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The anion exchange of metal complexes—XI application of the constant ionic medium method to the mercury halide system
J. Inorg. Nucl.
Chem.,
1963, Vol. 25, pp. 1465 to 1470. Pergamon Press Ltd. Printed in Northern
Ireland
THE A N I O N E X C H A N G E OF METAL COMPLEXES--XI* A P P L I C A T I O N OF T H E C O N S T A N T I O N I C M E D I U M M E T H O D TO T H E M E R C U R Y H A L I D E SYSTEM I. ELIEZER and Y. MARCUS Radiochemistry Department, Israel Atomic Energy Commission, Soreq Research Establishment, Rehovoth, Israel (Received26 March 1963; in revisedform 10 May 1963)
Al~traet--The applicability of the constant ionic medium method to the study of metal complex formation by exchange has been investigated, using the mercury(II) halide system as an illustration. The distribution of mercury(II) tracer has been measured between C molar (NaX + NaC10,) solution and (RX ÷ RC104) Dowex 1 resin, for C = 0"3, 0"5 and 3'0 M and X = CI-, Br- and I-. The stability constants for the resin phase and for the 0"3 and 3 M solutions have been calculated. The general applicability of the method for anion exchange studies has been discussed. THE constant ionic medium method ~1) has often been used to study complex formation in solution. It has been used successfully in conjunction with the cation exchange method ~lb) but less successfully with the anion exchange method. FRONAEUS,~2) in introducing anion exchange as a quantitative method for studying metal complexes, mentioned that if a constant neutral salt medium is used, considerable anion exchange takes place when the ligand concentration is varied within wide limits, and the metal distribution will be a too complicated function of the ligand concentration. Subsequent quantitative treatments of the anion exchange method~3, 4) have usually dispensed with a constant ionic medium, and tried instead to evaluate the activity coefficient terms. A detailed examination of the applicability limits of the constant ionic medium method seemed desirable, because of the known difficulties with the evaluation of activity coefficients. While this work was in progress, FRONAEUS et al. ~ published an account of the use of this method obtaining the stability constants in the resin phase for the cadmium bromide system, without however evaluating it in a general way. Earlier, SONESSON~) studied the gadolinium glycolate system using a constant ionic medium in the aqueous phase, while permitting the resin composition to vary considerably. The medium inside the resin was, therefore, far from constant, and stability * Previous paper in Series: D. MAYDANand Y. MARCUS: J. Phys. Chem. 67, 987 (1963). ~1~j. N. BRONSTED,Trans. Faraday Soc. 23, 416 (1927). t~bl F. J. C. ROSSOTTIand H. ROSSOTTI,Determination of Stability Constants. McGraw-Hill, New York (1961). ~ S. FRONAEUS, Svensk Kern. Tidskr. 65, 1 (1953). ~a~ y . MARCUS and C. D. CORYELL,Bull. Res. Council 8 A, 1 (1959) c4, K. A. KRAUS and F. NELSOr~, Structure of Electrolyte Solutions (Edited by W. J. HAMER), p.340 J. Wiley, N e w Y o r k (1959). ~ S. FRONAEUS, I. LUNDQVIST and A. SONr_.SSON,Acta Chem. Scand. 16, 1936 (1962). t0, A. SONESSON, Acta Chem. Scand. 15, 1 (1961). 1465
1466
I. ELmZERand Y. MARCUS
constants in the resin phase could be determined very approximately, using constants for the aqueous phase obtained by another method. Similarly, in the method proposed by WAKI, c7-9) substitution was permitted to proceed over the whole mole fraction range, and it is unlikely that the activity coefficient term remained constant. The differentiation used may therefore not be reliable. Further complications are introduced in WAKI'S experiments by the considerable loading of the exchanger by the metal used. It does not seem possible, in a completely general way, to vary the ligand concentration over a wide range and still have a constant ionic medium in the resin phase. In some particular cases, however, this may be possible. Namely, this is so where complex formation is relatively strong, requiring only low concentrations of the ligand, and where the affinity of the ligand for the resin is not too high, so that the resin remains essentially loaded with the medium ions. Using perchlorate ions for the medium, as is usually done, has the advantage of providing the resin with an anion of high affinity, competing favourably with most ligand ions. This requires high intrinsic affinity of the anionic metal complex for the exchanger, as otherwise distribution coefficients would be too small. In cases fulfilling the above requirements, it should be possible to determine stability constants for both phases, valid for the ionic medium chosen, and particularly also constants for the anionic complexes, which may not be always reliably determined by other methods. For other cases, in particular where complexes are weak and are formed only at high ligand concentration, the constant medium principle cannot be used, and other anion exchange methods ~4) should be used. The present work describes the application of the constant ionic medium method to the mercury halide systems, where the above conditions seem to have been met. The stability constants for mercury(II) with chloride, bromide and iodide have