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N U N - E Q U I L I B K I U M ~ X C I I A N G- ~~J S I K P I I O S
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The Exchange Adsorption of Ions from Aqueous Solutions by Organic Zeolites. III. Performance of Deep Adsorbent Beds under Non-equilibrium Conditions' BY G. E.
BOYD,'
L.s. A I Y E R S ,
Introduction During the p ; x t decade. the importance of a quantitative understanding of the operation of ac!.sorption towers has become increasiiigly eviilent:. L'sually, in thc practical use of adsorbent%a fluir.1 containing the aclsorbing,species is swept t hroiig'i a granular bed :LI: a velocity such that cquilibriurii conditions are far from being realized unless the rate of adsorption is extremely great. Large floiv velocities are requisite, for example, u-hi.n ionexchange materials are cinployetl in water demiiieralization, in t h e recovery and concentration of valuable traces, in purification and separations operations, etc. Presently, the factors wliicli tlctermine the uptake and discharge of ions lip tlcep, cylindrical beds of base exchangers reacting under unsteady state conditions are known only partially. However, the laws of classical or rate independent chromatography would be expected to apply, if a quasi-equilibrium can be made to occur by the employment of fine adsorbent particles, elevated temperatures, and/or excessively low flow velocities. I n principle, therefore, the beginnin;: o f a n understanding of the more general phenomenon of rate dependent chromatography may 1w claimed to exist. The first attempt to predict the extraction of ions from aqueous solutions by zeolite beds from theoretical considerations has been made only recently. In 19-11, fjeaton and Furnass conducted a n experimental study of the removal of cupric ions present in low concentration in sulfuric acid solutions by synthetic organic exchangers. In their treatment of the data the performance of the adsorbent bed was likened to a hcat exchanger in which a heated (or cooled) gas was passed through a bed of broken solids. The transfer of mass in the first instance was taken as strictly analogou!; to the transfer to heat in the latter, and the theoretical methods used in dealing with the latter problem6 were applied. However, no correlatioii of the parameters derived from the adsorptioii column studies with the rate and equilibriuni con(1) T h i s work was performed under t h e auspices of t h e Fvlanhattan District a t t h e Clinton Laboratories of t h e University of Chicago anll t h e M n n s a n t o Chemical C o m p a n y a t O a k Ridge, Tennessee. durin:: t h e period October, 1943, to J u n e , 1046. ( 2 ) On leave from t h e D e p a r t m e n t of C h e m i s t r y , University of Chicago. Present address: Clinton Laboratories, Oak R i d g e , Tenn. ( 3 ) Present a d d r e s s : I n s t i t u t e for Xuclear Studies, University of Chicago, Chicago. I l l . (4) Present a d d r e s s : D b p a r t m e n t of C h e m i s t r y , University of S o u t h e r n California, I.us Angeles, California. ( 5 ) R. H. Beaton arid C . C. F u r n a s , I n d . E n g . Chcm., 3 3 , l5Ol (1941 I . (fii C. C . F u r n a s . Bureau of Mines Bulletin No 362 (1932): th, aa. 7 2 1 i ~ O X l j
J R . , ~AND
\\.. A i D . u ~ s o K 4
stants determined by independent experiments w s attempted. Four su1)srquent attempts to understand the problem of the action of zeolites under dynamic conditiolis 1i;tve been published. An application o f the transfer theory approach to the water softening proldem has h e n reported wherein Ca+* ~ ion in iiiicro-concentr~tions was r e m o ~ e c l ,although tlie i1ct;iilcd experimental findings remain unpuhlishetl. X n iiidepcnclcrit stucly of the same qort in which a syiitlietic mineral zeolite was used r ~ t descri1,etl s t h t t same year.' I n this case, howIxtsetl upon an irreversible cvi'r, a rate pri) adsorption rc:iction w ~ postulated. s Although the fin:tl quatiori rvliich KIS tlcrivcd could be evaluated only by trial : m l error, charts were provided by Iiieans of wliicli n solution could be reached once certain dimensioiilctss quantities were computed. 