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Ion exchange properties of hydrous zirconia in mix solvents: Thermodynamics of alkali cation exchange in methanolic solutions
Colloids and Surfices. 7 (1983) 89-104 Elsevier
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Publishers
B.V.,
89
Amsterdam
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Printed
in The
ION EXCHANGE PROPERTIES OF HYDROUS SOLVENTS: THERMODYNAMICS OF ALKALl MET1IAKOLIC SOLUTIONS
N.Z. MISAK
Nuctcar
and
ZIRCONIA IN MlSED CATION EXCHANGE
IN
H.P. GHONEIMY
Ch frrrislry ihpartmcnt.
(Received
Neth+ands
9 September
1982;
A toniic accepted
Emvgy in final
Establishnw~lt.
Cairo (&yptJ
form 12 December
1982)
ABSTRACT Addition of methanol leads to o decrease of ab* and increase of J/P and AS’ for the exchange of both Na’ and Cs’ for Li’ in hydrous rirconia. Thus the incre.u;e of selectivity constant is due to an increase in entropy. In the cast of LilNa exchaugc, a selectivity reversal occurs ar 50% methanol. Changes in ionaolvcnt interactions in the liquid phase Icatl to an increase in Alp and as”. particularly at rclstivcly low methanol concctrtrations, but the main reason for this increase is probably conmctctl wilh changes in the solid ph~e, in. valving water rcmovnl from Na* and Cs* sorbed rrom the aqueous medium as solvent-rh;lrcd iun pairs. For the Li/No exchange in 30% mothnnol, the contribution to the increase of the selectivity constant from changes rclatcd to ionqolvent interactions in the liquid phase is much higtler than that rrorn chnn~es related trr interactions in ihc cxchunger phase. possibly because increases in AtI” and AS* due to the latter chnngcs Iar@g cancel each other out.
INTRODUCTION
Investigation on the ion exchange in hydrous oxides in aqueous and mixed media have been initiated in this laboratory in order to understand their ion exchange behaviour and their selcclivily. For this purpow, the ion cxchangc bchaviour of hydrous ceria in aqueous solution was studied in detail [I, 2, 31 and a comparison of the results obtained with those obtaintrl with other hydrous oxides, partioulnrly zirconia, has led to some useful conclusions rcgarding hydrous oxide sclcctivity txhnviour. Furttwrmoru the cffuct of nctdition of methanol on the capacity of zirconia for Li’, Na’, Cs*, Cl’, i3r- and NO;, and on the kinetics of exchange has been investigated 141. It was found fhnt in both aqueous and methanolic solutions, the ability of tlw alkali ions to replace H’ in zirconia decreases in the order: Li* > Na’ > Cs+, which is the order of the capacity values. However, the ability of Na’ and Cs’ to rcplace Li’ in the Li+ form of zirconia increases on adding methanol. In this paper the thermodynamics of Li/Na and Li/Cs exchange on hydrous zirconia in the presence of methanol, have been investigated from mcasurement.s of the equilibrium constant at various temperatures.
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ia
91
ability for replacing H+ in zirconia, acity.
which is the reason of the higher Li’ cap-
Li was determined by atomic absorption using a Pye Unicam SP 90A spectrophotomeler. Na and Cs in solution were determined by y-counting of the added tracers Naz* and Ca “*_ To determine Na and Cs in the solid, they were first eluted with 0.1 M HCI and then determined by atomic absorption. In the case where t.racers arc used, the activity was determined either directly in the solid or after its elution from the solid. The r-activity of Nazz and Cs”’ was counted by a Nal scintillation head connected to a scaler of the type Nuclear Chicago, h!odcI 186 A, USA. RESULTS AND DISCUSSXON
Alkali cation exchange IS] and anion exchange [G] on hydrous been already shown to be thcm~odynnmically revcrsiblc procusscs. selectivity coefficicnf, we have:
zirconia have lf K is the
tvhcrc q. is the maximum occupancy (capacity) of the W-form of zirconia by NR+ and Cs+, w. is the total modality of solution, q is the concentration of the sorbed ion in t.hc cxchangcr (mcq/g) and HI is its modality in solution. ‘I’hc values of q/q0 and nr/rnO arc taken from the ion cxcha~qp isotherms cxprcssing the variation of q/q, with ~rt/na~ for the replacsmcnt af Li’ in zirconia by Nn’ and Cs* in aqueous, 30% and 50% methanol soWions at 25, 45 and 65°C. As shown before 141, go for Nat and Cs* is equal, to 1.1 and 0.68 ~mx~/gin the aqueous solution, respcctivcly. ‘I’ho corresponding vnlucs for 30% and 50% methanol arc 1.12 a:ld 0.84, and 1.42 and 1.07 rcspcctivcly. Thcsc values arc practically indupcndent of tcmpuraturc in the range studied, To calculate the thcrmodytinmic equilibrium constant, the corrcctud sclcctivity cocfficiunt K' is first, calculated using the equation, 1
(2)
of the rcspwtivc where M is Na or Cs, y f is the mean activity coefficient clectrolutc in the corresponding aqueous or alcoholic solulion, the refcrcncu state being infinite dilution in the respective solution. ‘Chc thermodynamic equilibrium constant Ka is then obtained from the following equation, which applies at low total molalities a 0.1 ??afor both aqueous and mixed media (793): 1
log
K, =
J MK'd 0
(Q/QO)
(3)
92
The mean activity coefficients of LIOH, NaOH and C&H in 0.1 m aqueous solutions (Eq. (2)) are taken to be 0.760.766 and 0.802, respectively 19). In a mixture of two hydroxides, the activity coefficient of the hydroxide having the lower aAivity coefficient will be somewhat raised and that of the hydroxide having the higher activity coefficient will be somewhat lowered, Since the activity coefficients of the individual electrolytes are very close, the activity coefficient ratios can be taken as equal to 1, which is the usual practice when dealing with dilute solutions of l-l electrolytes (91. For the mixed solvent media, no data are available for the activity coeffiLit3 was found to be cients of the alkali hydroxides. However, r* N&l/r, equal to 1 in waterdioxane mixtuns of up to 82% dioxene where considerable ion pairing occurs as a result of ?he very lory dielect5c constant of dioxane [lo]. Moreover, according to Harned’s second rule ill], the activity coefficient ratio in a mixed solvent is the same as that in water and since in water this ratio for G 0.1 rr~ l-l electrolytes is equal to unity, the ratio may also be set equal to unity in the mixed solvent (81. This rule has been verified up to 90% methanol 1121 and the ratio r* NaCl/y, LiCl was taken equal to
Fig. 1. Variation of log h’ with zirconia at 25.45 and 65’C.
q/~,
for Li/Nn exchange
in aqueous solution
on
hydrous
93
unity in pure methanol solutions (13). Therefore, the activity coefflcicnt term in Eq. (2) was taken equal to 1 in all cases, and K’ = K. The variation of log K with CJ/~O is shown in Figs. l-3 for Li/Na exchange and in Figs. 4-6 for LI/Cs exchange. From Figs. 1-6, it can be seen that in
0.
