Dec., 1963
DONKAN EQUILIBRIA IZ: POLYMETHACRYLIC ACID-SODIGM CHLORIDE SYSTEMS
correlations it is possible to estimate the selective adsorptivity for the other pair of alcohols against agents. The numbers with bracket in Table I are the estimated values. The present results may be equally applicable
2549
for the adsorption a t the interface between the aqueous solution and the oleophilic phase. Acknowledgments.-We wish to thank Mr. S. Sugiura for his cooperation in this project.
DONNAN EQTJILIBRIA IN CROSS-LINKED POLYMETHACRYLIC ACID-SODIUM CHLORIDE SYSTEMS BY RICHARD L. GUSTAFSO~ Rohm and Haas Company, Research Division, Philadelphia 87, Pennsylvania Received April 22, 1968 Measurements of uptake of sodium chloride by a polymethacrylic acid resin which has been cross-linked with 57, divinylbenzene have been measured at various degrees of neutralization in aqueous solutions which were 1.0, 0.4,0.1,and 0.02 in ionic strength a t 25'. Mean molal activity coefficients, y** = yr,e"v/2RT, of sodium chloride in the resin phase have been calculated after suitable corrections have been made for salt occlusion on the surface and in the macro-pores of the resin. Values of y** have been shown to decrease with decreasing ionic strength at a constant degree of neutralization, C Y , of the carboxylic groups of the resin. It has been shown that this effect is not the result of anion-adsorbing impurities or resin heterogeneity. Similar variations of y*+ with ionic strength have been shown t o occur in cases oi rigid inorganic zeolites and in solutions of linear polyelectrolytes. The experiniental values of y** in the resin systems were found t o be in poor agreement with theoretical values of yri calculated on the basis of Katchalsky and Michaeli's theory of highly swollen polyelectrolyte gels. The discrepancies were particularly large a t low ionic strengths. Consideration of the equilibria involved suggests that the activity coefficient of the chloride ion in the gel phase decreases markedly with decreasing ionic strength a t a constant vallue of CY, whereas the activity coefficient of the sodium ion remains relatively constant.
Introduction Considerable disagreement exists concerning the nature of electrolyte sorption by ion-exchange resins. More than a decade ago, Baunian and Eichhornl pointed out that results concerning the sorption of hydrochloric acid from aqueous solution by crosslinked polystyrenesulfonic acid gels could not be explained on the basis of Donnan theory if it were assumed that the activity coefficient of HC1 in the gel phase remains high a t low external electrolyte concentrations. It was observed experimentally that abnormally large amounts of HCl were adsorbed by the resin phase from dilute solution. Since that time, several workers2-10 have shown that as the external electrolyte concentration approaches zero, the mean molal activity coefficient, yr+, of the sorbed electrolyte also approaches zero. This behavior is opposite to that observed in aqueous solutions of strong electrolytes, in which case activity coefficients tend toward unity a t infinite dilution. Freemaiill has suggested that the abnormal decrease of yrk with decreasing solution molality, m,, is caused by occlusioii of electrolyte on the bead surfaces aiid by the sorption of eo-ions by resin impurities. By the use of an iterative procedure, he has calculated the quantities of co-ion which must be occluded or sorbed by impurities in order to give good agreement with the equation log yrk = a f bm,, where a and bare constants. (1) W. C . Bauman and J. IEichhorn, J . Am. Chem. Soc., 69, 2830 (1947). ( 2 ) H. P. Gregor, F. Gutoff, and J. I. Bregman, J . Coollozd Scz., 6 , 243 (1951) ( 3 ) 11. 1'. Ciegor and h1. H. Gottlieb, J. rim. Chem. Soc., '76, 3539 (l9S3). (4) C. W. Dames a n d G. D. Yeoman, Trans. Paradag Soe., 49, 968 (1953). ( 5 ) J. S Maokie and P. Meares, Proc Rog Soc (London), A282. 485 (195.5). (6) G. J. Hills, P. W. ill. Jacobs and N. Lakvhminaraganaiah ?hid., 8262,257 (1961). (7) K. A. Kraus and G. E. Moore, J . AmAChem. Soc ,75,1457 (1 953). (8) M. H. Gottlieb a n d H. P. Gregoi, zbzd., '76,4639 (1954). (9) F. Nelson and X. A. Xraus, %bid.,80,4154 (1958). (10) J. Danon, J . Phys. Chem., 65, 2039 (1961). (11) D. H. Freeman zbzd., 64, 1048 (1960).
