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The Kinetics of Ion Exchange Accompanied by Irreversible Reaction. 11. Intraparticle Diffusion Controlled Neutralization of a Strong Acid Exchanger by Strong Bases
by R. A. Blickenstaff, J. D. Wagner, and J. S. Dranoff Department of Chemical Engineering, Northwestern University, Evalaston, Illinois
(Received September 20,1966)
An experimental study has been made of the neutralization of a strong-acid ion exchanger by strong-base solutions in the intraparticle diffusion controlled region. Data obtained in a well-stirred batch reactor were consistent with the theory of Helfferich and yielded reasonable values for intraparticle diff usivities. However, the results have also shown that the model fails to account properly for the effects of different co-ions.
Introduction This paper presents the results of an experimental study of the rate of neutralization of a strong-acid ion exchanger by strong-base solutions. Part 1’ presented a verification of theoretical models for this process under conditions of film diffusion control of the observable rate. Part I1 is concerned with the regime of intraparticle diffusion control. Results to be exhibited below indicate the theory of Helfferich2 to be essentially valid, with one exception, in this range as well. The data to be reported were obtained as outlined in part I and by an additional technique involving a specially constructed cage reactor.
Theory As before, the basic reaction under consideration is the neutralization illustrated in eq 1
H+
+ R1+ + OH- +%+ + HZO
(1)
where barred quantities represent species in the resin phase. The reaction is considered to take place in a well-stirred batch reactor under conditions of intraparticle diffusion control, i.e., high solution concentrations, large particle size, and vigorous solution agitation. Thus, there are no concentration gradients in the solution phase, while the presence of OH- ions there keeps the concentration of H+ ions essentially equal to zero everywhere outside the particle. (The OH- ions are virtually excluded from the interior of the resin beads by the Donnan effect.) The Journal of Physical Chemistrg
Therefore, the situation within the exchanger particles is exactly the same during neutralization as under conditions of ordinary ion exchange. The only difference js in the boundary condition at the particle surface. For neutralization, the concentration of H + ions at the surface remains negligible. However, this is true for ordinary exchange only in the case of “infinite solution volume.” Solutions for the infinite volume case have been previously obtained and reported by Helff erich and o t h e r ~ . ~ nThe ~ tabulated solutions numerically relate the fractional attainment of equilibrium, G(t), to time for a binary exchange in terms of the ionic diffusivities of the two components. More specifically, the solution involves the ratio of the two diffusivities as well as the absolute value of one of them. Now the rate law for the intraparticle diffusion controlled neutralization can be formulated in terms of the known G(t).2 If CV < CV
F ( t ) = G(t) IfCV>CV
cv
F(t) = -G(t)
cv
(1) R. A. Blickenstaff, J. D. Wagner, and J. S. Dranoff, J . Phys. Chem., 71, 1665 (1967). (2) F. Helfferich, ibid., 69, 1178 (1965). (3) M.S. Plesset, F. Helfferich, and J. N. Franklin, J . Chem. Phgs., 29, 1064 (1958). (4) F.Helfferich, ibid., 38, 1688 (1963).
KINETICS OF IONEXCHANGE ACCOMPANIED BY IRREVERSIBLE REACTION
for 0 It It,, and
F(t) = 1
(4)
for t 2 to, where F(t) is the fractional conversion of the resin during neutralization and 2, represents the time for complete reaction. The goal of this study was to test eq 2-4 by experimental measurement of F(t) and comparison with the theoretical solution. This requires selection of appropriate values for DHand the ratio of &/&. The ratio may be determined after certain assumptions. One assumes first that the ratio of diffusivities of the two ions within the solid exchanger is the same as in liquid solution
&/DM
=
D~/DM
(5)
It is then assumed that the Nernst-Einstein equation can be used to relate ionic mobility at infinite dilution to diffusivity US=
DiF/RT
(6)
This leads to an expression for the diffusivity ratio (given in eq 7) in terms of existing ionic mobility data.6
curve experimentally by the infinite solution volume
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within the cage as well as vigorous mixing of the external solution. Reaction could be quickly initiated by lowering this device into reactant solution and terminated as quickly by lifting it out of solution again. The extent of reaction achieved was measured by displacing and then titrating the unreacted H+ ions from the resin sample. Displacement was accomplished by immersion of the entire cage in concentrated NaN03. Regeneration was similarly achieved with acid solution.
Results and Discussion The applicability of eq 2 was first tested using two different bases, two volumes of resin, and two resin particle sizes. Fractional approach to equilibrium was determined directly a t various time intervals from the continuous traces of solution conductivity vs. time generated by the apparatus. The experimental data points were then compared graphically with the theoretical G(t) curve for each system. The diffusivity ratios used in determining the latter were: &/& = 6.98 and &/& = 4.76. G(t) curves for
V=50mt., re =0.0t79cm. Run A
-0
Run E-.
