ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT
Kinetics of Nonaqueous Ion Exchange HYDROGEN-BUTYLAMMONIUM EXCHANGE IN ETHANOL-WATER MIXTURES STAFFORD WILSON'
AND
LEON LAPIDUS
Deparfmenf o f Chemical Engineering, Princefon Universify, Princefon,
A
FORMIDABLE amount of basic research has been conducted on the ion exchange process. Both equilibrium and kinetic studies have been made, but with few exceptions, these investigations have dealt with reactions taking place in aqueous media. Theories of varying complexity which describe the exchange process have been developed as a result of these studies. It is only within the last few years however, that any investigations have been made of nonaqueous systems. Bhatnagar, Kapur, and Puri (1) appear to be the first to have performed any work with nonaqueous systems. These investigators considered the adsorption of benzoic acid from 50 cc. of a 0.01639N benzoic acid solution by 0.5 gram of a phenolformalin resin. They carried out static equilibrium experiments using as solvents ethanol, acetone, carbon disulfide, carbon tetrachloride, and water Further equilibrium measurements have been made by a number of investigators (2, 3, 10, 11, 14, 15). While investigation of equilibria in nonaqueous systems is limited, kinetics studies are almost nonesistent. Two kinetic investigations have been reported each carried out as a columnar operation. Chance, Boyd, and Garber ( 7 ) were interested in determining if the rates of exchange were sufficiently fast t o be of industrial interest. Using a column packed 0ith onc of several commercial resins, they investigated the removal of sodium and bromide ions from several alcohols and from dioxane, glycol, acetone, benzene. ethyl acetate, and carbon tetrachloride. A correlation of some of these data was obtained by plotting the percentage of resin capacity versus the solution's conductivity to the one third power divided by its viscosity. The exchange was found to be sufficiently rapid t o allow possible industrial application. S'ermeulen and Huffman (17) investigated the adsorption of amines from nonaqueous solvents by the hydrogen form of an exchange resin. This work was carried out in a small column packed with commercial Dosex 50 resin. The solvents used were absolute glycol, acetone, benzene, water, and two aqueous acetone mixtures of 2 and 10% by volume of water. Ethanolamine was used as the solute in all solvents except in the case of benzene where, due t o the low solubility of ethanolamine in benzene, cyclohexylamine and n-butylamine were used. I n considering the results of this latter work, the investigators assumed that the rate of adsorption was controlled by the diffusion of material from surface of the resin particles t o the active sites within the resin, This assumption of particle or solid phase diffusion control seemed justified because of the small extent of ionization in nonaqueous systems and the high solute concentration maintained in the liquid phase. Particle diffusion coefficients were calculated for each system and illustrate the Rignificant effect of the solvent composition on the exchange rate. Even trace quantities of water in the solvent or in the resin had an appreriable effect. However, no means of quanI
Deceased.