Glueckauf and W a t t ~ ~ have ~ - l ~recently published several papers which support the theory that the observed abnormalities are produced by variations in the degrees of cross-linking within a resin sample. By the assumption of an appropriate distribution of concentrations of functional groups within the resin, it is possible to obtain agreement with experiment on the basis of constant resin activity Coefficients. The validity of the assumption of the high degree of heterogeneity required to obtain a fit of the data is questioned on the basis of proton magnetic resonance studies of Gordoiil6.16 which indicated that several commercially available cation and anion exchange resins possess a high degree of homogeneity. It has been shown by Barrer aiid Meierll' on the basis of data concerning sodium chloride sorption by aluminosilicates, that the ideal Donnaii law based on constant activity coefficients in the zeolite phase is apparently obeyed. It was suggested that the differences in electrolyte sorption that are observed between rigid zeolites and organic ion-exchange resins are associated with the swelling properties of the latter materials. An important point, whicli often seems to have beeii overlooked, is that similar decreases of mean activity coefficients with decreasing electrolyte concentration have been reported1*-21 for a variety of linear polyelectrolytes in aqueous solution. I n these cases the distribution of polymer chains is governed only by (12) E. Gluecktruf and R. E. Watts, Natuie, 191, 904 (1961). (13) E. Glueckauf and R. E. Watts, Proc. Roy. Soc. (London), 8 2 6 8 , 339 (1962). (14) E. Glueckauf, ibid., 8268, 3.50 (1962). (15) J. E. Gordon, Chem. I n d . (London), 267 (1962). (16) J. E. Gordon, J . Phys. Chem.. 66, 1150 (1962). (17) R. M. Barrer and W. $1. Meier, J . Chem. Soc., 299 (1958). (18) A. Xatchalsky and S. Lifson, J . Polymer Sei., 11,409 (1953). (19) G. P. Strauss and P. Ander, J . Bm. Chem. Soc., 80,6494 (1958). ( 2 0 ) Z. Alexandrowicz, J. Polgmer Sci., 43, 337 (1960); 56, 11.5 (1962). (21) &I. Nagasa\va, M. Izumi, and I. Kagawa, ibid., 3'7, 375 (19.59).
RICHARD L. GUSTAPSON
2550
statistical factors and the systems are not heterogeneous in the Glueckauf sense. Several authors have investigated various aspects of the behavior of cross-linked polymethacrylic acid (PMA) gels. Gregor, et U Z . , ~ have ~ studied the swelling characteristics and hydrogen ion equilibria of resins which contained 0.25 to 24% divinylbenzene (DVB) and have discussed the qualitative aspects of their data. Fisher and have determined the apparent dissociation constants of acrylic and methacrylic acid polymers of varying degrees of cross-linking and have demonstrated the validity of the modified forni of the Henderson-Hasselbach equation, pH = pK - n log (1 - a ) / a , for these systems. Katchalsky and Michaeli26,26 have studied in detail the nature of swelling, electrolyte adsorption, and hydrogen ioii equilibria for two highly swollen polymethacrylic acid gels and have found satisfactory agreement between their experimental data and behavior predicted on the basis of their theoretical treatment. Hills, et have calculated activity coefficients of KOH in completely neutralized PMA gels and have noted steadily decreasing values of the mean molal activity coefficient of KOH in the resin phase with decreasing external hydroxide ion concentration. Recently, Chatterjee and Marinskyz7I28have studied the hydrogen ion equilibria and osmotic properties of 1 and 5% copolymers of diviiiylbenzene and methacrylic acid. However, in none of the aforementioned studies were attempts made to calculate activity coefficients of inorganic salts in the resin phases as fuiictioiis of the ionic strength and degree of neutralization of the acidic groups. I n the present study, measurements of the uptake of sodium chloride by a polymethacrylic acid resin which has been cross-linked with 5% divinylbenzene have been measured a t various degrees of neutralization in solutions which were 1.0, 0.4, 0.1, and 0.02 in ionic strength a t 25'. Corrections for the amounts of electrolyte occluded on the surface and in the macropores of the resin have been made, and it has been ascertained that negligible amounts of anion-exchange capacity are present in the resin. Mean molal activity coefficients of NaC1 in the resin phase have been calculated, and these values have been compared with similar quantities calculated on the basis of the theory of Katchalsky and L i f s ~ n . ~ s ~ ~ ~ Experimental Materials.--4 sample of PMA resin, which contained 5.0 and 4.1% of divinylbenzene and ethylvinylbenzene, respectively, was placed in a glass column and treated three times with alternate washings of 1 M NaOH and HCl. Resin of -30 +40 mesh was used in the equilibrium studies. The acidified resin was washed with water until chloride-free, and air-dried. .4 solids content of 87.49 ==! 0.047, was determined by oven drying 1-g. samples for 24 hr. at 110'. I n order to determine the resin capacity, the resin was first equilibrated with an excess of standard, carbonate-free sodium hydroxide. The resin was then filtered from the solution and washed with alcohol. The amount of excess KaOH present in equilibrium with the resin was deH. P. Grepor, PI. J. Hamilton, ,I. Becher, and G. Bernstein, J . Phys. 69,874 (1955). S.Fisher and R. Kunin, ibid., 60, 1030 (1956). R. Kunin and S. Fisher, ibid.. 66, 2275 (1962). ( 2 5 ) A. Katchalsky and I. Michaeli, J . Polymer Sei.. 16, 69 (1955). (26) I. Michaeli and A. Katchalsky, ibid., 23,683 (1957). 127) A. Chatterjee and J. A . Marinsky, J . Phys. Chem.. 67, 41 (1963). (28) J. A. Marinsky and 4.Chatterjee. ibad., 67,47( 1 9 6 3 . (29) A. Katchalsky, Progr. Biophys. Biophgs. Chem., 4 , l (1954).
