The fractional attainment of the isotopic equilibrium between
a Cd(N03)2 solution and a 115Cd-labelled CdX zeolite has been
measured as a function of time, particle size of zeolite and temperature.
The experimental kinetic data have been interpreted in
terms of the Brown-Sherry-Krambeck model and the self-diffusivities
and diffusional activation parameters of Cd++ ions in zeolite
CdX have been calculated

I. D. Paligorić

I. J. Gal

M. B. Todorović

V . M. Radak

English

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CROATICA CHEMICA ACTA CCA-1332 CCACAA 55 (3) 287-293 (1982) YU JSSN 0011-1643 UDC 546.4/.5.48 Original Scientific Paper Self-diffusion of Cd++ Ions in Hydrated CdX Zeolite M. B. Todorovic, I. J. GaI, I. D. Paligoric, and V . M. Radak Boris Kidric Institute of Nuclear Sciences, Belgrade and Department of Chemistry, Faculty of Sciences, University of Belgrade, Yugoslavia Received September 3, 1981 The fractional attainment of the isotopic equilibrium between a Cd(N03)2 solution and a 115Cd-labelled CdX zeolite has been measured as a function of time, particle size of zeolite and tem-perature. The experimental kinetic data have been interpreted in terms of the Brown-Sherry-Krambeck model and the self-diffusi-vities and diffusional activation parameters of Cd++ ions in zeolite CdX have been calculated. INTRODUCTION Ion-exchanged synthetic zeolites containing transition metal ions instead of sodium counter-ions are potentially useful catalysts and molecular sieves for industrial chemical processes. The thermodynamics of ion exchange in zeolites is generally well understood and in the case of Cd++-Na+ exchange has been extensivelly studied1- 4 . This however does not apply to the kinetics of ion exchange. In order to obtain fundamental data on the mobility of cations in hydrated zeolites, as, for example, the ionic self-diffusivities (self--diffusion coefficients), one depends on a suitable model which interprets the kinetics of the isotopic exchange. Thus, Dyer and coworkers5- 7 assumed that the isotopic exchange of Ca++,and Co++, Ni++ Zn++ in X and Y zeolites is governed by a single diffusion process of these ions in the solid particles, whereas Hoinkis and Levis--9 interpreted their isotopic exchange data on alkaline earth ions in zeolite X and A in terms of two independent diffusion processes. Later, Gaus and Hoinkis10 modified their model by assuming a temperature dependent distribution of cations over the zeolite lattice. Brown and Sherry11 interpreted the isotopic exchange of Na+ ions in X and A zeolite in terms of two kinetic steps: diffusion of mobile cations coupled to a intracrystalline exchange between mobile and bound cations (the Brown--Sherry-Krambeck model12). That model has also been applied to Zn++ 1in A zeolite13 and X zeolite14, and Cd++ in A zeolite15• The present paper reports the isotopic exchange kinetics of Cd++ ions measured between a Cd(N03)z solution and a CdX zeolite. A radio chemical technique using 115Cd-labelled X zeolite has been applied to measure the rate of isotopic exchange. In the interpretation of data, the Brown,-Sherry-Kram-beck (BSK) model12 gave good agreement with the experimental kinetic curves and allowed us to calculate the self-diffusivities of Cd++ ions in X zeolite, as well as the activation parameters for diffusion. 