J. Bbys. Chem. 1980, 8 4 , 21-24
Acknowledgment. This work was partially supported by the Robert A. Welch Foundation, the Organized Research Fund d UTA, and the National Science Foundation. The authors are grateful to C.I. Weathers for pre1iminar:yanalytical measurements, and to M. W. Lutes for technical assistance. References and Nates (1) Abstracted in part from V. Napoleone's thesis, University of Georgia, 19'79. (2) L. J. Beckham, W. A. Fessler, and M. A. Kise, Cbem. Rev., 48, 366 (19151). (3) Cf. the review article by H. Schmid, Chem. Z f g . , Cbern. Appar., 86, 809 (1962), and references therein; E. D. Hughes, C.K. Ingold, and G. H. Ridd, J . Cbem. SOC., 58 (1958). (4) H. Schmid and G. Muhr, Monatsb. Cbern., 93, 102 (1962). (5) Z. A. Schelly, J . Phys. Cbem., 74, 4062 (1970). (6) D. Y . Chao and Z. A. Schelly, J . Phys. Chem., 79, 2734 (1975).
21
(7) M. Eigen and L. DeMaeyer in "Techniques of Organic Chemistry", Vol. 8, 2nd ed, Part 2, S. L. Friess, E. S.Lewis, and A. Weissberger, Ed., Wiley, New York, 1963, p 895. (8) The stoichiometric coefficients v,,by definition, are posthe for products and negative for reactants. (9) C. C. Addison and R. Thompson, J . Cbem. SOC., 218 (1949). (10) C. W. Wittaker, F. 0. Lundstrom, and A. R. Merz, Ind. Eng. Cbem., 23, 1410 (1931). (11) M. M. Wong and Z. A. Sbhelly, Rev. Sci. Insfrum., 44, 1226 (1973). (12) Without structure breakers and at certain density differences of the liquids to be mixed, the time required for homogeneous mixlng may be much longer than 1 ms. This is evidenced by disturblng schlieren-effects. (13) There is a measurable amount of ions in HCI-HOAc (I. M. KoHthoff and A. Willman, J . Am. Cbem. SOC.,56 1007 (1934)). However, in a mixture wkh CCI, this ionization is conskably reduced. Although, the activity coefficients of ion pairs with large dipole moment depend strongly on ionic strength especially in solutions of low dielectric constant (J. G. Kirkwood, J . Cbem. Pbys., 2 , 351 (1934)), at the low ionic strength of our sollrtions, for simplicity, all activity coefficients were assumed to be unity.
Kinetics of Ion Exchange. A Radiochemical Study of Rb+-H+ and Ag+-H+ Exchange on Zirconium Arsenophosphate Narendra J. Singh," J. Mathew,+ and S. N. Tandon Department of Chemistry, University of Roorkee, Roorkee-247 672, India (Received September 22, 1978; Revised Manuscript Received August 1, 1979)
This communication reports a study of the kinetics of ion exchange of Rb+ and Ag+ on the H+form of zirconium arsenophosphate by the "limited bath technique". The slow step which determines the rate of exchange at concentrations 10.1 M is diffusion through the exchanger particles. The values of interdiffusion coefficients, energy of activation, and entropy of activation have been calculated. The data obtained have been comp,ared with those on organic resins and other inorganic ion exchangers. The rates of exchange for Rb+ and Ag+ on zirconium arsenophosphate have been found to approach to those on some organic resins and inorganic ion exchangers. Introduction The rate-controlling step in ion exchange is diffusion either through the exchanger particle (particle diffusion) or an adherent liquid layer (film diffusion) and under an intermediate range of conditions both mechanisms may contribute to the rate-determining step.' Of the various types of ion-exchange processes, particle-diffusion-controlled exchange has been studied thoroughly and has adequate theoretical understanding. It is observed that, in a process where an ion A is exchanged with an ion B in solution, there occurs an electric coupling of the opposite fluxes of the two ions, so that the rate of interdiffusion is dependent on the state of conversion of exchanger from form A, to form B, and the diffusion coefficient in the exchanger is not constant with time. However, an approximate indication of the rate may be obtained if an average constant mobility is assumed (constant-diffusivity model). In isotopic exchange this assumption is of course very nearly correct. The particle-diffusion equation developed by Boyd et a1.l for isotopic exchange was found to be valid for binary ion exchange also, at higher concentrations in which the composition of the external solution is assumed to be constant and not time dependent. Studies on the kinetics of ion exchange are mostly directed toward organic resins and thus leaving their inorganic clounterparts still to be exploited. Some of the im-