'I~LVO theoretical papers9 have appeared wherein solutions of tlie general differential equations have l m ~ attempted. Each of these treatments was 1):rsi.d upon ;Lconsideration of the rate as governed by n birnolecular mechanism formulated in accordance with the mass law equation for the exchange rvaction. In the latter paper, complete solution? mere givcn for special limiting cases of this reaction. X concise review of the status of ni:m traiisicr theories has been published recently, also.I0 The factors governing the rate of adsorption of cations from solution by resinous base exchangers am1 the quantities removed at equilibrium have becn discussed in two previous communications.l l It was shown that the exchange adsorption of univalent cations could be described by the mass law when the thermodynrtmic activities of the ions in the exchanger were defined assuming the formation of a solid solution. The adsorption affinity was observed to he dependent upon the ionic charge, as was anticipated. I n a sequence o f constant ionic charge, the extent of the exchange was governed by the hydrated radius. The standard irce energy per ion for the exchange of univalent cations was of the same order of magnitude as kT. In the rate studies i t was found that the velocit!r of uptake of ions was governed by diffusion, either ( 7 ) R. J. Myers, D. S. H e r r a n d R. W. A t t e h e r r y , Verbal r e p o r t , .4merican Chemical Society Meeting, April, 1943. ( 8 ) J. d u D o m a i n e , R. L. Swain a n d 0. A. Hougen, Ind. E7rg. C h c m . , 35, 546 (9) (a) H . C. T h o m a s , THISJ O U R N A L , 66, 1664 (1944); (b) J. E. Walter, J . Chem. Phys., 13, 229 (1945). (10) E . W.Thiele, I n d . Eng. Chcm., 38, 646 (1946). (11) (a) G. E. Boyd. J. S c h u b e r t a n d A. W. Adamson, THIS J O C R N A L . 69. 2818 (1947); (h) G. E. Boyd. A. W. Adamson a n d L. S. Myers. Jr.. i b i d . , 69, 2836 (1947).
(1943).
in anti through the adsorbent particle, or else The desorption of micro-components from a through a thin enveloping liquid film about the saturated bed was studied, and thy transfer theparticle. For conditions of constant tcmpcraturc, ory equations were foun(1 to apply also. I t is particle ji7e and flow of liquitl past the particle thercforc possiblt: to stucly tllc changes in the bountlary, it was shomn that the size of the ecpi- shape of a11ulsorhe(1 bantl :is it is moved clown libriuin distribution co(’fficietit, 6, tlcterniincd the ward through at1 :Itlsorption t , o w r h v tht, action rate mechanism: large valurs of 6 favoretl a rate of :~n c~liitrinntsoliltion. determined by film rather than particle diffusion. Theoretical Considerations The rate law for film permeation was shown to be first order, resembling that for a unimolecular re General.-Consider the dynamic system obaction. tained by passing a solution containing an adThis comrnunication will report the results from sorbate through a deep bed of unsaturated adsorban experimental study in which the exchange ad- e n t ; in the regular tlevelopnlent of such n case sorption of micro-amounts of these same alkali the solution becomes progressively impoverished metal cations by deep beds under dynamic con- in solute as it passes through the bed, a n d thc ditions were determined. Again, by use of radio- adsorbent becomes correspondingly enriched. isotope indicator techniques, a quactitative esti- This continuous sequence of changes may be mation of the ion-exchange could be effoctecl ac- approximated by a series of single-stage adsorpcurately and conveniently. X method for the tion steps where the solution and adsorbent are continuous monitoring of the radiations emitted divided