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Equilibrium studies on natural ion-exchange minerals—I. Caesium and strontium
J. lnorg. Nucl. Chem., 1956, Vol. 2, pp. 403 to 414. Pergamon Press Ltd., London
EQUILIBRIUM
STUDIES
ION-EXCHANGE CAESIUM
AND
ON
NATURAL
MINERALS--I STRONTIUM
C. B. AMPHLETTand (Miss) L. A. MCDONALD Atomic Energy Research Establishment, Harwell, Didcot, Berks (Received 27 January 1956)
Abstract--The uptake of Cs+ and Sr2+ ions has been studied on a Lower Greensand soil of good exchange properties; slight fixation of Cs4 is observed, but not of Sr2~. Isotherms have been obtained for the system Cs---Sr2+--soil at two different ionic concentrations; from these a value of 9.3 >~ 10-~ has been derived for the thermodynamic equilibrium constant of the exchange reaction 2CsX-~ Sr2+ ~SrX2 ~ 2Cs ~ where X represents the exchange complex within the soil. Other relevant thermodynamic data have been calculated for this system, and the results are compared with those of other workers on the pure clay mineral montmorillonite. THE ion-exchange properties of soils are of fundamental importance in plant nutrition and for purposes of liming and fertilization, and have been studied for over a century since their importance was first realized. (1) They have been traced in large part to the presence of clay minerals within the soil complex. (2) In clays, the negative charges arising from the replacement of Si zv by A111t, and of A1~H by Mg H, are balanced by the presence of positive ions such as Ca 2+, and to a lesser extent Na +, K +, Mg 2+, and other ions. The ion-exchange properties of soils and clays arise from the exchange of these ions with ions present in the solution with which the material is in contact. The cation-exchange capacities of clays vary enormously, from <."10 milliequivalents (meq)/100g for kaolinite to > 1 0 0 meq/100g for certain montmorillonites, other clays haying intermediate values; soils will possess a capacity depending upon the type and amount of clay mineral which they contain, and in addition may possess additional capacity arising from the presence of other mineral constituents and of organic matter. For a full discussion of the mechanism of ion exchange in clays, reference should be made to standard texts on the subject. ~3) It has been suggested ~4) that use should be made of the high capacity of montmorillonite for treatment of the highly active fission-product wastes arising from the processing of irradiated nuclear fuels. A logical extension of this approach is to consider the use which might be made of natural soils for similar purposes. (5) The latter case is also of interest in assessing the likely fate of active material which may be deposited on the soil as a result of accidental contamination. It was therefore decided to investigate the behaviour of certain typical fission products in relation to soils likely to be useful for such purposes; the present paper deals with caesium and strontium. Roy. Agr. Coll. Engl. II, 68 (1850); WAY,ibid., p. 313. (2) KELLEY,"Cation Exchange in Soils", Reinhold, New York, (1948). ¢3) GR1M."Clay Mineralogy", McGraw-Hill,New York, ch. 7 (1953). (a~ HAxc~, American Scientist41, 410 (1953); GINELL,MARTIN,and HAJ-CH,Nucleonics 12 (12), 14 (1954). /:,) AMPHLETT, l?esearch 8, 355 (1955). 403 /J/ THOMPSON, J .
404
C . B . AMPHLETT and (Miss) L. A. McDONALD EXPERIMENTAL
Characterization and treatment of the soil. The soil used in these experiments was a Lower Greensand soil from Nuneham Courtenay, Oxon, which was known to possess good exchange properties. The natural soil, which possessed varying amounts of coarse, pebbly matter, was sieved to --40 mesh after air-drying; approximately 1 kg of sieved material was then thoroughly mixed for use in the experiments. Although natural soils are far from homogeneous, the good agreement between results obtained with different samples suggests that mixing was efficient and that representative results were obtained. The soil sample thus prepared gave a slightly acid reaction (pH 5.5-6.0), and contained very little organic matter, so that its cation exchange capacity should be largely due to its clay mineral content; the capacity was determined with 1 N ammonium acetate at pH 7 and found to be 30'7 meq]100 g. X-ray examination of the clay fraction (particle size < 2/~) showed the principal clay minerals to be montmorillonite and illite, together with a little kaolinite and other minerals. Uptake experiments. The uptake of Cs and of Sr on natural soils, and the displacement of one of these ions by the other, was followed by means of experiments using small columns packed with soil. An accurately weighed quantity of soil, usually 1-3 g, was slurried with tap-water into a weighed 1-cm diameter glass column plugged at the lower end with glass-wool. After draining, the wet column was weighed, and the pore space within the column determined from the increase in weight and from the weight of soil taken, assuming unit density for the liquid within the pores. This method is only approximate, since it neglects the change in swelling for different salt solutions and also the change in weight when one ion is replaced by another. However, provided the pore space makes only a small contribution to the o'~erall volume of liquid passed on saturating the column (as will be the case for appreciable capacities), errors in pore-space determination will affect only slightly the overall accuracy of the results. In work on montmorillonite with the mixed system (Cs + + Sr 2+) it has been found possible, ~6) by labelling both species and estimating them individually, to derive a more satisfactory value for the pore space; this method was found to give values in good agreement with those obtained by the simpler method. After preparation of the column, a solution of the species being investigated, labelled with a suitable tracer, was allowed to percolate slowly down the column under a head of several centimetres, giving a flow-rate of 8-12 ml/h. Samples of approximately 2 ml were collected in measuring cylinders, their volumes were noted, and 1.0-ml aliquots were counted under reproducible conditions with a standard Geiger-M~iller tube and counting equipment ; 1-0-ml samples of the original solution were also counted. Curves were drawn of effluent concentration (in meq/ml) against effluent volume (ml/g soil), the latter being plotted at the mid-points of samples; the uptake was estimated from the area over the breakthrough curves, corrected for the pore space. Displacement runs were made on active columns with inactive solutions of the same concentration as that originally used to saturate the column, and were continued until the effluent was of negligible specific activity. In many cases mass balances were checked between material on the column, total material used, and that in the effluent. Cs + solutions were prepared by dissolving known weights of dried AR CsNO3 in distilled water and adding suitable amounts of tracer ~37Cs as nitrate solution (supplied by the Radiochemical Centre, Amersham); the final pH of the solution was adjusted by adding acid or CsOH solution, a small correction being applied for the added Cs + ion in the latter case. Sr ~+ solutions were prepared from SrCO3 which had been irradiated in B.E.P.O. at Harwell to produce 89Sr; this was dissolved in dilute nitric acid and the pH adjusted by the addition of acid or of inactive SrCOa. 9°Sris unsuitable as a tracer because of the activity of its daughter-product 90y, which in the absence of carrier yttrium will give a spuriously high reduction in the activity of the effluent. RESULTS T y p i c a l u p t a k e curves for Cs + a n d Sr e+ are s h o w n in Fig. 1 ; i~ general, there is a fairly s h a r p b r e a k t h r o u g h followed b y a s m o o t h s i g m o i d curve t r a i l i n g t o w a r d s s a t u r a t i o n ; s t e p p e d curves were o c c a s i o n a l l y o b t a i n e d , b u t were u s u a l l y traceable to d i s t u r b a n c e s d u r i n g the r u n . V a r i a t i o n s i n slope a n d shape b e t w e e n different t6) GAINES, Thesis,
Yale, 1954; J. Phys. Coll. Chem., in course of publication.
