by comparing the changcs oi entropy and hcat capacity for the dissociation process with the altcratiori in gross st ructural fcaturcs of the amine moleculc.1 15verett and his eo-wor.kcrs19e20 and Evans and IIamann' have rorisidered these matters in somc detail arid have been able to identify several factors that appear to be of primary importance in determining t,he sign and magnitude of the (19) D. 11. Everett and R. R. W. Pinsent, Proc. Roy. Sac. (London), 3168, 416 (1962).
(20) D. 13. Everett, D. A. Landsman and U. R. W. Pinsent. ibid.,
alar, 403 (1952).
(21) A. G. Evans and S. D. IIamann, Trans. Faraday Soc., 4?, 34 (1951).
thermodynamic quantities associatcd with the ionization process. The most illuminating comparisons, howcvcr, utilize the changes of these quantities upon passing from onc mcmber. to thc ncxt in a series of compounds of similar structure. An interpretation of the differences be tween tris-(hydroxymethy1)-aminomethane and 2-amino-2-methyl-1,3-propanediol therefore should be postponed until similar data for all four members of this series are available. The base with one hydroxyl group, namcly, 2-amino-2methyl-1-propanol, has been studied recently by Everett, and Timimi,12 and a similar study of the last member of the scrics (t-butylamine) already has been undertaken in this Laboratory.
RARE EAItTH CHELATE STABILITY CONSTANTS OF SOME A&lIKOPOLYCARBOXYLIC ACIDS1 BY J. L. MACKEY, M. A. RILLER AND J. E. POWELL Institute for Atomic Research and Department of Chemistry, Iowa State University, Ames, Iowa Received Seplember 85, 1961
Stability constants of the complexes formed between the rare earths and 1,2-bis-[2-di-(carboxymethyl)-aminocthoxy]ethane (ICGTA) and 2,2'-bis-[di-( carboxymethyl)-amino]-diethyl ether (EEDTA) have been determined by the polarographic and mercury elcctrode methods a t a temperature of 20" and an ionic strength of p = 0.1. Some of thc trends in the stabilities of rare cttrth aminopolycarboxylate chelates have been discussed.
Introduction and diethylenetriaminepentaacetic acid The interaction of lanthanide ions with amino- (DTPA).' The Present authors have extended the polycarboxylic acids is of practical interest because measurement Of rare earth chelate stability conthe use of chelating agents in conjunction with ion- stants to two additional chelating agents, 1,Zbisexchange resins has proved to be an effective method [2-di-(carboxYmethYl)-aminoethoxY]*thane (EGfor separating rare earths. Stability constants of TA) and 212'-bis-[di-(carboxYmethYl)-amino]-diindividual rare earth chelates indicate the appli- ethyl ether @EDTA) I and have considered Some cability of the respective chelating agents to this of the trends in rare earth chelate stability separation process. On a theoretical level studies sequences. The structures Of EXDTA and EGTA of chelation have been made for the purpose of are given below. A discussion of these chelating relating metal-chelate stability to the structure of the chelating agent and to the nature of the metal H o O C ' ~ z c ~ - ~ H z - ~ ~ ~ r ~ ~ ~ ~ z I-1oocr-I-c ion.2 The tervalent rare earth ions, having the EEDTA same electronic configuration in the outer orbitals, provide a unique opportunity for study of the effects of ionic size and inner elecS-CIIz-CEIz-(rCHz-CHz-O-C€Iz-CH2-r\T HOOCI12C tronic structure on chelate formation. EGTA Studies of stability constants of rare earth aminopolycarboxylate chelates have been limited agents as eluents for rare earths has been presented to ethylenediaminetetraacetic acid (EDTA),3t4 el~ewhere.~ 1,2- diamino-cyclohexane- K, K,X', K'- tetraacetic Methods of Measurement.