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Theoretical treatment of the elution system of rare-earth with dilute H.E.D.T.A. eluant
J. inorg,nucl,Chem,,1970,Vol.32, pp. 291 to 307. PergamonPress. Printedin Great Britain
THEORETICAL SYSTEM
TREATMENT
OF
THE
OF RARE-EARTH WITH H.E.D.T.A. ELUANT
ELUTION DILUTE
ZENZI H A G I W A R A and H I D E O OKI Faculty of Engineering, Tohoku University, Sendal, Japan (First received 24 March 1969; in revised form 1 May1969) A b s t r a c t - T h e elution of a single rare-earth from cation exchange resins has been investigated by means of 0-015 M H.E.D.T.A. buffered solutions at pH-values ranging from 4.9 to 8-8. After the attainment of dynamic equilibrium in the exchange system by moving the rare-earth band through the hydrogen-retaining bed, the constituents in the aqueous and resin phases of the formed bands were determined, and fundamental correlations of the experimental data were found. Also, theoretical treatments of all the species involved in the exchange system have been made, applying material balance, electrical neutrality and other theories. Thus, several theoretical curves were finally obtained in order to check the experimental data. The agreement was excellent. Also, major selectivity coefficients related to the present exchange system were evaluated in detail. INTRODUCTION
USING polyaminoacetic acid eluants buffered with ammonium hydroxide, the separation of the rare-earths has been widely carried out by ion exchange. A solution of N'-(2-hydroxyethyl)-ethylenediamine-N,N,N'-triacetic acid[l] (H.E.D.T.A. or H3Ch) buffered with ammonium hydroxide is effective as the eluant for the heavier rare-earth group [2] as well as the lighter rare-earth group, as shown by the differences in the stability constants of rare earth-H.E.D.T.A. chelates. Recently, one of the authors[3] made theoretical studies of the elution system with heavier rare-earth mixtures, at a high temperature, employing high concentrations of H.E.D.T.A. eluants. It may be valuable to understand the elution mechanisms involved in the ion exchange system of the rare-earth with dilute eluant and with hydrogen-retaining bed. The purpose of this study was to deduce some theoretical relations relating to the species present in each equilibrium band, applying material balance, electrical neutrality and chemical thermodynamics and to predict what is occurring in the exchange columns during an actual separation. Employing 0.015 M H.E.D.T.A. eluants in the pH range of 4.9-8.8, the elution experiments of rare earth are carried out at room temperature in such a manner that equilibrium is obtained through the whole exchange system. Under the experimental conditions described later, the adsorption of H.E.D.T.A. species on the resin in the rareearth band is not so high that the differences in the total concentration of H.E.D.T.A. species between the eluant and the aqueous phase of the rare-earth band, is controlled to a minimum degree. 1. J. R. Morton and D. B. James, J. inorg, nucl. Chem. 29, 2997 (1967). 2. J. E. Powell and F. H. Spedding, Trans. metall. Soc. A.I.M.E. 215, 457 (1959). 3. Z. Hagiwara, J. inorg, nucl. Chem. 31, 2933 (1969). 291
292
z. HAGIWARA and H. OKI
THEORETICAL TREATMENT OF THE RARE-EARTH ELUTION WITH DILUTE H.E.D.T.A. ELUANT It was confirmed that, when the concentrations of rare earth, ammonium and hydrogen ion were plotted against the eluate volume passed through exchange columns, typical flat-top elution curves were obtained over a fairly wide range of dilute H.E.D.T.A. eluants buffered with ammonium hydroxide and over a fairly wide range of pH, which is a function of ammonium hydroxide added to the H.E.D.T.A. eluant. The concentration of all species in the eluates from adsorption bands remained unchanged, within experimental error, after the ion-exchange system had reached steady state. Once equilibrium had been attained in the rare earth band, its length was maintained at a constant value while progressing down the exchange column. Of course, in such a state, all constituents involved in the exchange system, were fixed at their respective values. When a saturated band with the rare earth is displaced down the hydrogen retaining bed for a proper distance to stretch the band to its equilibrium length, several types of adsorption bands are steadily formed in the column, as shown in Fig. 1. If one regards the above exchange system as at equilibrium, it is possible to calculate the equilibrium compositions of all species in both phases of the formed bands by applying electrical neutrality and material balances and by using the ion-exchange equilibrium constants involved in the system. The compositions of species present in the aqueous and resin phases of each band, can be found as a Eluont,Vt.
I
t
ChT
ChT
8
Ch~r
C
D
T Eluate
Fig. l. Elution system with the H.E.D.T.A. eluant buffered with ammonium hydroxide. A: Eluant band; B: Rare earth band; C: H.E.D.T.A. adsorption band: D: Hydrogen
retainingbed.
Theoretical treatment of the elution system
293
function of the eluant composition. In the present study, the adsorption of H.E.D.T.A. on the resin is assumed to be so small that the amount can be neglected in material balance equation (See Chr-values in Table 3).
Notations used Chr = total concentration of anionic species of H.E.D.T.A. in the eluant N H~r = total concentration of ammonium in the eluant total replaceable hydrogen in the eluant Lnr = total concentration of rare-earth species in the rare-earth eluate or the aqueous phase of the rare-earth band Chr = total concentration of anionic species of H.E.D.T.A. in the rare-earth eluate or the aqueous phase of the rare-earth band total concentration of replaceable hydrogen in the rare-earth eluate or the aqueous phase of the rare-earth band Ch'r = total concentration of all H.E.D.T.A. species in the eluate from the H.E.D.T.A. adsorption band LII3 + = amount of rare-earth in the resin phase of the rare-earth band NH4 + = amount of ammonium in the resin phase of the rare-earth band H + = amount of hydrogen in the resin phase of the rare-earth band kl, k2, k3 = dissociation constants of H.E.D.T.A. (H3Ch) Kh = hydrolysis constant due to the reaction:
H'~=
NH4++ H~O ~-~ NH4OH + H + Ln 4 = KNH
apparent exchange constant due to the reaction: Ln3++ 3NH4 + ~ Lna++3NH4 ÷
K ~ H" =
apparent exchange constant due to the reaction: NH4++
H+ ~
N'---'H4++ H +.
The concentrations of the aqueous and resin phases are expressed in moles/l and equivalent fraction, respectively, and the superscript barred quantities denote the resin phase of indicated species.
(1) Analysis of the eluant Generally, the H.E.D.T.A. solutions of 0.015 to 0.018 M as Chr have been employed to separate rare-earth mixtures at room temperature. These solutions were buffered with ammonium hydroxide to desired pH's. Electrical neutrality leads to the following relationship: N'H4r + Hr = 3C"~hr.
(1)
Further NH4r, Hr and Chr are given in the forms --~
NH4T= [NH4 +] + [NH4OH] = [NH4 +]-t
[NH4 +]
[H+~Kh.
(2)
Hr = [H +] + 3 [ H 3 C h ] + 2 [ H 2 C h - ] + [HCh 2 - ] - [ N H 4 O H ] = [H +] + 2 [ C h 3- ]
[NH4 [H+]+] Kn.
Ch"~r= [H3Ch] + [H2Ch-] + [HCh 2- ] + [Ch 3-] = Y[Ch 3-]
(3) (4)
294
Z. HAGIWARA and H. OKI
where Kh is the hydrolysis constant due to the hydrolysis of ammonium in the eluant with a high pH. Kh =
[NHaOH] [H +] [NH4+]
(5)
and ? and Z are expressed as a function of hydrogen ion concentration. Y=
[H+] 3 , [H+] ~_ [H + ] _ -r---r ~-r 1. k,'k2"k3 k2"k3 3
2=3[H+]3'
2[H+32
(6)
[H+]
k.k2.k3-r k2--~k~ 4 ~
(7)
Combining Equations (1-4), one obtains
~ir=3C'-~hr_N"~4r= [H+] + ~ ~'~r
NH4T'Kn [H + ] + Kh
(8)
Equation (8,.~)c a n b e use,....,dto calculate the hydrogen ion concentration for given values of Chr, Hr or NH4r. In addition, various ionic species present in the eluant can be found. One example is represented in Fig. 2, in which pH is plotted against N"~4r. At Ch"~= 0"015 M the data points are close to the theoretical line. Io
86 C'h=0"015~ r i
4
Z o
~
r_h,o,
J
•
I
l
I.O
I
Exp.