Volume 71, Number 6 Mav 1867
R. A. BLICXENSTAFF, J. D. WAGNER,AND J. S. DRANOFF
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these ratios were interpolated from existing tabulated result^.^ The appropriate values of b~ were found for each set of data by a graphical matching technique.6 The conditions and values of b~for each experiment are presented in Table I. An average & value was then calculated for each system. With this parameter known, a single graph may be constructed for all of the data for each base by plotting F ( r ) us. T ) where r = &t/ro2. Such plots are shown in Figures 1 and 2 for NaOH and KOH, respectively. Also shown on each figure is the theoretical line.
Table I: Experimental Values of Counterion
Na Na Na K
K K
ZH
-
v,
70,
ml
cm
25 50 25 25 50 25
0,0179 0.0179
OH x
los, cml/sec
0.0388
1.12 1.16 1.07
0.0179 0,0179
1.35 1.25
0.0388
1.41
C = 0 , 4 N KOH,
E,=
1 . 3 4 ~ 1 0 ~ ~ ~ ~
V = Z J ~ I . , ~ , = Ocm.. O I ~o~ v=25 ml., ~=0.0388cm.-0 V = 5 0 m l . , r,=0.0179 cm.- A
0.2
0.4
-r
0.6
Figure 2. Experimental test of eq 2 with KOH.
These figures indicate that reproducibility of the experiments was good and that the theoretical model agrees quite closely with the experimental results for each system. The magnitude of the b~ values also seems appropriate. There are some deviations exhibited between the theoretical line and the points, which are probably due to experimental errors (especially at the very beginning of the reactions where imperfect dispersion of the resin partides may have influenced the data) and the failure of the approximations of ecl5 and 6 to apply exactly. In the last connection, the difference in the magnitude of DH as measured in the NaOH and KOH experiments must be due to such a failure, since one would otherwise expect the diffusivity to be the same in both cases. Further experimental evidence will be necessary before a complete picture of the influence of the exchanging ion on this parameter can be explained. It should be noted that Hering and Bliss* have previously reported similar difficulty in applying the theoretical model for intraparticle diffusion (based on the Nernst-Planck flux equations) to data for several different exchanging systems. They did not use eq 7 to determine the diffusivity ratio but rather chose the values of the two diffusivities to give the best fit t o data from exchanges run in both directions. They found the values determined in this way to depend strongly on the ion pair involved. It thus appears that this effect is a general one and that further modiThe Journal of Physical Chemiatry
fication of the Nernst-Planck model may be necessary to account for it. Some experiments were made under similar conditions with NaN03 solution in order to demonstrate experimentally the difference between ordinary ion exchange and that coupled with reaction. The resultant data for the smaller particles are shown as F(t) us. actual time in Figure 3 along with some of the NaOH data and the theoretical curve from Figure 1. With NaN03, F(1) = 1.0 does not correspond to aomplete exchange of the resin as long as P is significant because of the equilibrium limitations. Figure 3 shows that these two processes follow somewhat different rate laws, with ordinary exchange being surprisingly faster until F(t) exceeds about 0.8. It was not possible to estimate DH from the NaN03 data because a suitable rate law does not yet exist for the finite solution volume case studied here. Finally, experiments were made to determine experimentally the G(t) us. 1 plot for the H+-Na+ exchange by means of the infinite solution technique described earlier. This was done as a check on the basic applicability of the model to the experimental data obtained in this work. Results obtained for the larger particle size with 0.4 N NaNOa are shown in Figure 4. Determination of these points was found to (8) B. Hering and H. Bliss, A.I.Ch.E. J.,9 , 495 (1963).
KINETICS OF ION EXCHANGE ACCOMPANIED BY IRREVERSIBLE REACTION
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C =0.4&, r' =0.0179cm.
= 25ml.
NaN03:
V = 50mi.