-The r3re carth acid (DCTA), 4 N-hydroxyethylethylenediamine- aminopolycarboxylatc stabili t,y constants have been tetraacetic acid (HEDTA),6 nitrilotriacetic acid determined generally either by the modified p1-I (1) Contrihution No. 963. Work was performed in the " u n a method3'6'8 Or by polarographic Lahorntory of the U. S. Atomic Energy Commission. Recently the mercury electrode has been used to (2) (a) 9. Chabcrek and A . E. Martell, "Organic Sequestering determine stable chelate constants."J,11 I n the Agents," John W h y and Sons, New York, N. Y.,19.59, pp. 124-170; (b) A. E. Martell and M. Calvin, "Chemistry of the Metal Chelate Compounds," Prentice-Hall, Inc., New York, N. Y., 1952. (3) E. H. Wheelwright, F. H. Spedding and G. Sehmarzcnbach, J . Am. Chem. Soc., 75, 4196 (1953). (4) G. Schwnrsenhach, R. Gut and G. Anderegg, Helu. Chim. Acta. 37, 937 (1954). (5) I". €1. Spedding, J E. Powell and E. J. WhePlwrisht. J . A m . Chcm. S o c . , 78, 34 (1956)
(6) G. Sohwarzenbach and R. Gut, Helu. Chim. Acta, 39, 1589 (1956). (7) G. Anderegg, ibid., 43, 826 (1960). (8) R. Harder and 9. Chaberek J . Inorg. R. NucZear Chern.. 11, 197 (1959). (9) J. E. Powell, "Separation of Rare Earths by Ion Exrhange" i n F. H. Spedding and A. If. Daane. "The Rare Earths." Chap. 5 , John Wilvy RE Sons, New York, N. Y., 1961
J. L. MACKEY, 14. A. HILLER AND J. E, POWELL
312
present work the mercury electrode (pHg) was used to determine rare earth chelate stability con&ants for EEDTA and EGTA. These constants also have been measured independently by the polarographic method. The pHg Method.-In the pHg method equimolar amcunts of rare earth and mercury(1.T) ions are mixed with an amount of chelating agent equal tc: about half the sum of the concentrations of the two metal ions. The basic reaction which takes place is shown by eq. I R+3
+H g Y - Z
RY-
+ Hg2+
(1)
R3* in this equation represents rare earth ion and Y4-is the anion of the aminopolycarboxylic acid H4Y,which can be either EEDTA or EGTA. The equilibrium constant for reaction I can be written as
KI is calculated from the equilibrium concentrations of the four ionic species in 1. The mercury(I1) concentration and pH are measured directly and the other coscentration terms are evaluated from material balance equations which describe the concentrations of all species in a solution of the two metals and a chelating agent. These equations are [Rlt = [R"]
+ 2[R>Y2+]+ [RHgY+]h +
[H&Yh-']
(2)
h==O
IHglt =
&'+I
+ 2[Jkz2+l + IRHgY+l +
c P
[H,HgYP-*l
(3)
P-0
h
[Ylt
[HhRyb-l]
P
+
h=O
[HpHgYP-21
4
P-0
5
[H,Yl
n=O
[Hlt = [H+] - [OH-]
2
p=0
+ IRzY2+1+ [RHgY+l
+h
h
h[HhRYn-l]
(4)
+
=0
P [ H , H ~ Y ~ -4~I
5 nL"Y1
(5)
n= 0
I n their general form these equations are difficult to solve; however, for the chelating agents and circumstances studied here, some of the terms are negligible and may be omitted. The metal chelates considered here are very stable (KRY> and in all cases K H ~ Y . > ~ O ~ K R YDue . to these conditions the concentrations of free mercury ions are so small that they do not affect the material balance equan
tions to ai1 appreciable extent. The term n=O
[HnY]is insignificant due to the high stability of the chelates and the presence of excess metal ions. For chelating agents of the type studied, it is necessary to consider only singly-protonated metal che1atesl2; however, values for K H M Y= [HMY]/ (IO) C. N. Reilley and R. W. Schmid, J . A m . Chem. Soc., 78, 5513 (1956). (11) G. Schmrzenbach and G. Anderegg, H e k . Chim. Acta, 40, 1773 (1957). (12) G. Schwsrzenbach, H. Senn and G. Anderegg. ibid., 40, 1886 (1957).