* Department Geology and Geophysics, University Roorkee, Roorkee-247 672, India. 2623 North Ravenswood St., Chicago, Ill. 60613. 0022-3654/80/2084-0021$01 .OO/O
portant contributions in this direction may be cited by mentioning the work on synthetic zeolites,' zirconium p h ~ s p h a t e , "hydrous ~ zirconium oxide," zirconium antim ~ n a t etin , ~ antimonate,8 tantalum arsenate? and iron antimonate.l0 Most of these studies have been directed toward the investigation of the diffusion coefficients, since it can describe the mobility of the ion in the exchanger and, in addition, it might give a clue to the "degree of openness" of the channels through which diffusion takes place.'l Recently zirconium arsenophosphate (ZAP)" has been synthesized in chemical laboratories and was found to possess good ion-exchange properties. The material showed appreciable resistance toward high temperature, chemical attack, and ionizing radiations. The practical utility of the material was shown by achieving several metal ion separations of analytical and radiochemical interest. The present communication reports our findings OD the kinetics of Rb+-H+ and Ag+-H+ exchange systems on the material. The rate of exchange of Cs+ was found to be too slow to obtain any meaningful results. Experimental Section ZAP was prepared at pH -2 by the method reported elsewhere.l2 The diameters of the particles of two different sieved fractions were measured with a micrometer microscope for 100 particles of each fraction. The mean radii cm (within -4% error). were 2.16 X lo-' and 6.35 X The ion-exchange capacity measured at pH 2 by the radiometric method for Rb+ and Ag+ was found to be 1.26 and 1.17 mequiv/g, respectively.
0 1980 American Chemical Society
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The Journal of Physical Chemistry, Vol. 84, No. 1, 1980
Singh, Mathew, and Tandon M
10
I
- 1.4
-
2.5
1.2
- 1.0 -as
01
- 0.6
-
t,mn
Figure 1. Effect of the concentration of external solution on the rate of Rb+ exchange on ZAP (particle size, r = 2.16 X cm).
Radiotracers &Rb, llOmAg,and '"Cs were procured from Bhabha Atomic Research Centre, Bombay, India. Radiometric assays were made by using a y-ray spectrometer (ECIL, India) connected to a well-type NaI(T1) scintillation detector. The rates of exchange were determined by the method reported earlier.8 The studies were conducted a t 25, 35, 45, and 55 "C (fO.l "C). The amount exchanged with time is given by the expression F = So - S,/So - S ,
Figure 2. Effect of variation of temperature and particle size on the rate of Rb+ exchange with H+ on Z A P (0) r = 2.16 X lo-' cm; ( 0 ) r = 6.35 X cm.
-7.9
where F is the fraction exchanged at time t , Sois the count rate a t t = 0, St is the count rate at t = t , and S, is the count rate after -100% exchange. The experimental data were analyzed by the least-squares method13 and the estimated error was within 5 % for each measured value of the diffusion coefficient and other thermodynamic parameters.
Results The conditions for the present investigations were set to study the particle-diffusion mechanism only. The experimental data were tested for particle diffusion by using eq 1 given by Boyd et al.' and later modified by Rei6 - 1 F = 1- - C - exp(-n2Bt) (1) r2n=in2 chenberg,14where F is the fractional attainment of equilibrium at time t , n is an integer and
B = r2Di/?