Equilibrium studies on natural ion-exchangeminerals--I
405
breakthrough curves are probably due to heterogeneity of individual samples as regards particle size, and in this respect the kinetics will be far from ideal; despite this, however, agreement between different values of the exchange capacity was good. Mass balance tests showed agreement to within 2 ~, except in one case where it
cr or"
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,-
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EFFLUENTVOLUME,mr. FIG.
i
12
14
16
1.--Uptake of Cs and Sr.
exceeded 4 ~. Since samples were counted for a sufficient number of counts to give a statistical accuracy of ~-~1~, and since the errors in planimetry and in estimating the volumes will be no greater than this, it is likely that the major sources of error arise from (a) difficulty in estimating the shape of the curve over the trailing portion, and (b) retention of activity within the measuring cylinders after emptying and rinsing out to make up to a standard volume for estimation of the total eluate specific activity. It is noteworthy that the total specific activity summed from the curve and from the eluate was always less than that of the original solution, and that it was found possible to remove activity from the cylinders on further rinsing with chromic acid. It is expected that the individual values of exchange capacity are correct to better than ± 5 ~ ; comparison of the whole series suggests that the bulk soil-exchange capacity may be expressed to an accuracy of ~ 7 ~, which accords with the results of determinations made by other methods. 9B
406
C . B . AMPHLETT and (Miss) L. A. McDONALD
Apart from three high values, the pore space per gram of soil is reasonably constant at 0.60-0.80 cm3/g, 60~o of the values lying between 0.72 and 0.80 out of a total of twenty-four determinations; this suggests a fairly uniform degree of packing and of particle-size distribution. In one experiment the effect on pore space o f substituting one cation for another was measured, with the following results: Increase in weight of dry column after percolation of tap-water ~--- 2.0746 g Increase in weight of dry column after saturation with CsNO3 solution -~ 2.1311 g Weight increase due to replacement of Ca 2+ by Cs+ --~ 56.5 mg. From the known exchange capacity of the soil, the expected weight increase when Cs+ replaces Ca 2+ is 67.9 mg; the variation in pore-space weight when Cs+ replaces Ca 2+ is therefore no greater than 12 mg in a total of ~2.0 g.
Uptake of Caesium and Strontium Individually Eleven determinations of Cs-uptake were made, and five of Sr-uptake, the solution concentration varying from 0.02 to 0.05 N, and the pH from 1.4 to 8.8; the variation in exchange capacity with pH is shown in Fig. 2. Caesium-exchange capacities were determined on natural soil, on soil which had been converted to the Sr form, and also by isotopic exchange on inactive soil in the Cs form. The capacity for Cs is approximately constant above pH 3.5, and decreases rapidly below this value; uptake of Sr is more critically dependent upon pH, and for satisfactory removal of this element the pH should be above 5. Other workers ~7' s) have also found that in the case of Sr both the initial uptake and the saturation capacity are. strongly pH-dependent, much more so than in the case of Cs. The mean value of the cation-exchange capacity derived from the Cs results is 27-3 ± 2 meq/100 g, while that from the complete series of experiments with Cs and Sr is 27.1 ~ 2, compared with the value of 30.7 obtained with NH4OAc. Although the whole of the strontium exchanged on the soil may be displaced by treatment with a salt solution, it was never found possible to displace caesium completely in this way. Thus, if a soil saturated with tracer-active Cs were treated with an inactive Cs solution until the effluent possessed negligible specific activity, further treatment with dilute acid (3-6 N HNO3) removed additional activity corresponding to 1-2 ~o of the amount originally on the column. The activity removed by dilute acid gave an aluminium absorption curve identical with that of la7Cs, showing that it was not due to an impurity in the original material, and blank experiments showed that the activity adsorbed on the glass was negligible. The removal of Cs+ by acid appears to indicate that the ion is "fixed" to a slight extent upon this soil, i.e. that it is rendered relatively nonexchangeable towards ions other than the H + ion. Potassium fixation is a well-known phenomenon in soil chemistry, and both rubidium and caesium are fixed appreciably on the clay mineral vermiculite. ~9) The isotopic exchange of Cs on montmorillonite is completely reversible, c1°) but in view of the structural similarity ~7~ SEEDHOUSE,unpublished results. ~s~ BROCKETTand PLACAK,Proceedings of the 8ih Industrial Waste Conference, Purdue University, 1953. ~9) BARSHAD,Amer. Miner. 33, 655 (1948); 34, 675, 1949. Ilo} FAUCHER,SOUTHWORTH, and THOMAS,J. Chem. Phys. 20, 157 (1952).
Equilibrium studies on natural ion-exchange rninerals--I
407
between vermiculite and illite some fixation on the illite fraction of the present soil is not urdikdyJ m In the experiment in which traced Cs + ion was exchanged on an inactive Cs soil, the activity subsequently removed by acid was appreciably less than in the other runs; this would be expected, since the "fixed" Cs will largely be that derived from the original treatment with inactive solution, so that the traced Cs subsequently taken up should be almost completely exchangeable.
30
~
25
$'2o E
O
O
©
/
/ /
f
/
/
4m
/
0 13.
Sr
/
8
/
e.o to X Isl
5
3
4 5 6 7 pH of equilibrating solution
Fr~. 2.---Exchange capacity as a function of pH.
The Mixed System Cs--Sr--Soil Elution and displacement experiments showed that Cs was more strongly held on the soil than Sr, and isotherms for the system were derived in two ways. (a) Elution technique. A sample of soil was saturated with tracer-active Cs and the capacity determined from the breakthrough curve in the usual manner. Caesium was then eluted with an inactive Sr solution of the same concentration as the original Cs solution, giving an elution curve with a trailing rear boundary (Fig. 3). GLUECKAUF has shown (12) that it is possible to derive the isotherm from such a curve by means of the expression q- = I u C 1 . Co
q0 where
and
+
v0) Cot q0x
q -- capacity of exchanger for one species present at concentration C; in the present case q and C refer to Cs, q0 -- total capacity at concentration Co ( = total concentration), u = area under elution curve frGm the value of C/C o chosen to complete elution, V = volume of eluting solution corresponding to tl~e value of C/C o chosen, Vo = pore-space volume, x = mass of exchanger.
(11) DR. R. K. SCHOFIELD, private c o m m u n i c a t i o n . i]2~ GLUI~CK,~tJF, J. Chem. Soc. 3282 (1949).