already been measured by other methods. ~1°-12) The values obtained by the anion exchange method may thus be compared with previously reported values. EXPERIMENTAL Materials. Radioactive mercury, 2°SHg, obtained from O.R.N.L. in form of a nitrate solution was used, diluted so that the total mercury concentration was in all cases 10-4-10-e M. The resin used was Bio-Rad Dowex-1 A.G., 8 per cent crosslinked, 100-200 mesh. It was converted to the appropriate halide form, using hydrochloric acid, sodium bromide or iodide, after having been passed through the usual acid-base conditioning cycles. All other reagents were of analytical grade. Methods. Selectivity coefficients, KXclo4= (X-)(C104-)/(C104-)(X-), parenthesis denoting concentrations, barred symbols the resin phase, and X a halide ion, were measured in experiments where known quantities of resin in halide form were equilibrated for 24 hours with known quantities of perchlorate solutions at room temperature, 23 ± 3°. The coefficients were calculated from the measured capacity of the resin, its water content (obtained by the centrifugation method) ~13~and the concentration of halide in the resin and the solution phases at equilibrium. Mercury distribution coefficients were measured in similar experiments. Weighed amounts of ~7~H. WAKI,Bull. Chem. Soc. Japan 33, 1469 (1960); 34, 829 (1961). ~8~H. WAKI,Bull. Chem. Soc. Japan. 34, 1842 (1962). c9~j. YOSHIMURA,H. WAKIand S. T.~SHIRO,Bull. Chem. Soc. Japan 35, 412 (1962). ~10)L. G. SIt.LEN,Acta Chem. Scand. 3, 539 (1949). ~11~Y. MARCUS,Acta Chem. Scand. 11, 599 (1957). cx2JC. L. VAN PANTALEONVAN ECK, Thesis, Leiden (1958). ~8) K. W. PEPPEg D. REICHENBERGand D. K. HALE,J. Chem. Soc. 3129 (1952).
The anion exchange of metal complexes--XI
1467
resin in halide fo:m were equilibrated with solutions containing 0.01 M perchloric acid (to prevent hydrolysis of mercury ions) and 0.29, 0'49 or 2.99 M sodium perchlorate. The radioactivity of aliquots of the solution, separated from the resin by filtering through glass wool plugs, was measured in a well-type scintillation counter, and compared with that of blanks, shaken under similar conditions but without resin. The distribution coefficients D (activity per gramme air dried resin/activity per ml solution) were calculated from these values c14). The concentrations of halide ions in solutions were determined by titration with silver nitrate, using the Mohr method for chloride and bromide, and eosin indicator for iodide. Halide concentrations in the resin were determined after displacement with excess sodium perchlorate. The results checked with those calculated from material balance within :L 3 per cent. RESULTS AND CALCULATIONS
Selectivity coefficients. The values obtained for K~alo~ were (3.3 ~ 0.4) :< l0 -2 for 0-5 M and (3-1 ~ 0.5) × l0 -2 for 0.3 M total concentration, the fraction of resin in Cl-form being in the range 0.01-0.1. N o value could be obtained for the 3 M series, because of the i m m e a s u r a b l y small concentration of chloride remaining in the resin. Although preliminary experiments indicated the possibility of a dependence of selectivity coefficients on the ionic strength of the solutions, (15~ 11o convincing p r o o f of this was obtained, and for similar systems, (16) no such dependence was found, the range investigated being 0.001-0.1 M only, however. The value K~o, -- 0.033 was, therefore, used for all calculations. F o r bromide and iodide the values (10 z~z 1) x 10 -2 and (33 4- 5) × 10 -2 respectively were found for KXo~ for 0.5 M total concentration. These agree fairly well with values in the literature (171 for 0.1 M solutions, and were therefore, used for all the concentrations studied. F r o m the selectivity coefficients, values of X = f ( X ) c could be calculated ( w r i t i n g ) ( -- (X-), the halide concentration in the resin, in moles per kilogram air dried resin, and X -~ (X-) in moles per litre solution): -- K(Xo4 C X / [ C - X(1 -- K X o ) ] (1) where C is the total concentration in solution (0.30, 0-50 and 3"00 M), and C is the capacity of the resin in millequivalent/gramme air dried resin. Mercury distribution. The results for the nine series of measurements are shown in Fig. 1. The a m o u n t s of resin and solution were chosen in such a way as to obtain maximal equilibrium halide concentrations of 0.10, 0-15 and 0.25 M for the three total concentrations 0.30, 0.50 and 3.00 M respectively, for each halide. As the measurements were made under conditions of a h r g e excess of halide over mercury, the only species present in appreciable a m o u n t s in both resin and solution phases are HgX2-, H g X a- and HgX42-. tl°) The following equilibria exist: HgX2 + X ~ HgXa-, equilibrium constant/£3
(2)
H g X 2 + 2 X - ~± HgX42-, equilibrium constant/£34
(3)
gXaH ~- HgX~, equilibrium constant K 0
(4)
and reactions corresponding to (2) and (3) in the resin phase, with equilibrium 114~I. ELIEZER and Y. MARCUS, Israel A.E.C. Semi-annual Report July-Dec. 1961. IA 726, p. 58 (1962). t15) I. ELIEZERand Y. MARCUS,Israel A.E.C. Semi-annual Report July-Dec. 1960. IA-620, p. 37 (1961). (in) H. P. GREGOR, J. E. BELLE and R. A. MARCUS, J. Amer. Chem. Soc. 77, 2713 (1955). t17) R. M. WHEATONand W. C. BAUMAN, Industr. Engng. Chem. 43, 1088 (1951).
