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The aqueous chemistry of hafnium (IV) solvent extraction and ion exchange studies
J. Inorg. Nucl. Chem., 1965, Vol. 27, pp. 2171 to 2181. Pergamon Press Ltd. Printed in Northern Ireland
THE AQUEOUS CHEMISTRY OF HAFNIUM (IV) SOLVENT EXTRACTION
AND ION EXCHANGE
STUDIES
R. G. DESHPANDE, P. K. KHOPKAR, C. L. RAO and H. D. SHARMA Radiochemistry and Isotope Division, Atomic Energy Establishment, Trombay, Bombay (Received 6 April 1964; in revised form 30 September 1964)
Abstract--Some aspects of the solution chemistry of hafnium (IV) have been investigated by TTA solvent extraction and shallow bed ion exchange resin techniques. The stability constants of hafnium (IV) with chloride (ill 0"7, flz 0"48), nitrate (ill 0.8), sulphate (fla 110, r2 5 × 103) and fluoride (ill 4"2 × 104) ions have been determined and they are all lower as compared to the corresponding zirconium (IV) complexes. The rates of exchange of hafnium species on a cation exchange resin at various molarities in HCI, HNOa and HC104 media have also been determined. A model for the variation of diffusion coefficients with acidity has been suggested. THE chemical behaviour o f zirconium (IV) ions in aqueous solutions is quite complex as summarized in a review article by SOLOVKIN and TSVETKOVA.(1) The interest has largely been in its complexing behaviour and its existence as either unhydrolysed or hydrolytic p o l y m e r species in aqueous mcdia. There have been similar investigations, although n o t as exhaustive as those on zirconium ions, on the solution chemistry o f h a f n i u m viz. complex formation with chloride, nitrate, fluoride, oxalate and sulphate ions b y ion-exchange and solvent extraction techniques ~-5) and on the nature o f its hydrolytic species by ultra-centrifugation ~8) and ion exchange. (7) The present data on the determination o f stability constants for complex formation with various anions by 'solvent extraction m e t h o d ' and the rate o f exchange o f hafnium species on a cation exchange resin at various acidities, using the shallow bed technique, were collected during 1955 and 1957 with a view to finding better methods o f separation f r o m its analogue, zirconium. The values o f the stability constants o f hafnium complexes obtained, have been c o m p a r e d with those o f other workers for zirconium and h a f n i u m ; the existence o f hydrolytic species in solution, as studied by the measurement o f the rate o f exchange in different media, has been discussed. EXPERIMENTAL Hafnium-181 was used as a tracer in all experiments. The tracer was prepared by the irradiation of specpure HfO~ with neutrons at BEPO, Harwell, and subsequent dissolution of the hafnium in a platinum dish on a hot water bath with a mixture of HNO3 and HF. The resultant solution was then fumed with concentrated H~SO4 to eliminate fluoride ions. The hafnium was then precipitated ~a~A. S. SOLOVrdNand S. V. TSVETKOVA,Uspenskhi Khimi, 31, 655 (Nov. 1962). ~2~I. N. MAROVand D. I. RYABCrIII
2172
R . G . DESHPANDE,P. K. KHOPKAR, C. L. RAO and H. D. SHARMA
with NH4OH, repeatedly washed with water and dissolved in any one of the desired acids. It was re-precipitated with NH4OH, washed and dissolved in the desired acid, this process being repeated to ensure complete removal of sulphate ions. For the solvent extraction experiments, the hafnium hydroxide was dissolved in 4 M perchloric acid. In other experiments, stock solutions were made in corresponding 4 M acids. The concentration of hafnium in the tracer solution was determined by evaporation of 1 ml of the stock solution in a platinum crucible, subsequent ignition and weighing it as HfO~. TTA from Penn Research Corporation, U.S.A. was purified by recrystallization from thiophenefree benzene. Freshly prepared solution of the purified TTA in benzene of the desired molarity was used in all solvent extraction experiments.
T
. . . .