I
2.0
I
I
3-0
N NH4T/Ch T
Fig. 2. Calculated pH-values of the eluants
prepared.
(2) Analysis of the eluant band During elution, the eluant itself would be expected to be close to equilibrium with the resin phase of the eluant band, and the ion-exchange reaction involved may be expressed as follows: N H 4 + + H + ~- N H 4 + + H +.
Theoretical treatmentof the elutionsystem
295
The barred symbols refer to the resin phase and the unbarred symbols to the aqueous phase. The selectivity coefficient is written by
KN.,
[NH4 +] [H +] = [NH4+] [H+]"
(9)
Introducing the relation that the sum of NH4 ÷ and H ÷ is equal to unity in the resin into Equation (9), we have [NH4 +] -
[NH4+] " KNH4 [H +] + [NH4 +] K~H,"
(10)
In the experimental conditions described in Table 2, the concentrations of hydrogen and ammonium ions in the eluant are 10-5-10 -8 and 1.8 × 10-2 to 3.8 × 10-2 moles/l respectively. Therefore, ammonium ion in the resin is approximately equal to unity. In other words, the resin phase of the eluant band is saturated with ammonium. At the front boundary of the eluant band, the ammonium ions are transferred into the resin phase in order to displace the rare-earth ions into the aqueous phase of the rare-earth band, according to the exchange reaction: 3NH4 + + Ln 3+ + Ch a- ~ 3NH4 + + L n C h .
(11)
In the beginning of the elution step, ammonium ion as well as hydrogen ion in the eluant band, leaks slowly into the saturated rare-earth band so that spreading takes place to reach the equilibrium band whose composition is finally dominated by the eluant itself. In such a system, at the front edge of the eluant band, all of ammonium ion present in the aqueous phase deposits on the resin behind the rareearth band in order to substitute for the tripositive rare-earth ions. Let us consider the material balance of ammonium ion at the front boundary of the eluant band. When V(l) of the eluant is passed, the front moves down the column corresponding to E equivalents, and the ammonium ion balance is represented in the form: ( V - - f E ) N H 4 r = E.NH4 +
(12)
where f denotes the volume (/) of the eluant surrounding one equivalent of the resin bed, and NH4 + is equal to unity. The term f E in Equation (12) can be neglected. Thus, when there is no leak of ammonium ions, the front boundary of the eluant moves at the following rate: E
i-7= NH4r.
( 13 )
A similar relation [4] was observed in the elution of the rare-earth with 0.1 per cent citric acid buffered with ammonium hydroxide. 4. F. H. Speddingand J. E. Powell,J.Am. chem. Soc. 76, 2545 (1954).
296
z. HAGIWARA and H. ()K1
(3) Analysis of the rare-earth band After the establishment of equilibrium through the rare-earth band, the exchange equilibrium should be maintained between the species in both phases. The main reaction is Ln3++ 3NH4 + ~ Ln3++ 3NH4 + and the exchange constant is given Ltl KNH4
[ L--fi3+] [NH4+]3 [Ln3+] [~-~4+] 3.
(14)
Further the ion exchange between ammonium ion and hydrogen ion on the resin is expressed by NH4++H +~ NH4++H + and the exchange constant becomes
K~H,= [~q--fl,÷] [Iq÷]
[NH4+][R+]"
(15)
The formation of Ln-H.E.D.T.A. chelate is expressed Ln 3+ + Ch 3- ,~ LnCh and KLnChis written by [LnCh] KLnCh= [Ln3+] [Ch~_].
(16)
In the aqueous phase of the rare-earth band, the following species are mainly present:
LnCh, Ln 3+, NHa ÷, H ÷, Ch 3-, HCh 2-, H2Ch-, H3Ch. As already noted in the previous section, by passing through V(l) of the eluant, the front boundary of the eluant band progresses down the column proportional to E equivalents. Since there is no net transport of ammonium ion through both boundaries of the rare-earth band at equilibrium, all of the ammonium ion in the solution are considered to deposit on the resin at the front of the rare earth band. Thus we have the material balance equation NH4TV = N H +E
(17)
where NH4T in the rare-earth band is assumed to be present completely in the dissociated form. All of the rare earth in the resin may be transferred into the aqueous phase and picked up again on the resin at the front boundary. Thus, we have the following relationship:
Theoretical treatment of the elution system 3LnrV = LnS+E.
297 (18)
Further, the material balance for hydrogen may be expressed by (HT-- H r ) V = Ft+E
(19)
Introducing Equation (13) into Equations (17-19), the constituents in the resin phase are written in the forms L---fi3+ = 3Lnr NH4r NH4 + =
(20)
[NH4+]
(21)
NH4T
~t + __ Hr-- Hr
NH4r
(22)
Combination of Equations (20, 21 and 14) gives Lnr-
3+
Ln
[Ln ]KNH , 3 (N,-.~,r) 2
(23)
From Equations (15, 21 and 22), we see that H r = HT-F [~H~+H ] • m
(24)
O n the other hand, Lnr, Hr and Chr in the rare-earth aqueous phase are expressed
as follows: Lnr = [LnCh] + [Ln s+] Hr = [H +] + [HCh 2-] + 2 [ H 2 C h - ] +3[H3Ch]
(25) (26)
Chr = [LnCh] + [Ch 3-] + [HCh 2-] + [H2Ch-] + [HsCh] = [LnCh] ~ f'[Ch3-].
(27)
From Equations (16, 23 and 25), we find that [Ch3_ ] = K ~ , - 3(N"~4T) 2 3 (N~4T) 2" KLnCh"
(28)
Introducing Equations (7) and (24) into Equation (26), one obtains 1
[ H +] -- 1--KNm ( H , r - Z [ C h s- ] ).
(29)
298
z. HAGIWARA and H. ()KI
Combining Equations (6) and (16) into Equation (27), Chr is found
Chr = ( [Ln3+]KLnch + Y) [Ch3-].
(30)
At the present time, Chr in the aqueous phase of the rare-earth band is assumed to be approximately equal to that of Chr in the eluant. This is due to the following reasons. First, though the utilization of a dilute H.E.D.T.A. eluant causes the sorption of H.E.D.T.A. species on the resin, the degree is not large under the present experimental conditions. Secondly, a dilute eluant has no serious effect on the equilibrium condition. Phenomena such as swelling or shrinking observed in the exchange reactions are not so predominant in the present system that the change in ChT is kept to a small extent. Thus, Equation (30) is written in the form
Chr = ( [Ln 3+] KLnch + re) [Ch3-].
(31)
Since a solution should remain neutral, the sum of the positive charges of the ions must be equal to that of the negative charges. Thus, we may write [NH4 +] + [H +] + 3 [ L n 3+] = [H2Ch-] + 2 [ H C h 2-] + 3 [ C h 3-] = )([Ch 3-]
(32)
where .,~- [H+] 2 ~_2[H+] +3" k~.k3 k 3
(33)
If the compositions of eluant and the ion-exchange constants involved in the elution system are known, it is possible to find the concentrations of all species in either the resin or the aqueous phase of each adsorption band, as a function of the eluant composition. The right hand term is known, it is possible to calculate [Ch 3- ] from Equation (28). [H ÷] can be found from Equation (29). [Ln 3+] and [NH4 ÷] can be found from Equations (31) and (32), respectively. In addition, the other species in both phases can be calculated with the aid of the relations described. (4) Analysis o f the H.E.D.T.A. adsorption band When the rare-earth band is eluted down the hydrogen-retaining bed by means of a dilute solution of buffered H.E.D.T.A. with ammonium hydroxide, the H.E.D.T.A. adsorption band is formed between the retaining bed and the rare earth band due to the association of hydrogen ion with the H.E.D.T.A. species on the resin. The adsorbed form is close to HsCh 2+, which is formed by the reaction: H3Ch+2IT-I + ~---HsCh z÷ (C---hr'/E* ~ 0.5 in Table 1). The HsCh2+-band was studied by Powell et al.[5], and the more general treatment[6] on the sorption of H.E.D.T.A. species on the resin was made by the authors in a fairly wide range of the H.E.D.T.A. concentrations. Therefore, we only refer to the material balance of the H.E.D.T.A. species and the rate of growing of the H.E.D.T.A. band. 5. J. E. Powelland F. H. Spedding,Chem. Engng Prog.,Symp. Ser. 55, 101 (1959). 6. Z. Hagiwaraand H. Oki,Bull. chem. Soc. Japan. To be published.