into portions and each portion of solution by the radio-isotope tracer ions contained in the is shaken in turn with each portion of adsorbent. solutions flowing from the adsorbent greatly facil- The larger the number of fractions (each correitated these measurements. The transfer theory spondingly smaller) the closer, in principle, the of Anzelius and Schuman was re-interpreted in conditions within the column may be approached. terms of the constants occurring in the rate equa- Adsorption column operatior1 may be equilibrium tion believed to be valid. The rate and equilib- or non-equilibrium. In terms of the foregoing rium constants determined by the deep bed were “single-stage” approximation, equilibrium condicompared with those obtained by independent tions would correspond to the shaking of each pormeasurement. good agreement was found in tion of the solution with each aliquot of adsorbent the values obtained for the equilibrium constants until equilibrium was reached, whereas non-equiin the two types of experiments; the deep bed librium operation would correspond to the employrate constants, however, were from five to tenfold ment of a limited shaking time. Non-equismaller than those determined by the “shallow- librium operation has been observed with deep adbed method” used previously. This variance was sorbent beds pafticularly wherever the adsorbent expected from the known variation of the rate particle size was large, and/or wherever high flow constant with linear flow velocity. rates were used. On passing a solution through a bed of adsorbent, the concentration, C1,of adsorbable solute in the first portion of liquid to emerge will be lower than the influent concentration, Ct, but will gradually rise to this value with progressively larger volumes. The plot of the effluent concentration against the throughput volume, V (or the time t, for a constant flow rate), is termed a “concentration history.” Since generally there is a period during which an imperceptible amount of adsorbate emerges, followed by a more or less sharp rise in concentration, bed performances may be compared qualitatively using these “breakthrough curves. ’’ Concentration histories typical of equilibrium and of non-equilibrium column operation are shown in Fig. 1. The infinitely sharp rise predicted for equilibrium operation may be regarded as the limiting case of the Sshaped, non-equilibrium curve. Similar curves may be obtained for the plot of concentration in the adsorbent against the distance from tlie top :3 of the bed. Derivation of the Equations.--if i t is assumed 0.2 0.4 0.6 0.8 t h a t a lamina of solution passing through an CICO. adsorbcn t bed encounters a n irihiite number of Fig 1.--Typical conceiitration hiitories particles. the actual physical system can be
N ON-EQUILIBRIUM EXCHANGE ADSOKPT~ON IN DEEPADSORBENT BEDS
SOV., 194;
treated by the methods of calculus, and a basic general diffcreni.ia1 equation may be formulated. Let x
= distance froni top of column (cm.)
t
= time in seconds 1' = volume of :;ohtion in ml. = frxtional void space in the adsorbent bed (i. e . , intergranuLir space) :' = linear velocity o f flow of the solution in the bed (cin./sec 11. = volume Ao\r rate (cc./sq. cm./sec.) (W = z$) C.- = anivunt of adsorbate per ce. of adsorbent he-I (inoles/cc.)
f
=
@(Cl,1 )
L"
= coiicentrntim of adsorbate in solution (inoles/cc.)
6
= =
ccquilihr,iuiii distribution coenicient nioles :idsorlxite per cc. adsorbent bed moles adsorbate per cc. solution
-_.______
Further, it will be assumed that the concentration of adsorbate is such that the distribution coeflicient, 6 , is independent of this concentration (i. e . , Cs = 6 C . ) The conservation of matter relates the following processes which 'occur in an element of fluid contained i n >: portion of the adsorbent bed of unit cross sectioii m d length, dx .:tdwrbate imparted t o i the fluid element by ( t h e solid in time, dt !