III. TO . . SCALER .
Fro. 1.---Apparatus for diffusion experiments. A" Reactor cup B" Mechanical stirrer C: Sintered glass bed D: G . M . Flow Counter E: Capillary tubing. The equilibrations were carried out at 27 ± 2°C in sealed stoppered Pyrex test-tubes and the two phases were contacted by mechanically stirring the tube for 2 hr. Samples were drawn from the two phases and their radioactivity assayed using a NaI(T1) scintillation counting assembly. The extraction coefficient E is defined as: E=
Concentration of Hf in organic phase Concentration of Hf in aqueous phase
counts min -1 m1-1 (organic) counts min -1 m1-1 (aqueous)
Cation exchange resin, Zeokarb-225 (cross linkage 10 per cent), was used in the ion exchange experiments. About 20 g of the resin was converted to H + form by contacting the resin with 4 M HC1 and after washing with distilled water thoroughly, it was air dried under an infra-red lamp. The dried resin was then passed through standard sieves, and the fraction collected between 18 and 22 mesh size (B.S.S.) was used in the experiments. An apparatus (Fig. 1), similar to the one used by LISTER and MCDONALD,ca) was employed in the present experiments. The stock hafnium solution, prepared in the appropriate acid and brought to a known strength, was transferred to cup (A), wherein it was stirred with a known quantity of resin with a slow speed stirrer (B). The solution after passing through the sintered glass bed (C) ts) B. A. J. LISTERand L. A. MCDONALD,f. Chem. Soc. 4315 (1952).
The aqueous chemistry of hafnium (IV)
2173
was circulated in a G.M. flow counter (D) after which it was recirculated through the reaction cup by pneumatic transfer. The activity of the solution flowed through the G.M. counter was assayed at definite intervals of time. A constant flow-rate was maintained by adjusting the air pressure. RESULTS AND DISCUSSION (a) Extraction experiments (i) Hydrolysis. The extraction coefficient E was determined at various H + ion concentrations in 9erchlorate media. Figure 2 gives a plot of log E 0 (E0 being the 9
8
g,7
6
5
~o
I
-0'8
I
i
I
I
I
1
-0'6 -0'4 -0'2
I
i
I
I
0 + 0"2 log[H "I
I
I
0"4
=
I
I
I
I
0"6 0'8
Fio. 2.--Distribution coefficient vs. hydrogen ion concentration. extraction coefficient normalized to 1 M T T A concentration) vs. log [H+]. Following CONNICK and McVEY, (9) the equilibrium condition for the extraction of any metal ion with T T A is denoted as M(OH)m(T)~-~ -~ + (n -- p)HTorg ~ MTnorg + (n -- m - - p ) H + + mH~O Then, log E = log Kex ÷ (n -- p) log [HT] -- (n -- m - - p) log [H +]
(1) (2)
where, M stands for Hf; H T ----T T A ; Kex ----equilibrium constant for the reaction (1). A plot of log E vs. log [H +] at constant H T gives a curve with a negative slope (n - - m -- p) where m and p are the numbers of hydroxyl groups and T T A molecules attached to the metal ion in the aqueous phase. The fourth power dependence of log E on log T T A has already been established by H ~ A N and co-workers ~l°,xx~and therefore the value of p can be taken as zero. In Fig. 2 is shown the plot of log E 0 vs. ~9~R. E. CONNICKand W. H. McVEY,J. A. Chem. Soc. 71, 3182 (1949). tle~ E. H. HUrrMANand C. J. BEAUFArr,J. A. Chem. Soc. 71, 3179 (1949). txl~ E. H. HUFFMAN,G. M. IDDINGS,R. N. OSBORNEand G. V. SnAUMOFF,J. A. Chem. Soc. 77, 881 (1955).