992
N. J.
titatively predicting the rate of exchange from the nature of t h r solvent could be formulated. Present work undertakem to determine effect of solvent cornposition on rate of exchange
The adsorption of n-butylamine on the hydrogen form of 3 commercial monosulfonated polystyrene resin in aqueous ethanul mixtures was studied in a batch reactor. This system was chosen to allow a simple ana,lytical procedure and to prevent any solubility problems. The experiments were carried out using eit,ller Dowes 50 or Permutit Q as the resin; the moisture content of the reein being carefully controlled. Data were taken a t varying amine and solvent concentrations, resin cross linkage, and resin particle size. The rate of reaction was found to be particle diffusion controlled in the range of parameters considered; thus, confirming t8heassumption of T-ermeulen arid Huffman. Various theories, already in the literature, for the transient behavior of heterogeneous hatch ion exchange have been successfully used to correlate aqueous media data. These theories were used with varying success to correlate the present nonaqueous data. The particle diffusivities calculated from these data agreed in order of magnitude with values found in the literature for other systems. Thus, nonaqueous exchange systems may be characterized by a diffusion coefficient in the same manner as aqueous systems. In any kinet,ic st'udy, t.he extent of reaction is desired as a function of time. For an ion exchange reaction, such dat,a are easily obtained by follol.;ing the change in bulk solution concentration with time in a batch reactor. Because aolvent effects were of principal interest in this work, the exchange process chosen for study was made as simple as possible. The system used was the adsorption of n-butylamine from an aqueous ethanol solution on the hydrogen form of a commercial cation exchange resin. Equipment and Materials. The reaction rate studies mme carried out in a bat,ch reactor consisting of a 1-liter, three-necked, glass flask. Agitation of the reacting mixture was accomplished using a variable speed motor equipped xith a glass agitator. The agitator was introduced through the center neck of the reaction flask and allowed agitation speeds up to 1800 revolutions per minute. T o determine the temperature of the reacting misture, a thermometer n-as placed in one of the Bide necks of the flask. The third neck wa3 used for sampling. Additional equipment included a Westphal balance and the material used for titrations. The ethanol used in all mixed solvent runs was obtained from one lot which was procured early in the work. This lot of ethanol was found to have a density corresponding t'o 92% by weight of ethanol. The ot,her component was water. The adsorbate was standard research grade n-butylamine. Two varieties of ion exchange resins were used. Samples of 8 and 16% cross-linked Dowex 50 were supplied by the Dow
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 48, No. 6
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT Chemical Go. in the wet hydrogen form.
Cross-linked Permutit
Q of 3 and 15% was supplied in a similar form by the Permutit Co. Both of these resins are strong acid exchangers and are identical except for name. Each is essentially a monosulfonated, cross-linked polystyrene resin. Experimental Procedure. All resin samples were contacted three times in a batch flask with fresh portions of approximately 3N hydrochloric acid. The first two contacts were for 20-minute duration with the final portion for 24hour duration. The samples were then washed with distilled water until the effluent wash water showed no effect on litmus paper. Next, the samples were air dried to remove surface moisture, dried for an additional 48 hours in an oven a t 110" C., and then separated into size fractions using the Tyler screen series. A 35- to 40-mesh cut was taken of the Permutit Q resin, and a 50- to 70-mesh cut was taken of the Dowex 50. Average particle size was determined by measuring the diameters of GO randomly selected particles from each cut with a microscope having a calibrated eye piece. The dry, shed resin samples were then stored in a desiccator over calcium chloride until time for use. The solvent was prepared in 2-liter batches using the stock 92% ethanol solution and distilled water using a Westphal balance for determining composition. A sufficient quantity of n-butylamine was then added to the solvent to give the desired concentration. The exact amine concentration was determined by titrating a 10-cc. sample to the methyl orange end point with standard hydrochloric acid. Ten grams of dry resin sample were weighed out and placed into the reactor immediately before use. The agitator and thermometer were inserted into the reactor using rubber stoppers to close the openings in the flask and 500 cc. of amine solution added. Upon the addition of the amine solution, the agitator was started and the time was noted. T o ensure independence of agitation speed, all runs were made with an agitation speed of GOO r.p.m. or higher. Samples of solution, 10 cc., were withdrawn from the reactor every 2 or 3 minutes during the first portion of each run. After about 10 minutes, samples were taken at intervals from 10 to 40 minutes. The amine concentration in the samples was determined by titrating to the methyl orange end point with standard hydrochloric acid. A run was continued until the same amine concentration was found in two consecutive samples taken a t least 30 minutes apart This was assumed to be the equilibrium condition. T o prevent the removal of resin particles during sampling, the end of the sampling pipet was covered with a small piece of 200-mesh screen. The analytical procedure for the amine was checked against samples of known amine concentration in mixed solvent. The solvent was found to have no effect on the methyl orange end point so that i t was not necessary t o correct the titration results for solvent concentration. From the data obtained in the above manner, the extent of the reaction was determined as a function of time. The amount of amine adsorbed a t any time was calculated by a material balance on the bulk solution in which a correction myas applied for the amount of amine removed in each sample.