0.
0,
C
-0;
-a Yc
5
-0.;
- 0.1
-
0.:
-0.E
- 0.7 loY-
- 0.8
25.c 45’C 65’C
\
-0.9 Fig. 2. Variation at 26.45
of log 1: with 9/9. for LilNa and 6SC.
exchange
in 30% methanol
on hydrous
tirco:tio
l-
G_
,
3-
k .-
)0 Fig. 3, Variation of log K with q/q. zirconia at 25.45 and 65T.
Tar LIINa exchange in 60% methanol on hydrous
0.2
--_-
0
- 0.1
- 0.2
- a3 Y m @J - 0.4
-0.5
-0.6
- 0.7
- 0.e
- 0.9
- 1.l Fig. 4. Variation of log K with 9/9* for Li/Cs exchange in aqueous solution zirconia at 26.45 and 6S’C.
on hydrous
cases log K gcncrally dccruascs with increasing q/qo_ tbwevt’r, in 50% nn inurtl;tsc is slmwn at all tcmpuraturcs for the Li/Na exchange, and at. 30% methanol at 45 and 65*C for tbc same exchange, log K first inc’rcases reaching a maximum and then rapidly decreases with incrcasc of q/9O. For the I,i/Cs cxch~ngc, the only i~~reasu of tog K with incrcaso of g/q, is obscmed at- rciati-;ely high ~19~ values for the exchange in 30% methanoI at 25’C. The reason fnr the decrease of log K with increase of g/o0 is stmightforward; the sorkwd ions first occupy the sites of Mghest affinity for them and fIletI they occupy sites of prqpssivdy lower affinity. However, the increases of selectivity coefficients Ath increase of 4/40, which have been observed for orgiuk resit~s [ 1~1, 151, zeolitcs { 16 ] and zirconium phosphalc [ 171, show tllitt log K-4/4. plols call be highly co~~~ple~ for heterogeneous exchangcm and the shape of these plots drpends on the proportions and properties of the severnl groups of sites [ 161. The increase of log K with increasing q/&, obscrvccl in Il~ethanolic sotutions, may bc associated with changes of the wlativc eschangc site binding energies in zirconia on addilion of alcohol. Tlrv values of the thermodynamic equilibrium constants arc cakulatcd by grnpllka! integration, according to Eq. (31, (Figs. 1-6). The free energy most
~l~lllilll~l,
97
0:
0.
CC
*
01
z 0.s
0.; *Ox-
0.’
2s lc 4s ‘C 65 ‘C
(
Fig. 6. Variation of log K with q/q, rirconia at 25,45 and 66°C
for Li/Cs exchange
in 50% methanol
un hydrous
enthalpy and entropy changes arc calculated from the equilibrium using the following equations, A&* =
-RT
PW’-R AS” = (AH”
In K, d(ln K,)
df l/T) -
AIi”)/T
constants 14) (5) W)
is obtained from Figs. 7 and 8, which show the variation of log K, with l/T for Li/Na and Li/Cs exchanges, respectively, in the different conditions. The values of the thermodynamic quantities in the different solvents arc given in Table 1, In the case of the aqueous medium, As” was split into two components for the solution phase Ash and solid phase a using the procedure described by Sherry IlSJ, i.e., As” = ASh + D. ASh was obtained from the data of Rosscinsky for the entropies of ion hydration t193. The values of Ash and se for the aqugous medium arc given in Table 1. It should
Alp
98
0.;
0. 6-
0.’
0.;
2
goI 0
-I
-0.
-0-I L-
- 0.16-
/
I-
Aqueous
0 -
3 O%Mdhand
x-
SW.
I
- 0.13, Flg. 7. Variation of log ii, with l/T fur LiINa solutions on hydrous zirconia,
TABLE
exchange
in aqueous,
30% and 59% mathand
1
Thermodynamic
ent media
data at 25’C for LI~NR snd LI/Cs
_-
__,_- ____----.
exchanges on hydrous
-
______.________---~~. AIP kJ/md
Exchange reaction
Medium
Li/N8
Aqueous 30% methanol 50% methanol
Li/Cs
Aqueous
-0.02
t 0.08
-- 23.46
t 2
30% methanol
-1.42 -2.64
f 0.12 I 0.12
-12.86 -11.31
* 2 f 2
AP
~-
50% methanol
zlrconia in difCer-
kJtmn1 2.05 i 0.12 0.38 f 0.17 -0.88 f 0,12
-9.60 f 1 12.07 i 2 29.67 f 4
AS Jfmolldeg
ash
EP
-39.1 f 4 39.2 i 6 102.5 i 13
-31.4 --
-7.7 -
78.7
-38.4 -29.1
i
7
-82.1
i s
6 5
-
3.4
-
99
l
-
on-
Fig. 8. Variation of log Ka with l/T solutions on hydrous zirconia.
aqueous 30V.Methano 50’1; c
far Li/Cs exchange
in aqueous,
30% and 60% methanol
be mentioned that regardless of the values of the activity coefficient ratio in Eq. (2), the values of Aw remain the same if the change of this ratio with change of temperature from 26 to 65% is neglecti, which, according to Banner et al. f2OJ does not Tntroduce any significant error. Since Al+- is in all cases much smaller than Aw then errors introduced by approximating the activity coefficient ratio to unity will not significantly affect the resultant AS” values_ This is so because the values of As” are largely determined by the values of AH” which are independent of this ratio, Table 1 shows that Ar;” for the Li/Na exchange in aqueous solution is positive, indicating a preference for Lit over Na’, This is due to the large entropy-change which exceeds the enthalpy change which leads to a preference of Na+ over Li*. Similar behaviour was found for the same exchange in another preparation of zirconia (6) and in ceria (2). Table 1 also shows that m for thifsexchange has a small negative vahae. For the Li/Cs exchange in the aqueous medium, Table 1 shows that there is a littlc preference for Cs+ due to the enthalpy term and m has a very small positive value.