R.G. DESHPANDE,P. K. KHOPKAR,C. L. RAO and H. D. SHARMA
2174
log [H +] for perchlorate medium. It is seen that up to 1.5 M [H+] the curve has a slope of --3 indicating that the species in solution has an average charge of + 3 and above 1"5 M [H +] the slope is - - 4 showing that hafnium (IV) exists as species with a charge of + 4 . Thus, in 2M HC104, the equilibrium can be represented as follows provided activity coefficients of the reacting species do not vary considerably, H f 4+ + 4HT ~ HfT 4 + 4H +
(3)
which gives the fourth power dependence of E o on H + ion concentration. At concentration 10-4 M of hafnium in 1.5 M HC104, probably species of the type Hf(OH) ~are present in solution, while at higher acidities H f 4+ species are present if the assumptions connected with TTA method hold good as far as activity coefficients of the reacting species are concerned. Furthermore, the distribution coefficients in the experiments carried out at 2 M acidity did not change when the concentration of H f 4+ was TABLE 1 .--SOLVENT EXTRACTION DATA FOR THE DETERMINATION OF STABILITY CONSTANTS OF H f 4+
Conc. HSO4- ion (M)
Eo/E
Conc. NOn- ion (M)
0.01 0'02 0"03 0.04 0"05 0"06 0"07 0"08 0.09 0'10 0.12 0.15
1.67 2-75 3.67 5.30 6.62 9"22 11"02 12"85 14'59 18"01 22.66 34.86
0.1 0'2 0.3 0.4 0"5 0.6 0.7 0'8 0"9 1.0 . .
Conc. C1- ion (M)
Eo/E 1.13 1'12 1.25 1.34 1"41 1"49 1"52 1'60 1'72 1-86 . .
. .
0.1 0.2 0-3 0.4 0.5 0.6 0'8 0"9 . . . .
Conc. HF (M)
Eo/E 1.06 1'15 1.28 1.35 1"47 1'64 1'87 2.00 . .
. . . .
1 × 10-4 5 × 10-4 1 × 10-a 5 × 10-8 ----. . . .
Eo/E 18"52 116.3 238.1 666.7 -----
varied from 10-7 M to 1.6 × 10-3 M but thereafter they decreased rapidly at higher concentrations, the value of distribution coefficient being 10 4- 1 at the former concentrations and 1.5 at 10-8 M Hf(IV). Similarly at 1.4 M acidity up to a concentration of 6.65 × 10-4 M Hf(IV) essentially the distribution coefficients remained the same but at higher concentration they decreased showing that at 10-4 M (concentration of H f in the present studies) essentially monomeric species of H f 4+ and Hf(OH) a+ are present at these acidities. These results may be compared to those of CONNICK and McVEY (9) who reported by similar extraction studies that at tracer concentrations in 2 M HCIO4, zirconium (IV) exists chiefly in the form of the monomer Zr4+; and in the range 0.2-2-0 M HC104 the composition of zirconium (IV) ions correspond to the formula Zr(OH) 3+. According to LARSEN and WANG/7) zirconium (IV) species at 10-4 M also exists as Zr 4+ ion in 2 M HC104. (ii) Anion eomplexing. The complexing behaviour of hafnium (IV) with sulphate, nitrate, chloride and fluoride ions was studied by TTA method. All the experiments were conducted at constant ionic strength/, = 2 and constant acidity of 2 M, the
The aqueous chemistry of hafnium (IV)
2175
ionic strength being maintained constant by the addition of perchloric acid, so as to minimize the change in the activity coefficients of the anionic species. The concentrations of HSO4-, HF, NOa- and C1- have been used for the calculation of stability constants (vide Table 1). The stability constants flj were calculated from the extraction data obtained at various concentrations of ligands using the method of DAY and STOUGHTON (12) c o n s i d e r i n g the following equilibrium M ~" + j A -'~ ~ MA +(4-"~) MA + (4--n./) fl,. = [Ma+][A_,q~ where [A] = j = n = The fl~ values