methods proposed for correlating batch ion e x c h a n g e data
Numerous
Theory. I n all such theories, the transfer of mass, excluding transport due to liquid motion, is divided into five steps. These st,eps are: (1) diffusion of the reactant through the solution or film surrounding the resin particle up t o the particle surface; (2) diffusion of the reactant through the pores within the particle; (3) chemical reaction a t one of the randomly distributed exchange positions within the particle; (4)diffusion of the product from the reaction site out to the surface of the particle; and (5) diffusion of the product from the particle surface through the June 19.56
surrounding film and into the bulk solution. I n a given system the over-all kinetics are governed by the slowest step. The theoretical approaches t o this subject have progressed by assuming one of the above steps or a combination of steps as rate-determining. Experimentally ( 4 ) the chemical reaction step is always much faster than the diffusional steps and may thus be disregarded. Consideration must also be taken of the mode of experimentation. In some experimental techniques the solution concentration remains substantially constant whereas in other cases the solution concentration will be a function of the time of operation. The latter case is generally more common but the theoretical equations are much more complicated. Both cases will now be considered. Film Diffusion as Rate-Determining Step. Based upon a model of diffusion through a uniform film surrounding the ion exchange particles Boyd, Adamson, and Myers ( 4 ) derived the following equation:
where F Qp
= the fractional approach to equilibrium = amount of solute adsorbed per particle
Qp,
= amount of solute adsorbed a t equilibrium per
t R D a
Af
K
particle
= time = -3
-
0
%Zion
coefficient in the liquid
= particle radius
= film thickness = constant distribution coefficient between liquid
and solid phase
This solution was obtained with the following assumptions: a linear concentration gradient across liquid film equilibrium a t the particle surface negligible concentration gradients within the particles constant external solution concentration Reichenberg (14 ) has proposed the most convenient method of checking experimental data for a film diffusion mechanism when the solution concentration is a variable. Define a quantity Q as the amount adsorbed per unit volume of swollen resin. Then QP Q
=
4/38
and
(3) Initially, a t t = 0, the value of Cr,, is 0 . Therefore, if film diffusion is the controlling mechanism, the values of should be proportional to the bulk solution concentration. This is the criterion which should be applied to determine if a process is film diffusion controlled when the adsorbate is present as a macro-component. Particle Diffusion as Rate-Determining Step. I n this case, the film resistance to mass transfer is assumed negligible, and therefore, the concentration a t the particle surface is that of the bulk solution. Boyd, Adamson, and Myers started with the standard equation for diffusion into a sphere and with appropriate boundary conditions arrived a t the following solution
(4) where B
= Dp.ir2/aa
D , = internal particle diffusivity.
INDUSTRIAL AND ENGINEERING CHEMISTRY
993
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT Among the necessary assumptions required were a constant diifusivity throughout the interior of the particles; and constant solution concentration outside particles. Several items should be noted with regard to this solution. (1) For a given value of t , F is dependent only on D,/d; not dF dQ on the solution concentration. Likewise, &, - and - are indedt dt pendent of solution concentration. dP and t dQ - are proportional to B . (2) For a given value of F , d
where
S, = the nth root of S cot S
Also, B is inversely proportional to the square of the radius. Thus, the rate of exchange is inversely proportional to the square of the radius for all values of F .
a
3 where y VP
w
=
T
= D,t/aZ
dt
=
=
1f S Z 3w
5 a t equilibrium C
The series in the above solution converges very slowly for values of 7 less than one tenth. To avoid this difficult,y, Patterson derived an approximate solution which is valid when T is lesa than one tenth. This is fortunate since the value of the parameters encountered in ion exchange work generally are in this range. The approximate solution is
1A-
,
r
I
r----l--l---i
~
where
a: and @
are the roots of the quadratic equation 2 2
20
C
Figure 1.