1468
I. ELmZER and Y. MARCUS
constants g 8 and g ~ respectively. The distribution coefficient wiUthen be given by
4
g3x K° 1 + K z X + K ~ X z
= ~(rrgx,)
(5)
This relation is not sufficiently sensitive to permit the calculation of all five constants directly from it. Moreover, accurate values of Ks and K ~ in 0.5 NaC10 4 solution have been obtained previously, m) and it is o f little interest to redetermine them. Rather, these values can be combined with the data for the 0.5 M series, in order to reduce the number of the constants to be determined to three: the stability constants I
V V
I
V
I
V
I
V
I
O ~
I
V~V--
--V--V-- v 0 0 ~
1
~7 V ~7
V v V V V V V
--v--v--v--f
I
•
V~v--v-0 0
_._...~ o.~.o.~_ o.o.o o o o ~ ° ~ 8
~°-
A f
~
~3
-°--'--
££.s
4
~ A---A~"
....
8
,_
IZ
16 x 10.2
(X'), holide molarity
FIG. 1.--Distribution coefficients for tracer mercury (II) between Dowex-1 anion exchanger and halide-perchlorate solutions: /X chloride, © bromide, V iodide, full symbol C = 3-0 M, empty symbol C = 0-5 M, half-full symbol C = 0.3 M.
in the resin and the distribution constant of the neutral complex between the phases. Making use of the reported (Ix) Kz and K~, the denominator on the right hand of Equation (5) was calculated and the function t ----f(-~')0.5 (for (C = 0.5 M) obtained: t = [D(1 + K3X + K ~ X ~) -- Ko]/Ko : RaX + g~-~ ~
two side was (6)
The constant Ko was obtained simply by extrapolating the data to X = 0. Values of /~8 and K ~ were then obtained using the following methods. A plot of t X -1 vs..~gave R 3 as intercept and g ~ as slope, while a plot of tX -~ vs..~-1 gave/~3 as slope and g ~ as intercept. The constants could be obtained also by least squares calculation on
The anion exchange of metal complexes--XI
1469
these linear functions. Alternatively, curve fitting ~ts) was applied, comparing the experimental curve log t vs. log £ with a calculated curve log (v + v~) vs. log v, obtaining the constants from the position of the origin of coordinates when the curves coincide. TABLE 1 Medium Ligand Chloride
Bromide
Iodide
Constant log K0 (mlg-0 log Ks (M-0 log K84 (M -s) log Ko (mlg-0 log Ks (M-0 log Ks4(M-s) log Ko (mlg-0 log K3 (M-0 log Ks4(M-0
0.3 M
0.5 M
3.0 M
1.34 4- 0.08 1.I + 0.1 2.3 -4- 0"1 3.45 4- 0.07 2"5 4- 0"1 4"6 4- 0'1 5-0 4- 0"1 3"8 4- 0'3 6"4 4- 0"3
0.90 4- 0.07 0.95 c 2"00e 3.15 4- 0.09 2"27e 4'02c 4-85 4- 0-07 3.67e 6.04 e
0-70 ± 0-07 0.70 i 0.07 1.30 ± 0-07 2.18 ± 0.09 1'6 4- 0"1 2-6 ± 0"1 2"93 ± 0.08 3"0 4- 0'1 4"4 ± 0-1
resin (~12M) a b 2-15 ± 0.07 4.30 ± 0.08
1.55 3.10
2"7 ::k 0'1 4"7 4- 0-1
2"l 3"5
3"7 ± 0"1 5"6 ± 0'1
3'1 4'4
a Units of Ks and/~s4 in this column are kg resin mole-x and (kg resin) s mole-s respectively. b The values in this column have been calculated from the values in the previous column by converting the concentration units from moles/kg resin to moles per liter (internal solution). The conversion factor by which K3 or K3~½are multiplied, 0-25, has been obtained from the water content of the equilibrated resin ~. o From reference (11). Once the values o f R a and Ks4 have been obtained, and assuming that they are independent o f the ionic strength o f the external solution, values o f K a and Ka4 for total concentrations C = 0.3 and 3.0 M m a y be obtained from Equation (5) by a reverse process to the above. The constants thus obtained are shown in Table 1. DISCUSSION A l t h o u g h the mercury halide system is relatively simple, there being only three complex species in each phase, the expression for the distribution coefficient (5) turns out to be rather complicated, and did not permit an independent determination o f all five required parameters. This makes doubtful the possibility o f using the constant ionic m e d i u m m e t h o d independently on m u c h more complicated systems. On the other hand, the m e t h o d is highly valuable for obtaining the stability constants for the resin phase. ~5) Equation (5) may, o f course, be generalized by considering other species. It is interesting to compare constants f o u n d for various ionic media. The parameter K z for adding a singly charged halide anion to neutral mercury halide to form the singly charged complex anion involves a ratio o f activity coefficients of univalent ions, and the activity coefficients of the uncharged molecule. Ks = (HgXa-)/(HgX2)(X-) -- Ktherm s Y~gxs (Yx-/YHgXs-)