288 M. B. TODOROVIC ET AL. EXPERIMENTAL The CdX zeolite has been prepared from 13X zeolite (BDH) by exchanging sodium ions with cadmium ions. The composition of CdX obtained by chemical analysis is shown in Table I. TABLE I Composition of CdX Zeolite Cd'+ Na+ Al02 Si02 H20 sum wt 0/o 22.17 0.19 23.80 29.61 23.95 99.73 Unit cell composition : Two fractions of different particle size, of mean radius 32 ± 4 ~tm and 20 ± 2 pm , were obtained by sieving. The preparation of the exchanged zeolite, chemical analysis and particle size determination is described in previous papers3,13 • . The CdX zeolite particles were radioactively labelled by equilibrating them with a 115Cd(N03)2 solution at 90 °c for aproximately ten days. The labelled 115CdX zeolite has been stored in a desiccator over a saturated solution of ammonium chloride where its water content remained constant (see Table I). The rate of isotopic exchange between an inactive 0.01 mol dm-3 Cd(NOslz solution and a radioactive sample of CdX was followed radiometrically as described earlier13• The fractional attainment of isotopic equilibrium Ut is defined : Co-C, U t= ·- - - -Co-Coo (1) Here, C0, Ct and C00 are the concentrations of radioactive cadmium ions in the solid phase at zero time, at time t and at infinite time, when the isotopic equilibrium is established. C0, Ct and C00 have the same meaning for the liquid phase (C0 = 0 in the present case). In the aqueous phase, Ct is measured, whereas C00 is calculated from the known value of c: and the amount of Cd in both phases, assuming complete isotopic equilibrium. The rates of isotopic exchange, Ut vs. t, are shown in Figure 1. The points are experimental data, whereas the curves represent best fits calculated with the BSK model12 using a computer program13. RESULTS AND DISCUSSION A careful check of the experimental data of Fig. 1 has shown that the rate of isotopic exchange is not a single kinetic step, nor is it controlled by the film at the phase boundary16• Therefore, the BSK model12 has been applied in the quantitative interpretation, as before in the case of Zn++ in A 13 and X zeolite14, and Cd++ ~n A zeolite15• The model has been thor oughly described12 and often applied and discussed13- 15• Let it here be mentioned that the BSK model assumes a two-step kinetics: diffusion of mobile cations through the openings and cages of the zeolite framework coupled to a first-order exchange process betvveen mobile cations and cations bound to zeolite sites. In pratical application, no differentiation between different sites is made and SELT-DIFFUSION OF Cd(II)-IONS IN ZEOLITE 289 a single first-order »average« rate constant is used for all sites involved. Similarly, a single diffusional process is assumed over the whole lattice framework, since in an interconnected system of channels no separate diffu-sional paths are envisaged. According to the model, the dependence of U1 on t is given by: 0.8 0.6 0.4 0.2 0 0.8 0.6 0.4 0.2 0 /' / 20 40 l(---_..;A--20 60 r 60 80 100 120 t(min) h JI )C . x x r = 32 µm 80 100 120 t (min) Figure 1. U , against t at temperatures 0, 60; o, 45 and x, 25 oc. 290 M. B. TODOROVIC ET AL. 00 -~2 ""' 1 [ U n ( 1 + v" ) ,. L n2 (un - V11) k (l + K) exp (v 11 t) - v 11 n=l ( 1 + u " ) exp (u 11 t) J k (l + K) (2) un = - 21 -[ (1 + K) k + n2 B ] [ 1 -v 1 - 4 kn2 B J [(l + K) k + n 2 BF (3) 1 [ ][ v . 4kn2B- ] v,, = -- 2 (1 + K) k + n2 B 1 + 1 - [(1 + K) k + n2 B]2 (4) n = 1, 2, 3, ... Eqs. 2-4 represent the function U 1 = f(t) in terms of three time-independent parameters. One parameter is the frequency B , related to the diffusion step, and defined by B = n 2 D/r~ ('1) Here D is the ionic self-diffusivity and r is the mean effective radius of the solid particles. The second parameter is the frequency k , related to the first~order exchange between mobile and bound ions. The third parameter K is dimensionless, it is the equilibrium ratio between the number of bound and mobile ions involved in the kinetics. In principle, K could be obtained from crystallographic data of hydrated zeolite samples. Thus, in the case of X-ray analysis of NaX crystals, Olson1_7 