The negative value of a for Li/Na exchange in aqueous r?ipdium shows 118J that cithcr Na* has less degrees of freedom (stronger Knding) inside zirconin than Li’, or that Na’ drags more water molecules than Li” when it is bound to zirconia, This means that there is a net water transfer from solulion to solid and the entropy decreases since water molecules have less degrees of freedom inside zirconia than in the solution phase. The first assumption may be ruled out on the basis of the fact. mentioued before 141 that Li+ interacts more strongly with the zirconia matrix and that in certain sites this interaction is so strong that Na* cannot replace Li+, which is the reason for a higher Li+capacity. With regard to the second assumption, it has been found that alkali ions arc substantially dehydrated inside zirconin 14, 51. This was deduced from the similar water contents of the different alkali ion forms. Howvevcr, this substantial dehydration may not mean perfectly complcti shedding of the hydration sheUs of the alkali ions in all the exchange sites bccausc small differences in their hydrat.ion states will not be clearly reflected in the water contents. As already mentioned (41, zirconia is a very hctcrogcncous zxchanger and it may be supposed that. in some of the sites of re1ativcly low binding energy. Nat is bound as water-shared ion pairs with more watir molecules than
Li* f
In the case of LijCs exchange, Cs’ (41 is able to replace only tttosc Li’ that arc relatively weakly bound to zirconia (relatively strongly acidic sites) which is the reason for a much lower Cs+-capacity. This is probably the reason for the small prcfcrencc of zirconin to Cs+, since as already mentioned 121, the stronger the acidity of the exchange site and, consequently, the less the strength of its electrostatic interaction with the counter-ion, the more is the probability that it prefers the ion of a lesser hydration energy. The small increase of aS” in tlw Li/Cs exchange is probably due to slightly larger degrees of freedom of the more weakly bound Cs’ and it seiims that thcrc is no significant change in the water content of zirconia upon replacement in it of Lit by Cs’. As will bo seen later, Cs’ seems to be rctaincd from the ayur?ous medium at least partly as wntcr-sharnl ion pairs and it may, therefore, bc concluded that from this medium Lit in the sites of relatively weak binding is also retained, at least part-
ly, as
water-shared ion pairs,
Table 1 shows lhat the addition of methanol lcads to decrease of A&* (iucreasa of selectivity constant) and iucrcase of Alp and AS” for both Li/Na and Li/Cs exchanges. This indicates that the iucrcase of the sdcctivity constant is due to the entropy term. In the case of Li/Na exchange, thcrc is a selectivity reversal at 50% methanol. The increase of AH” and As” is much more profound in the case of LijNa exchange where both these quantities change sign in presence of methanoi. The change of Alp and As” (and consequently AF”) on addition of methanol may be account-ed for in terms of the effect of alcohol on ion-solvent interact.ions in the bulk solution and on the interactions occurring in the solid exchanger. Effects on ion-solvent interactions are related to the thermodynamics of transfer of ions from water to the respective alcoholic solution, while the effects on the interactions in the solid phase arc
101
related to the thermodynamics
of simitar transfer of the alkali ion forms of the exchanger, which depends on the solvent composition of the external solution and exchanger and on the extent of solvent imbibition by the cxchanger 17,8,21] . The effect of addition of methanol on ion-solvent interactions, may be obtained from the enthalpies Al’$ and entropies AL? of transfer of the alkali halides from water to water- methanol mixtures. The rcportcd enthalpies tif transfer (22,231 of LiCl from water to 10, 20.43 and 68% (by weight) of methanol are 3.77,6.46,2.72 and -1.63 kJ/mol, respectively, Those for NaC1 are 2.01,3.18, 2.85 and O-71 kJ/mol, respeclivcly, while those for CsCl are 0.67,0.88,0.38 and -2.47 kJ/mol, rcspect.ivcly. The change of AH’ of cxchange due to changes in ion-solvent interactions on addition of methanol can be put equal to AK (LiCI) - AIG (NaCI) in the ccascof Li/Na exchange where Na’ in solution is replaced by Li’, and to Ae(LiCl) - AN~(CsCI) in the case of Li/Cs exchange where Cs’ in solution is replaced by Li+. Thus, in the case of Li/Na exchange, changes in ion-solvent interactions due to adclition of 10 and 20% methanol lead to an increase of 1.76 and 2.27 kJ, respectively, in the value of AIP and a decrease of 0.13 and 2.34 kJ, at 43 and 68% methanol, respectively. Zn the case of Li/Cs exchange, increases of 3.1,4.57, 2.34 and 0,84 kJ arc obscrvcd nt 10, 20, 43 snd 68% methanol, rcspcctively. With regard to AS:, the available data [22-- 241 on the free cnergios and enthalpies of transfer give rise to the following results. The entropies of transfer of LiCl from water to 10, 20,43 and 68% mcthnnol are 7.96,8.38, -12.16 and -42.32 J/mol/dcg, respectively. For NaCl. these valucs are 0,42, - 2.1, -19.69 and -47.35, rcspectivcly. while for CsCl, wc have two values only, namely -4.19 and ---IO.06 for transfer from water to 10 and 20% methanol, respectively. Calculations similar to those for the cnthalpics of transfer reveal that incrcascs in AS” of 7.64, 10.48, 7,54 and 6.03 J/mol/dcg result in the case of Li/Na exchange due to changes in ion-solvent interactions on addition of 10, 20,43 and 68% methanol. respectively. in thE case of the Li/Cs exchange, increases of 12.16 and 18.44 J/mol/dcg arc exptwtcd for 10 and 20% methanol, rcspcctivciy. Tlws, changes in ion-solvent interactions in the liquid phase on addition of methanol may account for an increase of Aff” and As” in the presence of this solvent, Howwer, the above mentioned data of AK and AS; show that changes of AH’ and As” on account of ion-solvent interactions arc either less profound or even reversed (A@ for Li/Na exchange) at the rclativcly high methanol concentrations. This together with the fact (shown in Table 1) that large increases, that arc more profound with incrwse of methanol content, are observed in the values of AH” and AS”, particularly in the case of Li/Na exchange, show that other more important factors arc operating, namely those related to the changes in the interactions in the exchanger. Changes in the interactions in the solid that give rise to an increase in Alp and AS’ may occur as a consequence of imbibition of methanol. Such changes probably involve removal of water molecules from tho Na’ and Cs’ sorbed from the
