverse reaction is much less efficient and requires a large excess of regenerant chemical, HCI in this instance, for moderate regeneration levels be. With proper processing and regenerants, the ion exchange resins may be selectively and repeatedly converted from one ionic form to another. The definition of the proper processing requirements is based upon the selectivity and kinetic theories of ion exchange reactions 2.1 Selectivity When ion B, which is initially in the resin, is exchanged for ion A in solution, the selectivity is represented by Eq(5) InKa n(2A5-) where Zi is the charge and v is the partial volume of ion i. The selectivity which a resin has for various ions is affected by many factors. The factors include the valence and size of the exchange ion, the ionic form of the resin
Ion Exchange 389 2.0 THEORY The important features of ion exchange reactions are that they are stoichiometric, reversible and possible with any ionizable compound. The reaction that occurs in a specific length of time depends on the selectivity of the resin for the ions or molecules involved and the kinetics of that reaction. The stoichiometric nature of the reaction allows resin requirements to be predicted and equipment to be sized. The reversible nature of the reaction, illustrated as follows: Eq. (3) R - H' + Na'Cl- C= R - Na' + H'Clallows for the repeated reuse of the resin since there is no substantial change in its structure. The equilibrium constant, K, for Eq. (l), is defined for such monovalent exchange by the equation: IR-Na+] [H+Cl-l Eq. (4) [R-H+] [Na+Cl-] K= In general, if K is a large number, the reverse reaction is much less efficient and requires a large excess of regenerant chemical, HCl in this instanc,e, for moderate regeneration levels. With proper processing and regenerants, the ion exchange resins may be selectively and repeatedly converted from one ionic form to another. The definition of the proper processing requirements is based upon the selectivity and kinetic theories of ion exchange reactions. 2.1 Selectivity When ion B, which is initially in the resin, is exchanged for ion A in solution, the selectivity is represented by: where Zi is the charge and y. is the partial volume of ion i. The selectivity which a resin has for various ions is affected by many factors. The factors include the valence and size of the exchange ion, the ionic form of the resin
390 Fermentation and Biochemical Engineering Handbook of functional group and the nature of the non-exchanging iong n, the type he total ionic strength of the solution, the cross- linkage of th The ionic hydration theory has been used to explain the effect of some ofthese factors on selectivity. 20 According to this theory, the ions in aqueous lution are hydrated and the degree of hydration for cations increases with increasing charge and decreasing crystallographic radius, as shown in Table 2. 21] It is the high dielectric constant of water molecules that is responsible for the hydration of ions in aqueous solutions. The hydration potential of an ion depends on the intensity of the change on its surface. The degree of hydration of an ion increases as its valence increases and decreases as its hydrated radius increases. Therefore, it is expected that the selectivity of a resin for an ion is inversely proportional to the ratio of the valence/ionic radius for ions of a given radius. In dilute solution, the following selectivity series are followed Li< Na<K<Rb<o Mg Ca sr Ba F<Cl< Br <I Table 2. Ionic Size of Cations[21] Crystallographic Hydrated Ionization Radius(A) Radius(A) Potential 0.68 10.00 1.30 0.98 K 33 5.30 0.75 NH4 1.43 5.37 1.65 5.05 0.61 0.89 2.60 1.34 960 1.60 Ba 149 8.80 140 The selectivity of resins in the hydrogen ion or hydroxide ion form, however, depends on the strength of the acid or base formed between the functional group and the ion. The stronger the acid or base formed the lower is the selectivity coefficient. It should be noted that these series are not followed in nonaqueous solutions, at high solute concentrations or at high temperature
390 Fermentation and Biochemical Engineering Handbook the total ionic strength of the solution, the cross-linkage of the resin, the type of functional group and the nature of the nonexchanging ions. The ionic hydration theory has been used to explain the effect of some ofthese factors on selectivity.[20] According tothis theory, the ions in aqueous solution are hydrated and the degree of hydration for cations increases with increasing charge and decreasing crystallographic radius, as shown in Table 2.r2l] It is the high dielectric constant of water molecules that is responsible for the hydration of ions in aqueous solutions. The hydration potential of an ion depends on the intensity of the change on its surface. The degree of hydration of an ion increases as its valence increases and decreases as its hydrated radius increases. Therefore, it is expected that the selectivity of a resin for an ion is inversely proportional tothe ratio ofthe valencehonic radius for ions of a given radius. In dilute solution, the following selectivity series are followed: Li <Na < K < Rb < Cs Mg < Ca < Sr < Ba F < C1< Br < I Table 2. Ionic Size of Cations[21] Crystallographic Hydrated Ionization Ion Radius (A) Radius (A) Potential Li Na K NH4 Rb cs Mg Ca Sr Ba 0.68 0.98 1.33 1.43 1.49 1.65 0.89 1.17 1.34 1.49 10.00 7.90 5.30 5.37 5.09 5.05 10.80 9.60 9.60 8.80 1.30 1 .oo 0.75 0.67 0.61 2.60 1.90 1.60 1.40 - The selectivity of resins in the hydrogen ion or hydroxide ion form, however, depends on the strength of the acid or base formed between the functional group and the ion. The stronger the acid or base formed, the lower is the selectivity coefficient. It should be noted that these series are not followed in nonaqueous solutions, at high solute concentrations or at high temperature
Ton Exchange 39 The dependence of selectivity on the ionic strength of the solution has been related through the mean activity coefficient to be inversely proportional to the Debye-Huckel parameter, a [22 1+Ba° where, is the mean activity coefficient, A and B are constants, and u is the ionic strength of the solution. The mean activity coefficient in this instand represents the standard free energy of formation(-AF)for the salt formed by the ion exchange resin and the exchanged ion. Figure 4(231 shows this dependence as the ionic concentration of the solution is changed. As the concentration increases, the differences in the selectivity of the resin for ions ofdifferent valence decreases and, beyond certain concentrations, the affinity is seen to be greater for the lower valence ion 1.5 s1.2 MOLARITY OF SOLUTION
Ion Exchange 391 The dependence of selectivity on the ionic strength of the solution has been related through the mean activity coefficient to be inversely proportional to the Debye-Huckel parameter, where 'y* is the mean activity coefficient, A and B are constants, and ,u is the ionic strength of the solution. The mean activity coefficient in this instance represents the standard free energy of formation (-W) for the salt formed by the ion exchange resin and the exchanged ion. Figure 4[231 shows this dependence as the ionic concentration of the solution is changed. As the concentration increases, the differences in the selectivity of the resin for ions of different valence decreases and, beyond certain concentrations, the affinity is seen to be greater for the lower valence ion. f I I I I 0 0,4 008 la2 106 2,o MOLARITY OF SOLUTION Figure 4. Dependence of the activity coefficient on the ionic concentration of aqueous