40
60
80
120
IC0
Effect of solute concentration on the reaction rate
(3) This equation is most easily checked with experimental data vhen values of Bf,are tabulated for each value of F . Values of Bt from the table may then be plotted versus the corresponding experimental values of t. Provided the value of D, does not vary with F,a straight line.p-ith a slope of B should be obtained. The most satisfactory method of tabulating values of Bt versufi F nTas presented by Reichenberg (14). Reichenberg’s equations, giving errors in Bt less than those corresponding to a 0 001 variation in F , are as follows:
7 2 - In (1 - P )
;F
6
>
0.86
= 0
(9)
Equation 8 is most easily checked against experimental data, if a plot of F versus T with w as a parameter is prepared. Since w is fixed for a particular system, values of T may be determined for given values of F. The ratio D,/d may then be computed using the corresponding experimental values of t. For a particle diffusion controlled reaction, the ratio DJa2 should be constant with increasing F. This approximate solution of Patterson has been euccessfully used by Dryden and Kay (8)to correlate batch adsorption and desorption data for adsorbent carbon. Boyd and Soldano (5) have also been able to correlate their kinetics data for the selfdiffusion of cations by use of this solution. Thus, either Equation 4 or 8 presents a means of determining from experimental data whether a given exchange is particle diffusion controlled.
I
=
+ 3wx - 3w
I
(5)
I n this n-ay Equation 4 is easily checked against experimental data. To eliminate the assumption of constant solution concentration, the follomTing boundary condition is needed:
where V = volume of external solution W = weight, of ion exchange resin p = apparent resin density C = solution concentration c = solid concentration This condition relates the change in solute Concentration in the bulk solution with time t o the total amount of solute adsorbed by the resin. Patterson (IS) has solved the same system of equations (including Equation 6) for the corresponding heat transfer problem (6). By analogy, the solution t o the present problem is:
994
0
1
1
20
40
,
I
60 TIME
80
-
to0
‘20
MiNUTES
Figure 2. Effect of agitation speed on the reaction rate
Combined Solid and Film Diffusion. A rigorous solution to this problem has been presented by Edeskuty and Amundson (9). They solved the ion exchange probIem for a batch reactor assuming both particle diffusion and film diffusion significant. The resulting solution is:
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 48, No. 6
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT
+ +
c1
= (bl €)W/VP = D,/Ka
h
= -bi
e
= fractional internal void volume
D
E
e
OOUEX 5 0 . 8 % 5 0 - 100 M E S H
a
O V E N - 091ED A G I T A T I O N SPEED 120C REM. I SOLVENT. A B S O L ~ T E ETHANOL 0 A V I N E C C N C E N 7 R A T I O N : 0 4991 U 8 A M I N E C O N C E V T R A T l O N i 0.5089M 0 A M I N E CONCENTRATION * 0.4812 M . ( W I T H S A U P L E S TAKEN E V E R Y 20 MIN.)
-
= constant representing equilibrium between
bi
external and internal phases = external mass transfer coefficient 1)A* = the n t h root of X cot X = (’ X;2 -
K An
- 311
The convergence of this infinite series is rapid with the result that calculation is not too involved. If particle diffusion is assumed t o be the sole rate controlling mechanism, the resistance t o mass transfer across the film becomes negligible or the value of K becomes infinite. Thus, by taking the limit of Equation 10 as K approaches infinity or p approaches zero, a!-solution to the particle diffusion controlled case is obtained.
20
40
60
80
00
. MINUTES Figure 3. Reproducibility of data
120
140
TIME
The series in Equation 11 converges very slowly for the range of parameters usually encountered in ion exchange work. Its use for calculation is tedious. I n essence, Equation 11 is a somewhat more refined solution of PatterJon’s Equation 7 .