Theoretical treatment of the elution system
299
Table 1.6~T'/E*-values concerning the H.E.D.T.A. adsorption band Exp. No.
Chr'lE*
12 13 14 15 16
0.488 0-499 0-506 0-487 0.481
Chr' and E* are expressed in moles and equivalents, respectively, per small attached column.
After the passage of V(I) of the eluant, the material balance of the total: H.E.D.T.A. species at the boundary between the rare earth and H.E.D.T.A. band is given by 2(Chr' - C h r ) V = H~Ch 2+ . E.
(34)
Using H,~C h 2+ = 1.00 and E / V = N H4r, Equation (34) is rearranged in the form Chr' - N ~ -H4T ~-ChT.
(35)
Thus, if C h r is equal to ~ r , Chr' can be expressed as a function of the composition of eluant. On the other hand, at the front of the H.E.D.T.A. band, H s C h 2÷ is formed, and its band is steadily expanded with the increase in time, as seen in Fig. 3. When V(l) of the eluant is passed through the top of a column, the front of the H.E.D.T.A. band moves to a distance proportional t,o E' equivalents in the column. IOO
50
_1
o
5.0
I0.0
Eluote volume, I
Fig. 3. Movement of boundaries in the column.
15-0
300
Z. H A G I W A R A and H. OK1
2ChT'V =
H5C~2+E
'
or
(36)
2ChT'V = E'.
Combining Equations (35) and (36), the rate of growing is given by Et
--~ = NH4T+ 2ChT.
(37)
Comparing Equation (13) with (37), the rate of movement of the front of H.E.D.T.A. band is greater than that of rare-earth band, and the difference is equal to 2Chr. EXPERIMENTAL
Materials. The erbium oxide was prepared in a pure state by means of ion exchange and its purity was greater than 99.99 per cent. The citric acid employed for pre-conditioning the resin was reagent grade. Using analytical grade H.E.D.T.A. (H3Ch), 0.015 M eluants as C--~.were prepared, and these solutions were buffered with ammonium hydroxide in the pH range of 4.9-8.8. All other reagents used were analytical grade. A sulfonated styrene-divinylbenzene coploymer, Dowex 50W, X-8, 100-200 mesh, was used as ion exchanger. Experimental method. The ion-exchange columns were constructed of I.D. 1.5 cm-pyrex glass tubing. The bottom of each column was closed with a sintered glass disc in order to support the resin bed containing Dowex 50W, X-8, 100-200 mesh. The columns were back-washed with water, treated with 2 M HCI and 5 per cent citric acid solution. These were finally washed with water. The resulting resin beds were 66-79 cm in length, as listed in Table 2. Samples of erbium oxide were dissolved with a little excess of HC1 by heating, and these chloride solutions were kept slightly acidic by dilution with water. These solutions were then adsorbed on the hydrogen form beds to prepare the erbium type column. The columns were then washed with distilled water until free of chloride. The dimensions of the prepared beds are listed in Table 2. The Er-adsorption bed was connected to the hydrogen retaining-bed, and small appendages, with a bed dimension of 1.5 cm (I.D.) × 5 cm in the hydrogen form, were attached to determine the composition of resin phase (Fig. 4.). The elution of erbium was made with the H.E.D.]'.A. eluant at a definite flow rate, and the eluates from the formed bands were collected into small fractions by means of a fraction collector. These fractions were analyzed by the following methods. ,4nalytical Methods (a) Aqueous phase. Total H.E.D.T.,4. species. Total anionic species of H.E.D.T.A. in the eluant or the eluate from the H.E.D.T.A. adsorption band were determined by chelometry with a standard Table 2. Experimental conditions used for the elutions of Er-band Composition of eluant (mole/l) Exp. No.
C'-hr
N~H4T
pH
12 13 14 15 16
0.01500 0.01500 0.01500 0.01500 0.01500
0.03096 0.03104 0.03830 0.02611 0.01840
7.43 7.45 8.82 5.92 4-91
Column length* (cm) Er-adsorption Retaining bed (sated. form) bed (H-type) 17.8 17.3 17.3 17.3 18.5
79.1 69.7 69.7 69.7 66.0
Linear flow rate (cm/min) 0.45 0.85 0.85 0.85 0.91
*I. D.-I.5 cm column. Resin used: Dowex 50W, X-8,100-200 mesh; elution temperature: 25°C.
Theoretical treatment of the elution system
301
F.luant
A
\
D
collector
Fig. 4. Schematic representation of ion exchange columns. A: Rare earth adsorption column; B: hydrogen retaining bed; C: small columns for the determination of constituents in the resin phase; D: sintered glass disc as resin supporter; resin used: Dowex 50W, X-8,100-200 mesh. solution of ZnC1 z and with E.B.T. indicator. The titration was made in the presence of the NH4CINH4OH buffer solution (pH = I0). Er-determination. Total erbium in the rare-earth fraction was precipitated as the oxalate and then ignited to the oxide for weighing. Ammonium-determination. Total ammonium in the eluant or the eluate was determined by the usual Kjeldahl method. Methyl purple was used as the indicator for the titration of ammonia with the standard HCI. Chf-determination. The excess of H.E.D.T.A. species, which are present in the uncombined form with erbium, was titrated with a standard solution of ErCI3, using Arzonoazo-indicator [3-2(2-arzono~ phenylazo)-4,5-dihydroxy-2,7-naphthalene-disulphonicacid]. For the titration, pyridine was added to keep the pH between 5-5 and 6.0. (b) Resin phase After the elution system had approached an equilibrium state, small appendages attached to the main column were taken off for the analysis of resin phase. The small appendages for the H.E.D.T.A~ adsorption band were eluted with 2 M NH4C1, and the total anionic species of H.E.D.T.A. in the eluates were determined by chelometry, according to the described method. The constituents in the erbium band were determined after eluting them with 3 M NaCI. The content of erbium was determined gravimetrically using a method similar to that mentioned in the pre+ ceding section. Ammonium ion was determined by the Kjeldahl method, and hydrogen ion was measured using a glass electrode. RESULTS AND DISCUSSION
(1) E l u t i o n c u r v e s . In the initial step of elution, the length of the Er-band stretched to some extent, due to the leakage of ammonium ion or hydrogen ion in the eluant band through the rare-earth band, and then approached a steady state. On the other hand, the leading edge of the H.E.D.T.A. adsorption band
302
Z. H A G I W A R A and H. OKI
progressed down the column at a constant rate, and the rear boundary moved steadily, but more slowly than the leading edge, as shown in Fig. 3. Equation (37) explains the above fact well. It is clear from a typical elution curve in Fig. 5 that the total concentration of Er or NH4 rose very sharply to values which remained almost constant until the tail end of the rare-earth band was eluted from the column. At this point, either the concentration of ammonium or the pH of the eluate approached quickly to their respective values in the eluant. (2) Composition of both phases. The elution results are given in Table 3, which shows that the erbium concentration in the eluate decreased with decreasing ammonium ion in the eluant, while the erbium content in the resin increased with increasing NH4r. Further, due to the adsorption of H.E.D.T.A. on the resin, the total concentration of anionic species.~of H.E.D.T.A. (ChT) increased slowly with the increase in the concentration of N H4r. In order to check Equation (35), some calculations were made, as tabulated in Table 4, in which the agreement is observed between the terms Ch'r and [(N"H4T/2) + Ch'-~T]. The values of [~'H4r/2+ Chr] are always slightly higher than the Ch~-values owing to the sorption of H.E.D.T.A. on the resin. Material balance Equations (17) and (18) were checked with the aid of the experimental
30 ~
Exp.No.12 o
1
C~r
~
_e2o E E
P
I
o
•
~r"------'-'!8 6
, .
.
.
.
.
/-
c IO o tO
I
0
7
I 8
I
i 9
I I0
~t I II
0
12
F'luatevolume,l. Fig. 5. Total elution curves obtained by the elution of Er with 0.015M H.E.D.T.A. eluant (Exp. No. 13). ~, : Position where small appendages were taken off.