found the following distribution of Na+ ions per unit cell (total of 86 sites) : 16 in Sr and Sr' positions, and 24 on all Sn sites. The rest, 46 Na+ ions are mobile hydrated cations in the supercage (Sm sites). In that case, the ratio of bound to mobile cations should be about 0.87. This ratio is not of course, necessarilly valid for the divalent Cd++ ions. First, our CdX sample has only 42 Cd++ ions instead of 43 (two Na+ ions per until cell are probably bound on Sr sites and inaccessible for the exchange). Thus, if the above conjecture is valid for CdX, the ratio K shouM be about 0.83. As explained by the authors of the model12 , in the specific case of Na+ in hydrated NaX, if a single value of K is used, i t is 0.23 for NaX. However, this value is only valid if the exchange step is faster than the diffusional step (i.e. k > B), which is, indeed, the case of NaT in NaX. In the case of divalent ions, as a rule, the opposite is true (k < B), and the value of K = 0.23 is a not correct. We shall consider one more possi-bility by taki:ng into account only the ratio of sites Su and Sm, and by assuming that the exchange between Su and S1 sites is a relatively fast step performed by a single »jump«. In that case, K = 0.52. The BSK model (eq. 2-4) has been fitted to our e:{per imental data by means of a computer program in which no a priori assumptions about the parameters B, k and K have been introduced. The best fit is obtained with the parameters listed in Table II. The U1 vs. t. curves in Figure 1 are the best fits obtained with those parameters. The sum ~ in eq. 2 has been n extended in our program up to a value of n specifed so that the next member of the sum, (n + 1), gave a difference of j Ut (n) - U1 (n + 1) I< 0.001 , which is negligible compared to the accuracy of experimental U 1 values of ±0.01-0.02. SELT-DIFFUSION OF Cd(II)-IONS IN ZEOLITE 291 TABLE II Kinetic Parameters particle temp/K radiu:; B=F/s- 1 k=1=/s- 1 K D/m2 s-1 rhtm 298 32 8.3 x 10-4 1.6 x 10-6 0.7 8.64 x 10-1• 318 32 1.5 x 10-3 1.0 x 10-• 0.7 1.56 x 10·13 333 32 2. 1 x 10-3 3.0 x 10 " 0.7 2.24 x 10-1" 298 20 1.6 x 10-3 2.5 x 10-• 0.7 6.08 x 1u-14 318 20 3.3 x 10-3 3.a x 10-5 0.7 1.33 x 10·13 333 20 3.8 x 10-3 5.0 x 10 5 0.7 2.35 x io-•3 ::J:: These values are accurate within about ± 5°/o. As seen from Table II, the diffusional step is faster than the exchange step, since the parameter R is always about two orders of m agnitude larger than k. Similar behav ior has been noted in ZnX 14 • As m entioned earlier, the parameter K has been obtained without any a priori assumptions based on structural crystalographic data. However, one restriction has b een imposed in the computer program with r espect to the K value : it is a common para-meter for all calculated curves U1 vs. t. (Such a restriction h as not been applied, of course, to the B and k parameters.) The best fit obtained for K is 0.7, w hich seems to be a reasonable value, between the values of 0.8 and 0.5 discussed previously. The ionic self-diffusivities D in Table II are ob tained from the B para-meters with eq . 5. They are close to the values reported for ZnX14 (calcu-lated with the same model), but m ore than an order of magnitude h igher than the corresponding v alues of Cd+<- in CdA zeolite, in agreement w ith the fact that A zeolite has smaller channels an d a higher charge-density of lattice framework than X zeolite. The self-diffusivities (D) in Table 2 ar e self-con-sistent in that they depend on temperature, but not on particle size. All six D values of T able II obey a common Arrhenius type of plot as shown in Figure 2. From this plot the diffusional activation energy Eo and the para-meter D 0 h as been obtained : D = D0 exp (- E0 /RTl E 0 = 26 kJ mo1-1 The activation energy E0 is close to the corresponding values for ZnX (23.6 kJ mol-1) obtained also with the BSK model1e. However, Dyer and Townsendr., using a single diffusion model obtained En = 89.6 kJ mo1-1 for ZnX. With the D0 v alue given above, the diffusional activation entropy /), S~ can be caulculated using the equation: k Td2 D0 = 2.718 --\--exp <"" S~ IR) 292 LogD -12.5 -13.0 -13~5 M. B. TODOROVIC ET AL. 3.00 3.20 Figure 2. Arrhenius plot, log D against T-1. o 32 µm Cl 20 µm Here, ks, h and R are the Boltzmann, Planck and gas constants, whereas d is the ionic jump distance (taken as d = 0.5 nm13•14). One obtains ~ S~ = -63 J mo1-1 K-1. The values of k in Table II show remarkable irregularities and do not obey the Arrhenius equation. This behavior seems to reflect the fact that we are dealing with several types of sites on which the Cd++ ions are bound. A decrease of the rate constant k implies that here exists a stronger bOIIld of the cation to its negative site, and vice versa. In the present case, the model is simplified by taking an average value of k over all different sites on which the cations are bound, and for such an average value one can hardly expect it to obey the Arrhenius equation. In principle, to each type of sites holding cations, a specific k value should be assigned, but such a model would be too complicated and of little practical value. Thanks are due to the Serbian Council for Scientific Research for financial support. REFEREN CES 1. I. J . Ga 1, 0 . Jank o vi c, S. Ma 1 c i c, P. Rado van o v, and M. Tod o-r o vi c, Trans. Faraday Soc. 67 (1971) 999. 2. V. M. Rad a k and I. J. Ga 1, Proc. III Int. Conf. Molecular Sieves, Zurich 1973, p. 201. 3. I. J. Ga 1 and P. Rado van o v, J . Chem. Soc. (Faraday I), 71 (1975) 1671. 4. A. Maes and A. Cremers, J. Chem. Soc. (Faraday I), 71 (1975) 265. 5. A. D ye r and S. A. I. B arr y, J . Inorg. Nucl. Chem. 39 (1977) 1061. 6. A. Dyer and R. P. Townsend, J. Inorg. Nucl. Chem. 35 (1972) 3001. 7. A. Dyer and A. B. 0 g den, J. Inorg. NucL Chem. 37 (1975) 2207. 8. E. Ho ink is and H. W. Levi, Z. Naturforsch. A 22, (1967) 226. 9. E. Ho ink is and H. W. Levi, Ion Exchange in the Process Industries, Society of the Chemical Industry, London, 1970, p. 339. SELT-DIFFUSION OF Cd(II)-IONS IN ZEOLITE 293 10. E. Gaus and Ho ink is, Z. Naturforsch. A 24, (1969) 1511. 11. L. M. Brown, H. S. Sherry, J. Phys. Chem. 75 (1971) 3855. 12. L. M. Brown, H. S. Sherry, and F. J. Kramb e ck, J. Phys. Chem. 75 (1971) 3846. 13. V. M . Rad a k, I. J. Gal, J. J. Sa 1 a i, J. Chem. Soc. (Faraday I), 72 (1976) 1150. 14. V. M. Rad a k, I. J. Ga 1, M. B. Todor o vi c, and L. Vu j is i c, VI Int . Conf. Molecular Sieves, Recent Research Reports, Chicago 1977, p. 71. 15. M. B. Todor o vi c, I. J. Ga 1, V. M. Rad a k, and L. Vu j is i c, VI Int. Conf. Molecular Sieves, Recent Research Reports, Chicago 1977, p. 104. 16. F. He 1 ff er i ch, Ion Exchange, l\'Ic Graw-Hill, New York 1962, p. 255. 17. D. H. 01 son, J. Phys. Chem., 74 (1970) 2758. 18. M. B. Todor o vi c, Ph. D. Thesis, University of Belgrade, Faculty of Sciences, Belgrade 1981. SAZETAK Samodifuzija CdH jona u hidratisanom CdX zeolitu M. B. Todorovic, I. J. Gal, I. D. Paligoric i V. M. Radak Frakciono dostizanje izotopske ravnoteZe izmedu Cd (N03)2 u rastvoru i CdX zeolita obelezenog sa 115Cd, mereno je u funkciji vremena, veliCine zrna zeolita i temperature. Eksperimentalni kineticki podaci interpretirani su pomocu modela Brown-Sherry-Krambeck i izracunati su koeficijenti samodifuzije i aktivacioni parametri za proces difuzije Cd++ jona u CdX zeolitu. 

Self-diffusion of Cd++ Ions in Hydrated CdX Zeolite

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