408
C.B. AMPHLETTand (Miss) L. A. McDONALD
Values of V corresponding to different values of C/Co were taken from Fig. 3, all being normalized to one g of soil; qo was taken as the value determined by Cs uptake. Values of u were taken to an arbitrary point and corrected for the difference between the measured capacity to this point and the known total capacity; this avoided
"3
'
0'9 08 o
~07 c"
o
0.6
~u 0 - 5 f-
8 o.4 m 0
o-3 02 0'1 _
5
10 15 E f f l u e n t v o l u m e m l l g . o f soil Fi~. 3.--Elution of Cs+ by Sr2+. Sr=÷ = 0-050 N.
o
_
20
pursuing the trailing rear boundary to complete elution. The isotherm obtained in this way is given in Fig. 5. (b) Equilibrium technique. The derivation of isotherms from elution data depends on the assumption that at all points on the elution curve the system is in complete equilibrium. It has been shown c1°) that this is not so in the case of montmorillonite, and a method has been developed by which isotherms obtained from elution curves may be corrected on the basis of results of isotopic exchange experiments, where the deviations from equilibrium are readily calculated. Another disadvantage in the derivation of isotherms from elution data is that the accuracy is poor at low values of (?]Co, since V and V0 are then comparable in size; since at low values of C/Co the isotherm is most steeply curved, considerable errors may arise in denying thermodynamic data by integration over the complete isotherm. For these reasons it is preferable to carry out a series of equilibrations with solutions of the same total concentration Co and of varying relative Cs concentration C/Co, determining values of q/qo in individual experiments. If both ions are traced, then q and (qo -- q) may be determined independently, either by chemical separation or by absorption experiments; an unequivocal determination of the pore space is also possible in this case. t6) In the present work we have traced only one ion, viz. Cs. Values of q were obtained by integration over the breakthrough curves; we feel that in view of the possibility of variations between different samples of soil, this gives a better check on the reliability
Equilibrium studies on natural ion-exchange minerals--I
409
of individual runs than the method used by THOMAS in the case of montmorillonite, viz. to saturate the clay, displace the traced ions with an inactive salt solution, and count an aliquot of the eluate. In this way a series of uptake curves was obtained at different values of C/C o, for
o
II/
c 0"03~-----~
~002 g "d
r
4il
~J 001
L 1
10
20 30 Effluent, volume ml/g soil
40
50
FJo. 4.--Uptake of Cs in presence of Sr. Co = 0.05 N. 0.500 (curve 4) C/Co = 0.046 (curve 1) 0.759 (curve 5) 0.126 (curve 21 1.000 (curve 6) 0.234 (curve 3) TABLE ].--RELATIVE CONCENTRATION IN SOLID AND SOLUTION PHASE
(from equilibrium experiments)
Run i
Total concentration
i Cs concentration C, meq/ml
q, meq/lO0 g.
Cs uptake
C/C9
q/q9*
'i Co, meq]ml 15 13 12 14
0.0200 0.0200 0.0201 0.0201
0'00195 0"00499 0"01014 0'01509
7.9 14.6 20.5 24.3
0.097 0.249 0.506 0.752
0'29 0"54 0"76 0"89
26 25 21 18 24
0.0501 0.0501 0.0494 0.0500 0.0500
0"00232 0"00631 0'01157 0"02502 0.0380~
6'5 14.0 18.6 23.0 25.6
0.046 0.126 0.234 0.500 0.761
0'24 0"52 0'68 0"84 0"94
* Based on q0 ~ 27.1 meq/100 g.
410
C.B.
AMPHLETT and ( M i s s ) L .
A. McDONALD
C o ~ 0.02 and 0.05 N; Fig. 4 shows the curves for C o ~ 0.05 N, and values of q/qo as a function of C/C o are given in Table 1. The isotherms are plotted in Fig. 5, together with those for the system C s - - S r - - m o n t m o r i l l o n i t e : 6) The value o f qo used in these determinations is the mean ~¢alue o f 27.1 meq/100 g referred to above.
09
@0,8 -~. v
~ o.7 O f-
g 0.6 E U
0-5 A O.050N ,, [] 0 0 5 0 N (elution run) Monfa~:rillonite (ref 6 ) V O ' 0 5 0 N (equilibriumruns) X O ' 0 5 0 N (elution run)
0
,o_ c 04 C
o.s E 0 0 •>
02
rr 0.1
S 0-1
' 0"2
0"3 Relative
0'4 0"5 06 0"7 0 8 0"9 concentration of Cs in solution (C/Co)
FIG. 5.--The Cs-Sr isotherm on Lower Greensand.
Comparison of the elution and the equilibrium isotherms at 0.05 N total concentration shows that the error involved in the former is 5 % or less from C/C o ~_ 0.3 onwards, rising rapidly below this value to ~-~30 % at C/Co ~ 0.1 ; since the isotherm over the range C/Co ~ 0.3-1.0 only covers a range of 0-73-1.0 in q/qo, considerable errors would arise in deriving data from the whole of the elution isotherm. The discrepancy between the two isotherms is much less than in the case of montmorillonite, presumably because of the much higher flow-rates used in the latter work. DISCUSSION
The isotherms for montmorillonite and for the soil are not greatly different, and in fact are coincident up to a value of C/C 0 ~_ 0.12. If we consider the soil as possessing two kinds of exchange centres, viz. those of montmorillonite and those of illite, then'the smoothness of the uptake curves and of the elution curves indicates that the system is behaving as a pseudohomogeneous exchanger, i.e. that the rates of exchange at the two centres are similar, even though the saturation capacities
Equilibrium studies on natural ion-exchange minerals--I
411
differ greatly. If there were a considerable difference in uptake rate for the two types we would expect irregular curves, unless the flow-rate were sufficiently low to ensure equilibration with the centre having the lower exchange rate. It is perhaps fortunate that in this work the flow-rates have been low, and that the clay fraction of the soil is predominantly montmorillonite and illite, both of which exchange relatively slowly, while kaolinite exchanges much more rapidly. (3~ It would appear that up to a value ofq/qo ~ 0.5 (corresponding to C/C o ~ 0.12), exchange on the montmorillonite centres predominates; above this value, exchange on the soil favours Sr more than on the pure clay, although the overall effect is still to favour Cs relative to Sr. It seems reasonable to infer that this effect is due to the presence of illite in the soil, and that the negative free-energy change in the exchange Cs clay + Sr 2~ =7 Cs +
Sr clay
is greater for illite than for montmorillonite. Since the saturation capacities ofillite and montmorillonite are so widely different (assuming roughvalues of 100 and 20 meq/lO0 g respectively, saturation of a 50 ~ mixed clay would result in 83 ~ of the ions being exchanged on montmorillonite) we must assume that the difference between the equilibrium constants for exchange on montmorillonite and on illite is quite large. The Equilibrium Constants
If we denote the clay by X, we may write the exchange equilibrium involving Cs and Sr as follows: 2CsX +
q
Sr 2~
v-~: 2Cs ~ +
SrX~
( c o - c)
c
(qo - q)
C and (C o - - C) are the concentrations of Cs + and Srz~- ions in solution in equilibrium at total concentration C o with a clay containing q and (q0 -- q) meq per unit weight of Cs and Sr respectively, the total cation-exchange capacity of the clay being qo. If concentrations in solution and in the solid phase are expressed as fractions of C o and of q, respectively, the thermodynamic equilibrium constant may be written as "v 2 f'~r K ~ - K , , ' . ,c~ • , , ,
(1)
7s,. ./'c~
where K/is the apparent equilibrium constant derived from the observed concentrations, 7 is the ionic activity coefficient in solution, a n d f t h a t in the solid phase. K / i s given by the expression Kc'=
(1 -- q/qo)(C/Co) 2 C°" (q/qo)2(1 __ C/Co)'
(2)
and in addition we have the relationships s" K ~-~ I(~. f=--;, Jc~
and
K,. =- K~ ' . 7c''~z .