102
aqueous medium as water-shared ion pairs, with a subsequent stronger intcraction of thesr?ions with the exchange sites in zirconia. \VaCcrremoval, presumably connected with exchange sites of relatively low binding energy, is expected to increase (probably by involving site5 of lower binding wm-gy) with increase of methanol concentration. This water removal means that the water content of the h’s’ and Cs’ forms of zirconia become increasingly lass as we go from water to solutions of increasing methanol content, which implies an increase of the entropy of the system in presence uf methanol. The fact that the increase of entropy, relative to the value in water, is higher in t.he Li/nTa exchange than in the Li/Cs exchange (Table 1) may be due to a larger decrease, on going from t‘he aqueous to the mixed medium, of the water content of the Na*-form, compared to the Cs*-form. This implies that in the aqueous medium, Cs’ is, at least partly, retained in zirconia as solvent-shard ion Ilairs, It is not possible to judge the state of Li’ inside zirconia in the presence of methanol but taking into consideration that the capacity of the Li’-form of zirconia for Na+ and Cs’ increases on addition of methanol [43 and that its stability in the watcl-methanol mixtures, where it is predominantly solvat by water moIccuIc5, is higher than in water while that of Na’ and Cs* is mostly lower than in water [ZS], it may bc assumed that in the presence of the mixed solvent, Li’ inside zirconia retains at least the water molcculcs involved in its binding as solvent-shard ion pairs from the aqueous medium, For the case where the change of ion--solvent interactions in the liquid phase is the only factor affecting the ion exchange equilibrium on addition of the organic solvent, the thermodynamic equilibrium constants in water and in ii.!? mixed solvent arc interrelated through the medium effects (or the free cnergics of transfer) for the uxchangc pair of ions. If K,W and KY arc the thcrnlodynamic equilibrium constanls ior rcplaccmont of ion A* in the cxchanger by B’ frotn solutiora in water and the mixed solvent, rcspcctively, then we have the following relationship [7, S] : log
K,m = log K, + log
mYB+ 7
m7A
(7)
lvhere , yA + and ,l,yB+ are thu medium effects for transfer of thr! ions A* and B’ from water to the mixed medium and they arc related to thr?free cnergics of transfer by lhe following equation5 [7, ZB] : AF; (A’)
= H1’ln m7A+
AfiT (B’) = RT In myB+
(81 (9)
For the results in the lwescnt. work, Eq. (7) could be applied only to the Li/Na exchange in 30% methanol since only in t.his case is the capacity for the sorbed ion (Na’) practically the 5ame in both water and the mixed solvent and, thus, the standard states for the exchanger phase are consistent. The medium effects (or free energies of transfer) given in the literature for Li’ and Na’ are
largely different. However, the vaIuc_s of the ratio of the medium effects are nearly constant. Thus, vah~cs oi 0.26 [27], 0.26 (281, and 0.24 [ZS] for Iog (myNa+/myLi+) at 25’C are obtained, for transfer to 30% methanol, from literature data either directly or by interpolation. Using an average value of 0.25 for this quantity and the value 0.44 for Kr (corresponding to AF’ given in Table 1 for Li/Na exchange in water) and applying Eq. (7), we obtain a vaIUC of 0.78 for the equilibrium constant of the Li/Na exchange in 30% methanol, KF. Taking into consideration that the value obtained experimentally for this constant (corresponding to Atr” given in Table 1) is 0.86, it can be concluded that changes of ion-solvent interactions in 30% methanol contribute much more to the increase of the selectivity constant of Li/Na exchange than the changes occurring in the solid phase. Howcvcr, as already mentioned+ increases in AIP atuld AS” of exchange occur at 30% methanol due to changes occurring in the solid, involving remova! of water molecules from the sorbed Na’. It is thcrcforc possible that these increases largely cancel each other out at this aIcohol concentration. With the increase of methanol concentration, log(,,,rNa’/,yLi l) increases [ ZZ-283 + Moreover, chmlges in the solid, leading also to increase of the selectivity constant, arc expected to bc more profound, 9lld thus the SckctiVity COI’IStaIlt COlltitlUcS to increosc. ThC V~~UC Of l~g(~yCs*/~~Li’) is positive and increases with increase of methanol concentration 124) and the results in t.ho cast’ of the Li/Cs cxchangc sccn~ to bc quditativcly similar to those in the case of the Li/Na exchange.
10 11 12 13 14 15 16 I7 18 19 20 21
N.Z. Misak and EM. hlikhail. J. Appl. Chcm. Biutcchnul., 28 (1978) 499. N.Z. hfbak and E.hl. hlikhail, J. Inorg. Nucl. Chem., 43 (1081) 1063. N.Z. Misuk and B.lri_ Mikhail, J_ fnorg. Nucl. Chem., 43 (1981) 1903. N.Z. Misak and 1I.F. Ghoneimy, J. Chem. Technol. Uiutcchmd., 32 (1982) 709. D. Britz and G.11. Naneollas, J. Inorg. Nucl. Chcm.. 31 (19G9) 3861. G-11. Nancullas and R. Paterson. 3. Inurg. Nurl. Chem., 29 (1967) 565. AR. Gupta, J. Phys. Chcm., 75 (1971) 1152. A.M. El_Yrincc and K.L. Babcock, J. Yhys. Chcm., 79 (1975) lSS0. IIS. Jinrned and B.B. Gwen, The J’hysical Chemistry of Electrolyte Solutions, Reinhold, Kcw York, 1958. Z. Dizdar, J. Inorg. Nucl. Chem.. 34 (1972) 1069. 1f.S. #farned, J. Phys. Chem., 66 (19fi2) 689. R-D_ Lanicr, J. Phys. Chcm., 69 (19trS) 2097. A_ Schwarz, J. Phyr. Chem.. 72 (1988) 789. E. Ekedahl. E:, Ifogfcldt and L.G. Sillen, Acta Chcm. Stand.. 4 (1950) 556. O.D. Bonncr and FL. Livingston, 3. Plays. Chem., 60 (1956) 530. 11.M. Barrcr and J. Klinowski, Trans. Faraday Sac.. 1 (1972) 73. A. Ruvarac and V. Vcscly, J. Inorg. Nucl. Chem., 32 (1970) 3939. H.S. Stacrry, in J.A. hlarinsky (Ed.) Ion Exchange, Vol. 2, Dekker. New York, 1969. Chap. 3. D.R. Rosseinsky, Chem. Rev., 65 (1905) 467. O.D. Bonncrand L.L. Smith, J. Phys. Chem., 61 (1957) 1614. D. Nandan and A.R. Gupta, 3. Phys. Chem.. 79 (1975) 180.
104 22 23 24 25 26 27 28
D. Feakins, In F. Franks (Ed.), PhysicoChemical Processe s In hiired Aqueous Sdvenfs, Heinemann, London, 1967, pp. 71- -89. D. Feakins and P. Watson, J. Chem. Sot., (1963) 4734. A.L. Andrews, ILP, Rennetto, D. Feakins, K.G. Lawrence and R.P.T. Tomkins, J. Chem. Sue., IA) (I 968) 1486. D. Bax, C.L. DeLigny and M. Alfcnaar, Rec. Trav. Chim. Pays-Bas, 91 (1972) 462. 0. Popovych, Crit. Rev. Anal. Chem., 1 (1970) 73. 0. Akerlov, J. Am. Chem. Sot., 62 (1930) 2353. R.P.T. Tomkins, The&. Birkbeck Coll~go. London (1966).