This limiting operation leads to Preliminary work established that reaction i s not film controlled
n-hereS(A,)-l
+ 1) + A:
= 9q(~
= the nth root of
An
X cot
X = 1
Since an ionization process was being investigated, it was evident that one of the important solvent characteristics was polarity. The three solvents finally chosen ranged from a nonpolar material, benzene, to a reasonably polar substance, ethanol,
+ 37x2
0
c
TIME
Figure 4. lune 1956
-
MINUTES
Comparison of 15% cross linkage data with theory
INDUSTRIAL AND ENGINEERING CHEMISTRY
99s
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT
TiKE
Figure 5.
. MINUTES
Comparison of 3% cross linkage data with theory
to a highly polar compound, water. Furthermore, these three substances were convenient in that the benzene-ethanol and the ethanol-water systems are completely miscible. This allowed the possible investigation of the reaction rate in mixed solvent systems. The solute selected, n-butylamine, is soluble in each of the solvents and has sufficient ionic character t o take part in an ion exchange reaction. This substance is adsorbed by the hydrogen form of a cation exchanger, and the lack of any reaction product greatly simplifies the diffusion step. I n order to define the important parameters in these exchange systems, an exploratory program was undertaken. Air dried resin Dowex 50, having an 8% cross linkage and a particle size range of from 50 t o 100 mesh, was contacted with amine solutions of absolute alcohol, Four runs were made varying the amine concentration from 0.05306 to 0.8797% and using an agitation speed of 600 r.p.m. I n addition the effect of agitation speed was checked by repeating one of the runs a t an agitator speed of 1200 r.p.m. From the results of these runs, Figures 1 and 2, it is evident that (for agitation speeds above 600 r.p.m.) the reaction rate is independent of the bulk amine concentration According to theory (Equation 3), the initial rate of exchange in a film diffusion controlled reaction should be proportional t o the initial concentration of solute in the solution The absence of such a proportionality is clearly illustrated in Figure 1. The reaction rates independence of changes in agitation speed (Figure 2 ) confirms the absence of a film diffusion controlling mechanism. If film diffusion were controlling, increased agitation speed would cause portions of the film surrounding each particle to be sheared away. This would decrease the resistance to mass transfer across the film, and higher reaction rates would be observed TI ith increasing agitation speeds. Thus, it was concluded t h a t this reaction was not film diffusion controlled; the film resistance t o mass transfer being either negligible in all cases, or reduced by shearing forces to insignificance a t agitation speeds above 600 r.p.m. The reaction was investigated in the water system and the benzene system, Again, the resin used was 50 to 100 mesh, 8% cross-linked, air dried Dowex 50. A run was made using pure mater as the solvent and an initial amine concentration of 0.470334. The first sample, taken 1 minute after the start of the run, showed the amine concentration in solution to be 0.3577M. Samples taken during the next 35 minutes were identical. Thus, 996
the reaction reached equilibrium in less than 1 minute when pure water was used as the solvent. This was much too rapid t o follow using the present experimental technique. D a t a obtained using benzene as the solvent were Rignificantly different. A run made with pure benzene as the solvent and an initial amine concentration of 0.4399M showed that no appreciable adsorption took place for the first 2 days. After 7 days, the reaction was still incomplete, but the bulk solution concentration, 0.3832~1/1,indicated that adsorption had occurred. Thus, a t room temperature, the reaction rate may be altered by varying the solvent composition so that instead of reaching equilibrium in less than 1 minute, several weeks or months are required. The accuracy of the sampling technique was investigated by making two runs under identical conditions but with different sampling intervals. I n the first, samples were taken every 2 or 3 minutes for the first 10 minutes of the run and then a t intervals from 10 t o 30 minutes for the remainder of the run. I n the second run, samples were taken a t 20-minute intervals. I n Figure 3, the removal of sizable portions of bulk solution for sampling purposes had no effect on the observed rate of reaction. Another run was made (Figure 3 ) to show the degree t o which data could be reproduced. The method of calculation was a point to point material balance on the solution. I n these calculations a correction was made for the volume of solution removed in the form of samples. Thus, the scattering of the points at high values of time is due to the accumulated errors in the preceding data.
Figure 6.