(3)
7s,,
It will be noted that K~' is dependent upon the total concentration Co; this is always observed in exchange involving ions of different valency, and results in exchange
412
C.B.
AMPHLETT a n d (Miss) L. A. McDONALD
favouring the ion of lower valency at higher total concentrations, as will be seen from the isotherms in Fig. 5. GAINES and THOMASc6' 13~ have recently given a comprehensive treatment of the thermodynamics of ion-exchange systems, in which the equilibrium constant K for a 1 : 2-valent system such as the present one is given by the expression lnK=--l+lnT-w-~,+
lnKo.d
q
--2
Ns..dlna~,
(4)
,s
where the integration is carried out at constant total normality (C o constant). A represents pure Sr clay in equilibrium with Sr 2+ solution; B is pure Cs clay in equilibrium with Cs solution. N~ is the water content of the clay in moles per exchange equivalent, and a s the water activity. In the absence of data concerning the relevant activity coefficients, it is customary to make certain approximations as follows: (i) fsr (A) =fcs (B) = 1, i.e. the activity coefficients of Sr and Cs in the pure mono-ion clays in equilibrium with dilute solutions of the respective ions are unity; this is equivalent to assuming a negligible change in the water activity of the clay from infinite dilution to the salt concentration employed. (ii))JCs2/Tsr~--- 1, i.e. K ~ = K~'. Although this is not strictly true, the error involved should not be large, and in the absence of data for activity coefficients in mixed salt solutions, the approximation is justified. Equation (4) then becomes lnK~--1
+
lnK~. d
--2
N ~ . d l n a s.
(5)
~0
In the absence of data for the water activity of clays, the second integral is neglected, giving an expression identical with that derived earlier by BONNER et al. ta4) Fig. 6 shows the variation in In K~' with q/qo, values of K~' being calculated from Fig. 5. Since estimation of K~' is difficult at the ends of the isotherm, the values corresponding to q/qo --- 0 and 1 were calculated from the limiting slopes of the isotherm at these points. If S is the slope, then it may be shown t6) that Limit (ln K~') = In C o -- 2 In S
(6)
C--+0
Fig. 6. also gives the curve for montmorillonite, c6) and the values of K are given in Table 2. The constants for montmorillonite and for the soil are of the same order of magnitude, although the soil favours Sr uptake more than does the clay. The very small change in In K over a concentration range of 0-02-0.05 N may indicate that the water-activity term in equation (5) is unimportant under these conditions, or it may be due to compensating factors involving the other terms. Within the accuracy of these experiments we may state that K, as determined above, is constant over this range of concentration.
Activity Coefficient~ in the Solid Phase By extending the treatment above it may be shown ~6' 13) that for any value of O31 GAINES and THOMAS,J. Chem. Phys. 21,714, (1953). o4~ BONNER, ARGERSlNGER, and DAVIOSON, J. Amer. Chem. Soc. 74, 1044 (1952L
413
Equilibrium studies on natural ion-exchange minerals--I i
I
I
I
I
I
i
'O " " "a.,.
"
6 M o n t m o r i l l o n i t e (nef. 6 ) Co= O'OSN ~7 - - - - L o w e r Gpeensond
-0
Co:O-OSN. A - - - -
t-
LoweP Greens(] nd Co-- O-02N. 0
I
F
I
I
I
I
I
0.4
0'2
I
I
0.6
I
0.8
1"0
q/qo FIG. &--Variation of In K~" with q/q,,.
TABLE 2.--THERMODYNAMIC EQUILIBRIUM CONSTANTS FOR THE EXCHANGE
2CsX 4 Sr 2+ ~" 2Cs + - SrX.~.
Co~
Exchanger
Lower Greensand soil Lower Greensand soil Montmorillonite 6
equivts./1
In K
0-02 0.05 0.05 "
--6'96 --7.00 -7-32
10a K
9-5~ 9"13 6"6~
i
q/q, at a point Q on the isotherm the solid-phase activity coefficients in the present system are given by the expressions In f.,. (Q) = In .f'~,. ( A ) -
L) (:,) q
+<>--
¢'
i . R~.ln (Q)-~-.,,)
INK<. . d
-. 2 .
In I,,? (Q)
(')
(7) .dlna~,
: In .1{,~2 (B) + (S) -
-
i/
(j
In A~.. d q
-
.dlna,.
414
C.B.
AMPHLETT a n d (Miss) L. A. NIcDONALD
By introducing the same simplifying assumptions as before, we obtain values of fs, andfcs as functions ofq/qo, where q again refers to Cs uptake; these are plotted in Fig. 7, together with the values for montmorillonite. It will be ~een that in general the behaviour of Cs is not far from ideal over the whole range, but that Sr becomes I
I
I
I
I
I
I
I
I
Montmopillonitte (ref.6) 0-05N
0
cs 0
g -..~
s,~ 0
L o w e P GPeensand
O'05N
Lower Greensand
O-02N
Cs[]
~:~_..
Cs A
SrO Sr
-~ "- "Ck.
1-0
V
. . . .
~.
_
o
t)
# >
O'E
I
I
0-2
I
I
I
0"4
I
0'6
I
I
I
CsX
0"8
q/qo FIG. 7.--Solid-phase activity coefficients in mixed soils. Standard state: pure mono-ion soil in contact with solution of corresponding ion at infinite dilution.
progressively less ideal as its concentration in the clay increases. It is difficult to estimate the degree of ideality with certainty, since the derivation is based on fsr and fcs being unity in the pure clays in contact with solutions not at infinite dilution.
Acknowledgements--We
are indebted to Mr. G. BROWN, of Rothamsted Experimental Station, for X-ray examination of clay fractions of the soil, and to Professor H~NRe C. THOMAS,of Yale University, for permission to quote from work in course of publication.
