2704
The Journal of Physical Chemistry, Vol. 62, No. 25, 1976
G. E . Boyd
Thermodynamic Property Changes in Lanthanide(II1) Cation Exchange Reactions with Poly(styrenesu1fonic acid) Type Cation Exchangers G. E. Boyd Department of Chemistry, University of Georgia, Athens, Georgia 30602 (Received July 18, 1978) Publication costs assisted by the University of Georgia
Calorimetric and equilibrium distribution measurements at 298.1 K were employed to estimate standard Gibbs energy, enthalpy, and entropy changes in the ion-exchange reactions between 13 of the lanthanide(II1) cations and yttrium(II1) ion in dilute aqueous perchlorate solution and a strong-acid type cation exchanger. A plot of the lanthanide atomic number dependence of AGO for the reaction LnR3 + Ce(II1) = CeR3 Ln(II1) showed discontinuities at 2 = 64 (Gd) and between 2 = 60-61 (Nd-Pm) and 2 = 67-68 (Ho-Er) indicating a “tetrad” effect superimposed on the effect of the lanthanide contraction. No such 2 dependence was found with the AHo values but rather a maximum exothermic effect was reached at approximately the middle of the rare earth series followed by a linear decrease in the heat evolved from Tb to Lu. The dependence of AGO on 2 can be explained in terms of a slight modification of the effect of the lanthanide contraction by interelectronic repulsion effects in the Ln(II1) cations. The unusual 2 dependence of AHo can be rationalized by assuming that the coordination number for water in the primary hydration sphere of La(II1) ions changes from 9 to 8 and that strong ion-pair complexes are formed between the sulfonate groups of the ion exchanger and Ln(II1) cations with only inner sphere hydration.
+
Introduction Values of the thermodynamic property changes in the ion-exchange reactions of the trivalent lanthanides appear to be largely unknown in spite of the fact that it has been recognized for a long time that temperature is an important factor in determining the separation of these elements by liquid ion-exchange chromatography.1,2 Because of the great chemical similarities of the rare earths with one another it has been assumed that the enthalpy changes in their reactions with one another will be so small that temperature changes will be ineffective in changing their relative ion-exchange affinities. Apparent support for this view is found in the observation that the relative retention times (i.e., separation factors) in liquid chromatographic separations of the rare earths with poly(styrenesu1fonic acid) type cation exchangers and aqueous buffer solutions of weak organic acids are almost the same at 100 as at 25 OC. In contrast, however, efficiency of both rare earth and a ~ t i n i d eseparations ~,~ are strikingly improved by operation at the higher temperature. The retention time for a given lanthanide at constant temperature and pH in liquid chroqatography with weak acid buffers is determined to a first approximation by the balance between the affinity of the lanthanide for the ion exchanger Ln3+ + 3MR = LnR3
+ 3M+
(1)
and the degree of the dissociatiop-of its complex ion with the anion of the buffer eluant LnAn3-nz= Ln3+ + nA-z (2) The separation factors, a , for two or more lanthanides will be determined by the appropriate ratios of the equilibrium constants for reactions 1 and 2. The enthalpy and heat capacity changes in these reactions will govern the change in their equilibrium constants with temperature and hence the temperature dependence of a. The possibility for the development of temperature-programmed liquid ion-exchange chromatographic separations will depend on the magnitudes of the differences in the temperature dependence of 01. 0022-365417812082-2704$01.OO/O
A substantial amount of data on the Gibbs energy, enthalpy, and entropy changes for a wide variety of ligands reacting according to eq 2 has become available during the past 20 yearst5 but virtually none exist for eq 1. Accordingly we have conducted sensitive calorimetric and equilibrium distribution measurements with all of the trivalent lanthanides except promethium to obtain AHo, AGO, and ASo values for the ion-exchange reaction of these cations with one another in dilute aqueous acid perchlorate solutions. The procedure followed in the equilibrium constant determinations differed from an earlier studysa in which only tracer concentrations of lanthanide ions in 0.110 m HC104 solutions were employed in that the equivalent fraction of Ln(II1) in the exchanger was varied from zero to unity. More importantly, ion exchange enthalpy changes and equilibrium constants were compared directly by measurements on the reactions between pairs of lanthanide ions. This approach is much more convenient and yields more accurate equilibrium constant values than measurements on eq 1with a singly charged reference ion such as the hydrogen ion because of the very large and very similar affinities of lanthanide ions for ion exchangers. Thermodynamic equilibrium constants and enthalpy changes therefore were measured for the reaction Ce3+ 4- LnR3 = CeR3 + Ln3+ The choice of cerous as the reference ion was based on the accuracy and convenience with which it could be determined by redox titration in aqueous perchloric acid solutions.