(4)
(5)
concentration of ligand number of ligands attached to the metal ions charge of the ligand. were determined for the following equilibria from the experimental data: H f a+ + HSO 4- ~- HfSO4 ~+ + H + H f 4+ + 2HSO4- ~-- Hf(SO4)2 + 2H + H f 4+ q- C1- ~ HfCI 3+ H f 4+ q- 2C1- ~ HfClz~+ H f 4+ + NO 3- ~-- HfNO33+ H f 4+ + H F ,~- H f F 3+ + H +
(6) (7) (8) (9) (1(3) (11)
Table 1 gives the extraction data for the various systems studied from which the various stability constants have been evaluated; and Table 2 gives the values of the stability constants of H f 4+ with sulphate, chloride, fluoride and nitrate ions, and the values for both H f 4+ and Zr 4+ reported by other workers.(e,3,4,5,%13,14,TM As seen from Table 2, the first and second stability constants for hafnium complexes are generally lower than those for zirconium; this is expected as the ionic radius for Zr 4+ is smaller than that for H f 4+. The lower values of fll and fl~ for sulphate complexes of hafnium compared to those for zirconium are also consistent with the observed elution characteristics of hafnium and zirconium from the cation exchange columns with sulphuric acid. In the case of nitrate complexes our lower value of fl~ (0.8) for H f 4+ appears to be reasonable compared to 8.2 for the same ion reported by PROKI-IOROVAand BV,~ZHNnVA(3) who used the tributyl phosphate (TBP) solvent extraction method. The TBP solvent extraction method is found to give higher values for the stability constants if [TBP] alone is used in the calculation as against [HNOa-TBP]. t16) The values for the stability constants of fluoride and chloride complexes obtained by us using T T A method are in general agreement with those reported by other workers, although the fluoride system has not been studied very exhaustively in the present studies. (12~R. A. DAY and R. W. SxooG~rroN,J. A. Chem. Soc. 72, 5662 (1950). ~13~I. N. MAROV,Candidate's thesis, Vernadski Institute of Geochemistry and Analytical Chemistry, Moscow, 1961 (as cited in Reference 1). (14JA. S. SOLOVKIN,Zh. Neorff, Khim. 2, 611 (1957). ~13~S. ARm.ANt)and D. KAPaViDS,B. NOV.EN,Acta Chem. Scand. 17, 411 (1963). ~18~T. S. LAXMINARAYANAN,S. K. PATmand H. D. SHARMA,J. Inorg. Nucl. Chem. 26, 1001 (1964).
Fluoride
Nitrate
Sulphate
Ligand
-
0.7
-
0.8 -
42 x104 _
4
2
2
2 2 2 2 4 4
2
4-
3
-
-
2.33
2
-
110 -
B1
___----92
-
-
z -
-
0.48
-
o-90 2.18 0.6 8,2
0.95 24
-
_
1.87 x 104
--_---__-_
-
-
108
5x108 -
-
/%
x
3.6
_
108
0.12 3.21
0.55 1.0
0.12 1.18
-
_
2.12 x103 _
Ba
Hafnium
z 0.19 -
0.01 ;25
_
10’4
x
x
10”
1,95
1
3.35
1
I 0.03 119
0,08 0.05
_
_
_
81 -
Others
x
I 10’6
q
121
-
-z
_
_
-
85
x
10’8
2.31
z
6;s
z -
-1
_
_
f%
x 105
-
3.2 x 10’0
-
1.32 x 10’0
0x6 0.14
0.92 2.0 O-88 -
6.3x 106
0.12 z
_ 2.4 x 104 3.48 x 108 5.0 x104
pa -
0.95 1
x 102
4.6 x 102 4.66 x 10=
/?I -
/!& -
-
-
s.a x 10’8
-
-
OTOl 0.05 32
-
_ 2.4 x104 3.92 x106
Zirconium
OF Hf4+ AND ZI?+ BY SOME INORGANIC LIGANDS
-
/%
110
TABLE 2.-COMPLEXING
Ba
This work
2
2 2
Ionic strength ,u
-
-
-
-
-
15-
0.08 -
-
-
-
_ -
/Y4 -
extraction
Ion exchange
TI’A extraction and Potentiometry.