Table 3. Composition of both phases obtained by the elutions of Er-band with 0.015M H.E.D.T.A. buffered solutions in the pH range of 4.9-8.8
Exp. No,
E-~a+
12 13 14 15 16
0-818 0-811 0"925 0.702 0"393
*Cht = C h r - ErT.
Resin phase (eq. fraction) NH4 + 0.172 0,177 0,064 0,283 0.589
1~+
0.010 0"013 0"011 0"015 0"018
Err
0-00857 0.00866 0"01230 0"00612 0'00240
Aqueous phase (mole/l) NH4r Chr Chl* 0-00540 0.00578 0"00249 0"00761 0-01090
0.01541 0'01589 0"01596 0"10529 0.01504
0.00684 0"00724 0.00367 0.00918 0'01267
pH 3'25 3-27 3' 17 3'28 3"29
Theoretical treatment of the elution system
303
data, and the results are tabulated in Table 5. The agreement between Er3+/3Err and N H4+/N H4v was excellent. (3) Ion-exchange reaction involved in the system. As already noted in Section (3), if the composition of eluant is known, all of the compositions involved in the exchange system can be found by assuming true equilibrium in the system. In this Lrl case, it is necessary to know the values of the exchange constants such as KNn4 and K NH', which are dependent on ionic strength of the solution, the composition of the resin phase and the temperature. The exchange constants, K NH', found from the elution experiments are listed in Table 6, in which the resin and aqueous phases are expressed in the Table 4. Comparison of Chr' with NH4r/2 + ChT
Exp. No.
(mole/l)
Chr,
NH4r/2 + Chr (mole/l)
N~H4r/2 + C"thr* (mole/l)
12 13 14 15 16
0.03013 0.03060 0.03424 0.02816 0.02386
0.03089 0.03141 0.03511 0.02834 0.02424
0.03048 0.03052 0.03415 0.02806 0.02420
* Chr = Chr (Calcd., neglecting the adsorption of H.E,D.T.A.). Table 5. Material balance of ammonium and rare earth expressed by Equations (17 and 18). Exp. No.
Er 3+ 3Err
NH4+ NH4r
12 13 14 15 16
31.8 31.2 25.1 38.2 54.6
31.9 30.6 25-7 37-2 54.0
Resin phase: equivalent fraction. Aqueous phase: equivalent per liter. Table 6. Selectivity coefficient, K Nn, obtained from the elution experiments
Exp. No.
Kr~n', (25°C)
12 13 14 15 16
1'7 1.3 1.6 1.3 1.5
304
Z. H A G I W A R A and H. OKI
equivalent fraction and moles/l, respectively. Bonner[7] investigated the ion exchange equilibria for the NH4-H system, using various degrees of cross-linked resins, and the rational thermodynamic constant / ~ n , was found graphically to be 2.0 for Dowex 50, X-8, employing log/("Nn, = f~ log K~ H, dNNH, where N is the equivalent fraction of indicated species in the resin. In order to study the elution system, the mean value of K~ a, = 1.5 was used without any trouble (Figs. 6 and 7). To calculate the "~NH4/L ' nin Equation (14), the concentration of tripositive rare earth ions should be found. However, the amount is too small to determine directly. It is possible to calculate [Ln 3+] as follows: Combination of Equations (16, 25 and 27) yields ~'[LnCh] [Ln3+] = KLnch(Chr--Lnr) "
(34)
[LnCh] is approximately equal to Lnr at [LnCh] >> [Ln3+]. Y'.Lnr [Ln3+] = KLnch(Chr--Lnr)"
(35)
Introducing Equation (35) into Equation (14) L. _ [NH4+]3[ E-fi'~+](Chr-- LnT)KL.ch [NH4+] 3 . LnT. Y
KNH 4 - -
(36)
The K rr -values were found from Equation (36). The results are listed in Table 7. Table 7. Selectivity coefficient, KNn, rr obtained from the elution experiments
Exp. No.
Er KNH4 (25°C)
12 13 15
42 49 49
The following experiments were carried out in order to determine the reliability of the KNr[i,-values obtained from the elution experiments. Under almost similar experimental conditions to Exp. 12-13, the erbium band was eluted down the hydrogen-retaining bed, and the erbium eluate from the column was used as the aqueous phase for the batch equilibrium experiment. The composition of Ereluate was as follows: Err = 8-69 mmol/l; [NH4 +] = 5.29 mmol/l; Chr = 15-67 mmol/l; pH = 3,27. 7. O. D. Bonner, J. phys. Chem. 58, 318 (1954).
Theoretical treatment of the elutiou system
305
On the other hand, saturated resins with Er o r NH4 were prepared separately by the column method, using Dowex 50W, X-8, 50-100 mesh. They were dried at 50°C for 24 hr under a reduced pressure. The exchange capacities of the prepared resins were as follows: Er-type of resin = 3.75 meq/g-resin (Er-form); NH4-type of resin = 4.33 meq/ g-resin(NH4-form). Both types of resins were taken so that the constituents in Table 8. K~,-values obtained by equilibrium experiment
Exp. No. 1 2
Resin phase (eq. fraction) E-r~+ N H 4-~ H+ 0-77% 0-7776
0.2012 0.2025
0.0192 0-0199
Err 8-59 8'59
Aqueous phase (mmole/l) NH~r Chr 5.55 5-68
15'30 15'32
pH
KNmEr (25°C)
3'39 3.40
43 45
the resin were kept to 0.8 as Er and 0.2 as NH4 equivalent fraction. A total of approximately 5 g of the two kinds of resins were mixed up with about 500 ml. o f the above Er-eluate, and the resulting mixture was maintained at 25°+__0. I°C for 48 hr in a thermostat under occasional stirring. After equilibration, both phases were separated for analysis. The results are shown in Table 8. Although the ion exchange study with polyvalent ions so far has not been developed well, the exchange constants in Table 7 appear to be reasonable from a comparison of the K~,-values obtained from both methods. Really, an approach to equilibrium is a remarkable fact in such a complexed elution system. (4) Solution of the rare earth band as a function of the composition of eluant As already mentioned in Section 3, when the composition of eluant is known the concentrations of all species present in both phases of the rare-earth band can be calculated under the assumption of true equilibrium in the exchange system. In the present calculations, the following values are used:
pka = 2"39; pk2 = 5"37; pk3 = 9-93 [8] KEtch = 1"48 × 101~[9]; KNH4 _ g r __ 45*; K~u4 = 1"5" Further, Chr is assumed to be the same as Chr, neglecting the sorption of H.E.D.T.A. on the resin of the rare-earth band. Figure 6 shows that the experi~ mental plots related to the aqueous phase of the rare-earth band are consistent with the calculated lines, whereas in a region greater than 30 mmole/l as N'H~r the observed values of Chr are greater than the calculated values due to a tendem cy for increased sorption of the H.E.D.T.A. species into the resin with an increase in NH4r. * Found from the present investigation. 8. T. Moeller and R. Ferrus, J. inorg, nucl. Chem. 20, 261 (1961). 9, F. H. Spedding, J. E. Powell and E. J. Wheelwright, J. Am. chem. Soc. 78, 34 ~1956).
306
Z. H A G I W A R A and H. OKI 40
/
C'hT: O" 015 M
\\
30
/
c,;
',~ ,7" m o E E ?
Z,
%
~o
u
I% % •
o
,o
¢,, .
. I
~
1
0
I0
20
3O
40
5O
NH4rr, m m o ~ l l
Fig. 6. Plots of the experimental data related to the aqueous phase against ~-~"n4r. Theoretical lines are shown by solid and dotted lines.
0.8
go6 e
R+ A
Solid lines: Theor.
Q.
c 0"4
~ 0'2
0
I0
20
30
40
50
NH4T, mmole/l
Fig. 7. Plots of the experimental data related to the resin phase against NH~r.
Theoreticaltreatmentof the elutionsystem
307
Furthermore, all of the constituents in the resin phase of the rare-earth band are calculated as a function of the eluent composition, as represented in solid lines in F ~ . 7, in which is kept to 0.015M. The plots of E--~3+,~-~4 + and H+ against N H4r are on the related theoretical curves. | t is concluded from the described results that the compositions of both phases of the formed bands in the elution system are fixed by the composition of eluant itself. The agreement of the experimental and calculated values indicates that the ion-exchange system described is considered to be close to equilibrium under the elution conditions" used.