1.i
or - (aC'/atkl.i.tli
-
Adsorhate carried 1 iu by the flo\ring = liquid Change in amount of adsorbate in the fluid
i
(BC1/ax)7fdxdt = (dCJ/dt)fdrdt
:w,w -I- t!(aci/ax)
+ (i/f)(ac*/at)= o
technique was employed, the adsorption of the alkali metal cations from dilute electrolyte solutions (i. e., >.. J (-:>lto Icss than a *lOyo variation.ls The only reliable way to clctermine the adequacy of the assuniptims appears to be by experimentation. Several criteria may be employed to test the validity vi the theory when applied to the description oi rate dcpcticleiit ion-exchange adsorption plienoinena : i ;i c:ii.h experimentally determined "break-throiq!i c'iirv~" should have the shape of but one oi tiit. rurvc's computed from theory; (11) a5 the u h r b e n t 1 ~ x 1 depth varies the same v:iliic~~ of fi a n t 1 6 h ) ~ i l I)c~ l obtained; (c) the nuxnerical value.; [ i f k :inti 6 01)served with adsorption towers i l l i t i h l I)c i n agrcement with experimental errw JVILII indcperitlciit experimental determinations o i tlicw quantities: (d) the value oi k ~ 1 l 1 ) ~tllt cl l ~ : ~U( Il) O : I tht: i l o \ ~ rate, particle size antl tlistributioi; manner predictable from Equ;itiori Other iinplicit a1)I)r"siiiiatioris some of which are ntbt rculil!- ;iiiic' (17) T h e t e r m a / : ' i n t h e ex[m,,icui I1 -- f. most always nexligil,l) srndll. fllr t h e tinir r c q i i : r e J for t h e h r r t por tion ,>f t h e solution 11, tr:ivvr\t' t h i . 1 1 ~ , 1 . (18) An d t ~ ~ n : i t i vt icl t I1c c ~ i r ~ ~ - n ~ : ~; ~tr cwIc i, l~~ inr, ~ c> f, I ~ i i r r i a ~ h a s been sugjie5trd b y \ l r (; I: Q?iiiiii \ I I I ~ , h . i , c ~ ~ n ~ t r u ci it rcrctrd plot 01 t h e ther,rrtic;il curvch i,y tirbt 1,Iotling .! : t ~ a i n i !3 J f i r ~ l r lrcted vaIuc\ uf L / ' C u.1~1: 1:ig. 2 . a n d t h e n p I , ~ t r > u . ,:. . t x ; b 1 r i \ 1 .Y = 9 ' 0 . = f a ' i /(%':,lrivhcre t h e rrfc,re,i,c,, \ 3 i- ~ : I ~ ; L . I I for C/C8 = 0 I ' I h e 1,ittcr ~ r , i l > h I - I . I I I ~ , ~ , , \ P . t~ o l i n < l i, ,11111 t h e flt h r . r.1ic. c , i i i ~ l ~ i i i1t5 d c t c r ; I ,
mined
Nov., 1947
NON-EQUILIBRIUM
EXCHANGE -kDSORPTION
IN
DEEPADSORBENT BEDS
2853
perimental testing, may be enumerated: (1) It depth were formed. In each case, the lower end of the cylinder was fitted with a one-hole rubber stopper was assumed t h a t the volume of solution and solid glass carrying a glass outlet tube. The bed was supported do not change with concentration. This assump- above this stopper by a small plug of glass wool covered tion should be obeyed closely in the ion-exchange with a disc of heavy, coarse-weave glass filter cloth. The system. (2) The assumption t h a t the distribu- flow rate was regulated by means of a screw clamp piaced upon a section of Transflex tubing in the effluent line. tion coefficient, 6, is independent of the adsorbate Employment of a no. OOOO Rotameter in series permitted concentration will be true strictly only for in- a convenient control and accurate measurement of this finitely dilute solutions. On the other hand, it flow. The top of the column was fitted also with a onemay be taken as an approximation valid within hole rubber stopper containing a glass inlet tube which was connected by means of tubing t o the large g!ass experimental error for dilute solutions, or, for normally storage bottle used as the reservoir for the influent solusolutions in which the adsorbing ion is present in tions. The influents, maintained at an approximately conlow thermodynamic activity. ( 3 ) In the deriva- stant hydrostatic head of six feet, consisted of either: (a) tion of the equations above it was assumed that 0.001 M HC10, containing 14.8 h KaP4or 19.5 d Rb*c or, ( b ) 0.001 M CsCl or 0.1 M CsCl containing the fluid advanced uniformly through all the in- tracer; 14.8 h Na*’tracer. These influents were allowed to percoterstices in the bed (i. e . , rate of flow does not vary late downflow through the adsorbent bed. across any given plane normal to the long axis of Preparation and Analysis of Solutions.-Considcrable the bed). It is likely that this assumption will not care must be exercised in the purification of all the reagents be valid for flow through beds made up of non- employed, owing t o the possibility of very great effects by minute amounts of cationic impurities. For spherical particles, since in this case the interstices caused example, the laboratory distilled water could not be used will be quite irregular in shape. (4) Any effects because of the presence of several p: p. m. of C u + + and arising from the nature of the surface of the ad- Fe+++ ions; consequently, it was further demineralized sorbent particles are ignored (i. e., surface rough- using large columns of the resinous exchangers, Amberlite IR-1 and IR-4 in the recommended