Effect
Qf
particle size on the reaction rate
This preliminary work established that the reaction was not film controlled, and thus, the initial amine concentration was an unimportant variable. Likewise, the pure benzene and pure water systems could not be investigated without radically changing the experimental procedure. Because of the difference8 in time required to reach equilibrium in the water, ethanol, and benzene systems, the solvent composition was kno-xn to have a great influence on the reaction rate. I n addition, the reaction gave all indications of being particle diffusion controlled. According to theory (Equation 4) the over-all reaction rate in such a reaction is independent of the initial solute concentration, and is inversely proportional to the particle radius squared. Important variables in a particle diffusion controlled reaction are the particle diameter and the resin crom linkage. The size of the pores and the amount of voidage within the resin particles are functions of the cross linkage and affect the over-all reaction rate through the internal diffusion coefficient. These considerations suggested that the effect of solvent composition, particle
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
voi. 48,
N ~ 6.
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT
WEIGHT
Figure 7.
size, and cross linkage on the reaction rate using an ethanolwater system be investigated. Nonaqueous systems may be characterized by a particle diffusion coefficient, as are aqueous systems
To permit the use of larger sized particles, the following work was carried out using samples of 35- t o 40-mesh Permutit Q resin. This shift t o a larger particle size increased the relative importance of particle diffusion as compared to the case of the 50- to 100-mesh particles through the relationship between reaction rate and particle size mentioned. Furthermore, the use of larger particles tended toward the practical application of this reaction in a column where pressure drop considerations would become important. Since the solvent composition was a critical variable, the moisture within the resin particles was removed, as much as possible, before use. Possible variations in resin properties were minimized by handling all samples in an identical manner. Runs were made with both 3 and 15% cross-linked Permutit Q using an amine concentrationof 0.2500Mand varying the solvent composition from 71 t o 92% ethanol. The results of these runs are shown in Figures 4 and 5. T o determine the effect of particle size of the reaction rate, a n additional run was made using 16y0 cross-linked Dowex 50 resin having a size range of 50 t o 70 mesh. In Figure 6, this run is compared with another in which the same solvent composition, but a larger particle size was used. The average diameter of the dry resin particles and of the wet particles a t the end of a run were determined. From these data, the swollen volume of the resin appears to be independent of solvent composition. However, rewetting of the dried, spherical resin particles caused many of them to crack. No attempt was made to remove these shattered particles from the samples so that some error was introduced due to the presence of irregularly shaped particles. Since the experimental conditions were those of a finite bath or variable solution concentration, the equation of most interest was the Patterson solution (Equation 8). The equilibrium constant y, was estimated from the final equilibrium condition for each run. The curve predicted by the Patterson solution did not correlate the experimental data, but indicated a rapidly increasing value of D, over the entire length of each run. The Amundson solution for a particle diffusion controlled reaction (Equation 11) was tried. The fractional void volume, E, was approximated from the wet and dry resin diameters by assuming the void volume of the dry particles to be negligible. The June 1956
PER
CENT
ETHANOL
Calculated values o f particle size diffusion coefficients
constant for the adsorption isotherm was estimated, as in the case of the Patterson solution, from the final equilibrium values. Because of the extremely slow convergence of the series in 'the Amundson solution, more than six terms of the series were found to be required to yield a value of F of any accuracy. Thus, additional calculation was considered impractical and other methods of correlation were investigated. As an alternate approach, the Boyd, Adamson, and Myers solution (Equation 4) was considered. I n Figures 4, 5, and 6, this equation provided an excellent means of correlating the results of the present work. With the exception of the initial portion of each run, the predicted curve is in good agreement with the experimental data. This is especially true for the runs made with 15 and 16% cross-linked resin. High exchange rates made it very difficult to follow a reaction with the sampling technique being used. This explains the scattering of the data in Figure 5 where a 3y0 cross-linked resin was used. From this correlation, a value of the particle diffusion coefficient was determined for each run. These values are shovm in Table I.
Table 1.
Particle Diffusion Coefficients of n-Butylamine (Sq. om./min.)