Ch"~
THEORETICAL SYSTEM
TREATMENT
OF
THE
OF RARE-EARTH WITH H.E.D.T.A. ELUANT
ELUTION DILUTE
ZENZI H A G I W A R A and H I D E O OKI Faculty of Engineering, Tohoku University, Sendal, Japan (First received 24 March 1969; in revised form 1 May1969) A b s t r a c t - T h e elution of a single rare-earth from cation exchange resins has been investigated by means of 0-015 M H.E.D.T.A. buffered solutions at pH-values ranging from 4.9 to 8-8. After the attainment of dynamic equilibrium in the exchange system by moving the rare-earth band through the hydrogen-retaining bed, the constituents in the aqueous and resin phases of the formed bands were determined, and fundamental correlations of the experimental data were found. Also, theoretical treatments of all the species involved in the exchange system have been made, applying material balance, electrical neutrality and other theories. Thus, several theoretical curves were finally obtained in order to check the experimental data. The agreement was excellent. Also, major selectivity coefficients related to the present exchange system were evaluated in detail. INTRODUCTION
USING polyaminoacetic acid eluants buffered with ammonium hydroxide, the separation of the rare-earths has been widely carried out by ion exchange. A solution of N'-(2-hydroxyethyl)-ethylenediamine-N,N,N'-triacetic acid[l] (H.E.D.T.A. or H3Ch) buffered with ammonium hydroxide is effective as the eluant for the heavier rare-earth group [2] as well as the lighter rare-earth group, as shown by the differences in the stability constants of rare earth-H.E.D.T.A. chelates. Recently, one of the authors[3] made theoretical studies of the elution system with heavier rare-earth mixtures, at a high temperature, employing high concentrations of H.E.D.T.A. eluants. It may be valuable to understand the elution mechanisms involved in the ion exchange system of the rare-earth with dilute eluant and with hydrogen-retaining bed. The purpose of this study was to deduce some theoretical relations relating to the species present in each equilibrium band, applying material balance, electrical neutrality and chemical thermodynamics and to predict what is occurring in the exchange columns during an actual separation. Employing 0.015 M H.E.D.T.A. eluants in the pH range of 4.9-8.8, the elution experiments of rare earth are carried out at room temperature in such a manner that equilibrium is obtained through the whole exchange system. Under the experimental conditions described later, the adsorption of H.E.D.T.A. species on the resin in the rareearth band is not so high that the differences in the total concentration of H.E.D.T.A. species between the eluant and the aqueous phase of the rare-earth band, is controlled to a minimum degree. 1. J. R. Morton and D. B. James, J. inorg, nucl. Chem. 29, 2997 (1967). 2. J. E. Powell and F. H. Spedding, Trans. metall. Soc. A.I.M.E. 215, 457 (1959). 3. Z. Hagiwara, J. inorg, nucl. Chem. 31, 2933 (1969). 291
292
z. HAGIWARA and H. OKI
THEORETICAL TREATMENT OF THE RARE-EARTH ELUTION WITH DILUTE H.E.D.T.A. ELUANT It was confirmed that, when the concentrations of rare earth, ammonium and hydrogen ion were plotted against the eluate volume passed through exchange columns, typical flat-top elution curves were obtained over a fairly wide range of dilute H.E.D.T.A. eluants buffered with ammonium hydroxide and over a fairly wide range of pH, which is a function of ammonium hydroxide added to the H.E.D.T.A. eluant. The concentration of all species in the eluates from adsorption bands remained unchanged, within experimental error, after the ion-exchange system had reached steady state. Once equilibrium had been attained in the rare earth band, its length was maintained at a constant value while progressing down the exchange column. Of course, in such a state, all constituents involved in the exchange system, were fixed at their respective values. When a saturated band with the rare earth is displaced down the hydrogen retaining bed for a proper distance to stretch the band to its equilibrium length, several types of adsorption bands are steadily formed in the column, as shown in Fig. 1. If one regards the above exchange system as at equilibrium, it is possible to calculate the equilibrium compositions of all species in both phases of the formed bands by applying electrical neutrality and material balances and by using the ion-exchange equilibrium constants involved in the system. The compositions of species present in the aqueous and resin phases of each band, can be found as a Eluont,Vt.
I
t
ChT
ChT
8
Ch~r
C
D
T Eluate
Fig. l. Elution system with the H.E.D.T.A. eluant buffered with ammonium hydroxide. A: Eluant band; B: Rare earth band; C: H.E.D.T.A. adsorption band: D: Hydrogen
retainingbed.
Theoretical treatment of the elution system
293
function of the eluant composition. In the present study, the adsorption of H.E.D.T.A. on the resin is assumed to be so small that the amount can be neglected in material balance equation (See Chr-values in Table 3).
Notations used Chr = total concentration of anionic species of H.E.D.T.A. in the eluant N H~r = total concentration of ammonium in the eluant total replaceable hydrogen in the eluant Lnr = total concentration of rare-earth species in the rare-earth eluate or the aqueous phase of the rare-earth band Chr = total concentration of anionic species of H.E.D.T.A. in the rare-earth eluate or the aqueous phase of the rare-earth band total concentration of replaceable hydrogen in the rare-earth eluate or the aqueous phase of the rare-earth band Ch'r = total concentration of all H.E.D.T.A. species in the eluate from the H.E.D.T.A. adsorption band LII3 + = amount of rare-earth in the resin phase of the rare-earth band NH4 + = amount of ammonium in the resin phase of the rare-earth band H + = amount of hydrogen in the resin phase of the rare-earth band kl, k2, k3 = dissociation constants of H.E.D.T.A. (H3Ch) Kh = hydrolysis constant due to the reaction:
H'~=
NH4++ H~O ~-~ NH4OH + H + Ln 4 = KNH
apparent exchange constant due to the reaction: Ln3++ 3NH4 + ~ Lna++3NH4 ÷
K ~ H" =
apparent exchange constant due to the reaction: NH4++
H+ ~
N'---'H4++ H +.
The concentrations of the aqueous and resin phases are expressed in moles/l and equivalent fraction, respectively, and the superscript barred quantities denote the resin phase of indicated species.
(1) Analysis of the eluant Generally, the H.E.D.T.A. solutions of 0.015 to 0.018 M as Chr have been employed to separate rare-earth mixtures at room temperature. These solutions were buffered with ammonium hydroxide to desired pH's. Electrical neutrality leads to the following relationship: N'H4r + Hr = 3C"~hr.
(1)
Further NH4r, Hr and Chr are given in the forms --~
NH4T= [NH4 +] + [NH4OH] = [NH4 +]-t
[NH4 +]
[H+~Kh.
(2)
Hr = [H +] + 3 [ H 3 C h ] + 2 [ H 2 C h - ] + [HCh 2 - ] - [ N H 4 O H ] = [H +] + 2 [ C h 3- ]
[NH4 [H+]+] Kn.
Ch"~r= [H3Ch] + [H2Ch-] + [HCh 2- ] + [Ch 3-] = Y[Ch 3-]
(3) (4)
294
Z. HAGIWARA and H. OKI
where Kh is the hydrolysis constant due to the hydrolysis of ammonium in the eluant with a high pH. Kh =
[NHaOH] [H +] [NH4+]
(5)
and ? and Z are expressed as a function of hydrogen ion concentration. Y=
[H+] 3 , [H+] ~_ [H + ] _ -r---r ~-r 1. k,'k2"k3 k2"k3 3
2=3[H+]3'
2[H+32
(6)
[H+]
k.k2.k3-r k2--~k~ 4 ~
(7)
Combining Equations (1-4), one obtains
~ir=3C'-~hr_N"~4r= [H+] + ~ ~'~r
NH4T'Kn [H + ] + Kh
(8)
Equation (8,.~)c a n b e use,....,dto calculate the hydrogen ion concentration for given values of Chr, Hr or NH4r. In addition, various ionic species present in the eluant can be found. One example is represented in Fig. 2, in which pH is plotted against N"~4r. At Ch"~= 0"015 M the data points are close to the theoretical line. Io
86 C'h=0"015~ r i
4
Z o
~
r_h,o,
J
•
I
l
I.O
I
Exp.