manner. The perness, etc.). ( 5 ) The effect of longitudinal or axial chloric acid was of A. R. grade ( J . T. Baker & Co.) and diffusion has been assumed to be negligible. (6) was diluted to prepare solutions of the desired concentrnThe performance of the cylindrical bed was as- tion. The cesium chloride, purchased from Maywood sumed to be independent of its diameter. Owing Chemical Co., was purified by successive recrystallization. sodium and rubidium tracers were prepared by a sixtyto the finite particle size, however, there must be The hour irradi:ition of A. R. grade sodium carbonate with some minimum value of the diameter below which slow neutrons in the former case, and by a sixty to ninety this assumption wi.11 not be good. The inaccuracy day irradiation of rubidium carbonate in the latter. The thus resulting is related to the violation of the rubidium salts used were purified by successive re-preand recrystallization. The radiochemical purity assumption made by the application of the meth- cipitation of the radioactivities used was established by means of ods of differential calculus to a physical system half-life and beta-ray energy determinations. The chemical analyses for perchloric acid and for cesium containing a finite number of adsorbent particles. ( 7 ) Diffusion in and through the adsorbent par- were made using standardized procedures. I n the experiments where the concentration history was measured by ticles is assumed to be sufficiently rapid that any assaying the radioactivity contained in aliquots of the particle may be considered as being at a uniform effluent, a ~ t a n d a r d i z e d ’mounting ~ and counting techconcentration a t any instant. (8) The transfer of nique was employed. Experimental Procedure.-The adsorbent bed, conadsorbing ion to the exchanger by streaming a t a predetermined amount of either the hydrogen the particle boundary is assumed to be negligible taining or cesium form of the exchanger, was first back-washed compared to the uptake by diffusion through the with demineralized water t o remove the “fines” (or color) and to ensure the removal of any air so as t o prevent thin fluid film. Experimental--Materials and Procedures In order to test the theory developed above i t is necessary to obtain the ratio of the concentration of the adsorbing ion in the effluent from the bed to that in the influent as a function of time. If a large reservoir of solution at constant concentration be employed for the influent, then, all that is necessary experimentally is to obtain the concentration history in the effluent. Preparation of Adsorbent -The adsorbent employed was the phenol-formaldehyde synthetic cation exchanger, Amberlite IR-1. This material, received as the sodi6m form in a wet condition in a 40/60 mesh particle size range, was placed in large glass columns and successively converted t o the hydrogen form with 6 ,V hydrochloric acid and then back to the sodium form with 647, sodium chloride in order t o be certain that the exchanger was free from all soluble reaction products. After removal from the column and air-drying, aliquots viere pulverized in a ball-mill and sieved until sufficient quantities of 70/80 mesh particles were produced. Quantities of this latter product were placed in glass tubes of 10 mni. diameter (0.79 sq. cm.) until various adsorbent beds of approximately the desired
channeling. Next, the adsorbent was “pre-conditioned” by allowing solution of thc same co;npoiition as was to be employed in the experiment, except containing no radioactivity, to pass through the bed until the effluent was of the same composition as the influent. The desired tracer was added then to the influent reservoir, and the thinwalled Transflex tube carrying the effluent was coiled about a glass-walled G. M.tube (Eck and Krebs) mounted inside a heavy lend shield so that the growth of the radioactivity in the effluent could be detected and recorded. A schematic diagram of the experimental arrangement and of the components of the measuring and recording units is given by Fig. 3 . The continuous record of the brcakthrough of tracer activity was obtained by usc of a pen a n d ink electronic recorder (Esterline-Angus). Owing to the very great sensitivity w i t h which sm:t!l quantities of certain radio-isotopes may be detected, it was possible to estimate relative concentrations down to 5 X 10-4‘30 and smaller. \\lth the NJ*‘ and RbE6 the minimum value recorded for C/C,, was usually about 0.01. I n the preparation of the concentration history plots for comparison with the theoretical curves, the recorded data were corrected for counter background, counting losses, changcs in counter sensitivity :tnd for radioactive decay. A small
(19) G. E. Boyd and D. N. H u m e . Chaprer V I . Manhattan Technical Series (to he published).
