Synthetic inorganic ion-exchange materials—IV

J. lnorg. Nucl. Chem,, 1964. Vol. 26, pp. 297 to 304. Pergamon Press Ltd. Printed in Northern Ireland

SYNTHETIC INORGANIC ION-EXCHANGE MATERIALSmlV EQUILIBRIUM STUDIES WITH MONOVALENT CATIONS AND ZIRCONIUM PHOSPHATE C. B. AMPHLETT,P. EATON,L. A. MCDONALD and A. J. MILLER Chemistry Division, Atomic Energy Research Establishment, Harwell, Berks. (Received 6 May 1963; in revised form 25 July 1963)

Abstract--Equilibrium studies with zirconium phosphate and 0'1 N solutions containing pairs of cations have shown that the systems Cs+/Rb ÷ and Cs+/K+ give normal rectilinear isotherms, while S-shaped curves are obtained for exchange between H + ions and either Cs+ or Rb + ions, with pronounced reversal of selectivity. This behaviour is tentatively ascribed to steric factors which may arise when the exchanging ions differ appreciably in size. Values are given for the free energies of the exchange reactions, and in the Rb+/H + and Cs+/H+ systems for the heats and entropies also. THE ion-exchange behaviour of zirconium phosphate and similar inorganic cation exchangers has been described by several authors, ~1~ and much attention has been paid to the former material. Measurements of distribution coefficients for the alkali metal cations on zirconium phosphate ~2) show it to possess considerable specificity towards rubidium and caesium. Equilibria involving the ions Li +, Na + and K + upon the hydrogen form of zirconium phosphate have been measured by LARSEN and VISSARSta) in solutions in which the alkali metal was a trace component, and the thermodynamic functions for the exchange have been calculated assuming that the logarithm o f the selectivity is a linear function of the mole fraction o f exchanged cation in the solid phase. The quantitative significance of this extrapolation is doubtful, particularly in the case o f a rigid exchanger such as zirconium phosphate; it is well known in the zeolite series t4) and in the clay minerals t6~ that the selectivity may be a complex function o f exchanger composition, and that in some cases sigmoid isotherms are obtained, so that measurement over the whole range of exchanger composition is necessary in order to calculate thermodynamic data. Data have also been presented ts) for a number o f cation-pairs in tracer solution and in macroconcentrations, but as the latter apply to a limited range of composition it is again not possible to evaluate unambiguously the thermodynamic equilibrium constants for exchange. This paper reports the exchange behaviour of a number o f 1 : l-valent cation pairs over the complete range of exchanger composition, from which the appropriate thermodynamic data may be derived. c~ e.g.K.A. KRAUSand H. O. PrnLLII,S,J. Amer. Chem. Soc. 78, 694 (1956); C. B. AMPHLETT, Proceedings International Conference on the Peaceful Uses of Atomic Energy, Geneva, 1958, Vol. 28, p. 17, United Nations (1959); L. B~'rSL¢.and D. HuYs, J. lnorg. Nucl. Chem. 21, 133 ( 1961). ~2~C. B. AMPI~LETT,L. A. McDo~tALDand M. J. REDraAN,J. Inorg. Nucl. Chem. 6, 220 (1958). ~3, E. M. LARSENand D. R. VtSSAgS,J. Phys. Chem. 64, 1732 (1960). t4~ See, for example, R. M. BARREX,Proc. Chem. Soc. 106 (1958). ~5~j. A. FAtJCHERand H. C. THOMAS,J. Chem. Phys. 22, 258 (1954); G. L. GAINESand H. C. THOMAS, Ibid. 23, 2322 (1955). c6, L. BAE'rSLLJ. Inorg. Nucl. Chem. 25, 271 (1963). 297