Ethanol
in Solvent.
Wt. % 71 78 83 Bb 89
92
-___
Resin Cross Linkage
3%
4.48X'lO-6 3.57 X 10-6
2 . 6 4 ' 2 10-6 1.74 x io-'
15%
16
T
3.17 X 10-8 3.99 X 10-4
2 . 1 6 X 10-6 1 50 x 1 0 - 0 7.50 X 10-7 3 . 1 0 x 10-7
2.21'x'10-7
As the solvent composition goes from 78 to 92Yc by weight of ethanol, the values of the diffusion coefficient ranges from 4.48 X 10-6 to 1.74 X lo-&and from 3.99 X 10-8 to 3.10 X 10-7 for the 3 and 1570 cross-linked resins, respectively. These values show the tremendous effect of cross linkage and solvent composition on the rate of reaction. Since small differences in cross linkage have a negligible effect on the porosity of highly cross-linked resins, the diffusivities found using 15 and 16% cross-linked resins in 92% by weight of ethanol are significant in establishing the particle diffusion controlling mechanism. A diffusivity of 3.1 X 10-7 sq. cm. per minute was obtained using a 15% cross-linked resin having an average particle
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
997
ENGINEERING, DESIGN, AND
PROCESS DEVELOPMENT
diameter of 0.544 111111. Using a 16% cross-linked resin with an average particle diameter of 0.3 18 mm., the calculated diffusivity was 2.21 X 10-7 sq. em. per minute. These two values are in excellent agreement considering the possible experimental errors and the slight difference in cross linkage. This agreement in addition t o the correlation obtained using Equation 4 establishes the rate controlling mechanism of the reaction as particle diffusion. While the correlation is good, a deviation from theory is noticeable in the initial portion of each curve. This variation may be explained on the following basis. I n each expeiiment the resin was placed into the reactor in the dry form. Upon the addition of amine solution a t the beginning of each run, the resin particles began to swell. This caused the pores within the particles t o become larger and made more and more active sites available to the amine molecules. Thus, during this swelling period, the diffusion coefficient, and consequently the rate of reaction, increased. Theory assumes a constant diffusivity over the entire length of a run. The calculated values represent the diffusivity in the range where swelling was complete. On this basis, the experimental values of F for the initial portion of each run are understandably lower than the theoretical onea. The presence of this error was recognized prior to the start of experimental work. To avoid this, the resin should have been contacted with the pure solvent before adding any amine. However, for calculation purposes, the amine concentration and the initial volume of solution had to be known with as much accuracy as possible. Unknown quantities of solvent in the resin or the addition of concentrated amine to the solvent-resin mixture in the reactor introduced experimental errors of too large a magnitude. For these reasons, the swelling of the dry resin was allowed t o take place as the reaction proceeded. The Boyd, Adamson, and Myers equation for particle diffusion controlled reaction (Equation 4)assumes a constant solution concentration. I n the present work, this assumption was continually violated. I n all of the mixed solvent runs, the initial concentration of amine in solution was 0.2800M n-hile the equilibrium solution concentration was about 0.2OX. Keglecting the initial portion of each run the correlation holds over a range in which the amine concentration changes from about 0.24 to 0.201M. Several theories may be postulated t o explain this behavior; however, data are not available to confirm any of them. Perhaps the most significant of these theories pertains t o the over-all reaction time. In aqueous systems, where these equations have been tested, the total time to reach equilibrium is never more than 5 minutes. The total ieaction time considered here is a duration of several hours. While the bulk solution concentration changes appreciably during this time, the solute concentration at the particle surface changes so slo~vlythat the concentration gradient through the particle is approximately constant at all times. Under this condition, the reaction kinetics would conform to the infinite bath. Vermeulen and Huffman confirm the fact that neither Patterson’s nor Edeskuty and Amundson’s theory is applicable. No data on particle diffusion coefficients were found in the literature for n-butylamine in water and ethanol. For comparison purposes, it was necessary to extrapolate the calculated values of diffusivity in mixed solvent to pure solvent composition. The values for pure water were obtained by assuming a linear variation of diffusivity with solvent composition and finding the
998
least square line through the existing data (Figure 7 ) The values of the particle diffusion coefficient of pure water for the 3 and 1.5% cross-linked resins xere 1.92 X 10-4 and 1.56 X 10-8 sq. em. per minute, respectively. By extrapolating to absolute ethanol, the diffusivities for the 3 and 15yocross-linked resins were found to be 3.80 X and 5 X 10-8 sq. em. per minute, respectively. Vermeulen and Huffman ( 1 7 ) have reported values for the particle diffusion coefficient of ethanolamine, a solute whose diffusion coefficient is approximately equal t o that of n-butylamine, in both ethanol and water. These investigators carried out their work with an 8% cross-linked Dowex 50 resin. Thus, for a given solvent, the values of the particle diffusion coefficient determined in the present work for n-butylamine using 3 and 1570 cross-linked resins might be expected to bracket the values found for ethanolamine by Vermeulen and Huff man. The comparison of these values is shown in Table 11.