TTA extraction
TTA extraction
TTA extraction Ion exchange TTA extraction ‘ITA extraction Ion exchange TBP extraction
TTA extraction TTA extraction Ion exchange TTA extraction Ion exchange TBP extraction
Ion exchange
Ion exchange
=A
TT’A extraction
TTA extraction
Method
(15)
(4)
(9)
-
(9)
(9) (2) (14)
(15)
(13)
(9)
(5)
-
Reference
The aqueous chemistry of hafnium (IV)
2177
(b) Diffusion experiments The quantity of hafnium, adsorbed on the resin at any time t, is related to the diffusion coefficient in the resin phase, by the relationship(m Q' - 6 J ( - ~ ) Q o - - Q ° Q ~ r Q~o
(12)
where
D -----diffusion coefficient, r = radius of the resin bead Q0 = original amount of hafnium Qt and Qo~ = amount of hafnium taken up at time t and at equilibrium respectively. This relationship is valid only if the particle diffusion is the controlling mechanism as against the film diffusion. (17) The diffusion experiments suggest the former mechanism as indicated by the linear relationship observed between Qt/Q~o and ~/t for the perchlorate system, shown as a typical case in Fig. 3. 1'0 0
0'9
0'8 P
0'7 ~0'6 0"5 0"4 0'3 0'2 0"1 I
0
I
2
I
1
4
I
I
6
I
I
8
I
vT
I
10
I
I
12
I
l
lk
I
I
16
I
18
FIo. 3.--Uptake of hafnium (IV) with time [Hf] = 0.0019 M [HC104] = 1-0 M The values of D calculated from the data given in Tables 3, 4 and 5 show that D increases with acid concentration in all the cases. When log D is plotted against log M, M being the molarity of the various acids, linear plots are obtained as shown in Fig. 4, except in the case of the HNO3 system where corrections have been applied for the ~a~)T. R. E. KRESSMANand J. A. KITCm,rER, Disc. FaradaySoc. 7, 90 (1949).
2178
R. G. DF..SI"IPANDE,P. K. K.HOPKAR,C. L. RAO and H. D. SHARMA TABLE 3.--DIFFUSIONOF Hf (IV) IN HC1 IN ZEOKARB-225(H+ FORM)
No. 1 2 3 4 5 6 7 8
[Hf] = 0'001 M Conc. (M) D x 101°(cm2/sec) 0"73 0"88 1"09 1"35 1"65 2"01 2"37 3"09
0"53 1"45 6"96 32"24 73"31 190'30 424"80 1550"00
incomplete dissociation o f the acid as given by HESFORD a n d McKAY. cls) D can be expressed b y the relationship
D = Do M~
(13)
where D, D O = diffusion coefficients at acid molarities M a n d 1 respectively, a n d n = c o n s t a n t (slope of the line). TABLE 4.--DIFFUSIONOF Hf (IV) IN HNO8 IN ZEOKARB-225(H+ FORM)
No. 1 2 3 4 5 6
[Hf] = 0"0012 M Conc. (M) D × 101°(cm~/sec) 0"89 1"18 1'45 1"9 2"3 2"8
0'19 0"75 6"30 96-87 201"0 351'8
I n T a b l e 6 are given the values o f D o a n d n for the various systems. It is seen that the values o f n range f r o m 5.2 to 6.6, while D Ovalues differ by a large factor, between 3.98 × 10 -1° for HC1 system a n d 4 × 10-12 for H C 1 0 4 system. D values were also d e t e r m i n e d for h a f n i u m (IV) in 1 M HNO8 with varying fluoride c o n c e n t r a t i o n as presented in T a b l e 7. TABLE 5.--DIFFUSIONOF Hf (IV) IN HC104 IN ZEOKARB-225(H + fORM)
No. 1 2 3 4
[I-If] = 0.0019 M Conc. (M) D × 101°(cm~/sec) 1"0 2.0 3.0 4"0
0.04 10.74 76"21 456-2
~18)E. HESFORDand H. A. C. McKAY, Transaction of Faraday Soc. 54, 573 (1958).
The aqueous chemistry of hafnium (IV)
2179
Effect of size and shape of the ion The diffusion of a spherical particle in a cylindrical pore is retarded due to friction with the pore walls o f t h e ion exchange resin. The reduction in the mobility is expressed by a drag factor F in the FAXEN equation.ttg) F -~ I - - 2.104 ~ + 2.09 (r~p)' -- 0.95 (r. I
I' \rpl
rp
(14)
where r I = diameter of the diffusing species, rp = pore diameter. A large variation of r i has to be assumed, in order to explain the large variation in the diffusion coefficients. As r~ is not likely to vary to such an extent in the range of acidities above 1-5 M, the above relation does not satisfactorily explain the present
10
z
1
I
0"1
I
I
IIIill
I
I
I
1
~ttll[
I
10
I
i
iiii1|
I
D X 1010 100
i
i
iiii1|
1
t
t
, LII
1000
FIG 4.--Variation of diffusion coefficient of hafnium (IV) with acid molarity. A HC104 system × HC1 system © HNO3 system • HNO8 system (corrected; see text) experimental observations. It m a y be emphasised that none of the theoretical relations which have so far been developed seem to explain the experimental results. (~°) TABLE 6 System
n
Do × 101°(cm~/sec)
HC1 HNO8 HCIO4
5-2 6"6 6"6
3"98 0"35 0'04
(19)H. FAXEN,Ann.Physik, 68, 89 (1922). (~o)F. HELEFERICH,Ion Exchange,p. 303. McGraw-Hill, New York (1962).