298

C . B . AMPHLETT, P. EATON, L. A. McDONALD and A. J. MILLER

EXPERIMENTAL The systems examined were Cs-H, Rb-H, Cs-Rb and Cs-K; in some cases batch techniques were employed and in others column equilibrations. In the former, weighed amounts of the hydrogen form of zirconium phosphate (0.25 g) were equilibrated with 25 ml of the appropriate solution for 4 hr at a controlled temperature (25 or 40°C); The solution and exchanger were then separated by filtration or centrifuging and the decrease in concentration of the solution measured. Ecrlier experiments have shown (a) that the uptake is reversible, (b) that uptake of the cation from solution is accompanied by release of an equivalent amount of hydrogen ion from the exchanger to solution, and (c) that equilibrium is complete within 4 hr. Solutions used for uptake were 0"1 N with respect to total cations, the proportions of the two cations being varied to provide a range of values of relative concentrations. The solutions were prepared by mixing accurately-measured volumes of standard solutions of the appropriate salts (prepared from weighed dried salts) and of HNO3 (standardized by titration). Caesium and rubidium solutions were analysed radiometrically using tracer 8~Rb and mCs. Column equilibrations were carried out in some cases, by passing a solution of the mixed salts through a column of material in the hydrogen form until the effluent composition and influent composition were the same. A breakthrough curve for the traced component may then be drawn from measurements of effluent composition as a function of time, and hence the capacity for that component determined at the particular solution composition taken. The details of this technique have been given elsewhere.(;~ In order to avoid decomposition of the exchanger and loss of phosphate ions to solution, all experiments were carried out under conditions where the pH did not exceed 3; under these conditions no phosphate was detectable in the solution. Two samples of zirconium phosphate were used, one (CE 3) prepared in Chemical Engineering Division at A.E.R.E., and the other (BDH 5) supplied as an experimental batch by British Drug Houses, Ltd. Although the two samples differed appreciably in many of their properties, particularly with regard to rates of exchange, comparison of the Cs/H exchange on the two samples showed that they gave similar isotherms. Saturation capacities were measured by repeated batch equilibration with the exchanging ion until no further uptake occurred, followed either by analysis of the combined solutions or by elution of the cation from the exchanger for analysis. Values obtained from several sets of duplicate determinations were 1"64 4. 0.02 meq/g for CE 3 and 1.33 4- 0.01 meq/g for BDH 5. RESULTS

The isotherms are shown in Figs. I-3, those for the systems Cs/H and Rb/H being measured at 25 and 40°C. In these the relative uptake q/qo (q being the uptake and q0 the saturation capacity, both in meq/g) is plotted against the relative concentration C/Co in the solution at equilibrium (c being the concentration of the exchanging cation and co the total concentration, both in meq/ml). From these, values of the equilibrium quotient Ko' have been calculated as a function of the exchanger composition. For the exchange AX + M + ~ MX + A + KC r ~

[M+I[A +] = q(c o - - c)

[M+][~,+]

C(qo -- q)

where the barred terms refer to concentrations in the solid phase and the others to solution concentrations at equilibrium. All data in this paper refer to the case where Cs+ is the displacing cation except for the Rb/H system, where it is Rb +. The individual points for the Cs/H exchange on CE 3 are omitted in Fig. 3 for the sake of clarity, and in view of the absence of data at low concentrations no attempt has been made to derive thermodynamic data in this case. (7) e . g . J . A . FAUCHER,R. W. SOUTHWORTHand H. C. THOMAS,d. Chem. Phys. 20, 157 (1952).

Synthetic inorganic ion-exchange materials--IV

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299

t

0"8

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0"6

i

O'4

0'2

0.2

0.4

0-6

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RELATIVE CONCENTRATION~ C/C o

FIG. l.--Cs/Rb and Cs/K isotherms on zirconium phosphate (CE 3, 20°C)

I'0

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CONCENTRATION,

1.0

C/Co

Fie;. 2.--Rb/H isotherms on zirconium phosphate (BDH 5) at 25°C (C)) and 40°C (X).