(2)
in which Di is the interdiffusion coefficient for the exchanging ion inside the exchanger and r is the radius of the exchanger particle. Plots of F and Bt vs. t at different concentrations of external solution for Rb+-H+ exchange as a representative system are given in Figure 1. Plots of Bt vs. t with varying temperature and particle size are presented in Figure 2. Plots of log Di against 1/T (Figure 3 ) have been drawn to calculate the values of the energy
-a
t
I
I 3.1
3.2
I
3.3
3
l / T x IO3+
Flgure 3. Plots of log D v s . 1 I T .
of activation (E,) and preexponential constant (Do) employing an Arrhenius type equation
D = Do exp(-Ea/RV
(3)
The values of entropy of activation ( A S ) are calculated by substituting Do in the equation proposed by Barrer et a1.15
D = 2.72(kTd2/h) exp(AS*/R)
(4)
where 12 is the Boltzmann constant, T = 273 K, d is the ionic jump distance (the distance between two successive positions of ion in the process of diffusion) and is equal cm, h is Planck's constant, and R is the gas to 5 x constant. McKay plots (Figure 4) have been obtained by plotting log (1- F) against time t for Rb+-H+ exchange. Similar plots are obtained (not included in the text) for Ag+-H+ exchange also.
The Journal of Physical Chemistry, Vol. 84, No. 1, 1980
Kinetics of Ion Exchange
23
TABLE I : Kinetics of Ion Exchange on Zirconium Arsenophosphate and B and Di Values and Other Thermodynamic Parameters exchange E,, kcal A S , cal system r,a cm temp, "C 5,s - ' D , , cm2 s-' Do, cm, s" mol-' deg-' mol-'
-
Ag+H+
-
IEb+H+
a
2.l6 X 2.116 X 2.116 X 2.l6 X 6.35 x 2.116 X 2.l6 X 2.:L6 X 2.16 X 6.35 x
~ 25 lo-' 35 10''
lo-' 10-3 10" lo-'
lo-' lo-'
10-3
45 55 25 25 35 45 55 25
1.94 x 2.25 x 2.55 x 2.92 x 2.23 x 3.18 x 3.81 x 4-16 x 4-84 x 3.77 x
10-4 10-4 10-4 10-~ 10-3 10-4 10-4 10-4 10-4 10-3
9.19 x 10-9 1 . 0 6 X lo-' 1.21 x lo-' 1.38 X lo-' 9.10 x 10-9 1.51 X lo-' 1.71 X l o - * 1.97 X lo-' 2.29 X lo-' 1.47 X lo-'
-
7.47 x
lo-'
1.57 X
2.6
-21.56
2.8
-20.10
Particle size.
Flgure 4. McKay plot for Rbt-H+ exchange on ZAP (particle size r
= 2.16 X lo-? cm).
Discussion The Bt vs. t plots are linear and pass through the origin with a constant value for the interdiffusion coefficient at a concentration 20.1 M. At concentrations 10.05 M diffusion in the! initial stages of exchange seems not to be controlled by particle diffusion alone, while at concentrations 20.2 M, the slow step which determines the rate of exchange is particle diffusion as the concentration of external solution and the stirring conditions do not effect the rate of exchange. It can be seen from Figure 2 that the rate of exchange increases with increasing temperature. This can be attributed to an increase in ionic mobility at higher temperature. Further, the attainment of equilibrium is faster on smaller particles of the exchanger than on larger ones, where both have constant values for the interdiiffusion coefficient (within experimental error). This conforms to the relationship between the ratio of squares of radii and inverse ratio of B values from eq 2. The values of interdiffusion coefficients (Table I) on ZAP are much smaller than those on strongly cationic organic resins14 and appreciably higher than those for ze01ites.l~ However, the values are almost of the same order of magnitude as on some inorganic ion exchangers, e.g., on zirclonium antomonate7 the reported value for cm2s-l at 30 "C which is Rb+-Ht exchange is 4.86 X