I
2.0
I
I
3-0
N NH4T/Ch T
Fig. 2. Calculated pH-values of the eluants
prepared.
(2) Analysis of the eluant band During elution, the eluant itself would be expected to be close to equilibrium with the resin phase of the eluant band, and the ion-exchange reaction involved may be expressed as follows: N H 4 + + H + ~- N H 4 + + H +.
Theoretical treatmentof the elutionsystem
295
The barred symbols refer to the resin phase and the unbarred symbols to the aqueous phase. The selectivity coefficient is written by
KN.,
[NH4 +] [H +] = [NH4+] [H+]"
(9)
Introducing the relation that the sum of NH4 ÷ and H ÷ is equal to unity in the resin into Equation (9), we have [NH4 +] -
[NH4+] " KNH4 [H +] + [NH4 +] K~H,"
(10)
In the experimental conditions described in Table 2, the concentrations of hydrogen and ammonium ions in the eluant are 10-5-10 -8 and 1.8 × 10-2 to 3.8 × 10-2 moles/l respectively. Therefore, ammonium ion in the resin is approximately equal to unity. In other words, the resin phase of the eluant band is saturated with ammonium. At the front boundary of the eluant band, the ammonium ions are transferred into the resin phase in order to displace the rare-earth ions into the aqueous phase of the rare-earth band, according to the exchange reaction: 3NH4 + + Ln 3+ + Ch a- ~ 3NH4 + + L n C h .
(11)
In the beginning of the elution step, ammonium ion as well as hydrogen ion in the eluant band, leaks slowly into the saturated rare-earth band so that spreading takes place to reach the equilibrium band whose composition is finally dominated by the eluant itself. In such a system, at the front edge of the eluant band, all of ammonium ion present in the aqueous phase deposits on the resin behind the rareearth band in order to substitute for the tripositive rare-earth ions. Let us consider the material balance of ammonium ion at the front boundary of the eluant band. When V(l) of the eluant is passed, the front moves down the column corresponding to E equivalents, and the ammonium ion balance is represented in the form: ( V - - f E ) N H 4 r = E.NH4 +
(12)
where f denotes the volume (/) of the eluant surrounding one equivalent of the resin bed, and NH4 + is equal to unity. The term f E in Equation (12) can be neglected. Thus, when there is no leak of ammonium ions, the front boundary of the eluant moves at the following rate: E
i-7= NH4r.
( 13 )
A similar relation [4] was observed in the elution of the rare-earth with 0.1 per cent citric acid buffered with ammonium hydroxide. 4. F. H. Speddingand J. E. Powell,J.Am. chem. Soc. 76, 2545 (1954).
296
z. HAGIWARA and H. ()K1
(3) Analysis of the rare-earth band After the establishment of equilibrium through the rare-earth band, the exchange equilibrium should be maintained between the species in both phases. The main reaction is Ln3++ 3NH4 + ~ Ln3++ 3NH4 + and the exchange constant is given Ltl KNH4
[ L--fi3+] [NH4+]3 [Ln3+] [~-~4+] 3.
(14)
Further the ion exchange between ammonium ion and hydrogen ion on the resin is expressed by NH4++H +~ NH4++H + and the exchange constant becomes
K~H,= [~q--fl,÷] [Iq÷]
[NH4+][R+]"
(15)
The formation of Ln-H.E.D.T.A. chelate is expressed Ln 3+ + Ch 3- ,~ LnCh and KLnChis written by [LnCh] KLnCh= [Ln3+] [Ch~_].
(16)
In the aqueous phase of the rare-earth band, the following species are mainly present:
LnCh, Ln 3+, NHa ÷, H ÷, Ch 3-, HCh 2-, H2Ch-, H3Ch. As already noted in the previous section, by passing through V(l) of the eluant, the front boundary of the eluant band progresses down the column proportional to E equivalents. Since there is no net transport of ammonium ion through both boundaries of the rare-earth band at equilibrium, all of the ammonium ion in the solution are considered to deposit on the resin at the front of the rare earth band. Thus we have the material balance equation NH4TV = N H +E
(17)
where NH4T in the rare-earth band is assumed to be present completely in the dissociated form. All of the rare earth in the resin may be transferred into the aqueous phase and picked up again on the resin at the front boundary. Thus, we have the following relationship:
Theoretical treatment of the elution system 3LnrV = LnS+E.
297 (18)
Further, the material balance for hydrogen may be expressed by (HT-- H r ) V = Ft+E
(19)
Introducing Equation (13) into Equations (17-19), the constituents in the resin phase are written in the forms L---fi3+ = 3Lnr NH4r NH4 + =
(20)
[NH4+]
(21)
NH4T
~t + __ Hr-- Hr
NH4r
(22)
Combination of Equations (20, 21 and 14) gives Lnr-
3+
Ln
[Ln ]KNH , 3 (N,-.~,r) 2
(23)
From Equations (15, 21 and 22), we see that H r = HT-F [~H~+H ] • m
(24)
O n the other hand, Lnr, Hr and Chr in the rare-earth aqueous phase are expressed
as follows: Lnr = [LnCh] + [Ln s+] Hr = [H +] + [HCh 2-] + 2 [ H 2 C h - ] +3[H3Ch]
(25) (26)
Chr = [LnCh] + [Ch 3-] + [HCh 2-] + [H2Ch-] + [HsCh] = [LnCh] ~ f'[Ch3-].
(27)
From Equations (16, 23 and 25), we find that [Ch3_ ] = K ~ , - 3(N"~4T) 2 3 (N~4T) 2" KLnCh"
(28)
Introducing Equations (7) and (24) into Equation (26), one obtains 1
[ H +] -- 1--KNm ( H , r - Z [ C h s- ] ).
(29)
298
z. HAGIWARA and H. ()KI
Combining Equations (6) and (16) into Equation (27), Chr is found
Chr = ( [Ln3+]KLnch + Y) [Ch3-].
(30)
At the present time, Chr in the aqueous phase of the rare-earth band is assumed to be approximately equal to that of Chr in the eluant. This is due to the following reasons. First, though the utilization of a dilute H.E.D.T.A. eluant causes the sorption of H.E.D.T.A. species on the resin, the degree is not large under the present experimental conditions. Secondly, a dilute eluant has no serious effect on the equilibrium condition. Phenomena such as swelling or shrinking observed in the exchange reactions are not so predominant in the present system that the change in ChT is kept to a small extent. Thus, Equation (30) is written in the form
Chr = ( [Ln 3+] KLnch + re) [Ch3-].
(31)
Since a solution should remain neutral, the sum of the positive charges of the ions must be equal to that of the negative charges. Thus, we may write [NH4 +] + [H +] + 3 [ L n 3+] = [H2Ch-] + 2 [ H C h 2-] + 3 [ C h 3-] = )([Ch 3-]
(32)
where .,~- [H+] 2 ~_2[H+] +3" k~.k3 k 3
(33)
If the compositions of eluant and the ion-exchange constants involved in the elution system are known, it is possible to find the concentrations of all species in either the resin or the aqueous phase of each adsorption band, as a function of the eluant composition. The right hand term is known, it is possible to calculate [Ch 3- ] from Equation (28). [H ÷] can be found from Equation (29). [Ln 3+] and [NH4 ÷] can be found from Equations (31) and (32), respectively. In addition, the other species in both phases can be calculated with the aid of the relations described. (4) Analysis o f the H.E.D.T.A. adsorption band When the rare-earth band is eluted down the hydrogen-retaining bed by means of a dilute solution of buffered H.E.D.T.A. with ammonium hydroxide, the H.E.D.T.A. adsorption band is formed between the retaining bed and the rare earth band due to the association of hydrogen ion with the H.E.D.T.A. species on the resin. The adsorbed form is close to HsCh 2+, which is formed by the reaction: H3Ch+2IT-I + ~---HsCh z÷ (C---hr'/E* ~ 0.5 in Table 1). The HsCh2+-band was studied by Powell et al.[5], and the more general treatment[6] on the sorption of H.E.D.T.A. species on the resin was made by the authors in a fairly wide range of the H.E.D.T.A. concentrations. Therefore, we only refer to the material balance of the H.E.D.T.A. species and the rate of growing of the H.E.D.T.A. band. 5. J. E. Powelland F. H. Spedding,Chem. Engng Prog.,Symp. Ser. 55, 101 (1959). 6. Z. Hagiwaraand H. Oki,Bull. chem. Soc. Japan. To be published.