Science
Publishers
B.V.,
89
Amsterdam
-
Printed
in The
ION EXCHANGE PROPERTIES OF HYDROUS SOLVENTS: THERMODYNAMICS OF ALKALl MET1IAKOLIC SOLUTIONS
N.Z. MISAK
Nuctcar
and
ZIRCONIA IN MlSED CATION EXCHANGE
IN
H.P. GHONEIMY
Ch frrrislry ihpartmcnt.
(Received
Neth+ands
9 September
1982;
A toniic accepted
Emvgy in final
Establishnw~lt.
Cairo (&yptJ
form 12 December
1982)
ABSTRACT Addition of methanol leads to o decrease of ab* and increase of J/P and AS’ for the exchange of both Na’ and Cs’ for Li’ in hydrous rirconia. Thus the incre.u;e of selectivity constant is due to an increase in entropy. In the cast of LilNa exchaugc, a selectivity reversal occurs ar 50% methanol. Changes in ionaolvcnt interactions in the liquid phase Icatl to an increase in Alp and as”. particularly at rclstivcly low methanol concctrtrations, but the main reason for this increase is probably conmctctl wilh changes in the solid ph~e, in. valving water rcmovnl from Na* and Cs* sorbed rrom the aqueous medium as solvent-rh;lrcd iun pairs. For the Li/No exchange in 30% mothnnol, the contribution to the increase of the selectivity constant from changes rclatcd to ionqolvent interactions in the liquid phase is much higtler than that rrorn chnn~es related trr interactions in ihc cxchunger phase. possibly because increases in AtI” and AS* due to the latter chnngcs Iar@g cancel each other out.
INTRODUCTION
Investigation on the ion exchange in hydrous oxides in aqueous and mixed media have been initiated in this laboratory in order to understand their ion exchange behaviour and their selcclivily. For this purpow, the ion cxchangc bchaviour of hydrous ceria in aqueous solution was studied in detail [I, 2, 31 and a comparison of the results obtained with those obtaintrl with other hydrous oxides, partioulnrly zirconia, has led to some useful conclusions rcgarding hydrous oxide sclcctivity txhnviour. Furttwrmoru the cffuct of nctdition of methanol on the capacity of zirconia for Li’, Na’, Cs*, Cl’, i3r- and NO;, and on the kinetics of exchange has been investigated 141. It was found fhnt in both aqueous and methanolic solutions, the ability of tlw alkali ions to replace H’ in zirconia decreases in the order: Li* > Na’ > Cs+, which is the order of the capacity values. However, the ability of Na’ and Cs’ to rcplace Li’ in the Li+ form of zirconia increases on adding methanol. In this paper the thermodynamics of Li/Na and Li/Cs exchange on hydrous zirconia in the presence of methanol, have been investigated from mcasurement.s of the equilibrium constant at various temperatures.
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ability for replacing H+ in zirconia, acity.
which is the reason of the higher Li’ cap-
Li was determined by atomic absorption using a Pye Unicam SP 90A spectrophotomeler. Na and Cs in solution were determined by y-counting of the added tracers Naz* and Ca “*_ To determine Na and Cs in the solid, they were first eluted with 0.1 M HCI and then determined by atomic absorption. In the case where t.racers arc used, the activity was determined either directly in the solid or after its elution from the solid. The r-activity of Nazz and Cs”’ was counted by a Nal scintillation head connected to a scaler of the type Nuclear Chicago, h!odcI 186 A, USA. RESULTS AND DISCUSSXON
Alkali cation exchange IS] and anion exchange [G] on hydrous been already shown to be thcm~odynnmically revcrsiblc procusscs. selectivity coefficicnf, we have:
zirconia have lf K is the
tvhcrc q. is the maximum occupancy (capacity) of the W-form of zirconia by NR+ and Cs+, w. is the total modality of solution, q is the concentration of the sorbed ion in t.hc cxchangcr (mcq/g) and HI is its modality in solution. ‘I’hc values of q/q0 and nr/rnO arc taken from the ion cxcha~qp isotherms cxprcssing the variation of q/q, with ~rt/na~ for the replacsmcnt af Li’ in zirconia by Nn’ and Cs* in aqueous, 30% and 50% methanol soWions at 25, 45 and 65°C. As shown before 141, go for Nat and Cs* is equal, to 1.1 and 0.68 ~mx~/gin the aqueous solution, respcctivcly. ‘I’ho corresponding vnlucs for 30% and 50% methanol arc 1.12 a:ld 0.84, and 1.42 and 1.07 rcspcctivcly. Thcsc values arc practically indupcndent of tcmpuraturc in the range studied, To calculate the thcrmodytinmic equilibrium constant, the corrcctud sclcctivity cocfficiunt K' is first, calculated using the equation, 1
(2)
of the rcspwtivc where M is Na or Cs, y f is the mean activity coefficient clectrolutc in the corresponding aqueous or alcoholic solulion, the refcrcncu state being infinite dilution in the respective solution. ‘Chc thermodynamic equilibrium constant Ka is then obtained from the following equation, which applies at low total molalities a 0.1 ??afor both aqueous and mixed media (793): 1
log
K, =
J MK'd 0
(Q/QO)
(3)
92
The mean activity coefficients of LIOH, NaOH and C&H in 0.1 m aqueous solutions (Eq. (2)) are taken to be 0.760.766 and 0.802, respectively 19). In a mixture of two hydroxides, the activity coefficient of the hydroxide having the lower aAivity coefficient will be somewhat raised and that of the hydroxide having the higher activity coefficient will be somewhat lowered, Since the activity coefficients of the individual electrolytes are very close, the activity coefficient ratios can be taken as equal to 1, which is the usual practice when dealing with dilute solutions of l-l electrolytes (91. For the mixed solvent media, no data are available for the activity coeffiLit3 was found to be cients of the alkali hydroxides. However, r* N&l/r, equal to 1 in waterdioxane mixtuns of up to 82% dioxene where considerable ion pairing occurs as a result of ?he very lory dielect5c constant of dioxane [lo]. Moreover, according to Harned’s second rule ill], the activity coefficient ratio in a mixed solvent is the same as that in water and since in water this ratio for G 0.1 rr~ l-l electrolytes is equal to unity, the ratio may also be set equal to unity in the mixed solvent (81. This rule has been verified up to 90% methanol 1121 and the ratio r* NaCl/y, LiCl was taken equal to
Fig. 1. Variation of log h’ with zirconia at 25.45 and 65’C.
q/~,
for Li/Nn exchange
in aqueous solution
on
hydrous
93
unity in pure methanol solutions (13). Therefore, the activity coefflcicnt term in Eq. (2) was taken equal to 1 in all cases, and K’ = K. The variation of log K with CJ/~O is shown in Figs. l-3 for Li/Na exchange and in Figs. 4-6 for LI/Cs exchange. From Figs. 1-6, it can be seen that in
0.