(22) Chem., (23) (24)
Vol. 67
termined by titration with standard HC1. All steps in the capacity determination were carried out in a carbon dioxidefree atmosphere. In order to check for the presence of weak or strong base anion exchange capacity, the resin was equilibrated with a large excess of 0.1 N HC1, washed with alcohol to remove free chloride, and eluted with 1 M NaKOl to remove chloride, if any. The concentration of chloride ion in the NaN03 effluent was determined coulometrically with the use of a n Aminco-Cotlove chloride titrator. Duplicate results indicated a chloride concentration of 2.2 i 0.2 X meq. per meq. of resin. This negligible amount may be considered to be an upper limit since more efficient alcohol washing might have further reduced the amount of chloride ion imbibed in the resin. Equilibrations and Swelling Measurements.-Samples, 1.0000 rt 0.0002 g. (9.38 meq.), of air-dried hydrogen form resin were equilibrated for 5 weeks at 25.0" with 100-ml. aliquots of 1.0, 0.4, 0.1, and 0.02 m NaCl solution which contained the appropriate amounts of standardized, carbonate-free sodium hydroxide. The measurements of resin volumes were carried out pycnometrically. The determinations of the weights of swollen resin were made after centrifugation in a manner similar t o that described by Gregor, et aL30 Centrifugations were carried out for 10 min. a t 3000 r.p.m. The resin samples were held in 2.5-in. long, 0.5411. diameter Plexiglas tubes fitted a t the bottoms with 50 mesh stainless steel screens. The plastic tubes were suspended in stoppered, standard 4-in. X 1-in. glass centrifuge tubes. After centrifugations, the resin samples were rapidly transferred to tared weighing bottles and weighed. Triplicate measurements were made in all cases and gave results which had average deviations of less than 0.1%. The amount of water imbibed by each resin sample was calculated by difference. Measurements of Sodium and Chloride Concentrations.The imbibed chloride was eluted from the resins by repeated washings of the centrifuged resin samples with deionized water whose resistance was greater than 1 million ohms. Chloride determinations were carried out coulometrically. Solutions of reagent grade KC1 were used as reference standards. The precision of the analyses was within & 0 2 % in each case. Dilute hydrochloric acid was used to elute sodium ion from the resins which had been equilibrated with sodium chloride solutions which contained no sodium hydroxide. Sodium analyses were carried out with a Beckman DU flame spectrophotometer a t a wave length of 583 mp. The average deviations of these measurements were of the order of 1%. Measurements of Void Volumes.--Bqueous solutions (0.003 M ) of disodium indigodisulfonate were allowed to equilibrate with resin samples whose degrees of neutralization varied between 0.5 and 1.0 The resin phases were separated from the soiutions by centrifugation in exactly the manner described previously, and the resin samples were weighed. The dye was eluted from the resins with water, the solutions were made to volume, and the concentrations of dye were determined spectrophotometrically at a wai e length of 605 mp. With the knowledge of the densities and dye concentrations of the aqueous phases and the volumes of the resins, it was possible to calculate the apparent porosities of the resin samples. The calculated values represented the sums of the volumes of the macropores plus the solution occluded on the bead surfaces. 411 determinations of sodium and chloride ion content of the resin phases were corrected for the amount of ions present in the macropores. It was assumed that the composition of the solution contained in the voids was identical with that measured in the external solution.