EQUILIBRIUM
STUDIES
ION-EXCHANGE CAESIUM
AND
ON
NATURAL
MINERALS--I STRONTIUM
C. B. AMPHLETTand (Miss) L. A. MCDONALD Atomic Energy Research Establishment, Harwell, Didcot, Berks (Received 27 January 1956)
Abstract--The uptake of Cs+ and Sr2+ ions has been studied on a Lower Greensand soil of good exchange properties; slight fixation of Cs4 is observed, but not of Sr2~. Isotherms have been obtained for the system Cs---Sr2+--soil at two different ionic concentrations; from these a value of 9.3 >~ 10-~ has been derived for the thermodynamic equilibrium constant of the exchange reaction 2CsX-~ Sr2+ ~SrX2 ~ 2Cs ~ where X represents the exchange complex within the soil. Other relevant thermodynamic data have been calculated for this system, and the results are compared with those of other workers on the pure clay mineral montmorillonite. THE ion-exchange properties of soils are of fundamental importance in plant nutrition and for purposes of liming and fertilization, and have been studied for over a century since their importance was first realized. (1) They have been traced in large part to the presence of clay minerals within the soil complex. (2) In clays, the negative charges arising from the replacement of Si zv by A111t, and of A1~H by Mg H, are balanced by the presence of positive ions such as Ca 2+, and to a lesser extent Na +, K +, Mg 2+, and other ions. The ion-exchange properties of soils and clays arise from the exchange of these ions with ions present in the solution with which the material is in contact. The cation-exchange capacities of clays vary enormously, from <."10 milliequivalents (meq)/100g for kaolinite to > 1 0 0 meq/100g for certain montmorillonites, other clays haying intermediate values; soils will possess a capacity depending upon the type and amount of clay mineral which they contain, and in addition may possess additional capacity arising from the presence of other mineral constituents and of organic matter. For a full discussion of the mechanism of ion exchange in clays, reference should be made to standard texts on the subject. ~3) It has been suggested ~4) that use should be made of the high capacity of montmorillonite for treatment of the highly active fission-product wastes arising from the processing of irradiated nuclear fuels. A logical extension of this approach is to consider the use which might be made of natural soils for similar purposes. (5) The latter case is also of interest in assessing the likely fate of active material which may be deposited on the soil as a result of accidental contamination. It was therefore decided to investigate the behaviour of certain typical fission products in relation to soils likely to be useful for such purposes; the present paper deals with caesium and strontium. Roy. Agr. Coll. Engl. II, 68 (1850); WAY,ibid., p. 313. (2) KELLEY,"Cation Exchange in Soils", Reinhold, New York, (1948). ¢3) GR1M."Clay Mineralogy", McGraw-Hill,New York, ch. 7 (1953). (a~ HAxc~, American Scientist41, 410 (1953); GINELL,MARTIN,and HAJ-CH,Nucleonics 12 (12), 14 (1954). /:,) AMPHLETT, l?esearch 8, 355 (1955). 403 /J/ THOMPSON, J .
404
C . B . AMPHLETT and (Miss) L. A. McDONALD EXPERIMENTAL
Characterization and treatment of the soil. The soil used in these experiments was a Lower Greensand soil from Nuneham Courtenay, Oxon, which was known to possess good exchange properties. The natural soil, which possessed varying amounts of coarse, pebbly matter, was sieved to --40 mesh after air-drying; approximately 1 kg of sieved material was then thoroughly mixed for use in the experiments. Although natural soils are far from homogeneous, the good agreement between results obtained with different samples suggests that mixing was efficient and that representative results were obtained. The soil sample thus prepared gave a slightly acid reaction (pH 5.5-6.0), and contained very little organic matter, so that its cation exchange capacity should be largely due to its clay mineral content; the capacity was determined with 1 N ammonium acetate at pH 7 and found to be 30'7 meq]100 g. X-ray examination of the clay fraction (particle size < 2/~) showed the principal clay minerals to be montmorillonite and illite, together with a little kaolinite and other minerals. Uptake experiments. The uptake of Cs and of Sr on natural soils, and the displacement of one of these ions by the other, was followed by means of experiments using small columns packed with soil. An accurately weighed quantity of soil, usually 1-3 g, was slurried with tap-water into a weighed 1-cm diameter glass column plugged at the lower end with glass-wool. After draining, the wet column was weighed, and the pore space within the column determined from the increase in weight and from the weight of soil taken, assuming unit density for the liquid within the pores. This method is only approximate, since it neglects the change in swelling for different salt solutions and also the change in weight when one ion is replaced by another. However, provided the pore space makes only a small contribution to the o'~erall volume of liquid passed on saturating the column (as will be the case for appreciable capacities), errors in pore-space determination will affect only slightly the overall accuracy of the results. In work on montmorillonite with the mixed system (Cs + + Sr 2+) it has been found possible, ~6) by labelling both species and estimating them individually, to derive a more satisfactory value for the pore space; this method was found to give values in good agreement with those obtained by the simpler method. After preparation of the column, a solution of the species being investigated, labelled with a suitable tracer, was allowed to percolate slowly down the column under a head of several centimetres, giving a flow-rate of 8-12 ml/h. Samples of approximately 2 ml were collected in measuring cylinders, their volumes were noted, and 1.0-ml aliquots were counted under reproducible conditions with a standard Geiger-M~iller tube and counting equipment ; 1-0-ml samples of the original solution were also counted. Curves were drawn of effluent concentration (in meq/ml) against effluent volume (ml/g soil), the latter being plotted at the mid-points of samples; the uptake was estimated from the area over the breakthrough curves, corrected for the pore space. Displacement runs were made on active columns with inactive solutions of the same concentration as that originally used to saturate the column, and were continued until the effluent was of negligible specific activity. In many cases mass balances were checked between material on the column, total material used, and that in the effluent. Cs + solutions were prepared by dissolving known weights of dried AR CsNO3 in distilled water and adding suitable amounts of tracer ~37Cs as nitrate solution (supplied by the Radiochemical Centre, Amersham); the final pH of the solution was adjusted by adding acid or CsOH solution, a small correction being applied for the added Cs + ion in the latter case. Sr ~+ solutions were prepared from SrCO3 which had been irradiated in B.E.P.O. at Harwell to produce 89Sr; this was dissolved in dilute nitric acid and the pH adjusted by the addition of acid or of inactive SrCOa. 9°Sris unsuitable as a tracer because of the activity of its daughter-product 90y, which in the absence of carrier yttrium will give a spuriously high reduction in the activity of the effluent. RESULTS T y p i c a l u p t a k e curves for Cs + a n d Sr e+ are s h o w n in Fig. 1 ; i~ general, there is a fairly s h a r p b r e a k t h r o u g h followed b y a s m o o t h s i g m o i d curve t r a i l i n g t o w a r d s s a t u r a t i o n ; s t e p p e d curves were o c c a s i o n a l l y o b t a i n e d , b u t were u s u a l l y traceable to d i s t u r b a n c e s d u r i n g the r u n . V a r i a t i o n s i n slope a n d shape b e t w e e n different t6) GAINES, Thesis,
Yale, 1954; J. Phys. Coll. Chem., in course of publication.