0.
0,
C
-0;
-a Yc
5
-0.;
- 0.1
-
0.:
-0.E
- 0.7 loY-
- 0.8
25.c 45’C 65’C
\
-0.9 Fig. 2. Variation at 26.45
of log 1: with 9/9. for LilNa and 6SC.
exchange
in 30% methanol
on hydrous
tirco:tio
l-
G_
,
3-
k .-
)0 Fig. 3, Variation of log K with q/q. zirconia at 25.45 and 65T.
Tar LIINa exchange in 60% methanol on hydrous
0.2
--_-
0
- 0.1
- 0.2
- a3 Y m @J - 0.4
-0.5
-0.6
- 0.7
- 0.e
- 0.9
- 1.l Fig. 4. Variation of log K with 9/9* for Li/Cs exchange in aqueous solution zirconia at 26.45 and 6S’C.
on hydrous
cases log K gcncrally dccruascs with increasing q/qo_ tbwevt’r, in 50% nn inurtl;tsc is slmwn at all tcmpuraturcs for the Li/Na exchange, and at. 30% methanol at 45 and 65*C for tbc same exchange, log K first inc’rcases reaching a maximum and then rapidly decreases with incrcasc of q/9O. For the I,i/Cs cxch~ngc, the only i~~reasu of tog K with incrcaso of g/q, is obscmed at- rciati-;ely high ~19~ values for the exchange in 30% methanoI at 25’C. The reason fnr the decrease of log K with increase of g/o0 is stmightforward; the sorkwd ions first occupy the sites of Mghest affinity for them and fIletI they occupy sites of prqpssivdy lower affinity. However, the increases of selectivity coefficients Ath increase of 4/40, which have been observed for orgiuk resit~s [ 1~1, 151, zeolitcs { 16 ] and zirconium phosphalc [ 171, show tllitt log K-4/4. plols call be highly co~~~ple~ for heterogeneous exchangcm and the shape of these plots drpends on the proportions and properties of the severnl groups of sites [ 161. The increase of log K with increasing q/&, obscrvccl in Il~ethanolic sotutions, may bc associated with changes of the wlativc eschangc site binding energies in zirconia on addilion of alcohol. Tlrv values of the thermodynamic equilibrium constants arc cakulatcd by grnpllka! integration, according to Eq. (31, (Figs. 1-6). The free energy most
~l~lllilll~l,
97
0:
0.
CC
*
01
z 0.s
0.; *Ox-
0.’
2s lc 4s ‘C 65 ‘C
(
Fig. 6. Variation of log K with q/q, rirconia at 25,45 and 66°C
for Li/Cs exchange
in 50% methanol
un hydrous
enthalpy and entropy changes arc calculated from the equilibrium using the following equations, A&* =
-RT
PW’-R AS” = (AH”
In K, d(ln K,)
df l/T) -
AIi”)/T
constants 14) (5) W)
is obtained from Figs. 7 and 8, which show the variation of log K, with l/T for Li/Na and Li/Cs exchanges, respectively, in the different conditions. The values of the thermodynamic quantities in the different solvents arc given in Table 1, In the case of the aqueous medium, As” was split into two components for the solution phase Ash and solid phase a using the procedure described by Sherry IlSJ, i.e., As” = ASh + D. ASh was obtained from the data of Rosscinsky for the entropies of ion hydration t193. The values of Ash and se for the aqugous medium arc given in Table 1. It should
Alp
98
0.;
0. 6-
0.’
0.;
2
goI 0
-I
-0.
-0-I L-
- 0.16-
/
I-
Aqueous
0 -
3 O%Mdhand
x-
SW.
I
- 0.13, Flg. 7. Variation of log ii, with l/T fur LiINa solutions on hydrous zirconia,
TABLE
exchange
in aqueous,
30% and 59% mathand
1
Thermodynamic
ent media
data at 25’C for LI~NR snd LI/Cs
_-
__,_- ____----.
exchanges on hydrous
-
______.________---~~. AIP kJ/md
Exchange reaction
Medium
Li/N8
Aqueous 30% methanol 50% methanol
Li/Cs
Aqueous
-0.02
t 0.08
-- 23.46
t 2
30% methanol
-1.42 -2.64
f 0.12 I 0.12
-12.86 -11.31
* 2 f 2
AP
~-
50% methanol
zlrconia in difCer-
kJtmn1 2.05 i 0.12 0.38 f 0.17 -0.88 f 0,12
-9.60 f 1 12.07 i 2 29.67 f 4
AS Jfmolldeg
ash
EP
-39.1 f 4 39.2 i 6 102.5 i 13
-31.4 --
-7.7 -
78.7
-38.4 -29.1
i
7
-82.1
i s
6 5
-
3.4
-
99
l
-
on-
Fig. 8. Variation of log Ka with l/T solutions on hydrous zirconia.
aqueous 30V.Methano 50’1; c
far Li/Cs exchange
in aqueous,
30% and 60% methanol
be mentioned that regardless of the values of the activity coefficient ratio in Eq. (2), the values of Aw remain the same if the change of this ratio with change of temperature from 26 to 65% is neglecti, which, according to Banner et al. f2OJ does not Tntroduce any significant error. Since Al+- is in all cases much smaller than Aw then errors introduced by approximating the activity coefficient ratio to unity will not significantly affect the resultant AS” values_ This is so because the values of As” are largely determined by the values of AH” which are independent of this ratio, Table 1 shows that Ar;” for the Li/Na exchange in aqueous solution is positive, indicating a preference for Lit over Na’, This is due to the large entropy-change which exceeds the enthalpy change which leads to a preference of Na+ over Li*. Similar behaviour was found for the same exchange in another preparation of zirconia (6) and in ceria (2). Table 1 also shows that m for thifsexchange has a small negative vahae. For the Li/Cs exchange in the aqueous medium, Table 1 shows that there is a littlc preference for Cs+ due to the enthalpy term and m has a very small positive value.