Results Measurements of Macroporosity.--It has been noted previously by Conway, et al.,31 that P N X resin beads are microporous as evidenced by their opaque white appearance. Helium sorption measurements show that our sample has porosities of 14.9 * 0.6 and 19.1 =t O.lyoin the hydrosren and sodium forms, respectively. Yoid volumes in the s.il-ollenstate have been calculated on the basis of data concerning imbibition of indigo disulfonate froni 0.003 I l l solutions. An average (30) H. P. Gregor, Iy(4)
IIere rnrCOO - represents the molality of ionized functional groups in the resin p base and x is the fraction of imbibed chloride which is far enough removed from the polymer chains to be a t a zero electrical potential. Typical values of x as functions of experimentally determined quantities are presented in Table 11. It was expected that values of x calculated a t a constant concentration of functional groups would remain approximately constant and that, a t constant solution ionic strength, x would increase with increasing distance between functional groups. The lack of agreement between theory and experiment indicates that, a t least in the case of a nioderately cross-liiiked polymethacrylate exchanger, the Tye theory is inapplicable.
*ii
x
c3 0 -I
I
TABLE I1 CALCULATED VALUESO F THE PARAMETER x AS FUNCTIOSS OF mec1, mrcl-, AND mrcoo- FOR PMA-5% DVB GEL AT 25" Av. distance between ionized functional groups, A.
mSc1-
8.5 10.0 11.5 13.0 8.5 10.0 11.5 13.0 8.5 10.0 11.5 13.0 8.5 10.0 11.5 13.0
1.02 1.01 1.01 1.01 0.412 ,410 ,408 .408 .lo3 ,102 ,102 ,102 ,0207 ,0207 .0205 ,0206
- 7 0 0.0 01 m'cr 0.362 ,441 ,472 ,476 ,112 .135 ,158 ,171 ,0194 ,0215 .0253 ,0298 ,00196 ,00189 ,00231 .00276
m'coo-
3.35 2.30 1.70 1.29 3.29 2.16 1.56 1.16 3.25 2.09 1.47 1.08 3.23 2.08 1.44 1.05
X
0.150 ,159 .008 Kegative 0.190 .213 .241 .217 .166 .178 .203 .237 .088 ,083 .lo1 .120
Katchalsky and Lifsonls have derived the equation, 3V2€2
-In T~
=
~
Dkl' Zni(Kho2f 6h)
+-2DkT K€2
(5)
which permits the calculation of mean molal activity coefficients of 1:l salts in the presence of randomly kinked linear polyelectrolytes. Here v is the number of ionized functional groups per polymeric molecule, E is the electronic charge, D is the dielectric constant, k is the Boltzmann coilstant, T is the absolute temperature, Zlndis the average number of small ions associated with each polymer chain, K is the reciprocal of the Debye radius for a solution of ionic concentration equal to Zed, ho is the end-to-end distance in the reference state, and h is the same distance in the actual state. Excellent agreement between theory and experiment was foundlsmz9 for 0.05 N solutions of polymethacrylic acid in dilute NaC1. Subsequently, Katchalsky and Michaeli derived a similar expression
02
03
04
01
m:, . Fig. 1.-Plots of log y** vs. molal concentration of chloride ion in resin phase at various concentrations of ionized functional groups for PMA gel NaC1-H20 systems a t 25.0': 0, p = 1.0; 8 , p = 0.4; 8 , p = 0.1; 0 ,p = 0.02.
which may be utilized to calculate the activity coefficients of 1 : 1 salts imbibed in polyelectrolyte gels. In this case Y = a2 represents the average number of ionized functional groups between network junction points, 2 and Zn, are the average numbers of monomer units and monovalent ions between cross-links, respectively, ho and h are the distances between junction points in the reference and actual states, respectively, and -yok is the activity coefficient of NaCl in a solution whose ionic concentration is equal to the value of Zcl in the gel phase. Equation 6 has been employed by several workers in order to predict activity coefficients in resin phases. Mackie and Meares5 found reasonably good agreement between theory and experiment for systems containing halide or sulfate salts in equilibrium with sulfonated phenol-formaldehyde resins. At low concentrations of 1:1 electrolytes, however, the experimental values of yrs were considerably lower than the calculated values. Hills, et aZ.,la and Lakshminarayanaiaha5 found poor agreement throughout the entire salt concentration range in cases in which KOH was equilibrated with potassium polymethacrylate gels or in which various 1:1, 1:2, or 1:3 electrolytes were equilibrated with sulfonated phenol-formaldehyde gels. Values of -yrs have been calculated by both eq. 5 and 6 and are compared with experimental values of the mean molal activity coefficients of KaCl in the PMA gel in Table 111. A value of Z = 14.4 was used in the calculations. This value is equal to the average number of monomer units between cross-links provided that all of the divinylbenzene which was employed as (35) N. Lakshmnarayanaicch, J . Polymer Xcd., la, 139 (1963).
