ISOTOPIC EXCHANGE IN ZEOLITES
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n
Equations A12-A15 and eq A17 form the solution of eq A1 and A2 in terms of z(r, t ) and y(r, t). The average value of z y in the exchanger at any time, given by U ( t ) , can be calculated by applying the relationship
+
U(t) = 1 -
g3 f ( x + y)r2 dr
(AB)
Substituting eq A15 in eq A18 and integrating, we obtain
on = n2112D/R2
Mechanism and Kinetics of Isotopic Exchange in Zeolites.
11. Experimental Data by L. M. Brown and H. S. Sherry* Mobil Research and Development Corporation, Central Research Division, Princeton, N e w Jersey (Received M a y 17, 1971)
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Publication costs assisted by Mobil Research and Development Corporation
The kinetics of isotopic exchange of sodium ions in synthetic hydrated zeolites NaX and KaA were investigated by means of a radioactive-tracer technique. Exchange in these zeolites consisted of two observable steps involving structurally distinct cations. The experimental data were interpreted in terms of a new model containing two adjustable parameters representing the rate coefficients of the fast and slow isotopic exchange steps. The model assumes the rate-controlling processes are diffusion in the fast isotopic exchange of mobile ions and intracrystalline exchange (assumed to be first order) between bound and mobile ions in the slower isotopic exchange of bound ions. The behavior of NaX, in which bound and mobile ions in the large cages undergo isotopic exchange in a single apparent diffusional process, is explained by assuming that intracrystalline exchange is a t least as fast as diffusion. A rigorous test of the model for zeolite X shows that the rate of the fast step varies inversely with the square of the mean equivalent radius of the crystals and that the rate of the slow step was independent of the size of the crystals, as required mechanistically. Best values of the diffusivities and specific rates of exchange were derived from least-squares fits of the data on the model by use of the known distributions of cations over the different kinds of sites.
Introduction The rates of isotopic exchange of sodium ions in hydrated zeolites X and A have been measured by means of a radioactive-tracer technique. The primary objective of this study was to provide experimental data that could be used to ascertain the validity of the isotopic exchange model described previously. Earlier attempts2j3to investigate these systems were
limited by the immeasurably large rates in the small crystals available commercially. Measurable rates were achieved in the present study by the use of large single crystals of zeolites nTaX and NaA, which were (1) Part I : L. M. Brown, H. S. Sherry, and F. J. Krambeck, J . Phys. Chem., 75, 3846 (1971). (2) E. Hoinkis and H. W. Levi, Naturwissenschaften, 53, 500 (1966). (3) E. Hoinkis and H. W. Levi, Z . Naturforsch. A , 22, 226 (1967).
The Journal of Physical Chemistry, Vol. 76, N o . 26, 1971
L. M. BROWNAND H. s. SHERRY
3856 synthesized according to procedures developed by Charnell. Isotopic exchange in each of these zeolites involves more than one structurally distinct cation site. I n NaX there are three cation sites, consisting of mobile and bound sites in a three-dimensional network of large cages, and bound sites in an interconnecting network of small cages.jt6 In NaA, there are two cation sites, consisting of mobile and bound sites in a single three-dimensional network of large cages.6 One would therefore expect exchange in zeolite X to take place in a maximum of three steps and exchange in zeolite A to take place in a maximum of two steps. Experiment’~~ has shown that, with few exceptions, isotopic exchange of monovalent and divalent cations in these zeolites takes place in two observable steps. In all but one case these steps were thought to be independent diffusional processes. In the exchange of cesium ions in zeolite A,9 however, desorption of bound ions was considered to be rate controlling in the slow step. Data obtained in this study have been interpreted in terms of a different model’ which, we believe, is consistent with the crystal structure of the zeolites and accounts for all relevant modes of cationic migration. Briefly, the model states that the elementary isotopic exchange steps are not independent but are coupled processes. In zeolite A these processes consist of the diffusion of mobile ions in the fast step and of intracrystalline exchange between bound and mobile ions in the slow step. I n zeolite X, where intracrystalline exchange between bound and mobile ions in the large cages is assumed to be fast compared to diffusion, the fast step is an apparent uniform diffusional process involving these two kinds of ions, and the slow step consists of the intracrystalline exchange between bound ions in the small and large cages. The model further assumes the equilibrium distribution of cations among the different kinds of sites, as determined from X-ray diffraction dataj5r6is maintained during the approach to isotopic exchange equilibrium. Diffusivities and specific rates of intracrystalline exchange (assumed to be first order) were derived by means of a two-parameter fit of the data to the model for the known equilibrium distribution of cations. Data obtained for crystals of different radii show that the rate of the slow step in zeolite X is independent of particle size, consistent with the proposed model but inconsistent with the model that assumes diffusion to be rate controlling in the slow step.
Experimental Section The crystals of zeolites X and A were synthesized in accordance with procedures perfected by CharnelL4 These procedures yielded well-formed octahedra of NaX as large as 100 p in overall length and cubes of NaA as large as 60 p in edge length. X-Ray crystalThe Journal of Phusical Chemistry, Vol. 7 6 , X o . 15,1972
linities were obtained and found to be 150-160% of those for Linde 13X and Linde 4A crystals. Before they were used, the virgin crystals were washed once with a 0.1 N NaCl solution to ensure uniformity of the cation content and then washed carefully with distilled water until the pH of the slurry was in the range 10.5-11.0. The composition of each zeolite is shown in Table I.