300

C. B. AMPHLETT,P. EATON, L. A. h~IcDONALD and A. J. MILLER I-o O'g

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FIG. 3.--Cs/H isotherms on zirconium phosphate O B D H 5, 25°C. × B D H 5, 40°C. --CE 3, 20°C. DISCUSSION

While the Cs/Rb and Cs/K systems display normal rectilinear isotherms (Fig. 1), those for Rb/H and Cs/H exchanges are of the ogee type (Figs. 2 and 3), displaying very high selectivity for the alkali metal cation at low concentrations of the latter and changing to high selectivity for hydrogen ion as the fraction of the alkali metal on the exchanger increases. This behaviour has been observed on two different preparations of zirconium phosphate in the present work, and an independent investigation of the Cs/H system on a third sample of zirconium phosphate has revealed the same phenomenon, the isotherm being reversible throughout the entire composition range, cs) The extremely high selectivity towards caesium and rubidium at very low concentrations is shown by the curves in Fig. 4, which represent data from Figs. 2 and 3 at 25°C plotted on an enlarged scale up to a relative concentration of c / c o = 0-05; values of the distribution coefficient Kd (meq/g of exchanger -- meq/ml, of solution at equilibrium) are also shown. The reversal of selectivity occurs at a lower relative concentration for rubidium than for caesium, and in both cases increased temperatures favour hydrogen ion uptake relative to that of the other cation. The Cs/H curve is in fact very unsymmetrical, more so on BDH 5 than on CE 3, while the Rb/H curve is almost symmetrical about the line through the origin at 45 ° corresponding to an equilibrium constant of unity. It is obvious from the shape of these curves that any calculation of thermodynamic functions based on extrapolation from results over a narrow range of solution (s) .1. P. HARKIN, G. H. NANCOLLAS and R. PATERSON, 7. lnorg. N#cl. Chem. 26, 305 (1964).

Synthetic inorganic ion-exchange materials--IV I

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FIG. 4.--Uptake of Cs ÷ and Rb + ions on zirconium phosphate (BDH 5), H-form, 25~C at low concentrations. Total solution concentration 0-1 N. c o m p o s i t i o n is o f doubtful value. The t h e r m o d y n a m i c equilibrium constant K may

however be obtained tg~ from the relationship In K = where Ke is given by the expression

In Ko. d(q/q0)

Ke

K ' ~H

YM

where ~'Taand 7r~ are the activity coefficients of the ions H + and M + in solution, and In Kc is integrated over the entire composition range of the exchanger. The free energy of exchange may then be calculated from the expression AG = --RTln K, and the entropy of exchange is given by AG = AH -- T. AS, values of the heat of exchange being obtained for the Cs/H and Rb/H systems by applying the Van't Hoff isochore to the data for K,e ' at 25 ° and 40°C, assuming A H to be constant over this

range of temperature. In deriving K by integrating beneath the curve ofln Ke vs. q/qo, particular attention must be paid to the shape o f the curve at its extremities when the relationship is not

a simple one; in practice this involves measuring the limiting slope of the curve3 9) This is relatively simple as q/qo tends to zero, since small uptakes may be measured by the tracer method with an accuracy limited solely by counting errors, but as q/qo tends towards unity the errors increase, since the difference between q and q0 becomes comparable with errors in b o t h these quantities. A s s u m i n g that the slope o f the curve between q/qo ----- 0.90 and 1.0 is as s h o w n in Figs. 1-3, it is estimated that the error in determining K does not exceed 5 per cent.

Since Cs +, Rb + and K + ions have similar activity coefficients in 0.1 N solutions t*~G. L. G~at~r~and H. C. Tr~oM~, J. Chem. Phys. 21, 714 (1953).