RICHARD L. GUSTAFSON
2554
a cross-linker (5% DVB by weight) reacted with methacrylic acid. The value of ho was calculated by the relationship
ho2 = Zsb2 where s is the number of monomer units per chain element, and b is the hydrodynamic length of the monomer. We have assumed, as has Katchalsky25 in his treatment of polymethacrylic acid gels, that s = 10, and b = 2.55 X 10-8 cm. The value of h was estimated by the approximation
where V is the volume of the gel which was equilibrated in a given salt solution, and V o is the volume of the same number of milliequivalents of resin which was equilibrated with water. This value of Vo,rather than TABLE I11 VALUESOF THE MEANMOLALACTIVITYCOEFFICIENTS OF NaCl IN PMA-5yo DVB GEL, IONIC STRENGTHS, AND DEGREEOF NEUTRALIZATION AS CALCULATED BY EQUATIOES 5 AND 6 P
1 .oo 1 .oo 1 .oo 1 .oo 1 .00 0.40 .40 .40 .40 .40 * 10 .10 .10 .10 .10 .02 .02 .02 .02 .02
a
Y**
0.107 .320 .534 .748 .961 .lo7 .320 .534 .748 .961 .lo7 .320 .534 ,748 .961 .10T ,320 * 534 ,748 .961
(es. 5 )
0.406 .303 .259 .228 ,199 .477 .355 .298 ,255 .218 .533 .391 .319 .270 ,230 .553 .401 -325 .274 .232
(es. 6 )
Y’C
0.650 .668 .689 .715 .759 ,654 .642 .653 .674 .710 .663 ,635 .639 .656 .689 .667 .634 .636 .652 .631
Y**
=
meric network, an average of 10.3 methacrylic acid monomer units is calculated to be present between either EVB or DVB terminal points. Calculations of yr* by the use of eq. 6 with the assumpton that Z = 10.3, yield results which differ in nearly every case by less than 0.01 from results obtained by the use of 2 = 14.4. Katchalsky and Michaeli25 have studied swelling and salt sorption properties of two lightly cross-linked polymethacrylic acid gels which have averages of 200 and 308 monomer units between network bridges. In Table IV are listed values of y** which have been calculated on the basis of their data obtained in NaCl systems. Values of yr* calcuated by eq. 5 and 6 are included for comparison. In general, the agreement between experimental and calculated values of the activity coefficients improves as the ionic strength and average number of monomer units per chain segment increase. It should be pointed out that the pressurevolume term contributes little to the over-all value of y *+. In relatively highly cross-linked systems, the estimated differences between y** = yrie?rV/2RTand y** are less than 0.01 unit in most cases.
(exptl.)
0.744 .611 .592 .578 .557 .632 .521 ,496 ,469 .440 .472 .399 .362 .332 .304 .360 .304 .280 .246 .208
the value in the dry state, was chosen since the reference state was chosen to be one in which all fixed and free ions are considered to possess no charge, although the species in the reference state are assumed to have the same solubility, steric hindrances, and hydrogen bonding as the actual charged ions. The value of K was calculated by the relationship K2
Vol. 67
TABLE IV TKE MEANMOLAL ACTIVITYCOEFFICIENTS OF NzCl I N POLYMETHACRYLIC ACID GELSAT VARIOUS IOKIC STRENUTHS AND DEGREES OF NEUTRALIZATION AS CALCULATED BY EQUA-
VALVESOF TIOKS P
a
-tr*
(es. 5 )
z = 200
0.50
.IO
.008
.I0
.Ol
4ne2NZ C ~ lOOODkT
where N is the Avogadro number, and Zcc is the molar concentration of the monovalent ions in the gel phase. The data of Table I11 show that eq. 5 is completely inadequate in its prediction of experimental behavior and that eq. 6, although it describes the correct direction of the variation of yr* with ionic strength, fails a t high degrees of neutralization and low ionic strengths. The choice of Z = 14.4 in the calculations is open to question. The divinylbenzene used in the copolymerization contained 45% by weight of ethylvinylbenzene (EVB). If it is assumed that these “inert” monomer units are statistically distributed throughout the poly-
5 AND 6 (DATAO F ICATCHALSKY AND MICHAELI~~)
.9
0.200 .400 .566 .750 .850 .120 .315 .550 ,700 ,960 .310 ,498 ,690 .goo
0.42 .37 .34 .31 .30 .60 .50 .41 .37 .29 .52 .42 .35 .28
.250 ,440 ,582 .780 ,960 .210 .380 ,550 ,766 .955
Z = 308 .56 .49 .45 .39 .35 .63 .53 .44 .36 .29