(7)
where K~he~ is the t h e r m o d y n a m i c equilibrium constant which is o f course independent o f the m e d i u m concentration, and the y ' s are molar activity coefficients. If the ~8~ L. G. SILLEN,Acta Chem. Scand. 10, 186 (1956).
1470
I. ELIEZERand Y. MARcus
ratio is taken as approximately unity, or at least as invariant with medium concentration, the effect of changing the ionic strength of the perchlorate medium should be the same for K S, as for K0, the constant for transferring the neutral mercury halide to the invariant resin. Indeed, the difference log K0 -- log K 3 is found to be approximately independent of the ionic strength. The variation of K0 (or/£3) with ionic strength, however, is opposite to what is expected from the salting effect of sodium perchlorate on the mercury halides, measured by extraction with benzene. ~19) There a salting constant of +0.14 was found, independent of the halide used, but here the salting constants are approximately --0.3 and show some variation with the halide. No reason for this discrepancy is directly evident. Another point to be noted is the stepwise formation of the anionic species in the resin phase, as shown by the magnitude of the constants J(3 and gz4. This behaviour at relatively low ligand concentration in the resin, in presence of a large excess of perchlorate ions, is contrary to that found when only ligand ions are present in the resin, t~°) Although in the latter case the ligand activity varies also, because of electrolyte invasion, it is initially at such a high concentration that usually only a single anionic complex predominates in the resin. For the cadmium-bromide system it has been shown ~5) that the stabilities of the complexes with one to three ligands are considerably enhanced in the resin phase compared to aqueous solutions. The complex with four ligands, however, was approximately equally stable in both phases. This has been connected c5) with the changes of the stability of the complexes with ionic strength, observed in aqueous solutions. The ionic strength in the resin, approximately 12 M, is however quite outside the range of 1-3 M, on which the above conclusion is based, and additional factors may be important. Examination of the values in Table 1 for the mercury halide systems shows that as the ionic strength increases, the chloride shows a pronounced minimum in the constants, the bromide a somewhat less pronounced minimum, while the iodide shows decreasing constants with no clear minimum. An explanation for this trend may be sought in the competing action of the screening and dehydrating effects of the medium. The first factor should be independent of the ligand, while for the second, the effect for the chloride, bromide and iodide should decrease in this order. Thus for the more dehydratable chloride ligand, the complex formation in the resin should be enhanced as compared to aqueous solutions due to the highly dehydrating environment of the resin c~1) (particularly in the perchlorate form). No such enhancement should occur with the relatively non-dehydratable iodide ion. This is, in fact, confirmed by the data in Table 1. Acknowledgements--The technical assistance of Mrs. N. BAUMANand Miss S. YITSHAKIiS gratefully acknowledged. ~19~y . MARCUS,Acta Chem. Scand. 11, 329 (1957). ~20~I. ELIEZER and Y. MARCUS,J. lnorg. NucL Chem. 25, 867 (1963). t21~ y . MARCUSand D. MAYDAN,J. Phys. Chem. 67, 983 (1963).