close to 1.51 X cm2s-l observed on ZAP. For Na'-H+ exchange on the weakly cationic resin Amberlite IRC-50, cm2 s-l. On crysConway et aL18 gave a value 3.9 x 10-~ talline zirconium phosphate, however, for alkali metal ions the Di values are of the order of cm2 s-', Thus a comparison of the interdiffusion coefficient values obtained with those reorted earlier suggests that the rates of exchange on ZAP are approaching those of some organic resins and other gel inorganic ion exchangers. For Cs'-Ht exchange the very slow rate of exchange may be explained on the basis of the formation of too narrow intraexchanger channels to permit the diffusion of Cs+. Plots of log Di vs. 1/ T are linear, enabling one to estimate the energy of activation and the preexponential constant, The values of E , increase with increasing ionic size, Le., Agt (1.25 A) has a lower value compared to Rb+ (1.48 A). An analogous behavior was observed for the diffusion of alkali metal ions through analcitelg and Rb+ and Cs+ on antimonates of zirconium7and tin8 The values of entropy of activation20 are in part associated with changes in the hydration states of the ions as they leave the aqueous solution and enter the exchanger phase and vice versa. The negative values of AS* observed may be due in part to an overall increase in the hydration as the hydrogen ions replace larger cations (counterions) iin the solution, suggesting thereby a certain degree of dehydration of cations while diffusing into the solid phase. This is partly in agreement with the observation of Harvie and Nancollas4who found that Li+ and Na+ diffuse as hydrated species with the possibility of K+ being anhydrous on zirconium phosphate. This is a further indication that no significant structural changes occur in ZAP upon exchange of Rb+ and Ag+ for H+. The McKay plots21(Figure 4) are curves similar to those for independently decaying activities, suggesting thLe occurrence of a complex exchange reaction. This can be explained on the basis of the heterogeneity of functional groups as phosphate and arsenate are incorporated in the exchanger. Similar observations have been made by Tandon et al. on the antimonates of zirconium' and tine for Rb+ and Cs+ exchange and also by Rahman and Barrett22for the isotopic exchange of phosphate groups of zirconium phosphate.
Acknowledgment. The financial support from the University Grants Commission, New Delhi, India, under Scheme No. F.23-60/75(SRII) is gratefully acknowledged. References and Notes (1) G. E. Boyd, A. W. Adamson, and L. S. Myers, J . Am. Chem. Soc.,
69,2836 (1947). (2) L. V. C. Rees, Annu. Rep. frog. Chem., Sec. A , 67, 19 (1970). (3) G. H. Nancollas and R. Paterson, J. Inorg. Nucl. Chem., 2:2, 259 (1961). (4) S. J. Harvle and G. H. Nancollas, J . Inorg. Nucl. Chem., 30, 273 (1968).
J. Phys. Chem.
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(5) S. J. Harvie and G. H. Nancollas, J. Inorg. Nuci. Chem., 32, 3923 (6) (7) (8) (9) (10) (1 1) (12) (13)
(1970). E. Hallaoa, Z. Mlzak, and H. N. Salama, Indian J. Chem., 11, 580 (1973). J. Mathew and S. N. Tandon, Can. J. Chem., 55, 3857 (1977). J. Mathew, N. J. Singh, C. B. Gupta, and S. N. Tandon, Indian J. Chem., 16A, 524 (1978). J. P. Rawat and P. S. Thind, J. Phys. Chem., 80, 1384 (1976). J. P. Rawat and D. K. Singh, J. Inorg. Nucl. Chem., 40, 897 (1978). A. Dyer and M. J. Fawcett, J. Inorg. Nucl. Chem., 28, 615 (1966). N. J. Singh and S. N. Tandon, J. Radioanal. Chem., 49, 195 (1979). D. L. Harnett, "Introduction to Statistical Methods", Addison-Wesely, Reading, Mass., 1970.
(14) D. Reichenberg, J. Am. Chem. Soc., 75, 589 (1953). (15) R. M. Barrer, R. F. Batholomew, and L. V. C. Rees, J. Phys. Chem. Solids, 21, 12 (1961). (16) G. E. Boyd and 8. A. Soklano, J. Am. Chem. Soc.,75, 6091 (1953). (17) V. I. Gorshkov, 0. M. Panchenkov, and T. V. Ivanova, Zh. Fiz. Khim., 38, 1969 (1962). (18) D. E. Conway, J. H. S. Green, and D. Reichenberg, Trans. Faraday Soc., 50, 511 (1954). (19) R. M. Barrer arid L. V. C. Rees, Trans. Faraday Soc., 56, 709 (1960). (20) L. V. C. Rees, Annu. Rep. frog. Chem., Sec. A, 201 (1970). (21) H. McKay, Nature (London), 142, 977 (1938). (22) M. K. Rahmann and J. Barrett, J. Inorg. Nucl. Chem., 36, 1899 (1974).