0.61 .57 .54 .51 .50 .65 .55 .47 .42 .36 .52
.43 .36 .30 .60 .ti3 .49 .44 .40 .62 .52 .44 .36 .30
0.66 .61 .56 .56 .54 .67 .62 .54 51 .42 .21 .17 ’ 15 .12 .66 .63 .58 .58
.45 .66 .58 .52 .43 .38
Role of Co-Ion in Donnan Equilibria.-It was mentioned earlier that the sodium polyvinyl alcohol sulfate data of Napasawa, et aZ.,21are consistent with the concept that values of the activity coeEcients of the counter-ions decrease with decreasing concentration of added salt, while values of activity coefficients of the co-ions are approximately equal to corresponding values obtained in simple salt solutions. Although results of this type are to be expected in solutions which contain approximately equivalent amounts of polyelectrolyte and inorganic salt, such a conclusion seems
Dec., 1963
DONNAN EQUILIBRIA IN POLYMETHACRYLIC ACID-SODIUMCHLORIDE SYSTEMS
intuitively wrong in the case in which the concentration of added salt is small relative to that of the polyelectrolyte. In Fig. 2, calculated values of the single ion activity coefficient, yrNa.+, are plotted against the molal concentration of ionized functional groups a t various ionic strengths. The calculations were carried out by use of the relationship
and the assumptions that (1) the activity coefficient of KC1 is the same in a potassium chloride solution as in a sodium polymethacrylate gel of the same ionic molality and (2) y ~ =+ycl- in KC1 solutions. Large decreases of yrNa + with decreasing ionic strength are calculated a t constant values of the ionized functional group concentration, mrco0 -. The assumption that these large decreasles are produced by an increasing degree of sodium ion pairing, as the amount of imbibed salt decreases, appears to be unreasonable since the changes in the average values of yrNB+wouldbe expected to be small, even if the contribution of the imbibed NaCl to the total sodium ion activity were zero. Alternatively, it seems necessary to assume that y r N a + is relatively iindependent of ionic strength a t a constant functional group concentration, and that the variations of y*& under these conditions must be produced primarily by changes in the chloride ion activity coefficient. Two consideratioiia lend support to the concept that co-ion interactions are of major importance in Donnan equilibria. The first concerns correlations of calculated values of osmotic pressure with resin volumes. Values of P have been calculated with the use of the equation
Calculations were crarried out (a) with the use of the activity coefficients of sodium and chloride ions calculated according to eq. 7 , and (b) values of Y'N~+ and y r C l - calculated with the assumptions that y r ~+, is independent of ionic strength a t a constant value of = yrcl- = y** a t p = 1.0. Calcua, and that tions of P according to assumption a yielded a series of plots of V* us. n which were widely divergent (Fig. 3). Since the resin volume is a function of the osmotic pressure, it is expected that all of the points on a 'V* us. P plot should fall close to a single curve. The complete lack of such conformity in Fig. 3 strongly suggests that variations of y*& are not produced by corresponding variations of yrNa +. The results of calculations based upon assumption b are shown in Fig. 4,where it may be seen that the resudts obtained in 0.4,0.1, and 0.02 M solutions fall on a single curve although data obtained in 1.0 M NaCl solutions deviate markedly from this curve. The second consideration which emphasizes the importance of co-ion interactions concerns hydrogen ion equilibriaa6 in PMPL gel systems. The equilibrium constant for the dissociation of a polymeric acid may be represented by the following equation. (36) R. L. Gustafson, manuscript in preparation.
1.01
2555
\
0 . 0 1I
I
I
I
I
RICHARD L. GUSTA.FSON
2556
Vol. 67
3 .€I
2.6
V *. 2.2
I .8
-5
0
5
ll.
IO
15
20
Fig. 3.-Plot of volume, V*,of 9.38 meq. of PMA resin in NaCl solutions us. osmotic pressure calculated according to assumption a : 0, p = 1.0; 8 , p = 0.4; 8 , p = 0.1; 0 , p = 0.02.