Chem.,
1963, Vol. 25, pp. 1465 to 1470. Pergamon Press Ltd. Printed in Northern
Ireland
THE A N I O N E X C H A N G E OF METAL COMPLEXES--XI* A P P L I C A T I O N OF T H E C O N S T A N T I O N I C M E D I U M M E T H O D TO T H E M E R C U R Y H A L I D E SYSTEM I. ELIEZER and Y. MARCUS Radiochemistry Department, Israel Atomic Energy Commission, Soreq Research Establishment, Rehovoth, Israel (Received26 March 1963; in revisedform 10 May 1963)
Al~traet--The applicability of the constant ionic medium method to the study of metal complex formation by exchange has been investigated, using the mercury(II) halide system as an illustration. The distribution of mercury(II) tracer has been measured between C molar (NaX + NaC10,) solution and (RX ÷ RC104) Dowex 1 resin, for C = 0"3, 0"5 and 3'0 M and X = CI-, Br- and I-. The stability constants for the resin phase and for the 0"3 and 3 M solutions have been calculated. The general applicability of the method for anion exchange studies has been discussed. THE constant ionic medium method ~1) has often been used to study complex formation in solution. It has been used successfully in conjunction with the cation exchange method ~lb) but less successfully with the anion exchange method. FRONAEUS,~2) in introducing anion exchange as a quantitative method for studying metal complexes, mentioned that if a constant neutral salt medium is used, considerable anion exchange takes place when the ligand concentration is varied within wide limits, and the metal distribution will be a too complicated function of the ligand concentration. Subsequent quantitative treatments of the anion exchange method~3, 4) have usually dispensed with a constant ionic medium, and tried instead to evaluate the activity coefficient terms. A detailed examination of the applicability limits of the constant ionic medium method seemed desirable, because of the known difficulties with the evaluation of activity coefficients. While this work was in progress, FRONAEUS et al. ~ published an account of the use of this method obtaining the stability constants in the resin phase for the cadmium bromide system, without however evaluating it in a general way. Earlier, SONESSON~) studied the gadolinium glycolate system using a constant ionic medium in the aqueous phase, while permitting the resin composition to vary considerably. The medium inside the resin was, therefore, far from constant, and stability * Previous paper in Series: D. MAYDANand Y. MARCUS: J. Phys. Chem. 67, 987 (1963). ~1~j. N. BRONSTED,Trans. Faraday Soc. 23, 416 (1927). t~bl F. J. C. ROSSOTTIand H. ROSSOTTI,Determination of Stability Constants. McGraw-Hill, New York (1961). ~ S. FRONAEUS, Svensk Kern. Tidskr. 65, 1 (1953). ~a~ y . MARCUS and C. D. CORYELL,Bull. Res. Council 8 A, 1 (1959) c4, K. A. KRAUS and F. NELSOr~, Structure of Electrolyte Solutions (Edited by W. J. HAMER), p.340 J. Wiley, N e w Y o r k (1959). ~ S. FRONAEUS, I. LUNDQVIST and A. SONr_.SSON,Acta Chem. Scand. 16, 1936 (1962). t0, A. SONESSON, Acta Chem. Scand. 15, 1 (1961). 1465
1466
I. ELmZERand Y. MARCUS
constants in the resin phase could be determined very approximately, using constants for the aqueous phase obtained by another method. Similarly, in the method proposed by WAKI, c7-9) substitution was permitted to proceed over the whole mole fraction range, and it is unlikely that the activity coefficient term remained constant. The differentiation used may therefore not be reliable. Further complications are introduced in WAKI'S experiments by the considerable loading of the exchanger by the metal used. It does not seem possible, in a completely general way, to vary the ligand concentration over a wide range and still have a constant ionic medium in the resin phase. In some particular cases, however, this may be possible. Namely, this is so where complex formation is relatively strong, requiring only low concentrations of the ligand, and where the affinity of the ligand for the resin is not too high, so that the resin remains essentially loaded with the medium ions. Using perchlorate ions for the medium, as is usually done, has the advantage of providing the resin with an anion of high affinity, competing favourably with most ligand ions. This requires high intrinsic affinity of the anionic metal complex for the exchanger, as otherwise distribution coefficients would be too small. In cases fulfilling the above requirements, it should be possible to determine stability constants for both phases, valid for the ionic medium chosen, and particularly also constants for the anionic complexes, which may not be always reliably determined by other methods. For other cases, in particular where complexes are weak and are formed only at high ligand concentration, the constant medium principle cannot be used, and other anion exchange methods ~4) should be used. The present work describes the application of the constant ionic medium method to the mercury halide systems, where the above conditions seem to have been met. The stability constants for mercury(II) with chloride, bromide and iodide have already been measured by other methods. ~1°-12) The values obtained by the anion exchange method