Thermodynamics of Binding of Configurationally Different Iron( 111) Complex Ions by Sodium Dextran Sulfate in Aqueous Solution B. Pispisa" and S, Paolettl Isfltutodi Chimica Fisica dell'Universitg di Roma, Rome, Italy, and Istltuto di Chimica deii'Universit2 di Trieste, Trieste, Italy (Received May 29, 1979)
The binding process between sodium dextran sulfate (NaDS) and pseudo-octahedral trans- and cis-Fe(II1)complex ions in aqueous solution, around pH 7.5 and 5.7, has been studied by means of equilibrium dialysis, phaseseparation, and calorimetricmeasurements. Equilibrium dialysis data show that the affinity of NaDS for the complex counterions follows the order trans-[Fe(tetpy)(OH),]+> cis-[Fe(bmen)(H20)0Hl2+> cis-[Fe(bmen)(OH)2]+.Phase-separation experiments indicate, however, that [Fe(bmen)(HZ0)0Hl2+-NaDSexperiences a less intimate association process than does the [Fe(bme~~)(oH)~l+-NaDS system, owing to the higher charge density of the aquahydroxo species. Calorimetric results support the conclusion that the trans-[Fe(tetpy)(OH)z]+ compound forms the most stable and specific association complex with NaDS, the process being entirely entropy driven. Molecular models are consistent with the overall findings in that they suggest that the trans topology of [Fe(tetpy)(OH)z]+makes a close approach of the ions to the polymeric substrate less crowded than the cis configuration, thus allowing specific interactions which very likely involve also the tetrapyridyl ligand and hydroxylic groups of the polysaccharide chain,
Introduction complex counterions by this polymer and, second, to investigate the effect of their charge density on the mode Ionic polysaccharides have drawn attention in the past of binding. few years because of their important role in a number of Calorimetric and binding data, the latter obtained by biological phenomena.' For example, sodium dextran equilibrium dialysis and "phase-separation" measurements, sulfate (a sulfonated derivative of dextran) exhibits anshow a different affinity of NaDS for the complex ions, tithrombic activity. This property is very likely related which will be discussed in the light of their different toboth to the high charge density and saccharidic structure pology. of the polymer which allow extensive and possibly specific interactions with small ions. A number of studies on the Experimental Section behavior of these polyelectrolytes in aqueous ~ o l u t i o n ~ ~ ~ Materials. Sodium dextran sulfate (mol wt. 500000)wm as well as on the interaction with simple ions or purchased from Sigma Chemical Co. (USA) and dialyzed have been reported. against water in order to remove phosphate. The sulfur We present here the results of an investigation on the content of the purified and dried material was 17.2%, binding process between some pseudo-octahedral Fe(II1) which corresponds to an average of 2.02 sulfate groups per complex ions and sodium dextran sulfate (NaDS) in glucosyl residue. This gives a mean intercharge distance aqueous solution. The iron(II1) derivatives were trans(for the fully extended chain) of 2.6 A.2 The concentration [Fe(tetpy)(OH),]+, cis- [Fe(bme~~)(OH)~l+, and cis- [Feof the polymer was determined by weight after prolonged (bmen)(H,O)OHl2+, where tetpy = 2,2':6',2'':6",2"'drying under vacuum. Final concentrations were in the quaterpyridyl and bmen = N,N'-bis(2-methylpyridyl)range of 2 X to 6 X 10" M, referred to the monomeric ethylenediamine. unit (monomol/ L). The Fe(II1) complex ions were prepared as already deThe cis compound is a mononuclear species both in the solid state and in aqueous solution. According to OH potentiometric titrations, the protolytic equilibrium [Fetrans US-* (14) 6 [Fe(bme~~)(OH)~l+ + H+ has a pK, (bmen)(H2O)OHI2+ of 4.4 (20 "C), which increases to 6.4 f 0.1 in the presence The aim of the work was, first, to study the association of NaDS (C/Cp 0.1, C being the total concentration of process of configurationally different, relatively bulky, 0022-3654/80/2084-0024$01 .OO/O
0 1980 American Chemical Society