TABLE V VALUESOF pK,* CALCULATED BY USE AND b cz
0.214 ,214 ,214 .214 .427 ,427 ,427 ,427 .641 ,641 ,641 .641 .854 .854 ,854 ,854
P
1.00 0.40 .10 .02 1.00 0.40 .10 .02 1.00 0.40 .10 .02 1.00 0.40 .10 ,052
-log [ H + l ?ci-(a)
5.00 5.21 5.72 6.39 5.74 5.95 6.47 7.12 6.31 6.59 7.08 7.73 7.24 7.49 8.01 8.68
0.580 ,586 .592 .596 .572 ,574 ,576 ,578 ,571 ,571 ,572 ,572 .574 ,573 ,572 ,572
OF THE
/ I .4
0
20
Tr.
40
60
Fig. 4.-Plot of volume, V*,of 9.38 meq. of PMA resin in NaC1 solutions us. osmotic pressure calculated according to assumption b: 0, p = 1.0; 8 , p = 0.4; 8 , fi = 0.1; 0 , p = 0.02.
ASSUMPTIONS a
pK,*(a)
yrci-(b)
pK,*(b)
5.25 5.42 5.71 5.94 5.49 5.62 5.90 6.11 5.65 5.83 6.09 6.32 6.01 6.19 6.48 6.76
0.648 ,460 ,278 ,162 ,599 .431 ,240 .144 ,584 ,396 ,206 ,112 .568 ,364 ,179 ,091
5.29 5.31 5.38 5.37 5,51 5.50 5.52 5.50 5.66 5.68 5.65 5.62 6.01 5.99 6.00 5.96
with changes in ionic strength, but in which mean activity coefficients vary markedly. The results of Table V give additional support to the concepts that (1) the couiiterion activity is essentially constant and independent of the external electrolyte concentration (at least a t salt concentrations less than 0.4 N ) a t a given degree of neutralization, and (2) the decreases in the mean molal activity coefficients of salts in the resin phase with decreases in ionic strength are due primarily to decreases in the activity coefficients of the co-ions. The latter effect is a consequence of ai1 increasing degree of ion pairing of chloride with sodium ions as the ionic strength
decreases. Such an effect is consistent with the coiisequences of acceptaiice of the concept that, upon addition of neutral salt to the sodium resinate, the added sodium ions help to reduce the electrostatic potential of the polyion by screening carboxylate groups from their neighbors. I n order to maintain electroiieutrality, equal numbers of imbibed sodium aiid chloride ions, many of them in close proximity to the polymer chains, must be present. It is reasonable to assume that the degree of ion pairing of both sodium and chloride ions in the vicinity of the chains nil1 be quite high. As the concentration of iionexchaiige electrolyte n ithin the resin increases and the electrostatic potential of the polymer decreases, the affinity for additional sodium ion also decreases aiid a greater proportion of imbibed sodium and chloride ion is preseiit in the regions of low electrostatic potential further renioved from the polymer chains. The result is that, as the concentration of imbibed KaC1 increases, the degree of pairing of imbibed sodium and chloride ions decreases. Because the total concentration of sodium ions in the resin phase does not change appreciably with changes in external concentration (in the range 0-1 M ) the average degree of pairing of sodium ions would be expected to change little with external concentration. On the other hand, large variations in the concentrations of chloride ion iii the resin phase are observed and, under these conditions, the variations in the chloride ion activity coefficients are quite large and exert a considerable influence on the equilibria.
KINETICS OF HALOGEN EXCHAXGE
Dec., 1963
The importance of the role of the co-ion in Donnan equilibria has previously been overlooked. This has been due in part to the fact that much attention has been given to the more obvious interactions of polyions with counterions, some studies of which have seemed to illustrate the lack of importance of coion interactions. The aforementioned study of Nagasama, et aZ.,21showed that, whereas the activity coefficients of the sodiurn ion decreased, activity coefficients of the chloride ion increased with decreasing KaC1
2557
concentration, except in the cases of 0.005 and 0.001 ycl- decreased markedly, particularly at high polyelectrolyte concentrations. Such observations are consistent with the coiicepl outlined above, wherein, at low salt concentrations. the degrrc of intcmction of co-ions increases significantly. Acknowledgment.-The author expresses his appreciation to Dr. Robert Kunin for many helpful discussions during the course of this work.