Theoretical treatment of the elution system
299
Table 1.6~T'/E*-values concerning the H.E.D.T.A. adsorption band Exp. No.
Chr'lE*
12 13 14 15 16
0.488 0-499 0-506 0-487 0.481
Chr' and E* are expressed in moles and equivalents, respectively, per small attached column.
After the passage of V(I) of the eluant, the material balance of the total: H.E.D.T.A. species at the boundary between the rare earth and H.E.D.T.A. band is given by 2(Chr' - C h r ) V = H~Ch 2+ . E.
(34)
Using H,~C h 2+ = 1.00 and E / V = N H4r, Equation (34) is rearranged in the form Chr' - N ~ -H4T ~-ChT.
(35)
Thus, if C h r is equal to ~ r , Chr' can be expressed as a function of the composition of eluant. On the other hand, at the front of the H.E.D.T.A. band, H s C h 2÷ is formed, and its band is steadily expanded with the increase in time, as seen in Fig. 3. When V(l) of the eluant is passed through the top of a column, the front of the H.E.D.T.A. band moves to a distance proportional t,o E' equivalents in the column. IOO
50
_1
o
5.0
I0.0
Eluote volume, I
Fig. 3. Movement of boundaries in the column.
15-0
300
Z. H A G I W A R A and H. OK1
2ChT'V =
H5C~2+E
'
or
(36)
2ChT'V = E'.
Combining Equations (35) and (36), the rate of growing is given by Et
--~ = NH4T+ 2ChT.
(37)
Comparing Equation (13) with (37), the rate of movement of the front of H.E.D.T.A. band is greater than that of rare-earth band, and the difference is equal to 2Chr. EXPERIMENTAL
Materials. The erbium oxide was prepared in a pure state by means of ion exchange and its purity was greater than 99.99 per cent. The citric acid employed for pre-conditioning the resin was reagent grade. Using analytical grade H.E.D.T.A. (H3Ch), 0.015 M eluants as C--~.were prepared, and these solutions were buffered with ammonium hydroxide in the pH range of 4.9-8.8. All other reagents used were analytical grade. A sulfonated styrene-divinylbenzene coploymer, Dowex 50W, X-8, 100-200 mesh, was used as ion exchanger. Experimental method. The ion-exchange columns were constructed of I.D. 1.5 cm-pyrex glass tubing. The bottom of each column was closed with a sintered glass disc in order to support the resin bed containing Dowex 50W, X-8, 100-200 mesh. The columns were back-washed with water, treated with 2 M HCI and 5 per cent citric acid solution. These were finally washed with water. The resulting resin beds were 66-79 cm in length, as listed in Table 2. Samples of erbium oxide were dissolved with a little excess of HC1 by heating, and these chloride solutions were kept slightly acidic by dilution with water. These solutions were then adsorbed on the hydrogen form beds to prepare the erbium type column. The columns were then washed with distilled water until free of chloride. The dimensions of the prepared beds are listed in Table 2. The Er-adsorption bed was connected to the hydrogen retaining-bed, and small appendages, with a bed dimension of 1.5 cm (I.D.) × 5 cm in the hydrogen form, were attached to determine the composition of resin phase (Fig. 4.). The elution of erbium was made with the H.E.D.]'.A. eluant at a definite flow rate, and the eluates from the formed bands were collected into small fractions by means of a fraction collector. These fractions were analyzed by the following methods. ,4nalytical Methods (a) Aqueous phase. Total H.E.D.T.,4. species. Total anionic species of H.E.D.T.A. in the eluant or the eluate from the H.E.D.T.A. adsorption band were determined by chelometry with a standard Table 2. Experimental conditions used for the elutions of Er-band Composition of eluant (mole/l) Exp. No.
C'-hr
N~H4T
pH
12 13 14 15 16
0.01500 0.01500 0.01500 0.01500 0.01500
0.03096 0.03104 0.03830 0.02611 0.01840
7.43 7.45 8.82 5.92 4-91
Column length* (cm) Er-adsorption Retaining bed (sated. form) bed (H-type) 17.8 17.3 17.3 17.3 18.5
79.1 69.7 69.7 69.7 66.0
Linear flow rate (cm/min) 0.45 0.85 0.85 0.85 0.91
*I. D.-I.5 cm column. Resin used: Dowex 50W, X-8,100-200 mesh; elution temperature: 25°C.
Theoretical treatment of the elution system
301
F.luant
A
\
D
collector
Fig. 4. Schematic representation of ion exchange columns. A: Rare earth adsorption column; B: hydrogen retaining bed; C: small columns for the determination of constituents in the resin phase; D: sintered glass disc as resin supporter; resin used: Dowex 50W, X-8,100-200 mesh. solution of ZnC1 z and with E.B.T. indicator. The titration was made in the presence of the NH4CINH4OH buffer solution (pH = I0). Er-determination. Total erbium in the rare-earth fraction was precipitated as the oxalate and then ignited to the oxide for weighing. Ammonium-determination. Total ammonium in the eluant or the eluate was determined by the usual Kjeldahl method. Methyl purple was used as the indicator for the titration of ammonia with the standard HCI. Chf-determination. The excess of H.E.D.T.A. species, which are present in the uncombined form with erbium, was titrated with a standard solution of ErCI3, using Arzonoazo-indicator [3-2(2-arzono~ phenylazo)-4,5-dihydroxy-2,7-naphthalene-disulphonicacid]. For the titration, pyridine was added to keep the pH between 5-5 and 6.0. (b) Resin phase After the elution system had approached an equilibrium state, small appendages attached to the main column were taken off for the analysis of resin phase. The small appendages for the H.E.D.T.A~ adsorption band were eluted with 2 M NH4C1, and the total anionic species of H.E.D.T.A. in the eluates were determined by chelometry, according to the described method. The constituents in the erbium band were determined after eluting them with 3 M NaCI. The content of erbium was determined gravimetrically using a method similar to that mentioned in the pre+ ceding section. Ammonium ion was determined by the Kjeldahl method, and hydrogen ion was measured using a glass electrode. RESULTS AND DISCUSSION
(1) E l u t i o n c u r v e s . In the initial step of elution, the length of the Er-band stretched to some extent, due to the leakage of ammonium ion or hydrogen ion in the eluant band through the rare-earth band, and then approached a steady state. On the other hand, the leading edge of the H.E.D.T.A. adsorption band
302
Z. H A G I W A R A and H. OKI
progressed down the column at a constant rate, and the rear boundary moved steadily, but more slowly than the leading edge, as shown in Fig. 3. Equation (37) explains the above fact well. It is clear from a typical elution curve in Fig. 5 that the total concentration of Er or NH4 rose very sharply to values which remained almost constant until the tail end of the rare-earth band was eluted from the column. At this point, either the concentration of ammonium or the pH of the eluate approached quickly to their respective values in the eluant. (2) Composition of both phases. The elution results are given in Table 3, which shows that the erbium concentration in the eluate decreased with decreasing ammonium ion in the eluant, while the erbium content in the resin increased with increasing NH4r. Further, due to the adsorption of H.E.D.T.A. on the resin, the total concentration of anionic species.~of H.E.D.T.A. (ChT) increased slowly with the increase in the concentration of N H4r. In order to check Equation (35), some calculations were made, as tabulated in Table 4, in which the agreement is observed between the terms Ch'r and [(N"H4T/2) + Ch'-~T]. The values of [~'H4r/2+ Chr] are always slightly higher than the Ch~-values owing to the sorption of H.E.D.T.A. on the resin. Material balance Equations (17) and (18) were checked with the aid of the experimental
30 ~
Exp.No.12 o
1
C~r
~
_e2o E E
P
I
o
•
~r"------'-'!8 6
, .
.
.
.
.
/-
c IO o tO
I
0
7
I 8
I
i 9
I I0
~t I II
0
12
F'luatevolume,l. Fig. 5. Total elution curves obtained by the elution of Er with 0.015M H.E.D.T.A. eluant (Exp. No. 13). ~, : Position where small appendages were taken off.