Vol. 66
[HI [MY] were not available for the rare earth chelates studied here. Since protonated chelates are generally fairly strong a~ids,1~,13 the pH range for the measurement of constants was maintained sufficiently high that these protonated species could be neglected. Species of the form R2Y and RHgY also were neglected in our calculations. With these simplifications the equations easily were solved for the concentration terms required in (1). It should be noted that the validity of the above assumptions can be checked easily. If the assumptions are correct, the experimentally determined values of KRYcalculated from the simplified material balance equations should be constant in spite of appreciable changes in pH or the composition of the solutions on which the measurements were made. KRY can be found by applying eq. I, provided K H ~ has Y been determined independently. The mercury-chelate constants (KHgY. for EGTA and EEDTA) also were measured with the mercury electrode. The details of the method have been given by Schwarzenbach, et aZ.ll The values obtained in the present study are reported in Table I along with previously reported values.
Experimental Procedure Two separate series of solutions were prepared in the case of each chelating agent by mixing proper proportions of standardized solutions of rare earth nitrate, chelating agent, mercuric nitrate and enough potassium nitrate to adjust the ionic strength of each preparation to ~1 = 0.1. A drop of mercury was added to each solution and all were placed in a constant temperature-bath at 20' for 24 hr. Each solution then was placed in a titration cell and the pH.and potential of the mercury electrode were recorded periodically as the pH was varied from 3.5 to 4.5 by addition of KOH. The pH was measured by means of a Beckman G.S. meter using the regular scale. The potential of the mercury electrode was measured with a Rubicon potentiometer and can be represented by the equation E = Eo' X/2 log [Hg2+] (6) where Eo' = EO Ej Ej' S/2 log y ~ ~ ' + ( 7 ) I n the above equation EO is a term that consists of the reduction potential of Hga+ to HgO and the potential of a 0.1 M calomel cell, E, and E;' are liquid-liquid junction potentials, and S = 2.3026RT/F. E"' was evaluated by measuring the potential of a solution of known mercury(I1) ion concentration a t a n ionic strength of p = 0.1 (KNOJ). TheequilibriumHg Hga+ 4 Hgp+* must be accounted for. For a detailed description of how EO is found, the paper by Schwrtrzenbach and Anderegg should be consu1ted.l1 Polarographic Method.-In this method equimolar amounts of cadmium chelate and rare earth nitrate are combined. The rare earth ion and cadmium then compete for the complexing agent as shown in eq. J.T. The polarograph is used to measure the concentration of CdY2RZ+ Cd2+ RY(11)
+ + + +
+
+
+
uncomplexed cadmium ions in the equilibrated mixture. When the rate of formation and dissociation of the metal chelate is slow, both Cd2+ and CdY- are reduced a t the dropping mercury electrode, and a distinct reduction wave is observed for each species. The diffusion current, i d , of the first wave is proportional to the concentration of free cadmium ion in solution. The equilibrium constant for eq. I1 can be written as
(13) J. E. Powell, J. S. Fritz and D. B. James, Anal. Chem., 32, 954 (1960).