2180
R.G. DESHPANDE,P. K. KHOPKAR,C. L. RAO and H. D. SrIAman
In an attempt to explain the particularly large variations of D over a small acid range we have applied the Stokes' equation RT
D -- - -
67rNrlrs
(15)
R ----gas constant T = absolute temperature N = Avagadro number ~/= viscosity of the medium rs = Stokes' radius of the ion Assuming that the Stokes' equation for diffusion is applicable to the hafnium (IV) systems studied, the variation of D by a large factor (108 to 104), when acid strength changes from 1 to 4 M cannot be explained in terms of the variation of rs (it has
TABLE 7.--EFFECT OF ANION COMPLEXING SV H F ON DIFFUSION OF H f ( I V ) INTO CATION EXCHANGE RESIN
[HNOs] = [HF](M) D
1.0 M ×
0.00 5 × 10 -4
101°(cm2/sec) 18.00
30.8 28.0 164.5 173.7
5 × 10-3 1.25 × 10-2 2.5 x 10-2
already been shown from the TTA solvent extraction data that in > 1.5 M HC10 4 solution hafnium (IV) exists as unhydrolysed H f 4+ species). The viscosity of the medium is also not likely to vary by a significant factor over the small acid range (1 to 4 M). However, when diffusion of ions in the capillary pores of the ion exchange resin is considered, a drag similar to the viscous flow of liquids, may be experienced by the ions inside the resin pores. It may not be irrelevant to consider this in view of the fact that the fixed charges on the resin will certainly have a large number of oriented water dipoles. Similarly H f 4+ ion has a hydration sheath and therefore while passing through such a pore, it will encounter certain resistance. The size of the capillary and the size of the hydrated ion are an important factor in explaining the variation of diffusion coefficients of hafnium (IV) through the ion exchanger. This may be represented as inversely proportional to the fourth power of(rp -- rs) in place of the viscosity ~ in the Stokes' equation. The Equation (15) can thus be represented as D -- RT(rp -6¢rNrs
rs) 4
(16)
so that
(17)
The aqueous chemistry of hafnium (IV)
2181
where D x and D~ are the diffusion coefficients of any two ions having (rs)~ and (rs)y as Stokes' radii. The results of SOLDANOt21~ on the diffusion coefficients for Na +, Zn 2+, ya+ ions and LAGOS and KITCHNERt22~ for Na +, Cs+, Ag + and Ca ~ suggest that the above relationship is approximately valid. It may be emphasized that the effects of the medium on the resin matrix which in turn is heterogeneous, cannot be neglected and this simple relationship cannot alone account for the complicated phenomenon. A systematic study is necessary to test the validity of the relationship. Large changes in D values were also observed by LISTER and MCDONALD(s~ for zirconium (IV) system which cannot possibly be accounted for by hydrolytic polymerisation alone.