may thus be compared with previously reported values. EXPERIMENTAL Materials. Radioactive mercury, 2°SHg, obtained from O.R.N.L. in form of a nitrate solution was used, diluted so that the total mercury concentration was in all cases 10-4-10-e M. The resin used was Bio-Rad Dowex-1 A.G., 8 per cent crosslinked, 100-200 mesh. It was converted to the appropriate halide form, using hydrochloric acid, sodium bromide or iodide, after having been passed through the usual acid-base conditioning cycles. All other reagents were of analytical grade. Methods. Selectivity coefficients, KXclo4= (X-)(C104-)/(C104-)(X-), parenthesis denoting concentrations, barred symbols the resin phase, and X a halide ion, were measured in experiments where known quantities of resin in halide form were equilibrated for 24 hours with known quantities of perchlorate solutions at room temperature, 23 ± 3°. The coefficients were calculated from the measured capacity of the resin, its water content (obtained by the centrifugation method) ~13~and the concentration of halide in the resin and the solution phases at equilibrium. Mercury distribution coefficients were measured in similar experiments. Weighed amounts of ~7~H. WAKI,Bull. Chem. Soc. Japan 33, 1469 (1960); 34, 829 (1961). ~8~H. WAKI,Bull. Chem. Soc. Japan. 34, 1842 (1962). c9~j. YOSHIMURA,H. WAKIand S. T.~SHIRO,Bull. Chem. Soc. Japan 35, 412 (1962). ~10)L. G. SIt.LEN,Acta Chem. Scand. 3, 539 (1949). ~11~Y. MARCUS,Acta Chem. Scand. 11, 599 (1957). cx2JC. L. VAN PANTALEONVAN ECK, Thesis, Leiden (1958). ~8) K. W. PEPPEg D. REICHENBERGand D. K. HALE,J. Chem. Soc. 3129 (1952).
The anion exchange of metal complexes--XI
1467
resin in halide fo:m were equilibrated with solutions containing 0.01 M perchloric acid (to prevent hydrolysis of mercury ions) and 0.29, 0'49 or 2.99 M sodium perchlorate. The radioactivity of aliquots of the solution, separated from the resin by filtering through glass wool plugs, was measured in a well-type scintillation counter, and compared with that of blanks, shaken under similar conditions but without resin. The distribution coefficients D (activity per gramme air dried resin/activity per ml solution) were calculated from these values c14). The concentrations of halide ions in solutions were determined by titration with silver nitrate, using the Mohr method for chloride and bromide, and eosin indicator for iodide. Halide concentrations in the resin were determined after displacement with excess sodium perchlorate. The results checked with those calculated from material balance within :L 3 per cent. RESULTS AND CALCULATIONS
Selectivity coefficients. The values obtained for K~alo~ were (3.3 ~ 0.4) :< l0 -2 for 0-5 M and (3-1 ~ 0.5) × l0 -2 for 0.3 M total concentration, the fraction of resin in Cl-form being in the range 0.01-0.1. N o value could be obtained for the 3 M series, because of the i m m e a s u r a b l y small concentration of chloride remaining in the resin. Although preliminary experiments indicated the possibility of a dependence of selectivity coefficients on the ionic strength of the solutions, (15~ 11o convincing p r o o f of this was obtained, and for similar systems, (16) no such dependence was found, the range investigated being 0.001-0.1 M only, however. The value K~o, -- 0.033 was, therefore, used for all calculations. F o r bromide and iodide the values (10 z~z 1) x 10 -2 and (33 4- 5) × 10 -2 respectively were found for KXo~ for 0.5 M total concentration. These agree fairly well with values in the literature (171 for 0.1 M solutions, and were therefore, used for all the concentrations studied. F r o m the selectivity coefficients, values of X = f ( X ) c could be calculated ( w r i t i n g ) ( -- (X-), the halide concentration in the resin, in moles per kilogram air dried resin, and X -~ (X-) in moles per litre solution): -- K(Xo4 C X / [ C - X(1 -- K X o ) ] (1) where C is the total concentration in solution (0.30, 0-50 and 3"00 M), and C is the capacity of the resin in millequivalent/gramme air dried resin. Mercury distribution. The results for the nine series of measurements are shown in Fig. 1. The a m o u n t s of resin and solution were chosen in such a way as to obtain maximal equilibrium halide concentrations of 0.10, 0-15 and 0.25 M for the three total concentrations 0.30, 0.50 and 3.00 M respectively, for each halide. As the measurements were made under conditions of a h r g e excess of halide over mercury, the only species present in appreciable a m o u n t s in both resin and solution phases are HgX2-, H g X a- and HgX42-. tl°) The following equilibria exist: HgX2 + X ~ HgXa-, equilibrium constant/£3
(2)
H g X 2 + 2 X - ~± HgX42-, equilibrium constant/£34
(3)
gXaH ~- HgX~, equilibrium constant K 0
(4)
and reactions corresponding to (2) and (3) in the resin phase, with equilibrium 114~I. ELIEZER and Y. MARCUS, Israel A.E.C. Semi-annual Report July-Dec. 1961. IA 726, p. 58 (1962). t15) I. ELIEZERand Y. MARCUS,Israel A.E.C. Semi-annual Report July-Dec. 1960. IA-620, p. 37 (1961). (in) H. P. GREGOR, J. E. BELLE and R. A. MARCUS, J. Amer. Chem. Soc. 77, 2713 (1955). t17) R. M. WHEATONand W. C. BAUMAN, Industr. Engng. Chem. 43, 1088 (1951).