Table I : Composition of Zeolites NaX and NaA Amt Zeolite (site)
NaX ( 9 5 ~ ) NaX ( 7 7 p ) NaA (5311)
of Na,
mequiv/g
6.74 6.0 6.87
-Amt, mmol/gSi02 AlrOa
7.54 7.96 7.44
--Atom SUA1
3.45
1.1
3.20 3.44
1.23
1.08
ratiosNa/A1
0.98 0.97 1.0
The crystals were classified into fractions having narrow size ranges by means of elutriation. The apparatus, adapted from that of Alyl and Latimer,’o is shown schematically in Figure 1. It is a closed, selfsustaining system in which ethyl alcohol is circulated continuously by means of a variable-speed tubing pump (A) through a series arrangement of five Pyrex tubes (B) having diameters in the range 2-3.5 in. The return of the alcohol to the first tube (B) was effected by pumping liquid from the top of Pyrex tube (C). This tube, immersed in a beaker containing alcohol, contains a column of glass beads (D) to trap crystals that enter it through the side arm. The pump speed was maintained constant within 1% by means of a solid-state controller; flow rates were monitored by means of a flowmeter (E). Mean sizes of the samples used in this research are given in Table 11. Each result was obtained by measuring the dimensions of 300-500 crystals contained in calibrated photomicrographs of the type shown in Figure 2. The mean equivalent radii contained in Table I1 were used in analyses of the data. The isotopic exchange system consisted of the zeolite crystals (1/4 to ‘/s g) containing a trace amount of sodium-22 and a 0.1 N sodium chloride solution (600 ml). The reaction was performed in the apparatus shown schematically in Figure 3. The mixture was stirred (C) vigorously (5000 rpm) in a 1-1. resin flask (4) J. Charnell, J . Cryst. Growth, in press. (5) D. H. Olson, J . P h y s . Chem., 74, 2758 (1970). (6) L. Broussard and D. P. Shoemaker, J . Amer. Chem. Soc., 82, 1040 (1960). (7) E. Hoinkis and H. W. Levi, 2. Naturforsch. A , 23, 813 (1968). (8) E. Hoinkis and H. W. Levi, “Ion Exchange in the Process Industries,” Society of the Chemical Industry, London, 1970, p 339. (9) H. Gaus and E. Hoinkis, 2. Naturforsch. A , 24, 1511 (1969). (10) H. F. Alyl and R. ,M.Latimer, J . Inorg. Nucl. Chem., 29, 2041 (1967).
ISOTOPIC EXCHANQE IN ZEOLITES
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Table 11: Melean Sizes of Zeolitic Crystals Me*" length of octahedra or cabea. Zeolite
NaX NaA
P
95 77 53
* 10 * 10 *5
Mea" .Qui"
whetid radius. cm
2.7 X lo-' 2 . 2 x 10-1 2 . 7 X lo-*
I'
) . A
Figure 3. Experimental apparatus (schematic): A, 1-1. Pyrex vessel; B, filter holder; C, stirrer; D, plastic cell; E, NaI(TI) crystal and electron multiplier tube; F, pump; G, electrical lead to analyzer-rate meter.
Figure 1. Elutriation apparatus (schematic): A, pump; B, elutriatiiig tube; C, glass tube; I), glass beaas; E, flowmeter.
Figure 4. Relative activity of "Na 08. time in a test of the experimental method: open circles, relative activity of "Nn added at known rate to reaction vessel; curve A, measured activity; curve B, activity corrected for time constant of rate meter.
(A) immersed in a constnnt-temperature bath and pumped (F) rapidly (2 I./min) through a filter (R). The filtered solution then passed through a Plexiglas cell (D) that was inserted in an opening in a TI-doped NaI scintillation crystal (E) brforc returning to the resin flask. The U-shaped Plexiglas cell proved to be unsatisfactory, because bubblrs tendrd to accumulate therein and consequently preventcsd the measurement, of the true activity of the solution. This effect was eliminated by use of a steel tube, having a volume of 14 ml, that was mounted in another NaI crystal having a straight-through bore. Zrolite crystals were re-
tained in the flask by a Millipore Nylon filter contained in the holder (B); the average diameter of the filter pores was 14 p. The apparatus was modeled after that of Schwarz, et al." The volume of the rubber tubing external to the solution was approximately 22 ml. For a flow rate of 2 I./min, the solution in the steel tube was replaced once every 0.2 sec. The NaI crystal was sealed to a light-shielded electron multiplier tube, t,he output of which was fed sequentially into a preamplifier, pulse height, analyzer, and linear rate meter. The output of the last was displayed on a 10-mV recorder. A correction was applied to t,he recorded signal to compensate for the distortion of the true signal by the time constant of the rate meter, set a t 1.069 see, by use of the finite-difference method of Vincent.l* All such calculations were programmed for execution by an electronic computer. The sample standard deviation of the corrected relative activities from the least-squares smoothed curve through the data vaned from *0.01 to *0.04 for data obtained at the lowest to highest temperature. (11) A. Sehwam.
J. A. Marinsky, and K. 5.Spiegler, J . Z'hua. Chom.,
MI, 918 (1964).
(12) C . H. Vincent, J . Sei. Inatrum., 44, 241 (1967).
The J o w d of Physiml Chm&lru. Vol. 76. A'". M.1971
L. M. BROWN AND H. S. SHERRY
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Figure 5 . Dimensionless time parameter (diffusional model) (Bt)d vs. t h e for NaX (95 p ) .
The reliability of the overall experimental procedure was tested in a separate experiment. In this experiment 2