C.B. AMPtILETr, P. EATON, L. A. MCDONALD and A. J. MILLER

302

o f their nitrates 0'~=tMNO0 ----0"733, 0"734 and 0.739 respectively for 0"1 m solutions at 25°C~1°)), Ke has been set equal to Ke' in deriving values o f K for the Cs]K a n d C s ] R b systems. The activity coefficients for M N O a and H N O a differ significantly however (7~=tHNO0 ---- 0"791 at 25°C in 0.1 m solution), a n d appropriate corrections have been m a d e in the other systems to derive values o f Ke f r o m the experimentallydetermined ratios Ke'. Values o f 7~tcsso0, Yit~b~o0 and 7±tHNO0 at 25°C and 0.1m concentration have been used together with values ~1°) for the constants A and B at 25 ° a n d 40°C in the Debye-Hiickel equation a Izaz~l V I

--log 7 =

1 q- B~v/I

to derive data at b o t h temperatures for the activity coefficients as a function o f concentration. Interaction between M + and H+ is neglected as being insignificant between univalent cations in these relatively dilute solutions. The overall contribution o f the activity coefficient terms to the value o f K m a y be seen b y evaluating the integral \Tu/"

~

which converts

f0

lnKe'.d

() I0 ~q

to

()

l n K e . d ~q

.

This corresponds to a m e a n value for Y~/7~ o f 0.97 at 25°C, so that the correction to be applied is only 3 per cent, which is within the limits o f the experimental accuracy. T h e r m o d y n a m i c data obtained in this w a y are given in the Table; the data for THERMODYNAMICDATAFOR SOME 1:1 EXCHANGEREACTIONSON ZIRCONIUMPHOSPHATE K

AGO (kcal mole-~)

AH ° (kcal mole-~)

Rb --~ Cs, CE3 20°C.

0"56

0"34

--

K --- Cs, CE3 20°C.

0"10

1.35

--

System

25°

R b -*- H , B D H 5

Cs --* H, BDH5

1"78

4.83

40°

1.00

2.36

25°

--0"34

--0.93

AS°, 25°C. cal mole-Xdeg-~) --

q/qo --

--

--

--7.4 --7-1 --6"9

--23.5 --22.7 --21.8

0"16 0"2 0"3 0"4 0'5 0"6 0"7 0"8

40°

0.0

--0.53

- - 7.7

-- 24-8

-- 10"6 -- 10"2 --6"3 --5"4

-- 34-3 -- 33.0 --19.9 --17"0

--8"6 --7-4 --8"0

--25.8 --21.6 --23-7

--8"I

--24"1

--7"6 --9"1 --10"2 --9.1 --10"8

--22.5 --27"4 --31-1 --27.4 --33"2

0"1 0'2 0'3 0.4 0.5 0.6 0.7 0.8 0.9

noJ R. A, RomNsoN and R. H. STomsa, Electrolyte Solutions, Appendix 8.10. Butterworths, London 0959).

Synthetic inorganic ion-exchangematerials--IV

303

AG °, in conjunction with those of LARSEN and VISSARS(a) for other alkali metals, show that AG ° becomes progressively more negative as we descend the group. The values of AG ° in this table for the Cs/H and R b / H exchanges are less negative than those reported by BAETSLE(6) for exchange from tracer solutions, since Ke' decreases as the mole fraction of the alkali metal cation in the solid phase is increased. If, however, we compare BAETSLI~'s figures obtained at tracer concentrations of the alkali metal cations with om limiting value of Ke' when (q/qo) tends to zero the agreement is reasonably good, e.g. System