Table II.
Comparison of Diffusivities for Ethanolamine and n-Butylamine (Sq.cm./min.)
Solvent Water Ethanol
D %-Butylamine
3$
Cross Linkage 1 . 9 2 x 10-4 3 . 8 0 X 10-6
DI,Ethanolamine
8% Cross Linkage 7 . 2 X 10-6 1.50 x 10-
D n-Butylamine
16% Cross Linkage 1 . 6 6 X 10-5 5 x 10-8
These data show the expected trend with cross linkage and a large dependency on solvent composition. Thus, nonaqueous ion exchange systems may be characterized by a part,icle diffusion coefficient just as in the case of aqueous exchange. Vermeulen also reports a value of 3.78 X 10-8 sq. cm. per minute for the particle diffusion coefficient of n-butylamine for an 8% cross-linked exchanger using benzene as a solvent. This value appears much too high from the results of the present work with benzene. Literature cited Bhatnagar, S.S., Kapur, A. h-.,Puri, >I. L., J . Indiura Chem. SOC.13,679 (1036).
Bodamer, G. W., Kunin, R., IND.ENG.CHEM.45, 2577 (1953). Bonner, 0. D., Moorefield, J. C., J . PAys. Chem. 58, 555 (1954). Boyd, G. E., Adamson, A. Myers, L. S., J . Ana. Chem. SOC.69,2836 (1947). Boyd, G. E., Soldano, B. A., i b i d . , 75, 6091 (1953). Carslaw, H. S.,Jaegar, J. C., “Conduction of Heat in Solids,” p. 200, Oxford Univ. Press, London, 1948. Chance, F. S.,Jr., Boyd, G. E., Garber, H. J., IsD.CUG.CHEM., 45, 1671 (1953).
Dryden, G. E., Kay, W. B., I b i d . , 46, 2294 (1954). Edeskuty, F. J., Amundson, R. R., J . Phys. Chem. 56, 148 (1982).
Gregor, H. P., Nobel, D., Gottlieb, 11.€I., Ibid.,59, I O (1955). Kressman, T. R. E.. Kitchner, J. A,, J . Chem. SOC.194.9, p. 1211. Myers, F. J., IWD. ENG.CHEW35, 858 (1943). Patterson, S., Proc. Phys. SOC.(London) 59, 60 (1947). Reiohenberg, D., J . Am. Chen. SOC.75, 589 (1953). Robinson, D. h.,Nills, G. F., IKD.ENG. CHEII. 41, 2221 (1949).
Roehl, E. J., King, C. V., Kipnem, S.,J . Am. Chem. SOC.63, 284 (1941).
Vermeulen, T., Huffman, E. H., ISD. ENG.CHEM.45, 1858 (1963). RECEIVED for review December 1, 1955.
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
ACCEPTED X a h h 15, 1958.
Vol. 48, No. 6