Equilibrium studies on natural ion-exchangeminerals--I
405
breakthrough curves are probably due to heterogeneity of individual samples as regards particle size, and in this respect the kinetics will be far from ideal; despite this, however, agreement between different values of the exchange capacity was good. Mass balance tests showed agreement to within 2 ~, except in one case where it
cr or"
04(
i/~
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E O'O31
_
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,-
f
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u ~ 0.020 I-Z Idd
,,-e O.OIC
I,L
I.
Cs,O.O501N.,pH 7.O
0
Sr,O'!O'509N. pH
[]
7I
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,
i
4
6
8
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IO
EFFLUENTVOLUME,mr. FIG.
i
12
14
16
1.--Uptake of Cs and Sr.
exceeded 4 ~. Since samples were counted for a sufficient number of counts to give a statistical accuracy of ~-~1~, and since the errors in planimetry and in estimating the volumes will be no greater than this, it is likely that the major sources of error arise from (a) difficulty in estimating the shape of the curve over the trailing portion, and (b) retention of activity within the measuring cylinders after emptying and rinsing out to make up to a standard volume for estimation of the total eluate specific activity. It is noteworthy that the total specific activity summed from the curve and from the eluate was always less than that of the original solution, and that it was found possible to remove activity from the cylinders on further rinsing with chromic acid. It is expected that the individual values of exchange capacity are correct to better than ± 5 ~ ; comparison of the whole series suggests that the bulk soil-exchange capacity may be expressed to an accuracy of ~ 7 ~, which accords with the results of determinations made by other methods. 9B
406
C . B . AMPHLETT and (Miss) L. A. McDONALD
Apart from three high values, the pore space per gram of soil is reasonably constant at 0.60-0.80 cm3/g, 60~o of the values lying between 0.72 and 0.80 out of a total of twenty-four determinations; this suggests a fairly uniform degree of packing and of particle-size distribution. In one experiment the effect on pore space o f substituting one cation for another was measured, with the following results: Increase in weight of dry column after percolation of tap-water ~--- 2.0746 g Increase in weight of dry column after saturation with CsNO3 solution -~ 2.1311 g Weight increase due to replacement of Ca 2+ by Cs+ --~ 56.5 mg. From the known exchange capacity of the soil, the expected weight increase when Cs+ replaces Ca 2+ is 67.9 mg; the variation in pore-space weight when Cs+ replaces Ca 2+ is therefore no greater than 12 mg in a total of ~2.0 g.
Uptake of Caesium and Strontium Individually Eleven determinations of Cs-uptake were made, and five of Sr-uptake, the solution concentration varying from 0.02 to 0.05 N, and the pH from 1.4 to 8.8; the variation in exchange capacity with pH is shown in Fig. 2. Caesium-exchange capacities were determined on natural soil, on soil which had been converted to the Sr form, and also by isotopic exchange on inactive soil in the Cs form. The capacity for Cs is approximately constant above pH 3.5, and decreases rapidly below this value; uptake of Sr is more critically dependent upon pH, and for satisfactory removal of this element the pH should be above 5. Other workers ~7' s) have also found that in the case of Sr both the initial uptake and the saturation capacity are. strongly pH-dependent, much more so than in the case of Cs. The mean value of the cation-exchange capacity derived from the Cs results is 27-3 ± 2 meq/100 g, while that from the complete series of experiments with Cs and Sr is 27.1 ~ 2, compared with the value of 30.7 obtained with NH4OAc. Although the whole of the strontium exchanged on the soil may be displaced by treatment with a salt solution, it was never found possible to displace caesium completely in this way. Thus, if a soil saturated with tracer-active Cs were treated with an inactive Cs solution until the effluent possessed negligible specific activity, further treatment with dilute acid (3-6 N HNO3) removed additional activity corresponding to 1-2 ~o of the amount originally on the column. The activity removed by dilute acid gave an aluminium absorption curve identical with that of la7Cs, showing that it was not due to an impurity in the original material, and blank experiments showed that the activity adsorbed on the glass was negligible. The removal of Cs+ by acid appears to indicate that the ion is "fixed" to a slight extent upon this soil, i.e. that it is rendered relatively nonexchangeable towards ions other than the H + ion. Potassium fixation is a well-known phenomenon in soil chemistry, and both rubidium and caesium are fixed appreciably on the clay mineral vermiculite. ~9) The isotopic exchange of Cs on montmorillonite is completely reversible, c1°) but in view of the structural similarity ~7~ SEEDHOUSE,unpublished results. ~s~ BROCKETTand PLACAK,Proceedings of the 8ih Industrial Waste Conference, Purdue University, 1953. ~9) BARSHAD,Amer. Miner. 33, 655 (1948); 34, 675, 1949. Ilo} FAUCHER,SOUTHWORTH, and THOMAS,J. Chem. Phys. 20, 157 (1952).
Equilibrium studies on natural ion-exchange rninerals--I
407
between vermiculite and illite some fixation on the illite fraction of the present soil is not urdikdyJ m In the experiment in which traced Cs + ion was exchanged on an inactive Cs soil, the activity subsequently removed by acid was appreciably less than in the other runs; this would be expected, since the "fixed" Cs will largely be that derived from the original treatment with inactive solution, so that the traced Cs subsequently taken up should be almost completely exchangeable.
30
~
25
$'2o E
O
O
©
/
/ /
f
/
/
4m
/
0 13.
Sr
/
8
/
e.o to X Isl
5
3
4 5 6 7 pH of equilibrating solution
Fr~. 2.---Exchange capacity as a function of pH.
The Mixed System Cs--Sr--Soil Elution and displacement experiments showed that Cs was more strongly held on the soil than Sr, and isotherms for the system were derived in two ways. (a) Elution technique. A sample of soil was saturated with tracer-active Cs and the capacity determined from the breakthrough curve in the usual manner. Caesium was then eluted with an inactive Sr solution of the same concentration as the original Cs solution, giving an elution curve with a trailing rear boundary (Fig. 3). GLUECKAUF has shown (12) that it is possible to derive the isotherm from such a curve by means of the expression q- = I u C 1 . Co
q0 where
and
+
v0) Cot q0x
q -- capacity of exchanger for one species present at concentration C; in the present case q and C refer to Cs, q0 -- total capacity at concentration Co ( = total concentration), u = area under elution curve frGm the value of C/C o chosen to complete elution, V = volume of eluting solution corresponding to tl~e value of C/C o chosen, Vo = pore-space volume, x = mass of exchanger.
(11) DR. R. K. SCHOFIELD, private c o m m u n i c a t i o n . i]2~ GLUI~CK,~tJF, J. Chem. Soc. 3282 (1949).