Effect of valence and chemical nature of the species From the experiments it is clearly seen that at comparable acidities D in C1- > D in NO3- > D in C104- ions. The chloride and nitrate ions are known to complex Hf 4+ ions as shown earlier. It is also known that the equilibrium distribution coefficient in ion exchange resin for any metal ion is higher compared to its charged ion complex, e.g. Ko for Eu 3+ is ver ymuch higher as compared to 1(,ofor EuCI2+.c~a~ This may be explained on the basis that the diffusing species in the pores may be a complex ion of rs (eft), lower than that of the hydrated radius of the uncomplexed ion; but it would seem that predominantly the latter is taken up in the resin phase by excluding the ligand. The increase in D can be attributed to lower values of rs (eft) of the complex. This has been shown by the experiments with fluoride ion (Table 7) in low concentration which brings about a reduction in the size of the hydration sheath of the species present, resulting in high D values. A linear relationship between log D and log M is obtained in the present studies (Fig. 4). This behaviour is different from the observations on a similar study of zirconium (IV) ts~ where a plateau was obtained between certain molarities of nitric acid. Similar evidence of a polymerization plateau indicating low molecular weight species has been obtained for zirconium (IV) and hafnium (IV). t6~ Present results show that the size of the ion increases gradually, and therefore indicating continuous polymerization, thus supporting the hypothesis of SILLEN, (24) which has further been substantiated by the experiments of LARSENtT) and COW,rICK and McVEY. t°) Acknowledgements---The authors are thankful to D r K. A. KRAUS for his valuable comments and to SHRI S. K. PATIL for his help in calculations. i~1) B. A. SOLDANO, A/D/. N.Y. Acad. Sci. 57, 116 (1953). Iz2~ A. E. LAGOS and J. A. KITCI-~R, Trans. Faraday Soe. 56, 1245 (1960). ~8~ H. IRVlNO and P. K. KHOPKAR, J. Inorg. Nucl. Chem. 26, 1561 (1964). t24) F. GARNER and L. G. SILLEN, Acta Chim. Scand. 1, 631 (1947).
THE AQUEOUS CHEMISTRY OF HAFNIUM (IV) SOLVENT EXTRACTION
AND ION EXCHANGE
STUDIES
R. G. DESHPANDE, P. K. KHOPKAR, C. L. RAO and H. D. SHARMA Radiochemistry and Isotope Division, Atomic Energy Establishment, Trombay, Bombay (Received 6 April 1964; in revised form 30 September 1964)
Abstract--Some aspects of the solution chemistry of hafnium (IV) have been investigated by TTA solvent extraction and shallow bed ion exchange resin techniques. The stability constants of hafnium (IV) with chloride (ill 0"7, flz 0"48), nitrate (ill 0.8), sulphate (fla 110, r2 5 × 103) and fluoride (ill 4"2 × 104) ions have been determined and they are all lower as compared to the corresponding zirconium (IV) complexes. The rates of exchange of hafnium species on a cation exchange resin at various molarities in HCI, HNOa and HC104 media have also been determined. A model for the variation of diffusion coefficients with acidity has been suggested. THE chemical behaviour o f zirconium (IV) ions in aqueous solutions is quite complex as summarized in a review article by SOLOVKIN and TSVETKOVA.(1) The interest has largely been in its complexing behaviour and its existence as either unhydrolysed or hydrolytic p o l y m e r species in aqueous mcdia. There have been similar investigations, although n o t as exhaustive as those on zirconium ions, on the solution chemistry o f h a f n i u m viz. complex formation with chloride, nitrate, fluoride, oxalate and sulphate ions b y ion-exchange and solvent extraction techniques ~-5) and on the nature o f its hydrolytic species by ultra-centrifugation ~8) and ion exchange. (7) The present data on the determination o f stability constants for complex formation with various anions by 'solvent extraction m e t h o d ' and the rate o f exchange o f hafnium species on a cation exchange resin at various acidities, using the shallow bed technique, were collected during 1955 and 1957 with a view to finding better methods o f separation f r o m its analogue, zirconium. The values o f the stability constants o f hafnium complexes obtained, have been c o m p a r e d with those o f other workers for zirconium and h a f n i u m ; the existence o f hydrolytic species in solution, as studied by the measurement o f the rate o f exchange in different media, has been discussed. EXPERIMENTAL Hafnium-181 was used as a tracer in all experiments. The tracer was prepared by the irradiation of specpure HfO~ with neutrons at BEPO, Harwell, and subsequent dissolution of the hafnium in a platinum dish on a hot water bath with a mixture of HNO3 and HF. The resultant solution was then fumed with concentrated H~SO4 to eliminate fluoride ions. The hafnium was then precipitated ~a~A. S. SOLOVrdNand S. V. TSVETKOVA,Uspenskhi Khimi, 31, 655 (Nov. 1962). ~2~I. N. MAROVand D. I. RYABCrIII
2172
R . G . DESHPANDE,P. K. KHOPKAR, C. L. RAO and H. D. SHARMA
with NH4OH, repeatedly washed with water and dissolved in any one of the desired acids. It was re-precipitated with NH4OH, washed and dissolved in the desired acid, this process being repeated to ensure complete removal of sulphate ions. For the solvent extraction experiments, the hafnium hydroxide was dissolved in 4 M perchloric acid. In other experiments, stock solutions were made in corresponding 4 M acids. The concentration of hafnium in the tracer solution was determined by evaporation of 1 ml of the stock solution in a platinum crucible, subsequent ignition and weighing it as HfO~. TTA from Penn Research Corporation, U.S.A. was purified by recrystallization from thiophenefree benzene. Freshly prepared solution of the purified TTA in benzene of the desired molarity was used in all solvent extraction experiments.