The negative value of a for Li/Na exchange in aqueous r?ipdium shows 118J that cithcr Na* has less degrees of freedom (stronger Knding) inside zirconin than Li’, or that Na’ drags more water molecules than Li” when it is bound to zirconia, This means that there is a net water transfer from solulion to solid and the entropy decreases since water molecules have less degrees of freedom inside zirconia than in the solution phase. The first assumption may be ruled out on the basis of the fact. mentioued before 141 that Li+ interacts more strongly with the zirconia matrix and that in certain sites this interaction is so strong that Na* cannot replace Li+, which is the reason for a higher Li+capacity. With regard to the second assumption, it has been found that alkali ions arc substantially dehydrated inside zirconin 14, 51. This was deduced from the similar water contents of the different alkali ion forms. Howvevcr, this substantial dehydration may not mean perfectly complcti shedding of the hydration sheUs of the alkali ions in all the exchange sites bccausc small differences in their hydrat.ion states will not be clearly reflected in the water contents. As already mentioned (41, zirconia is a very hctcrogcncous zxchanger and it may be supposed that. in some of the sites of re1ativcly low binding energy. Nat is bound as water-shared ion pairs with more watir molecules than
Li* f
In the case of LijCs exchange, Cs’ (41 is able to replace only tttosc Li’ that arc relatively weakly bound to zirconia (relatively strongly acidic sites) which is the reason for a much lower Cs+-capacity. This is probably the reason for the small prcfcrencc of zirconin to Cs+, since as already mentioned 121, the stronger the acidity of the exchange site and, consequently, the less the strength of its electrostatic interaction with the counter-ion, the more is the probability that it prefers the ion of a lesser hydration energy. The small increase of aS” in tlw Li/Cs exchange is probably due to slightly larger degrees of freedom of the more weakly bound Cs’ and it seiims that thcrc is no significant change in the water content of zirconia upon replacement in it of Lit by Cs’. As will bo seen later, Cs’ seems to be rctaincd from the ayur?ous medium at least partly as wntcr-sharnl ion pairs and it may, therefore, bc concluded that from this medium Lit in the sites of relatively weak binding is also retained, at least part-
ly, as
water-shared ion pairs,
Table 1 shows lhat the addition of methanol lcads to decrease of A&* (iucreasa of selectivity constant) and iucrcase of Alp and AS” for both Li/Na and Li/Cs exchanges. This indicates that the iucrcase of the sdcctivity constant is due to the entropy term. In the case of Li/Na exchange, thcrc is a selectivity reversal at 50% methanol. The increase of AH” and As” is much more profound in the case of LijNa exchange where both these quantities change sign in presence of methanoi. The change of Alp and As” (and consequently AF”) on addition of methanol may be account-ed for in terms of the effect of alcohol on ion-solvent interact.ions in the bulk solution and on the interactions occurring in the solid exchanger. Effects on ion-solvent interactions are related to the thermodynamics of transfer of ions from water to the respective alcoholic solution, while the effects on the interactions in the solid phase arc
101
related to the thermodynamics
of simitar transfer of the alkali ion forms of the exchanger, which depends on the solvent composition of the external solution and exchanger and on the extent of solvent imbibition by the cxchanger 17,8,21] . The effect of addition of methanol on ion-solvent interactions, may be obtained from the enthalpies Al’$ and entropies AL? of transfer of the alkali halides from water to water- methanol mixtures. The rcportcd enthalpies tif transfer (22,231 of LiCl from water to 10, 20.43 and 68% (by weight) of methanol are 3.77,6.46,2.72 and -1.63 kJ/mol, respectively, Those for NaC1 are 2.01,3.18, 2.85 and O-71 kJ/mol, respeclivcly, while those for CsCl are 0.67,0.88,0.38 and -2.47 kJ/mol, rcspect.ivcly. The change of AH’ of cxchange due to changes in ion-solvent interactions on addition of methanol can be put equal to AK (LiCI) - AIG (NaCI) in the ccascof Li/Na exchange where Na’ in solution is replaced by Li’, and to Ae(LiCl) - AN~(CsCI) in the case of Li/Cs exchange where Cs’ in solution is replaced by Li+. Thus, in the case of Li/Na exchange, changes in ion-solvent interactions due to adclition of 10 and 20% methanol lead to an increase of 1.76 and 2.27 kJ, respectively, in the value of AIP and a decrease of 0.13 and 2.34 kJ, at 43 and 68% methanol, respectively. Zn the case of Li/Cs exchange, increases of 3.1,4.57, 2.34 and 0,84 kJ arc obscrvcd nt 10, 20, 43 snd 68% methanol, rcspcctively. With regard to AS:, the available data [22-- 241 on the free cnergios and enthalpies of transfer give rise to the following results. The entropies of transfer of LiCl from water to 10, 20,43 and 68% mcthnnol are 7.96,8.38, -12.16 and -42.32 J/mol/dcg, respectively. For NaCl. these valucs are 0,42, - 2.1, -19.69 and -47.35, rcspectivcly. while for CsCl, wc have two values only, namely -4.19 and ---IO.06 for transfer from water to 10 and 20% methanol, respectively. Calculations similar to those for the cnthalpics of transfer reveal that incrcascs in AS” of 7.64, 10.48, 7,54 and 6.03 J/mol/dcg result in the case of Li/Na exchange due to changes in ion-solvent interactions on addition of 10, 20,43 and 68% methanol. respectively. in thE case of the Li/Cs exchange, increases of 12.16 and 18.44 J/mol/dcg arc exptwtcd for 10 and 20% methanol, rcspcctivciy. Tlws, changes in ion-solvent interactions in the liquid phase on addition of methanol may account for an increase of Aff” and As” in the presence of this solvent, Howwer, the above mentioned data of AK and AS; show that changes of AH’ and As” on account of ion-solvent interactions arc either less profound or even reversed (A@ for Li/Na exchange) at the rclativcly high methanol concentrations. This together with the fact (shown in Table 1) that large increases, that arc more profound with incrwse of methanol content, are observed in the values of AH” and AS”, particularly in the case of Li/Na exchange, show that other more important factors arc operating, namely those related to the changes in the interactions in the exchanger. Changes in the interactions in the solid that give rise to an increase in Alp and AS’ may occur as a consequence of imbibition of methanol. Such changes probably involve removal of water molecules from tho Na’ and Cs’ sorbed from the