408
C.B. AMPHLETTand (Miss) L. A. McDONALD
Values of V corresponding to different values of C/Co were taken from Fig. 3, all being normalized to one g of soil; qo was taken as the value determined by Cs uptake. Values of u were taken to an arbitrary point and corrected for the difference between the measured capacity to this point and the known total capacity; this avoided
"3
'
0'9 08 o
~07 c"
o
0.6
~u 0 - 5 f-
8 o.4 m 0
o-3 02 0'1 _
5
10 15 E f f l u e n t v o l u m e m l l g . o f soil Fi~. 3.--Elution of Cs+ by Sr2+. Sr=÷ = 0-050 N.
o
_
20
pursuing the trailing rear boundary to complete elution. The isotherm obtained in this way is given in Fig. 5. (b) Equilibrium technique. The derivation of isotherms from elution data depends on the assumption that at all points on the elution curve the system is in complete equilibrium. It has been shown c1°) that this is not so in the case of montmorillonite, and a method has been developed by which isotherms obtained from elution curves may be corrected on the basis of results of isotopic exchange experiments, where the deviations from equilibrium are readily calculated. Another disadvantage in the derivation of isotherms from elution data is that the accuracy is poor at low values of (?]Co, since V and V0 are then comparable in size; since at low values of C/Co the isotherm is most steeply curved, considerable errors may arise in denying thermodynamic data by integration over the complete isotherm. For these reasons it is preferable to carry out a series of equilibrations with solutions of the same total concentration Co and of varying relative Cs concentration C/Co, determining values of q/qo in individual experiments. If both ions are traced, then q and (qo -- q) may be determined independently, either by chemical separation or by absorption experiments; an unequivocal determination of the pore space is also possible in this case. t6) In the present work we have traced only one ion, viz. Cs. Values of q were obtained by integration over the breakthrough curves; we feel that in view of the possibility of variations between different samples of soil, this gives a better check on the reliability
Equilibrium studies on natural ion-exchange minerals--I
409
of individual runs than the method used by THOMAS in the case of montmorillonite, viz. to saturate the clay, displace the traced ions with an inactive salt solution, and count an aliquot of the eluate. In this way a series of uptake curves was obtained at different values of C/C o, for
o
II/
c 0"03~-----~
~002 g "d
r
4il
~J 001
L 1
10
20 30 Effluent, volume ml/g soil
40
50
FJo. 4.--Uptake of Cs in presence of Sr. Co = 0.05 N. 0.500 (curve 4) C/Co = 0.046 (curve 1) 0.759 (curve 5) 0.126 (curve 21 1.000 (curve 6) 0.234 (curve 3) TABLE ].--RELATIVE CONCENTRATION IN SOLID AND SOLUTION PHASE
(from equilibrium experiments)
Run i
Total concentration
i Cs concentration C, meq/ml
q, meq/lO0 g.
Cs uptake
C/C9
q/q9*
'i Co, meq]ml 15 13 12 14
0.0200 0.0200 0.0201 0.0201
0'00195 0"00499 0"01014 0'01509
7.9 14.6 20.5 24.3
0.097 0.249 0.506 0.752
0'29 0"54 0"76 0"89
26 25 21 18 24
0.0501 0.0501 0.0494 0.0500 0.0500
0"00232 0"00631 0'01157 0"02502 0.0380~
6'5 14.0 18.6 23.0 25.6
0.046 0.126 0.234 0.500 0.761
0'24 0"52 0'68 0"84 0"94
* Based on q0 ~ 27.1 meq/100 g.
410
C.B.
AMPHLETT and ( M i s s ) L .
A. McDONALD
C o ~ 0.02 and 0.05 N; Fig. 4 shows the curves for C o ~ 0.05 N, and values of q/qo as a function of C/C o are given in Table 1. The isotherms are plotted in Fig. 5, together with those for the system C s - - S r - - m o n t m o r i l l o n i t e : 6) The value o f qo used in these determinations is the mean ~¢alue o f 27.1 meq/100 g referred to above.
09
@0,8 -~. v
~ o.7 O f-
g 0.6 E U
0-5 A O.050N ,, [] 0 0 5 0 N (elution run) Monfa~:rillonite (ref 6 ) V O ' 0 5 0 N (equilibriumruns) X O ' 0 5 0 N (elution run)
0
,o_ c 04 C
o.s E 0 0 •>
02
rr 0.1
S 0-1
' 0"2
0"3 Relative
0'4 0"5 06 0"7 0 8 0"9 concentration of Cs in solution (C/Co)
FIG. 5.--The Cs-Sr isotherm on Lower Greensand.
Comparison of the elution and the equilibrium isotherms at 0.05 N total concentration shows that the error involved in the former is 5 % or less from C/C o ~_ 0.3 onwards, rising rapidly below this value to ~-~30 % at C/Co ~ 0.1 ; since the isotherm over the range C/Co ~ 0.3-1.0 only covers a range of 0-73-1.0 in q/qo, considerable errors would arise in deriving data from the whole of the elution isotherm. The discrepancy between the two isotherms is much less than in the case of montmorillonite, presumably because of the much higher flow-rates used in the latter work. DISCUSSION
The isotherms for montmorillonite and for the soil are not greatly different, and in fact are coincident up to a value of C/C 0 ~_ 0.12. If we consider the soil as possessing two kinds of exchange centres, viz. those of montmorillonite and those of illite, then'the smoothness of the uptake curves and of the elution curves indicates that the system is behaving as a pseudohomogeneous exchanger, i.e. that the rates of exchange at the two centres are similar, even though the saturation capacities
Equilibrium studies on natural ion-exchange minerals--I
411
differ greatly. If there were a considerable difference in uptake rate for the two types we would expect irregular curves, unless the flow-rate were sufficiently low to ensure equilibration with the centre having the lower exchange rate. It is perhaps fortunate that in this work the flow-rates have been low, and that the clay fraction of the soil is predominantly montmorillonite and illite, both of which exchange relatively slowly, while kaolinite exchanges much more rapidly. (3~ It would appear that up to a value ofq/qo ~ 0.5 (corresponding to C/C o ~ 0.12), exchange on the montmorillonite centres predominates; above this value, exchange on the soil favours Sr more than on the pure clay, although the overall effect is still to favour Cs relative to Sr. It seems reasonable to infer that this effect is due to the presence of illite in the soil, and that the negative free-energy change in the exchange Cs clay + Sr 2~ =7 Cs +
Sr clay
is greater for illite than for montmorillonite. Since the saturation capacities ofillite and montmorillonite are so widely different (assuming roughvalues of 100 and 20 meq/lO0 g respectively, saturation of a 50 ~ mixed clay would result in 83 ~ of the ions being exchanged on montmorillonite) we must assume that the difference between the equilibrium constants for exchange on montmorillonite and on illite is quite large. The Equilibrium Constants
If we denote the clay by X, we may write the exchange equilibrium involving Cs and Sr as follows: 2CsX +
q
Sr 2~
v-~: 2Cs ~ +
SrX~
( c o - c)
c
(qo - q)
C and (C o - - C) are the concentrations of Cs + and Srz~- ions in solution in equilibrium at total concentration C o with a clay containing q and (q0 -- q) meq per unit weight of Cs and Sr respectively, the total cation-exchange capacity of the clay being qo. If concentrations in solution and in the solid phase are expressed as fractions of C o and of q, respectively, the thermodynamic equilibrium constant may be written as "v 2 f'~r K ~ - K , , ' . ,c~ • , , ,
(1)
7s,. ./'c~
where K/is the apparent equilibrium constant derived from the observed concentrations, 7 is the ionic activity coefficient in solution, a n d f t h a t in the solid phase. K / i s given by the expression Kc'=
(1 -- q/qo)(C/Co) 2 C°" (q/qo)2(1 __ C/Co)'
(2)
and in addition we have the relationships s" K ~-~ I(~. f=--;, Jc~
and
K,. =- K~ ' . 7c''~z .