Experimental Section Chemicals and Reagents. Approximately 1 N stock solutions of the trivalent rare earth perchlorates were prepared by dissolving ultrapure rare earth oxide (>99.9% by weight, American Potash and Chemical Co.) in reagent grade perchloric acid (70% by weight, J. T. Baker reagent). The pH of these solutions was adjusted from an initial value of ca. 1.5 to their equivalence point to establish a C104:Ln(III)ratio of 3.00. Some difficulty was experienced in dissolving the pure CeOz in HC104 to prepare the 0 1978 American Chemical Society
Ion-Exchange Reactions of Trivalent Lanthanides
Ce(C104)3solution so that pure anhydrous CeC13 (>99.9% Cerac, Menominee Falls, Wisc.) was evaporated with concentrated perchloric acid to near dryness to form the desired salt. During the latter phases of this research hydrated reagent grade Ce(C104)3became available (G. F. Smith Chemical Co.) and was used. All solutions and dilutions were made with water with a specific conductance mho cm-l. of less than 1 X Analytical grade poly(styrenesu1fonate) nominally cross linked with 8% by weight of divinylbenzene (BioRad AG 50W-X8) was employed as the cation exchanger. The exchange capacity of this preparation was 5.10 mequiv per gram of dry H form as determined by weight titration with standardized NaOH. The average particle diameter, determined microscopically, was 55 pm which agrees well with the vendor designated actual wet mesh range of 230-400 (U.S. Std.). A portion of this preparation was fractionated hydraulically to give a 20-40-pm size range which was used in addition to the unfractionated exchanger. No differences in the properties between the classified and the unclassified preparations were observed. The lanthanide salt forms of the ion exchanger, LnR3, were prepared as needed by treating the purified H form of the exchanger with 1 N Ln(C104), solution. Calorimetric System. The solution calorimeter and associated circuitry have been described.6b The response of the calorimeter was increased and the thermal mass was reduced by changing to a thin-walled, silvered glass Dewar vessel (0.6 mm) following Christensen, Izatt, and H a n ~ e n . ~ The heat leak from the calorimeter to its surroundings also was decreased by leaving the top-most inch of the vessel unsilvered. In studies of the rare earth ion-exchange reactions the calorimeter vessel was filled with 500 mL of 0.01 N Ce(C104)3or Ln(C10J3 solution weighed to i O . 1 g. Approximately 5 mequiv of LnR3 or CeR3 which had been brought to equilibrium with 0.01 N Ln(C104)3.0r Ce(C104)3solution was placed in a 3-mL glass pipet which was sealed before its submersion in the calorimeter vessel solution. The pipet was opened when a steady state temperature drift had been reached in the stirred solution and the ion-exchange reaction was initiated by the mixing of the exchanger with the solution. The thermal effect was complete within 5 min. The reaction temperature was 25.1 f 0.05 OC because of the need to increase the temperature of the calorimeter by 0.1 "C above that of the bath to achieve a convenient temperature drift rate. Electrical calibrations were made on the final state of the system in the calorimeter with an average precision in the electrical energy equivalent of f0.0570. The temperature sensitivity of the calorimeter was ca. 1 X deg corresponding to a limit of heat detection of 5 mcalth. A heat of pipet opening correction of 11 f 5 mcal exothermic was made in all determinations. Heat of dilution measurements were conducted with several 0.01 N Lr1(C10,)~solutions by diluting 10 mL initially in a large pipet into pure water. The derived apparent molal heat contents, @L, were in agreement with recent extensive heat of dilution measurements with rare earth perchlorate^^^^ which indicate conformity to the Debye-Huckel limiting law at concentrations below 0.006 m. Chemical Analyses. The exchanger was recovered quantitatively on completion of the calorimetric experiment and its ionic composition was determined by chemical analysis. The ions in the exchanger were eluted quantitatively with a 3 N H2S04solution and the eluant plus water rinse was made up to a known volume (200 mL) for determinations of total rare earths and Ce(II1) content. The resulting H form of the exchanger was washed with