G. E. BOYD,L. S. MYERS,JR., AND A . W. ADAMSON
2854
Vol. 69
1 .o
0.8
2 0.6
1;-
Scale of 1024
0.4 0.2 _.
. _100
1000
t , minutes.
Fig. 4.-EfRuent concentration of radio-sodium activity as a function of time and length of adsorbent bed. '
I- I
To Receiver
I:/
Fig. 3-Experiinental arrangement for adsorption column studies: 4, solution reservoir; B, adsorbent bed; C , flowmeter; D, Geiger-Muellcr counting tube; E, lead shicltl.
penetration of Na+ ion as tlie bed depth was increased. Qualitative agreement with the prediction from theory may be seen in the sense that the breakthrough curve becomes progressively steeper as the depth, x, increases. If the rate constant, k, were truly independent of bed thickness, the observed y value should increase linearly with x , all other variables bc'iiig held unchanged. The data of Table I for this series of experiments reveals this was not the case, for the rate constant decreasetl approxiinately fivefold when the depth increased iiinc-fold. 'Tlie distribution coefficient, 6, likewise should be constant within experimental error, although clearly a trend sccms to be present.
correction lor tlic t iiiie rcquirctl for thc tli~placcmciitof t h e hold-up in the adsorbent I)ed after the start of the passage of active solution was :ipplicd. The v:tlue of the depth of the bed, x , cinployed bclow wits iiiensurcd while the solution conraining the radio-isotope W:IS flowing. At the conTABLE I clusion of the experiment, the adsorbent w:is rttinoved from VARIATION OF TRANSFER THEORY CONSTANTS WITH BED the tube, n m h c d , dried, and its III:ISS tleterniiried by heating for two hundrcd hours a t 110". This datuin together DEPTHFOR THE ADSORPTION OF MICRO-AMOUNTS OF with the computed bed volurnc made possible the calculaSODIUM ION FROM 0.001 Jf CESIUM CHLORIDE SOLUTIONS tion of the factor required to convert the value of the disI~lowr:ite,0.10-0.12 ec./sq. cin./scc.: adsorbent p:irticle tribution cocnicient found in an equilihriuiti experiment so t h a t it might be compared with the v:ilue of 6 obtained size, 70-80 mesh ; teinperature, cn. 2,Y". d from the column. Bed depth, k X 101, moles/cc. bed A repetition of a particular esperiinent usually gave Expt. cm. y sec.-l (rnoles/cc. solution) duplicate results with good agreement ; the primary cause M-F 5.0 50 4.2 290 OF variation seeiiicd to result from ch:tngcs in bed density presurnably caused by slightly differciit cotitlitions during ht-5 9.3 50 1.6 330 the hackwashing :irid settling of the jxirticles under gravity. h.2-4 16.9 115 0.74 360 Although usu:illy ?;iiiooth coiicciitr:ition histories were olwxvcd whieli cc)rrc.spontlcti to :i .;ingle tr:iiisfcr theory The variation of the rate constant with depth is curve over tlic ~ i i t i r cr:ingc of rckitivc concentration, beliwed to be real for i t has been olmrvetl to ocoec:i~iwi,dlyii-rcgiil irit ici \iifigc\tivc of tlii. on,ct of ch:tnnnlinq were ~ i o t c r l . Siicli c ~ l T ~i v ~r r ~c ~c,\piv4 ~ > i l l y ~ v i t l ~ i i t cur previously with other systeins studied in these \ v l i c i ~ C ' Y o c \ c ~ ~ ~ lI).X~I. ctl . \ i i < l 1 1 i i r r.it1it.i. tiiI>rcx cniiiiiiott I:tlmratoric,s i l l greater clctail. Ikntoii and p(,culi.irity \v.is tlir liiiI i l l i i < ~ r : i t i , 1\1 1 1 . iiiim,:i\iii: I i i i i i * i - t ~ l i i i i r ( , c li c w