N solution. I n the latter cases, values of
KINETICS O F HALOGEN EXCHANGE BETWEEN IODIDE ,4ND IODOACETIC ACID AND BETWEEN BROMIDE AND BROMOACETIC ACID BY J. F. HINTOX ilKD F. J. JOHNSTON Department of Chemistry, University of Georgia, Athens, Georgia Received April 39, 1963 I n aqueous Bystems halogen exchange occurs between bromide and bromoacetic acid and between iodide and iodoacetic acid. Exchange rates are first order with respect to each of the exchanging species. Second-order rate constants for the bromide and iodide systems in 0.628 M nitric acid may be expressed as kx = k T / h exp[ - 13 4/ R] exp[ -18,98O/RT] and kx = kT/h exp[--14.6/R] exp[- 15,980/RT] 1. mole-' sec.-1, respectively. The rate constants are essentially independent of nitric acid concentration from 0.006 to 0.63 M . A comparison is made of these results with those for the chloroacetic acid--chloride system. Enthalpies of activation for the exchange reactions appear to depend linearly upon the C-X bond strength, while those for the hydrolysis reactions vary only slightly.
Introduction The kinetics of ha,logen exchange between chloride ions and chloroacetic acid' and between iodide ions and iodoacetic acid2 have been described previously. This report discusses in more detail the iodide-iodoacetic acid system and the corresponding bromide-bromoacetic acid system. These exchanges occur a t a measurable rate a t room temperature and have been studied over the range of 10 to 49.9'. Exchange rates increase in the order chloride, bromide, iodide. I n the chloride-chloroacetic acid system, exchange rates were conveniently measurable only above 70", and a significant hydrolysis occuirred simultaneously with the exchange. I n the bromide and iodide systems, no hydrolysis was detectable during the course of the exchange reaction. Reaction rates were evaluated in the usual way from plots of log (1 - 8') vs. t. A separation induced exchange prevented our obtaining satisfactory rate data for the iodide system a t total reactant concentrations above approximately 0.03 M . At the concentrations used in our experiments this exchange was always less than 10%. Prestwood and Wah13 have shown that if such background exchange is constant, the homogeneous exchange rate may still be obtained from the slope of a plot of log (1 - 8') vs. t with F being the apparent total fractional exchange. Experimental Eastman White Label iodoacetic and bromoacetic acids were used as reactant material. The iodoacetic acid was recrystallized from ether. The acid purified in this manner had a melting point range of 81 to 82.5'. The bromoacetic acid, with melting point range of 48 to 50" was not further purified. Labeled iodide for the iodide-iodoacetic acid system was prepared in the following manner. Sublimed, reagent grade iodine (1) R. A. Kenney and F. J. Johnston, J . Phys. Chem., 63,1462 (1959). (2) H. V. D. Stratten a n d A. H. Aten, J . Am. Cham. Hoc., 76, 3798 (1954). 13) R. Prestwood and A+C. Wahf, obid., 71, 3137 (1949).
dissolved in heptane was tagged by means of a heterogeneous exchange reaction involving equilibration with a dried sample of the sodium iodide-131 as obtained from the Oak Ridge Isotope Sales Department. An exchange of iodine between that in the liquid phase and the surface iodide ions occurs readily and produces labeled molecular iodine of controllable specific activity. This solution of iodine-131 in heptane was then equilibrated with reagent grade potassium iodide, producing the iodide-131 used as the iodide tracer in these experiments. For the bromide-bromoacetic acid system, potassium bromide82 as obtained from Oak Ridge, was used as a tracer without further purification. Experiments were carried out in 0.628 M nitric acid to ensure the presence of the haloacetic acid in the molecular form. Reactions were carried out over a temperature range of 10 to 49.9" with temperature control within &0.05". Aliquots of 10 cc. were withdrawn a t intervals from the reactant solution, placed on ice in a beaker to quench the reaction, and titrated potentiometrically with silver nitrate. All titrations were performed at 0" to reduce separation induced exchange. It was found that excessive background exchange occurred in the iodide-iodoacetic acid system unless the concentration of the iodoacetic acid was low, and unless the separation process was performed a t reduced temperature. For example, with 0.172 M iodoacetic acid and 0.089 M iodide, the exchange occurring during the silver iodide precipitation process amounted to 30%. It is felt that this background exchange occurs between iodoacetic acid and colloidal silver iodide formed during the early stages of the precipitation. Following precipitation, the solutions were filtered and diluted to a volume of 50 cc. Aliquots of 4 cc. of each solution were counted using a scintillation detector. The counting rate for a reactant solution was obtained by diluting 10 cc. of the original material to 50 cc. and counting 4-cc. aliquots. The fraction of equilibrium exchange a t time t was obtained from
Fg =
(specific activity of CH&COOH) (specific activity of total X ) t =
E
In every case the net counting rate was characterized by a standard deviation of less than 2%.
Results and Discussion Typical plots of log (1 - F ) vs. t are shown in Fig. 1