The Journal of Physical Chemistry, Vol. 82, No. 25, 1978 2705
2 N NaCl solution to displace the Ht ion which subsequently was titrated with a glass electrode to a pH of 8.6 with 0.1 N NaOH (carbonate free) which had been standardized with pure, dried potassium acid phthalate (J. T. Baker Analyzed reagent Primary standard). This determination gave the total milliequivalents of ion exchanger involved in the calorimeter reaction. Total rare earths in the initial and final calorimeter solutions and in the H2S04eluant from the ion exchanger were determined by photometric titrations with 0.01 M EDTA at pH 5 using xylenol orangelo as an indicator. Standardization of the EDTA (Fisher Scientific Co. Certified Reagent) solution was performed with 0.01 M Zn(NOJ2 or ZnClz solutions prepared from accurately weighed quantities of pure metallic zinc (NBS Standard reference material No. 728). The concentrations of Ce(II1) in the final calorimeter solution and in the sulfuric acid eluant from the ion exchanger were determined volumetricallyll by electrometric titration with standard 0.1 N arsenious oxide12 (G. F. Smith Chemical Co., As203Standard Reference for Cerate Oxidimetry, Purity assay 99.99%) after oxidation to Ce(IV) with (NH4),S2o8catalyzed by silver ion. A platinum wire plus a calomel electrode were employed in the titrations with Radiometer titration equipment (London Co., Westlake, Ohio) consisting of a stirred titration vessel fitted with an automatically driven 2.5-mL syringe buret SBU 1,a Titrator TTT-1,and a Titrigraph SBR-2. A titration curve is drawn by this equipment as a series of "stair-step" segments denoting the changes in the emf and milliliters of reductant solution. The result is a titration curve which appears to be continuous. It was possible with the aid of the Titrigraph and the use of Os04 catalyst to estimate the volume of 0.1 N AsOz- needed to reach the end point to 1 ppm. The same instrumentation was used in the photometric titrations where a TTA4 titration assembly was employed. Standard solutions of Ce(II1) for use in periodically checking the EDTA and Ce(IV)/As02- methods were prepared and analyzed gravimetrically by precipitation of perchlorate with tetraphenylarsonium chloride,13 or, by oxalate precipitation and ignition to Ce02. All volumetric glassware including the Radiometer syringe burets was calibrated for delivery at 25 OC. The foregoing analyses permitted an accurate estimate of the millimoles of reaction in the calorimeter as well as estimates of the composition of the equilibrium exchanger and final mixed electrolyte solution. The uncertainty in the amount of exchange reaction was i0.02 mmol; this was the largest source of error in the ion exchange enthalpy determination. The mass law concentration product ratio, KLnCe, for the ion exchange equilibrium was computed from the analyses which also were employed to obtain material balances needed to establish the purity of the calorimetric reaction (i.e., absence of side reactions). The experimentally measured heats of partial ion exchange, QLnCe, were expressed as defined calories per mole (1 calth 1 4.1840 J). The QLnCe values were found to be independent of the direction of the exchange reaction (i.e., QLnCe = -QceL") within experimental error. A minimum of two and sometimes as many as four calorimetric de(and Khce)were performed in which terminations of QhCe the equilibrium was approached from opposite directions.