(3)
7s,,
It will be noted that K~' is dependent upon the total concentration Co; this is always observed in exchange involving ions of different valency, and results in exchange
412
C.B.
AMPHLETT a n d (Miss) L. A. McDONALD
favouring the ion of lower valency at higher total concentrations, as will be seen from the isotherms in Fig. 5. GAINES and THOMASc6' 13~ have recently given a comprehensive treatment of the thermodynamics of ion-exchange systems, in which the equilibrium constant K for a 1 : 2-valent system such as the present one is given by the expression lnK=--l+lnT-w-~,+
lnKo.d
q
--2
Ns..dlna~,
(4)
,s
where the integration is carried out at constant total normality (C o constant). A represents pure Sr clay in equilibrium with Sr 2+ solution; B is pure Cs clay in equilibrium with Cs solution. N~ is the water content of the clay in moles per exchange equivalent, and a s the water activity. In the absence of data concerning the relevant activity coefficients, it is customary to make certain approximations as follows: (i) fsr (A) =fcs (B) = 1, i.e. the activity coefficients of Sr and Cs in the pure mono-ion clays in equilibrium with dilute solutions of the respective ions are unity; this is equivalent to assuming a negligible change in the water activity of the clay from infinite dilution to the salt concentration employed. (ii))JCs2/Tsr~--- 1, i.e. K ~ = K~'. Although this is not strictly true, the error involved should not be large, and in the absence of data for activity coefficients in mixed salt solutions, the approximation is justified. Equation (4) then becomes lnK~--1
+
lnK~. d
--2
N ~ . d l n a s.
(5)
~0
In the absence of data for the water activity of clays, the second integral is neglected, giving an expression identical with that derived earlier by BONNER et al. ta4) Fig. 6 shows the variation in In K~' with q/qo, values of K~' being calculated from Fig. 5. Since estimation of K~' is difficult at the ends of the isotherm, the values corresponding to q/qo --- 0 and 1 were calculated from the limiting slopes of the isotherm at these points. If S is the slope, then it may be shown t6) that Limit (ln K~') = In C o -- 2 In S
(6)
C--+0
Fig. 6. also gives the curve for montmorillonite, c6) and the values of K are given in Table 2. The constants for montmorillonite and for the soil are of the same order of magnitude, although the soil favours Sr uptake more than does the clay. The very small change in In K over a concentration range of 0-02-0.05 N may indicate that the water-activity term in equation (5) is unimportant under these conditions, or it may be due to compensating factors involving the other terms. Within the accuracy of these experiments we may state that K, as determined above, is constant over this range of concentration.
Activity Coefficient~ in the Solid Phase By extending the treatment above it may be shown ~6' 13) that for any value of O31 GAINES and THOMAS,J. Chem. Phys. 21,714, (1953). o4~ BONNER, ARGERSlNGER, and DAVIOSON, J. Amer. Chem. Soc. 74, 1044 (1952L
413
Equilibrium studies on natural ion-exchange minerals--I i
I
I
I
I
I
i
'O " " "a.,.
"
6 M o n t m o r i l l o n i t e (nef. 6 ) Co= O'OSN ~7 - - - - L o w e r Gpeensond
-0
Co:O-OSN. A - - - -
t-
LoweP Greens(] nd Co-- O-02N. 0
I
F
I
I
I
I
I
0.4
0'2
I
I
0.6
I
0.8
1"0
q/qo FIG. &--Variation of In K~" with q/q,,.
TABLE 2.--THERMODYNAMIC EQUILIBRIUM CONSTANTS FOR THE EXCHANGE
2CsX 4 Sr 2+ ~" 2Cs + - SrX.~.
Co~
Exchanger
Lower Greensand soil Lower Greensand soil Montmorillonite 6
equivts./1
In K
0-02 0.05 0.05 "
--6'96 --7.00 -7-32
10a K
9-5~ 9"13 6"6~
i
q/q, at a point Q on the isotherm the solid-phase activity coefficients in the present system are given by the expressions In f.,. (Q) = In .f'~,. ( A ) -
L) (:,) q
+<>--
¢'
i . R~.ln (Q)-~-.,,)
INK<. . d
-. 2 .
In I,,? (Q)
(')
(7) .dlna~,
: In .1{,~2 (B) + (S) -
-
i/
(j
In A~.. d q
-
.dlna,.
414
C.B.
AMPHLETT a n d (Miss) L. A. NIcDONALD
By introducing the same simplifying assumptions as before, we obtain values of fs, andfcs as functions ofq/qo, where q again refers to Cs uptake; these are plotted in Fig. 7, together with the values for montmorillonite. It will be ~een that in general the behaviour of Cs is not far from ideal over the whole range, but that Sr becomes I
I
I
I
I
I
I
I
I
Montmopillonitte (ref.6) 0-05N
0
cs 0
g -..~
s,~ 0
L o w e P GPeensand
O'05N
Lower Greensand
O-02N
Cs[]
~:~_..
Cs A
SrO Sr
-~ "- "Ck.
1-0
V
. . . .
~.
_
o
t)
# >
O'E
I
I
0-2
I
I
I
0"4
I
0'6
I
I
I
CsX
0"8
q/qo FIG. 7.--Solid-phase activity coefficients in mixed soils. Standard state: pure mono-ion soil in contact with solution of corresponding ion at infinite dilution.
progressively less ideal as its concentration in the clay increases. It is difficult to estimate the degree of ideality with certainty, since the derivation is based on fsr and fcs being unity in the pure clays in contact with solutions not at infinite dilution.
Acknowledgements--We
are indebted to Mr. G. BROWN, of Rothamsted Experimental Station, for X-ray examination of clay fractions of the soil, and to Professor H~NRe C. THOMAS,of Yale University, for permission to quote from work in course of publication.