.Feh., 1962
RAREEARTHCHELATESTABILITY OF AMINOPOLYCARBOXYLIC ACIDS
Since the reactants are combined in equimolar quantities, the following expressions hold a t equilibrium [RY-] = [Cd2+] (9) and [CdYz-] = [Ra+] = C - [Cdz+] (10) where C is the initial concentration of each reactant. Xubstituting these quantities into (8) gives [Cd2+I2 KII = (C - [Cdz'])' The rare earth-chelate stability constant can be calculated from eq. 12
Experimental Procedure.-The polarograms were obtained from solutions prepared by mixing 10 ml. of 0.0100 M R(NO&, 10 ml. of 0.0100 M Cd(NOa)z, 10 ml. of 0.0100 M tetrapotassium salt of the chelating agent, 10 ml. of 0.1 M sodium acetate, 10 ml. of 0.1 M acetic acid and enough ytassium nitrate to adjust the ionic strength to p = 0.1. he mixtures then Were diluted to a total volume of 100 ml. The acetic acid-sodium acetate mixture buffered the solutions at a pH of 4.65. After mixing, the solutions were allowed to equilibrate for 24 hr. in a constant temperature bath a t 20'. The measurements were made with a Sargent Model X X I polarograph. The cell was fashioned from a 100-ml. beaker, and a saturated calomel electrode was connected to the cell by a potassium nitrate-agar bridge. Helium or argon was bubbled through the cell prior to making measurements. Reference id values were obtained from solutions with 100% uncomplexed cadmium and 100% compleked cadmium. The stability constants were calculated from i d values by use of eq. 12. The cadmium-EGTA and EEDTA stability constants were determined by the pHg method. The values me based on the mercury-chelate stability constants, and are listed in Table I.
TABLE I STABILITYCONSTANTS OF THE CADMIUM AND MERCURY AT 20" AND IONIC STRENGTH OF p = 0.1 (KNOJ CHELATES KMY
KMY
313
by the pHg method are the maximum deviations from the mean of some ten determinations on two series of solutions in the pH range 3 . 5 4 . 5 . For the polarographic measurements the errors made in the determination of the per cent. uncomplexed metal ion amount to f.201,. This would introduce uncertainties of A0.08 t o 10.17 in the log KRY values in Table 11. The two methods give results of comparable accuracy. TABLE I1 STABILITY CONSTANTS OF THE RARE EARTHEGTA AND EEDTA CHELATES AT 20" A N D IONIC STRENGTH p = 0.1 (KNOa) Rare earth
EGTA , pHg Polar. log K R Y log KRY
EEDTA pHg Polar. log KRY log K R Y
La Ce Pr Nd Sm
15.55 I 0.20 15.84 16.00 1 0 . 2 0 16.29 16.69 f .IO 17.13 15.70 =k .10 16.06 16.05 f .OS 16.17 17.36 i .06 17.61 16.28 f .10 16.59 17.67 f .10 17.81 1 6 . 8 8 I . I 6 17.25 18.19 f .OS 18.25 Eu 17.10 f .10 17.77" 18.31 f .10 18.38" 18.13 f .OS 18.21 Gd 1 6 . 9 4 1 .1Q 17.50 18.31 f .1Q 18.31 Tb 17.27 f -10 17.80 18.21 f .20 18.29 Dy 17.42 f .04 17.84 Ho 17.38 f .05 17.90 18.13 1 .10 18.17 17.99 4 -15 18.18 Er 17.40 f .05 18.00 Tm 17.48 i .05 17.96 17.83 f .I1 18.01 Yb 17.78 zk .05 18.22 17.85 f .20 18.06 17.75 I .23 17.92 Lu 17.81 f .IO 18.48 1 7 . 5 4 f .10 17.79 Y 16.82 f .05 17.16 0 Europium could not be measured vs. cadmium because the half-wave potentials of the metals were too close. The value given here was obtained by comparing europium to neodymium, gadolinium afid dysprosium.