Treatment of Experimental Data Mass law concentration product quotients, K,' = KLnCe, derived for the ion-exchange reaction which occurred in the calorimeter, and the corresponding integral enthalpies of ion exchange, AH = QLnCe, are plotted in Figures 1 and 3, respectively, as a function of the atomic number of the
2706
The Journal of Physical Chemistry, Vol. 82, No. 25, 1978
lanthanide initially in the exchanger. The magnitudes of the Gibbs energy, enthalpy, and entropy changes, AGO, AHo, and ASo for the ion-exchange reaction at equilibrium a t 298 K when the products and reactants are in their standard states may be derived from K,' and QLnCe. This hypothetical but defined cerous-lanthanide(II1) cation exchange reaction may be written as LnR3.nHz0 ( a = 1, equil with 0.01 N Ln(C104),) + Ce(C104)3(as, a = 1) = CeR3-mH20( a = 1, equil with 0.01 N Ce(C10,)J + L I I ( C ~ O ~(as, ) ~ a = 1) + (m - n)HzO (3) The standard states of the hydrated exchanger salt forms, LnR3.nH20 and CeR3.mH20, are defined when they are in equilibrium with 0.01 N Ln(C104)3and 0.01 N Ce(C104)3, respectively. The standard states for the mixed electrolyte solution phase are chosen as the usual ones which make ion activities approach corresponding molalities as the solute content becomes vanishingly small. The reference states for the solvent are chosen so that the activity of the water, a,, in each phase is the same and a, = 1for the pure solvent. The assumption is made the perchlorate ion invades the exchangers to a negligible extent. Note, however, that allowance is made changes in the hydration of the exchanger. The standard Gibbs energy change per mole of reaction is given by 1
AGO = -RT In K, = - R T S In K, dxce 0
where the two definite integrals on the right follow as a special case of eq 17 of Gaines and Thomas.14 Because of the difference in our choice of standard states for the exchanger from that of Gaines and Thomas their "zero point" correction term, In [fCe(a)/fLn(b)], may be set equal to zero. The thermodynamic equilibrium constant, K,, is given by
Ka
3CCemLnYLlfCe/3CLnmCeYCefLn
= Kc(fce/fLn) (5)
where X J are the equivalent fractions of rare earth in the exchanger, and mJ are their molalities in the equilibrium mixed electrolyte. The quantities f J and yJ are the ionic activity coefficients in the exchanger and aqueous phases, respectively. The experimentally measured concentration product quotient, K,', is related to K , by K, = K,'(YLn/YCe) = K,'[y,(Ln)/ydCe)14
(6)
where y,(Ln) and yk(Ce) are the mean ionic activity coefficients for Lr1(C10,)~ and Ce(C10J3 in the mixed aqueous electrolyte solution. The activity coefficient ratio in eq 6 may be taken as unity to a good approximation for the 0.01 N mixed rare earth perchlorate solutions employed in this investigation. For example, our unpublished determinations of the osmotic coefficients for La(C104), and Gd(C1O4I3solutions at concentrations between 0.01 and 0.1 m show them to be identical to within 0.2%. These observations are supported by recent independent measurement~l~ on lanthanide perchlorate solutions a t concentrations generally slightly greater than 0.1 m. The last term on the right-hand side of eq 4 may be approximated by the mean value theorem as fi, In [a,(Ce)/a,(Ln)] where ii, is the average number of moles of water per equivalent in the exchanger and a,(Ce) and a,(Ln) are the respective water activities in the exchanger salts, LnR3-nHz0and CeR3.mHz0, each in their standard states. Because of the virtually identical osmotic coefficients of
G. E. Boyd
the aqueous electrolytes with which these salts are in equilibrium the values of a,(Ce) and a,(Ln) will be nearly identical and the logarithm of their ratio will effectively vanish. Equation 4 therefore simplifies to 1
AGO = -2.3RTS0 log K,' dxce = -2.3 log KLnCe(7) The standard state enthalpy change, AHo, for eq 3 will be given by
AHo = AH + AI$L
(8)