Rb ~ H Cs ~ H

AG O In K / (BAETSLL 2 0 C ) --2'28 kcal mole -t - 2 . 6 0 kcal mole -~

3.8 4-3

Lim(ln Kc')~,,o~o (this work, 2 5 C ) 3"6 4'8

Examination of the data as a function of exchanger composition shows that AH ° and AS ° are not constant, but vary together in such a manner that each tends to cancel the effect of the other. Although the accuracy in determining AH ° is probably not greater than 10 per cent, since each value is obtained from two values of Ke' which are only accurate to i 5 per cent, the maximum deviations observed exceed this figure and are considered to be significant. For the Rb/H exchange AH ° has a mean value of --7.6 kcal mole -1 (BAETSLi~quotes --9"56), which decreases abruptly to < - - 1 0 kcal at 50 per cent saturation and then increases sharply to ~ - - 5 kcal when the exchanger is predominantly in the rubidium form. In the Cs/H exchange, the mean value of --8.8 kcal compares with BAETSE~'s figure of --10.01, and appears to decrease slowly to ~ - - 11 kcal as the fraction of Cs in the exchanger increases. The mean entropies of exchange (--24.6 e.u. for Rb and --26.3 for Cs, compared with BAETSL~'Sfigures of --24.8 and --25.0 respectively) are somewhat greater than the entropies of the two ions in aqueous solution (--29.7 and --31.8 e.u.) and thus parallel the behaviour observed by LARSEN and VlSSARS for Na + and K -~ ions. The data presented in this paper are thus in qualitative agreement with those of other workers on similar systems, although a similar detailed treatment of other alkali metal-hydrogen ion exchange reactions is required before a full comparison can be made. Significant changes in AH ° as a function of exchanger composition have also been reported by BARRER et al. for the synthetic zeolite Linde Molecular Sieve 4A. (n~ In this case the heats of exchange were measured calorimetrically for a number of cation pairs, for some of which marked energetic heterogeneity was observed. The results in this paper differ quantitatively from those of HARKIN et al., ts) although the shapes of the isotherms are identical. However, there is no reason to expect close agreement, since the samples of zirconium phosphate were prepared by different methods. It is well known even for organic ion-exchange resins, where control of the chemical composition of the exchanger is reasonably well established, that variations in selectivity are observed when the degree of cross-linking is changed, particularly for pairs of ions which differ appreciably in size. Close control of the composition and detailed properties of the zirconium phosphate class of exchangers is not possible at present; although qualitatively two batches or even two different talj R. M. BARRER, L. V. C. RE~ and D. J. WARD, Proc. Roy. Soc. A 273, 180 (1963). 7

304

C.B. AMPHLETT,P. EATON,L. A. McDONALDand A. J. MILLER

preparations will generally be similar as regards relative affinities and total capacity, properties such as distribution coefficients and rates of exchange can vary significantly. This is due in part to lack of close control over chemical composition and over the degree of cross-linking in the polymer network. Under these circumstances the fairly close agreement between the different samples used in this paper must be regarded as fortuitous. The significant feature of the results in this paper and in that of HARKIN et al. ts~ is the shape of the isotherms and not the detailed quantitative results. The difference in shape between the isotherms for the systems Rb/Cs and K/Cs on the one hand and those for Cs/H and Rb/H on the other requires some comment. The ogee-shaped curves in the latter two instances are characteristic of equilibria in which exchange becomes progressively more difficult as the proportion of one of the cations in the solid phase is increased, leading ultimately to a reversal in selectivity. This may arise in a rigid exchanger which undergoes relatively little swelling, if there is a large difference in the sizes of the two cations. It has, for example, been observed in certain zeolites, e.g. the exchange between lithium and sodium on basic cancrinite: a2~ more open structures do not show this behaviour. The compact structure and resistance to swelling of zirconium phosphate are indicated by the relative slowness of exchange compared with ion-exchange resins, by the ion-sieve action which it exhibits, tls~ and by the fact that volume change on conversion from the hydrogen form to the sodium form is less than 5 per cent. The problem may also be treated as one arising from the limited solubility of the two end-members of the series over a certain range of composition. In the systems Rb/Cs and K/Cs the existence of normal rectilinear isotherms presumably indicates that differences in ionic size are not sufficiently great to cause limited solubility and reversals in selectivity. It would be interesting to study the K / H and Na/H systems in detail, since there is a sharp reduction in ionic radius in passing from potassium to sodium (Na + 0.95, K + 1.33, Rb + 1.48, Cs+ 1.69 A). Acknowledgements--Part of this work was carried out during the tenure of vacationstudentshipsat

Harwellby two of the authors(P. E. and A. J. M.), who wishto tendertheir thanksto theU.K.A.E.A. ~1~R. M. BARRERand J. D. FALCONER,Proc. Roy. Soc. A 236, 227 (1956). ~13~C. B. AUpnLErrand L. A. MCDONALD,Proc. Chem. Soc. 276 (1962).