-
-
NaOH: V=25ml.-O
V = 5Oml.- a Theoretical i
8
IO
12
14
0
Time(sec)
Figure 3. Comparison of ordinary ion exchange and neutraliation.
be more difficult than originally anticipated because of repeated resin bead fracture in the apparatus. Earlier experiments showed considerable scatter and subsequent microscopic examination of the resin particles showed that they had been severely fractured during repeated use because of the violent motion within the cage reactor and the great concentration changes to which the particles were necessarily subjected. The stirring rate was diminished somewhat and the data shown in Figure 4 were obtained. Examination of the particles used in this case revealed little breakage of the spherical beads, although they did develop a large number of cracks. It is felt that these cracks provide a relatively easy path for diffusing ions into the bead interior and hence should result in a faster rate of reaction than might otherwise be expected. Comparison of the experimental data and the theoretical curves shown in Figure 4 confirm this expectation. The two curves correspond to DE = 1.12 X cm2/sec (from the NaOH data shown cm2/sec (best fit to the earlier) and DEI= 1.36 X NaN03 data). It is clear that the latter provides an excellent fit to the data, confirming the essential validity of the theoretical model. The fact that the apparent diffusivity in this case is higher than that found for the neutralization reaction can be ascribed to the previously mentioned cracks and the resulting more
Figure 4. Experimental determination of G(t).
open structure of the resin beads used. Additional experiments under less violent conditions of agitation and/or with more stable resin particles will be necessary for further verification of this conclusion. Some attempts were also made to verify the validity of eq 3 and 4 for the case where the resin capacity exceeds that of the solution. No satisfactory data have been obtained in this region and further consideration of the basic equations seems to preclude their application. In this case, reaction should proceed until the solution is completely exhausted. However, as this condition is approached, solution concentrations will fall into the range where film diffusion can be expected to play a significant, if not controlling, role. Therefore, one might expect the initial stages of reaction to follow the intraparticle diffusion equations, but this model should cease to be effective as reaction proceeds. Further study of this phenomenon will be necessary in order to provide a suitable quantitative description.
Conclusions The experimental data obtained in this work indicate that the Helfferich's model for intraparticle diffusion controlled neutralization of acid-form resins by strong bases is essentially correct as long as exhaustion of the solution is avoided. The data are consistent with curves based on this model (differing Volume 71, Number 6 May 1967
G. 0. PRITCHARD AND R. L. THOMMARSON
1674
significantly from data for ordinary ion exchange) and yield reasonable values for intraparticle diff usivities. However, additional work is necessary to understand the effects of various co-ions on the measured diffusivities, as well as to uncover a model suitable for the case of low solution ionic capacity (CV < CV).
Notation Initial solution concentration Concentrations of fixed ionic groups in the solid exchanger Solution phase diffusion coefficient for speciesi Di,cm2/sec Intraparticle diffusion coefficient for species i D 1, cmz/sec F , coulombs/mole Faraday's constant
C, mequiv/ml
C,mequiv/ml
Fractional attainment of equilibrium during neutralization Fractional exhaustion of resin during ordinary exchange with infinite solution boundary condition Radius of exchanger particle TO, cm R, ergs/mole OK Gas constant Time t, sec Time for complete reaction to, sec Absolute temperature T, OK Mobility of species i ui,cmZ/sec v Solution volume V , ml Resin volume V, ml Dimensionless time 7
Acknowledgment. The authors wish to acknowledge with thanks support of this work by the National Science Foundation under Grant GP-2725.
The Photolysis of Fluoroacetone and the Elimination of Hydrogen Fluoride from "Hot" Fluoroethanesl
by G. 0. Pritchard and R. L. Thornmarson Department of C h a i s t r y , University of Californk, Santa Barbara, Ca&fornia 93106 (Received August 31, 1966)
Fluoroacetone was photolyzed in the region of 3130 A, and the rates of collisional stabilization vs. H F elimination of the "hot" fluoroethanes CJW" and C2H4Fz" produced in the system were examined as functions of the temperature and the pressure. The classical Rice-Ramsperger-Kassel theory of unimolecular reactions is shown to give a quantitative description of the decomposition of the "hot" molecules, as was demonstrated recently by Benson and Haugen2 for C2H4F2*. The reduction in the number of effective oscillators in C2H6F*,as opposed to C2H4F2*,results in the predicted enhancement of the rate of ilF elimination from C2H6F*. The values of the activation energies for H atom abstraction from the ketone are 4.6 and 6.7 kcal mole-' for CHBand CH2F radicals, respectively.
Introduction There has been much recent interest in the elimination of HF from vibrationally excited fluoroethanes, formed by methyl radical recombination,a-6 and the observed rates have been correlated with the decreasing number Of effective oscillators in the molecules with decreasing fluorine atom content.2 On this basis The Journal of Physical Chemistry
C2HsF*should show the greatest rate of HF elimination for a given set of experimental conditions.2 This (1) This work was supported by a grant from the National Science Foundation. (2) S. W. Benson and G. Haugen, J. Phys. Chem., 69, 3898 (1965). (3) G.0.Pritchard, M. Venugopalan, and T. F. Graham, ibid., 68, 1786 (1964).