Table 3. Composition of both phases obtained by the elutions of Er-band with 0.015M H.E.D.T.A. buffered solutions in the pH range of 4.9-8.8
Exp. No,
E-~a+
12 13 14 15 16
0-818 0-811 0"925 0.702 0"393
*Cht = C h r - ErT.
Resin phase (eq. fraction) NH4 + 0.172 0,177 0,064 0,283 0.589
1~+
0.010 0"013 0"011 0"015 0"018
Err
0-00857 0.00866 0"01230 0"00612 0'00240
Aqueous phase (mole/l) NH4r Chr Chl* 0-00540 0.00578 0"00249 0"00761 0-01090
0.01541 0'01589 0"01596 0"10529 0.01504
0.00684 0"00724 0.00367 0.00918 0'01267
pH 3'25 3-27 3' 17 3'28 3"29
Theoretical treatment of the elution system
303
data, and the results are tabulated in Table 5. The agreement between Er3+/3Err and N H4+/N H4v was excellent. (3) Ion-exchange reaction involved in the system. As already noted in Section (3), if the composition of eluant is known, all of the compositions involved in the exchange system can be found by assuming true equilibrium in the system. In this Lrl case, it is necessary to know the values of the exchange constants such as KNn4 and K NH', which are dependent on ionic strength of the solution, the composition of the resin phase and the temperature. The exchange constants, K NH', found from the elution experiments are listed in Table 6, in which the resin and aqueous phases are expressed in the Table 4. Comparison of Chr' with NH4r/2 + ChT
Exp. No.
(mole/l)
Chr,
NH4r/2 + Chr (mole/l)
N~H4r/2 + C"thr* (mole/l)
12 13 14 15 16
0.03013 0.03060 0.03424 0.02816 0.02386
0.03089 0.03141 0.03511 0.02834 0.02424
0.03048 0.03052 0.03415 0.02806 0.02420
* Chr = Chr (Calcd., neglecting the adsorption of H.E,D.T.A.). Table 5. Material balance of ammonium and rare earth expressed by Equations (17 and 18). Exp. No.
Er 3+ 3Err
NH4+ NH4r
12 13 14 15 16
31.8 31.2 25.1 38.2 54.6
31.9 30.6 25-7 37-2 54.0
Resin phase: equivalent fraction. Aqueous phase: equivalent per liter. Table 6. Selectivity coefficient, K Nn, obtained from the elution experiments
Exp. No.
Kr~n', (25°C)
12 13 14 15 16
1'7 1.3 1.6 1.3 1.5
304
Z. H A G I W A R A and H. OKI
equivalent fraction and moles/l, respectively. Bonner[7] investigated the ion exchange equilibria for the NH4-H system, using various degrees of cross-linked resins, and the rational thermodynamic constant / ~ n , was found graphically to be 2.0 for Dowex 50, X-8, employing log/("Nn, = f~ log K~ H, dNNH, where N is the equivalent fraction of indicated species in the resin. In order to study the elution system, the mean value of K~ a, = 1.5 was used without any trouble (Figs. 6 and 7). To calculate the "~NH4/L ' nin Equation (14), the concentration of tripositive rare earth ions should be found. However, the amount is too small to determine directly. It is possible to calculate [Ln 3+] as follows: Combination of Equations (16, 25 and 27) yields ~'[LnCh] [Ln3+] = KLnch(Chr--Lnr) "
(34)
[LnCh] is approximately equal to Lnr at [LnCh] >> [Ln3+]. Y'.Lnr [Ln3+] = KLnch(Chr--Lnr)"
(35)
Introducing Equation (35) into Equation (14) L. _ [NH4+]3[ E-fi'~+](Chr-- LnT)KL.ch [NH4+] 3 . LnT. Y
KNH 4 - -
(36)
The K rr -values were found from Equation (36). The results are listed in Table 7. Table 7. Selectivity coefficient, KNn, rr obtained from the elution experiments
Exp. No.
Er KNH4 (25°C)
12 13 15
42 49 49
The following experiments were carried out in order to determine the reliability of the KNr[i,-values obtained from the elution experiments. Under almost similar experimental conditions to Exp. 12-13, the erbium band was eluted down the hydrogen-retaining bed, and the erbium eluate from the column was used as the aqueous phase for the batch equilibrium experiment. The composition of Ereluate was as follows: Err = 8-69 mmol/l; [NH4 +] = 5.29 mmol/l; Chr = 15-67 mmol/l; pH = 3,27. 7. O. D. Bonner, J. phys. Chem. 58, 318 (1954).
Theoretical treatment of the elutiou system
305
On the other hand, saturated resins with Er o r NH4 were prepared separately by the column method, using Dowex 50W, X-8, 50-100 mesh. They were dried at 50°C for 24 hr under a reduced pressure. The exchange capacities of the prepared resins were as follows: Er-type of resin = 3.75 meq/g-resin (Er-form); NH4-type of resin = 4.33 meq/ g-resin(NH4-form). Both types of resins were taken so that the constituents in Table 8. K~,-values obtained by equilibrium experiment
Exp. No. 1 2
Resin phase (eq. fraction) E-r~+ N H 4-~ H+ 0-77% 0-7776
0.2012 0.2025
0.0192 0-0199
Err 8-59 8'59
Aqueous phase (mmole/l) NH~r Chr 5.55 5-68
15'30 15'32
pH
KNmEr (25°C)
3'39 3.40
43 45
the resin were kept to 0.8 as Er and 0.2 as NH4 equivalent fraction. A total of approximately 5 g of the two kinds of resins were mixed up with about 500 ml. o f the above Er-eluate, and the resulting mixture was maintained at 25°+__0. I°C for 48 hr in a thermostat under occasional stirring. After equilibration, both phases were separated for analysis. The results are shown in Table 8. Although the ion exchange study with polyvalent ions so far has not been developed well, the exchange constants in Table 7 appear to be reasonable from a comparison of the K~,-values obtained from both methods. Really, an approach to equilibrium is a remarkable fact in such a complexed elution system. (4) Solution of the rare earth band as a function of the composition of eluant As already mentioned in Section 3, when the composition of eluant is known the concentrations of all species present in both phases of the rare-earth band can be calculated under the assumption of true equilibrium in the exchange system. In the present calculations, the following values are used:
pka = 2"39; pk2 = 5"37; pk3 = 9-93 [8] KEtch = 1"48 × 101~[9]; KNH4 _ g r __ 45*; K~u4 = 1"5" Further, Chr is assumed to be the same as Chr, neglecting the sorption of H.E.D.T.A. on the resin of the rare-earth band. Figure 6 shows that the experi~ mental plots related to the aqueous phase of the rare-earth band are consistent with the calculated lines, whereas in a region greater than 30 mmole/l as N'H~r the observed values of Chr are greater than the calculated values due to a tendem cy for increased sorption of the H.E.D.T.A. species into the resin with an increase in NH4r. * Found from the present investigation. 8. T. Moeller and R. Ferrus, J. inorg, nucl. Chem. 20, 261 (1961). 9, F. H. Spedding, J. E. Powell and E. J. Wheelwright, J. Am. chem. Soc. 78, 34 ~1956).
306
Z. H A G I W A R A and H. OKI 40
/
C'hT: O" 015 M
\\
30
/
c,;
',~ ,7" m o E E ?
Z,
%
~o
u
I% % •
o
,o
¢,, .
. I
~
1
0
I0
20
3O
40
5O
NH4rr, m m o ~ l l
Fig. 6. Plots of the experimental data related to the aqueous phase against ~-~"n4r. Theoretical lines are shown by solid and dotted lines.
0.8
go6 e
R+ A
Solid lines: Theor.
Q.
c 0"4
~ 0'2
0
I0
20
30
40
50
NH4T, mmole/l
Fig. 7. Plots of the experimental data related to the resin phase against NH~r.
Theoreticaltreatmentof the elutionsystem
307
Furthermore, all of the constituents in the resin phase of the rare-earth band are calculated as a function of the eluent composition, as represented in solid lines in F ~ . 7, in which is kept to 0.015M. The plots of E--~3+,~-~4 + and H+ against N H4r are on the related theoretical curves. | t is concluded from the described results that the compositions of both phases of the formed bands in the elution system are fixed by the composition of eluant itself. The agreement of the experimental and calculated values indicates that the ion-exchange system described is considered to be close to equilibrium under the elution conditions" used.
Ch"~