1468
I. ELmZER and Y. MARCUS
constants g 8 and g ~ respectively. The distribution coefficient wiUthen be given by
4
g3x K° 1 + K z X + K ~ X z
= ~(rrgx,)
(5)
This relation is not sufficiently sensitive to permit the calculation of all five constants directly from it. Moreover, accurate values of Ks and K ~ in 0.5 NaC10 4 solution have been obtained previously, m) and it is o f little interest to redetermine them. Rather, these values can be combined with the data for the 0.5 M series, in order to reduce the number of the constants to be determined to three: the stability constants I
V V
I
V
I
V
I
V
I
O ~
I
V~V--
--V--V-- v 0 0 ~
1
~7 V ~7
V v V V V V V
--v--v--v--f
I
•
V~v--v-0 0
_._...~ o.~.o.~_ o.o.o o o o ~ ° ~ 8
~°-
A f
~
~3
-°--'--
££.s
4
~ A---A~"
....
8
,_
IZ
16 x 10.2
(X'), holide molarity
FIG. 1.--Distribution coefficients for tracer mercury (II) between Dowex-1 anion exchanger and halide-perchlorate solutions: /X chloride, © bromide, V iodide, full symbol C = 3-0 M, empty symbol C = 0-5 M, half-full symbol C = 0.3 M.
in the resin and the distribution constant of the neutral complex between the phases. Making use of the reported (Ix) Kz and K~, the denominator on the right hand of Equation (5) was calculated and the function t ----f(-~')0.5 (for (C = 0.5 M) obtained: t = [D(1 + K3X + K ~ X ~) -- Ko]/Ko : RaX + g~-~ ~
two side was (6)
The constant Ko was obtained simply by extrapolating the data to X = 0. Values of /~8 and K ~ were then obtained using the following methods. A plot of t X -1 vs..~gave R 3 as intercept and g ~ as slope, while a plot of tX -~ vs..~-1 gave/~3 as slope and g ~ as intercept. The constants could be obtained also by least squares calculation on
The anion exchange of metal complexes--XI
1469
these linear functions. Alternatively, curve fitting ~ts) was applied, comparing the experimental curve log t vs. log £ with a calculated curve log (v + v~) vs. log v, obtaining the constants from the position of the origin of coordinates when the curves coincide. TABLE 1 Medium Ligand Chloride
Bromide
Iodide
Constant log K0 (mlg-0 log Ks (M-0 log K84 (M -s) log Ko (mlg-0 log Ks (M-0 log Ks4(M-s) log Ko (mlg-0 log K3 (M-0 log Ks4(M-0
0.3 M
0.5 M
3.0 M
1.34 4- 0.08 1.I + 0.1 2.3 -4- 0"1 3.45 4- 0.07 2"5 4- 0"1 4"6 4- 0'1 5-0 4- 0"1 3"8 4- 0'3 6"4 4- 0"3
0.90 4- 0.07 0.95 c 2"00e 3.15 4- 0.09 2"27e 4'02c 4-85 4- 0-07 3.67e 6.04 e
0-70 ± 0-07 0.70 i 0.07 1.30 ± 0-07 2.18 ± 0.09 1'6 4- 0"1 2-6 ± 0"1 2"93 ± 0.08 3"0 4- 0'1 4"4 ± 0-1
resin (~12M) a b 2-15 ± 0.07 4.30 ± 0.08
1.55 3.10
2"7 ::k 0'1 4"7 4- 0-1
2"l 3"5
3"7 ± 0"1 5"6 ± 0'1
3'1 4'4
a Units of Ks and/~s4 in this column are kg resin mole-x and (kg resin) s mole-s respectively. b The values in this column have been calculated from the values in the previous column by converting the concentration units from moles/kg resin to moles per liter (internal solution). The conversion factor by which K3 or K3~½are multiplied, 0-25, has been obtained from the water content of the equilibrated resin ~. o From reference (11). Once the values o f R a and Ks4 have been obtained, and assuming that they are independent o f the ionic strength o f the external solution, values o f K a and Ka4 for total concentrations C = 0.3 and 3.0 M m a y be obtained from Equation (5) by a reverse process to the above. The constants thus obtained are shown in Table 1. DISCUSSION A l t h o u g h the mercury halide system is relatively simple, there being only three complex species in each phase, the expression for the distribution coefficient (5) turns out to be rather complicated, and did not permit an independent determination o f all five required parameters. This makes doubtful the possibility o f using the constant ionic m e d i u m m e t h o d independently on m u c h more complicated systems. On the other hand, the m e t h o d is highly valuable for obtaining the stability constants for the resin phase. ~5) Equation (5) may, o f course, be generalized by considering other species. It is interesting to compare constants f o u n d for various ionic media. The parameter K z for adding a singly charged halide anion to neutral mercury halide to form the singly charged complex anion involves a ratio o f activity coefficients of univalent ions, and the activity coefficients of the uncharged molecule. Ks = (HgXa-)/(HgX2)(X-) -- Ktherm s Y~gxs (Yx-/YHgXs-)