102
aqueous medium as water-shared ion pairs, with a subsequent stronger intcraction of thesr?ions with the exchange sites in zirconia. \VaCcrremoval, presumably connected with exchange sites of relatively low binding energy, is expected to increase (probably by involving site5 of lower binding wm-gy) with increase of methanol concentration. This water removal means that the water content of the h’s’ and Cs’ forms of zirconia become increasingly lass as we go from water to solutions of increasing methanol content, which implies an increase of the entropy of the system in presence uf methanol. The fact that the increase of entropy, relative to the value in water, is higher in t.he Li/nTa exchange than in the Li/Cs exchange (Table 1) may be due to a larger decrease, on going from t‘he aqueous to the mixed medium, of the water content of the Na*-form, compared to the Cs*-form. This implies that in the aqueous medium, Cs’ is, at least partly, retained in zirconia as solvent-shard ion Ilairs, It is not possible to judge the state of Li’ inside zirconia in the presence of methanol but taking into consideration that the capacity of the Li’-form of zirconia for Na+ and Cs’ increases on addition of methanol [43 and that its stability in the watcl-methanol mixtures, where it is predominantly solvat by water moIccuIc5, is higher than in water while that of Na’ and Cs* is mostly lower than in water [ZS], it may bc assumed that in the presence of the mixed solvent, Li’ inside zirconia retains at least the water molcculcs involved in its binding as solvent-shard ion pairs from the aqueous medium, For the case where the change of ion--solvent interactions in the liquid phase is the only factor affecting the ion exchange equilibrium on addition of the organic solvent, the thermodynamic equilibrium constants in water and in ii.!? mixed solvent arc interrelated through the medium effects (or the free cnergics of transfer) for the uxchangc pair of ions. If K,W and KY arc the thcrnlodynamic equilibrium constanls ior rcplaccmont of ion A* in the cxchanger by B’ frotn solutiora in water and the mixed solvent, rcspcctively, then we have the following relationship [7, S] : log
K,m = log K, + log
mYB+ 7
m7A
(7)
lvhere , yA + and ,l,yB+ are thu medium effects for transfer of thr! ions A* and B’ from water to the mixed medium and they arc related to thr?free cnergics of transfer by lhe following equation5 [7, ZB] : AF; (A’)
= H1’ln m7A+
AfiT (B’) = RT In myB+
(81 (9)
For the results in the lwescnt. work, Eq. (7) could be applied only to the Li/Na exchange in 30% methanol since only in t.his case is the capacity for the sorbed ion (Na’) practically the 5ame in both water and the mixed solvent and, thus, the standard states for the exchanger phase are consistent. The medium effects (or free energies of transfer) given in the literature for Li’ and Na’ are
largely different. However, the vaIuc_s of the ratio of the medium effects are nearly constant. Thus, vah~cs oi 0.26 [27], 0.26 (281, and 0.24 [ZS] for Iog (myNa+/myLi+) at 25’C are obtained, for transfer to 30% methanol, from literature data either directly or by interpolation. Using an average value of 0.25 for this quantity and the value 0.44 for Kr (corresponding to AF’ given in Table 1 for Li/Na exchange in water) and applying Eq. (7), we obtain a vaIUC of 0.78 for the equilibrium constant of the Li/Na exchange in 30% methanol, KF. Taking into consideration that the value obtained experimentally for this constant (corresponding to Atr” given in Table 1) is 0.86, it can be concluded that changes of ion-solvent interactions in 30% methanol contribute much more to the increase of the selectivity constant of Li/Na exchange than the changes occurring in the solid phase. Howcvcr, as already mentioned+ increases in AIP atuld AS” of exchange occur at 30% methanol due to changes occurring in the solid, involving remova! of water molecules from the sorbed Na’. It is thcrcforc possible that these increases largely cancel each other out at this aIcohol concentration. With the increase of methanol concentration, log(,,,rNa’/,yLi l) increases [ ZZ-283 + Moreover, chmlges in the solid, leading also to increase of the selectivity constant, arc expected to bc more profound, 9lld thus the SckctiVity COI’IStaIlt COlltitlUcS to increosc. ThC V~~UC Of l~g(~yCs*/~~Li’) is positive and increases with increase of methanol concentration 124) and the results in t.ho cast’ of the Li/Cs cxchangc sccn~ to bc quditativcly similar to those in the case of the Li/Na exchange.
10 11 12 13 14 15 16 I7 18 19 20 21
N.Z. Misak and EM. hlikhail. J. Appl. Chcm. Biutcchnul., 28 (1978) 499. N.Z. hfbak and E.hl. hlikhail, J. Inorg. Nucl. Chem., 43 (1081) 1063. N.Z. Misuk and B.lri_ Mikhail, J_ fnorg. Nucl. Chem., 43 (1981) 1903. N.Z. Misak and 1I.F. Ghoneimy, J. Chem. Technol. Uiutcchmd., 32 (1982) 709. D. Britz and G.11. Naneollas, J. Inorg. Nucl. Chcm.. 31 (19G9) 3861. G-11. Nancullas and R. Paterson. 3. Inurg. Nurl. Chem., 29 (1967) 565. AR. Gupta, J. Phys. Chcm., 75 (1971) 1152. A.M. El_Yrincc and K.L. Babcock, J. Yhys. Chcm., 79 (1975) lSS0. IIS. Jinrned and B.B. Gwen, The J’hysical Chemistry of Electrolyte Solutions, Reinhold, Kcw York, 1958. Z. Dizdar, J. Inorg. Nucl. Chem.. 34 (1972) 1069. 1f.S. #farned, J. Phys. Chem., 66 (19fi2) 689. R-D_ Lanicr, J. Phys. Chcm., 69 (19trS) 2097. A_ Schwarz, J. Phyr. Chem.. 72 (1988) 789. E. Ekedahl. E:, Ifogfcldt and L.G. Sillen, Acta Chcm. Stand.. 4 (1950) 556. O.D. Bonncr and FL. Livingston, 3. Plays. Chem., 60 (1956) 530. 11.M. Barrcr and J. Klinowski, Trans. Faraday Sac.. 1 (1972) 73. A. Ruvarac and V. Vcscly, J. Inorg. Nucl. Chem., 32 (1970) 3939. H.S. Stacrry, in J.A. hlarinsky (Ed.) Ion Exchange, Vol. 2, Dekker. New York, 1969. Chap. 3. D.R. Rosseinsky, Chem. Rev., 65 (1905) 467. O.D. Bonncrand L.L. Smith, J. Phys. Chem., 61 (1957) 1614. D. Nandan and A.R. Gupta, 3. Phys. Chem.. 79 (1975) 180.
104 22 23 24 25 26 27 28
D. Feakins, In F. Franks (Ed.), PhysicoChemical Processe s In hiired Aqueous Sdvenfs, Heinemann, London, 1967, pp. 71- -89. D. Feakins and P. Watson, J. Chem. Sot., (1963) 4734. A.L. Andrews, ILP, Rennetto, D. Feakins, K.G. Lawrence and R.P.T. Tomkins, J. Chem. Sue., IA) (I 968) 1486. D. Bax, C.L. DeLigny and M. Alfcnaar, Rec. Trav. Chim. Pays-Bas, 91 (1972) 462. 0. Popovych, Crit. Rev. Anal. Chem., 1 (1970) 73. 0. Akerlov, J. Am. Chem. Sot., 62 (1930) 2353. R.P.T. Tomkins, The&. Birkbeck Coll~go. London (1966).