t o one, this r;itio r:tliitlly inerc:tscil to 1.10 after ivhich iL grnt1u:tlly dccri,:iccd t oiwrd uiiity as iuorc solutiou w:is p i h d through the colutriti. \*cry srii.ill ainounts of a cliciiiitdly siiiiil~i-inipurity could produce this phenorne-
NON-EQUILIBRIUM EXCHANGE ADSORPTIONIN DEEPADSORBENTBEDS
Nov., 1947
sequence, y should be found virtually independent of flow. The data of Table I1 and Fig. 5 show how well this prediction holds over the narrow range examined.
1.0
TABLE I1 VARIATION OF TRANSFER THEORY CONSTANTS WTH FLOW RATE FOR THE ADSORPTION OF MICRO-AMOUNTS OF SODIUM I O N FROM 0 001 M C E S I U M CHLORIDE SOLUTIONS Adsorbent paticle size, 70j80 mesh; teniperature, ca. 25' Flow rate, cc./sq. cm./sec.
y
9.3
0.099
50
10.3
.35
(io
tixpt.
BeE" TRANSFER THEORY CONSTANTS WITII Influence of Temperature.--.~ltllougli tcniMACRO-COMPOKENT ION CONCENTRATION FOR THE ADpcrature must be recognized as an iiiiportant SORPTIOS OF h1lCRc.l-AMOVSTS O F SODIUM ION FROM factor in determining the pcrforin:incc of deep CEsruar CIILURIDE SOLUTIOVS adsorbcnt beds, i t was not csnininctl iii this work. Xtlsorberit I i u t i c l c sin., SO i i i i . \ I i : acls;nrl,crit he11 The value of ? ~ O u l ( be 1 cxpcctc~tlto ii1trc.nsc wit11 temperature, since y = ( : : D ' ) ' rh , , j ' )( x v i , and sincc the diffusion coefliciciit, D!, will incrcasc with temperature with an activation energ!- of approximately 5 kcal. mole-'. 51-4 0.11 0.0131 115 0.74 mo Intercomparison of Values for Rate Constants 1 XI-8 .01X 400 85.5 4.7 and Distribution Coefficients.--It is important I n predicting the behavior of adsurption col- t o compare the values of the characteristic conumns from changes in 6 it is to be remembered that stants obtained in colutnn csperimcnts with the results will bc L-alitl nnly for linear isotherms. those f o u i i t l by independent 111 Howevcr, witliin this range tlic i)erforniancc will This is afiortletl by TnlAe I V wlicrc the iiitlependnot change with changing microcomponent con- ently estiniatetl ratc constmit s listctl were nieascentration, m t l this has been verified in other es- u r d by tlic sh:tIlow bet1 nietlioti."b \7alucs for the perinicnts wherc tlic concentration varictl 111. IO4. distribution cocfficicnts werc clcterriiined in cquiSince the tliiiiensicmless parameter y is propor- libriuni experinleiits i n wliicli a sriiall amount of tional to the protluct k6. it is to b e c,xpectcti tli:it the adsorbent was shaken for twclve to twentyt h e :ictinii of t l l i , l > i . c l w i l l I>