where A4L is the relative apparent molal heat content difference (Le., heat of dilution difference), 4L[Ce(C104)3] - $~~[Ln(C10~ for ) ~the ] , aqueous rare earth perchlorate solutions at 0.01 N. These concentrations (Le., 0.00333 m) are sufficiently low that the prediction, A& = 0, from the Debye-Huckel limiting law is a fair approximation. Recent comprehensive enthalpy of dilution measurements at 25 OC on solutions of eight of the rare earth perchlorates from 0,001 m to saturation16 confirm this approximation to be satisfactory within h5 cal mol-l which is about the same order as the errors in the values of themselves. Computations of 4L for 0.00333 m solutions using the least-squares best fit equations reported give values of 298.2, 270.4, 276.2, and 269.3 for La, Pr, Gd and Lu perchlorates, respectively. Values for Ce(C1O4I3were not determined but a value of 282 cal mol-l for +L may be estimated by linear interpolation with the q+, values for La and Pr. The magnitudes of A$L estimated with the interpolated value for Ce(C104)3are then -16, 12, 6, and 13 cal mol-l for La, Pr, Gd, and Lu perchlorates, respectively, with an uncertainty in each of at least &7 cal mol-l. The quantity AH in eq 8 is the integral or total enthalpy for the conversion of the ion exchanger from the LnR3 form to the cerous salt form, CeR3. Its magnitude is given by the area under the differential heat of exchange, AH, vs. composition curve:
AH =
s 0
1
A H dxce =
Q
L
~
~
~
The quantity AR, like K,', was found to be constant independent of the composition within experimental error, hence AH = QLnCe. The standard entropy changes, AS",were derived from AGO and AHo. Numerical values for all of these quantities are summarized in Table I. Standard state thermodynamic property change values for the ion exchange reactions of the trivalent lanthanide ions are useful in that they may be employed to estimate standard Gibbs energies, enthalpies, and entropies for the reactions of these ions in aqueous solutions with other ions of lesser or greater charge. A subsequent paper will report measurements on the lanthanum-sodium ion exchange reaction in dilute aqueous perchlorate solutions which lead to AGO, AH", and ASo values which may be combined with the values of Table I. Discussion Equilibrium constants, KLnCe, for the exchange reactions between cerous ion in 0.01 N perchlorate solution and various lanthanide(II1) cations in the exchanger together with the corresponding standard Gibbs energy change values are given in columns 2 and 3 of Table I. The precision of the KLnCe values is approximately fl70 which reflects the propagation of analytical errors of 0.2-0.3 70 in the Ce(II1) determinations and the fact that the Ln(II1) concentrations were derived from differences between the
The Journal of Physical Chemistry, Vol. 82, No. 25, 1978 2707
Ion-Exchange Reactions of Trivalent Lanthanides
Kn Ce3t t LnR, = CeR, Go,cal mol-’ AH”, cal mol-’
TABLE I : Thermodynamic Property Changes in the Reaction at 298.1 Ln(II1)
KLn Ce
La Ce Pr Nd Pm Sm Eu Gd Tb
0.899 f 0.003 ( 3 ) 1.00 1.087 i: 0.008 ( 4 ) 1.147 i 0.012 ( 3 )
- 6 3 -L 1 0.0 49 i 3 81 i 5
1.270 i 0.012 ( 3 ) 1.397 i 0.007 (3) 1.538 f 0.008 ( 4 ) 1.758 + 0.004 ( 2 ) 1.876 i 0.047 (2) 2.045 t 0.013 ( 2 ) 2.163 i 0.041 ( 2 ) 2.271 i 0.021 (2) 2.337 i: 0.081 (4) 2.397 f 0.049 (2) 2.132 f 0.006 (2)
142 i 5 198 f 3 255 f 3 334j: 2 373 f 1 4 424 f 4 457 j: 1 4 486f 5 503 i 20 518 f 1 2 449 f 1
DY Ho Er Tm Yb Lu Y
-A
t
Ln3+ A S ” , cal mol-’ deg-I
- 0.4
-46 i: 1 2 ( 2 ) 0.0 39 (1) 22 j: 10 (2)
0.0 0.3 0.3
- 235 j: 1 2 (2) -435 i: 1 4 (2) -564 j: 17 ( 4 ) -691 f 2 ( 2 ) -658 j: 2 (2) - 595 f 5 ( 3 ) -472 i 21 ( 2 ) -341 i 11 ( 2 ) -258 f 4 (4) -153 f 15 (3) -556 j: 11 ( 2 )
-0.3
- 0.8 - 1.0 - 1.2 - 1.0 - 0.6
-0.1 0.5 0.8 1.2 - 0.4
a The uncertainties indicated are standard deviations. The number of independent determinations used to obtain the average values are given in parentheses.