(7)
where K~he~ is the t h e r m o d y n a m i c equilibrium constant which is o f course independent o f the m e d i u m concentration, and the y ' s are molar activity coefficients. If the ~8~ L. G. SILLEN,Acta Chem. Scand. 10, 186 (1956).
1470
I. ELIEZERand Y. MARcus
ratio is taken as approximately unity, or at least as invariant with medium concentration, the effect of changing the ionic strength of the perchlorate medium should be the same for K S, as for K0, the constant for transferring the neutral mercury halide to the invariant resin. Indeed, the difference log K0 -- log K 3 is found to be approximately independent of the ionic strength. The variation of K0 (or/£3) with ionic strength, however, is opposite to what is expected from the salting effect of sodium perchlorate on the mercury halides, measured by extraction with benzene. ~19) There a salting constant of +0.14 was found, independent of the halide used, but here the salting constants are approximately --0.3 and show some variation with the halide. No reason for this discrepancy is directly evident. Another point to be noted is the stepwise formation of the anionic species in the resin phase, as shown by the magnitude of the constants J(3 and gz4. This behaviour at relatively low ligand concentration in the resin, in presence of a large excess of perchlorate ions, is contrary to that found when only ligand ions are present in the resin, t~°) Although in the latter case the ligand activity varies also, because of electrolyte invasion, it is initially at such a high concentration that usually only a single anionic complex predominates in the resin. For the cadmium-bromide system it has been shown ~5) that the stabilities of the complexes with one to three ligands are considerably enhanced in the resin phase compared to aqueous solutions. The complex with four ligands, however, was approximately equally stable in both phases. This has been connected c5) with the changes of the stability of the complexes with ionic strength, observed in aqueous solutions. The ionic strength in the resin, approximately 12 M, is however quite outside the range of 1-3 M, on which the above conclusion is based, and additional factors may be important. Examination of the values in Table 1 for the mercury halide systems shows that as the ionic strength increases, the chloride shows a pronounced minimum in the constants, the bromide a somewhat less pronounced minimum, while the iodide shows decreasing constants with no clear minimum. An explanation for this trend may be sought in the competing action of the screening and dehydrating effects of the medium. The first factor should be independent of the ligand, while for the second, the effect for the chloride, bromide and iodide should decrease in this order. Thus for the more dehydratable chloride ligand, the complex formation in the resin should be enhanced as compared to aqueous solutions due to the highly dehydrating environment of the resin c~1) (particularly in the perchlorate form). No such enhancement should occur with the relatively non-dehydratable iodide ion. This is, in fact, confirmed by the data in Table 1. Acknowledgements--The technical assistance of Mrs. N. BAUMANand Miss S. YITSHAKIiS gratefully acknowledged. ~19~y . MARCUS,Acta Chem. Scand. 11, 329 (1957). ~20~I. ELIEZER and Y. MARCUS,J. lnorg. NucL Chem. 25, 867 (1963). t21~ y . MARCUSand D. MAYDAN,J. Phys. Chem. 67, 983 (1963).