Discussion
A comparisorr of the values obtained by the two methods shows that in both cases the polarographic values are higher than those of the pHg method. I n the case of EEDTA the two sets of values are within the limits of error, if the uncertainty of the cadmium-chelate stability constant is considered. Preparation of Solutions.-The EGTA and EEDTA used For EGTA the difference between the two sets of were obtained from Geigy Industrial Chemicals, Ardsley, New York and were further purified by double recrystalliza- constants is definitely greater than the experimental tion from ethanol. The solutions of chelating agents were error. The exact reasons for this difference in the standardized by the following two methods: potentiometric two sets of constants is not clear. A consideration titration with standard potaasium hydroxide; and complexo- of possible metal a,cetate complexes of cadmium metric titration against standard mercuric nitrate solution and the rare earths in the case of the polarographic using the mercury indicator electrode.14J6 The rare earths were supplied by the rare earth separation measurements would tend to increase rather than group at the Ames Laboratory of the Atomic Energy Com- decrease the difference. It might be noted that mic;sion and were 99.9% pure or better. Stock solutions of nitrates were prepared by dissolving the respective oxides in Schwarzenbach and Anderegg" also have reported nitric acid. Aliquots of each solution were titrated potentio- a difference between the calcium-EDTA stability metrically 1,o determine the pH of the neutral equivalence constant measured with the mercupy electrode and point and the solutions then were adjusted to that pH. the equally accurate pH method. In any case the Standardization was done gravimetrically by precipitation with oxalic acid followed by ignition to oxides. Carbonate- relative values of the constants determined by the free potassium hydroxide was prepared by the method of two methods are in good agreement. Both sets of Powell and Hillerla and was standardized against potassium constants for both ligands show a "gadolinium acid phthalate. break" and, in the case of EEDTA, an inflection is apparent in both sets at thulium. The use of the Results The results of the determination of the rare rare earth stability constants in obtaining separaearth-chelate stability constants are listed in Table tion factors in ion-exchange separations depends 11. The errors shown for the constants determined upon relative values so that either set of constants would suffice. (14) C. N. Reilley and R. W. Schmid, Anal. Chem., 26,1640 (1953)It is interesting to compare the stability con(15) J. 8. Fritz, hl. J. Riohard and 9. K. Karraker, ibid , 80, 1347 stants of the rare earth6 with EEDTA and EGTA (1958). (16) J. E. Powell and M. A. Hiller, J . Chem. Educ., 34, 330 (1957). with the stability constants of other rare earth Metal ohelate
This work
Lit.12
Hg-EEDT A Hg-EGTA Cd-EEDTA Cd-EGTA
22.88 I 0.10 23.12 f .I2 16.64 f .06 16.70 f . I O
23.09 23.20 16.27 16.73
3 14
J. L. MACICEY, M. A. HILLERAND J. E. POWELL
aminopolycarboxylate chelates. The stability sequences for DCTA and EDTA chelates of the rare earths show similar behavior. These constants increase rather regularly with increasing atomic number and decreasing ionic radius. The two sets of constants are nearly parallel with the DCTA constants somewhat higher than those for EDTA. The trend with EGThresembles that with HEDTA. Both sets of constants reveal an increase in chelate stability from lanthanum to europium; whereupon the values remain nearly constant up to erbium and then increase again from thulium to lutetium. Both the DTPA and EEDTA sequences show an unusual reversal in chelate stability. The heavier rare earth stability constants decline in magnitude and a few become lower than some of the light, rare earth stability constants. For DTPA the reversal in chelate stability occurs a t dysprosium, while for EEDTA i t occurs in the vicinity of europium. For almost all chelating agents there is a noticeable irregularity in the case of the gadolinium che, ~ this phenomenon in late. Spedding, et ~ l . noted the EDTA constants, and Schwarzenbach and Gut1’ called attention to the “gadolinium break” in the stability sequences of both DCTA and nitrilotriacetate (XTA) chelates. Many other properties of the rare earths also show a discontinuity at gadolinium. The irregularity is marked in both the EGTA and EEDTA rare earth-chelate sta,bility sequences. It is interesting to note the position of yttrium in stability constant series. In every case it falls below the position it should occupy from a consideration of its ionic radius. Furthermore, its position relative to individual rare earths changes with the chelating agent. I n all stability sequences the constants. increase rather regularly up to europium, but beyond europium they increase in some cases and decrease in others. Comparing the regular portions of the rare earth series, the increasing order of stability for the chelating agents is NTA < HEDTA < EDTA L EGTA