total rare earth concentration determined separately and that for cerous ion. The equilibrium constant values in Table I are probably more accurate than any of the few comparable results6J7J8 reported in the literature. A collation may be made with the work of Suds and ChoppinGawho determined distribution coefficients, Kdo, for the exchange reactions of trace concentrations of Ln(II1) ions in 0.110 m HC104 with the H form of a nominal 4 % DVB cross-linked poly(styrenesu1fonate) exchanger. Their values relative to that for Ce(II1) are in fair agreement with those in Table I for La(II1) through Gd(1II) but contrary to Table I their relative distribution coefficients show little or no increase from Tb(II1) through Lu(II1). The preferential uptake of Ce(II1) ion in its exchange reactions with all the Ln(II1) cations excepting La(II1) may be noted in Table I. The lanthanide contraction is reflected in the fact that the relative affinity of Ce(II1) increases progressively as the atomic number, 2, or weight, A , of the lanthanide increases. However, the relative affinity of the quasi-rare earth yttrium which lies between that for Ho(1II) and Er(II1) does not correlate with either 2 or A but rather with its ionic radius (0,900 A for CN = 6)19suggesting that an electrostatic model might correlate the data. The crystal radii of the Ln(II1) ions decrease approximately linearly by ca. 17% in going from Ce(II1) to Lu(II1) as the 4f subshell is filled so that a plot of log KhCeagainst Z should be useful. As may be seen in Figure 1the increase in the selective uptake of Ce(II1) with atomic number is not a monotonic function but discontinuities in slope occur at gadolinium (4P) and probably also between neodymium and promethium (4P-4f4) and between erbium and holmium (4f1°-4f11). This behavior which is superimposed on the effect of the lanthanide contraction has been observed frequently in other types of phase equilibria and has been given the name “tetrad”20,21or “double-double’’ e f f e ~ t .The ~ ~ perturbation ~ ~ ~ of the electrostatic contribution to AGO in Figure 1 is small and is of the same order as the experimental errors in the data, although one-half filled shell effect is clear. Because of the errors in our measurements and the absence of a value for Pm(II1) there can be no great certainty about concluding from Figure 1that discontinuities exist at and 3/4-filled4f shells. However, the data of Choppin and Silva4 on the ion-exchange chromatographic separation of the lanthanides with aqueous a-hydroxyisobutyric acid buffers when plotted as in Figure 1 clearly show discontinuities in the Nd-Pm region and a t Gd but apparently not in the Er-Ho region. These latter data, and other
La
I
C e P r Nd Pm Sm Eu Gd Tb Dy Ha E l Tm Y b
I
I
l
I
I
I
I
I
l
I
I
/
l
LY
I
0.4
DEPENDENCE OF MASS LAW PRODUCT QUOTIENT, K f i FOR THE REACTION LnR, + Ce” = CeR, +Ln3’ ON THE LANTHANIDE ATOMIC NUMBER 57 56 59 60 61 62 63 64 65 66 67 68 69 70 71
ATOMIC NUMBER ( 2 )
Figure 1. Dependence of log K L P on lanthanide(” cation atomic number (broken lines arbtrarily drawn to connect end members of tetrad groups).
considerations, lead us to conclude that it is probable that a “tetrad” effect exists in our AGO values for the Ln(II1) ion exchange equilibria. Theoretical attemptsZ4J5to account for the tetrad effect in the lanthanide(II1) and actinide(II1) series based on a quantitative assessment of interelectronic repulsions in their respective cations have enjoyed some success. The theory indicates in agreement with experiment that the logarithm of the phase equilibrium constant is diminished by about 1%because of the “tetrad” effect (Le., the effect decreased the stability) and that the one-half filled shell effect is about six times larger than the or 3/4-filled shell effects. The presence of a “tetrad” effect in ionexchange equilibria with the lanthanides indicates that the interelectronic repulsions in the Ln(II1) cations differ in the aqueous and ion-exchanger phases possibly because of differences in the “electron cloud expanding effects”25 of the sulfonate ion ligands in the exchanger and the water molecules of the hydrated ion in the aqueous phase. The appearance of the effect which is small therefore has significance because it suggests that the sulfonate groups of the ion exchanger either form inner sphere complexes with the lanthanide cations, or interact strongly with the primary hydration spheres of the cations. Ion-exchange chromatographic separation factors relative to Gd(II1) were computed from the equilibrium
2708
The Journal of Physical Chemistry, Vol. 82,No. 25, 1978 57 1
G. E. Boyd
ATOMIC NUMBER
58 59 60 61 62 63 64 65 66 67 68 69 70 71 1
1
1
I
I
I
I
I
I
l
l
1 1 1 3
Integral Heot of Ion for the Reoction CeStt(R E )R3+ CeR3+IR E
Lanthanide(m) Saporoilon Factors in the Absence and Presence of Complexing Agents
I J
i
wl
qy .
L-Lo a tlydroxy.8sobutyrate buffer a t 67'C Citrate buffer a t IOO°C A Perchlorate solution a t 25°C
Lo
Ce Pr
Nd Pm Sn Eu
Gd Tb
Dy HC Er Tm Yb Lv
LANTHANIDE
Flgure 2. Lanthanide(II1) separation factors in liquid chromatography in the absence and presence of complexing agents in the aqueous phase.
constants in Table I and these are plotted as a function of 2 in Figure 2 where they are compared with a. values derived from ion-exchange chromatographic separations of micro quantities of the rare earths with citrate buffer at 100 0C1,2and with a-hydroxyisobutyrate buffer at 87 0C.4 The substantial increase in a. caused by the formation of rare earth complex ions in the aqueous solution phase in equilibrium with the ion exchanger is readily apparent. The separation factors even for the rare earths in dilute perchloric acid solution are sufficiently large t o permit their efficient chromatographic separation from one another if speed (or eluant volume) were not the limiting factor. Values for the standard enthalpy changes, AH', are listed in the fourth column of Table I where an average precision of approximately A10 cal mol-' is indicated which includes errors in the calorimetry (mainly in the heat of pipet opening) and errors in the analysis for the number of moles of exchange reaction. Heat was evolved in all reactions in which Ce(II1) ion replaced a lanthanide(II1) ion excepting with Pr(III1 and Nd(III), where the thermal effects were barely detectable, A standard Gibbs energy decrease is accompanied by a standard enthalpy decrease in the ion-exchange reaction of Ce(II1) with all lanthanides heavier than Nd. No previous calorimetrically determined ion-exchange reaction enthalpy changes for the lanthanide(II1) ions have been published. Comparisons of the values in Table I with those derived from measurements of the temperature coefficients of equilibrium constants in two reactions can be made, however. An estimate of 170 cal mol-l for the exchange of Tm(II1) ion in aqueous solution with Lu(II1) in the exchanger can be derived from the work of Surls and Choppida which agrees well with the value 188 cal mol-' from Table I. Analogously, a value of -290 cal mol-' at 298.1 K for the reaction of La(II1) with EuR3can be derived from Table IV of Kraus and Riordanls which agrees in sign but not in magnitude with the estimate of -389 .cal mol-' from Table I. A plot (Figure 3) of the AH" values of Table I against the lanthanide atomic number shows unexpected features. Instead of a monotonic increase in exothermicity with 2 as is the case with the hydration s n t h a l p i e ~ ~of ~ , the ~' Ln(II1) cations a broad maximum occurs approximately at Tb(II1) beyond which AH" decreases almost linearly. The behavior exhibited in Figure 3 also contrasts sharply
9
ZOO
57 Lrr
58
Ce
59 PI
60 No
61
62
63
Pni
Srr
Eu
64
GO
65
66
Tb
Oy
67 Ho
68
Er
69
70
Tm
Yb
71 tu
Figure 3. Atomic number dependence of the integral heat of ion exchange of Ce(II1) with the lanthanide("
cations (error bars indicated
on symbols).
with the 2 dependence of the thermodynamic property changes previously observedze in ion-exchange reactions between equally charged cations such as in the alkali-metal or alkaline earth series of cations where the replacement of progressively more strongly hydrated cations by a less strongly hydrated reference cation always occurs with a progressively increasing negative AH" and ASo. The data of Table I in fact indicate that the general trend of the standard enthalpies and entropy of ion exchange of Ce(1II) with increasingly hydrated Ln(II1) ions is normal up to Gd(II1) beyond which some new interaction sets in which makes AH" less negative and AS" more positive. Conceivably changes in ion-solvent interaction may occur. The solvation of the trivalent rare earth ions in aqueous solution is believed to be a consequence largely of electrostatic forces typical of closed electron shell ions. The unfilled 4f subshell in these ions are inner orbitals which do not interact with surrounding molecules or ions, hence non-Coulombic or nonelectrostatic interactions contribute relatively little to the thermodynamic functions of hydration. Available evidence suggests that rare earth cations in strong-acid type cation exchangers exist as hydrated species. The water contents29 of the equilibrium exchangers are more than sufficient for them to retain their primary hydration spheres. Molal chemical NMR shifts30 measured on these exchangers indicate that the hydrated rare earth ions in them are quite similar to those in solution. The magnitudes of the hydration enthalpies and Gibbs energiesz6for Ln(II1) ions are extremely large indicating the presence of very strong ion-water forces. As the crystal radius of the rare earth ion decreases changes may occur in the number of water molecules in the primary hydration shell. Much indirect evidence for this possibility has been collected by Spedding and c o - ~ o r k e r s ~who ~ - ~have ~ suggested that the inner sphere coordination number for water progressively decreases through the rare earth series. In the La-Pm region CN = 9 approximately, while in the Tb-Lu region the number of nearest water neighbors to the cation is approximately 8 on the average. Compensating changes in the outer hydration sphere presumably take place so that the total ionic hydration (and hence hydrated ion size) increases regularly from Ce(II1) to Lu(II1). The atomic number dependence of AHo (Table I and Figure 1)can now be rationalized if the sulfonate groups of the ion exchanger may interact with Ln(II1) ions possessing only primary hydration layers as well as with ions having both inner and outer hydration spheres. Simple electrostatic considerations indicate that fully
Ion-Exchange Reactions of Trivalent Lanthanides
hydrated Ce(II1) ion will exchange with the other fully hydrated (larger) Ln(II1) ions with an energy (enthalpy) decrease. However, the exchange of Ce(II1) ion possessing only a primary hydration sphere with CN = 9 with a smaller Ln(II1) ion possessing CN = 8 must take place with an energy increase. The competition between these two types of exchange reactions appears to be sufficient to give the maximum in the heat evolved in the overall Ce(II1)Ln(II1) reaction plotted in Figure 1. Other types of measurements suggest that ion pairs between sulfonate groups and Ln(II1) cations shorn of their outer hydration spheres may be formed in moderately and in highly cross-linked ion exchangers. For example, the exchange reaction of La3+ with Na’ ion initially in the exchanger occurs with a relatively large volume increasez9 (AVO = 16.5 mL mol-l) suggesting that at least some of the outer sphere hydration of the rare earth ion is lost. The entropy increase%for the same reaction (AS” = 27 cal deg-l mol-l) also is large as expected if water were released. The report36that the sequence of equilibrium constants listed in Table I is reversed in the exchange reactions of the lanthanide ions in a polymethacrylic acid ion exchanger further suggests that anionic (i.e., COO-, for example) exchange groups sometimes may enter the primary hydration sphere and even form “contact” ion pairs with Ln(II1) cations. The results from thermochemical measurements with these kinds of systems will be of the greatest interest.
Acknowledgment. The considerable assistance of Q. V. Larson (deceased) in the various experimental parts of this research, particularly in the numerous chemical analyses required, is gratefully acknowledged. References and Notes (1) B. H. Ketelle and G. E. Boyd, J . Am. Chem. Soc., 69, 2800 (1947). (2) B. H. Ketelle and G. E. Bovd. J. Am. Chem. Soc.. 73. 1860 (1951). (3) G. R. Choppin, B. G. Hariey, and S. G. Thompson, J: Inorg: Nuci. Chem., 2, 66 (1956).
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