T
. . . .
III. TO . . SCALER .
Fro. 1.---Apparatus for diffusion experiments. A" Reactor cup B" Mechanical stirrer C: Sintered glass bed D: G . M . Flow Counter E: Capillary tubing. The equilibrations were carried out at 27 ± 2°C in sealed stoppered Pyrex test-tubes and the two phases were contacted by mechanically stirring the tube for 2 hr. Samples were drawn from the two phases and their radioactivity assayed using a NaI(T1) scintillation counting assembly. The extraction coefficient E is defined as: E=
Concentration of Hf in organic phase Concentration of Hf in aqueous phase
counts min -1 m1-1 (organic) counts min -1 m1-1 (aqueous)
Cation exchange resin, Zeokarb-225 (cross linkage 10 per cent), was used in the ion exchange experiments. About 20 g of the resin was converted to H + form by contacting the resin with 4 M HC1 and after washing with distilled water thoroughly, it was air dried under an infra-red lamp. The dried resin was then passed through standard sieves, and the fraction collected between 18 and 22 mesh size (B.S.S.) was used in the experiments. An apparatus (Fig. 1), similar to the one used by LISTER and MCDONALD,ca) was employed in the present experiments. The stock hafnium solution, prepared in the appropriate acid and brought to a known strength, was transferred to cup (A), wherein it was stirred with a known quantity of resin with a slow speed stirrer (B). The solution after passing through the sintered glass bed (C) ts) B. A. J. LISTERand L. A. MCDONALD,f. Chem. Soc. 4315 (1952).
The aqueous chemistry of hafnium (IV)
2173
was circulated in a G.M. flow counter (D) after which it was recirculated through the reaction cup by pneumatic transfer. The activity of the solution flowed through the G.M. counter was assayed at definite intervals of time. A constant flow-rate was maintained by adjusting the air pressure. RESULTS AND DISCUSSION (a) Extraction experiments (i) Hydrolysis. The extraction coefficient E was determined at various H + ion concentrations in 9erchlorate media. Figure 2 gives a plot of log E 0 (E0 being the 9
8
g,7
6
5
~o
I
-0'8
I
i
I
I
I
1
-0'6 -0'4 -0'2
I
i
I
I
0 + 0"2 log[H "I
I
I
0"4
=
I
I
I
I
0"6 0'8
Fio. 2.--Distribution coefficient vs. hydrogen ion concentration. extraction coefficient normalized to 1 M T T A concentration) vs. log [H+]. Following CONNICK and McVEY, (9) the equilibrium condition for the extraction of any metal ion with T T A is denoted as M(OH)m(T)~-~ -~ + (n -- p)HTorg ~ MTnorg + (n -- m - - p ) H + + mH~O Then, log E = log Kex ÷ (n -- p) log [HT] -- (n -- m - - p) log [H +]
(1) (2)
where, M stands for Hf; H T ----T T A ; Kex ----equilibrium constant for the reaction (1). A plot of log E vs. log [H +] at constant H T gives a curve with a negative slope (n - - m -- p) where m and p are the numbers of hydroxyl groups and T T A molecules attached to the metal ion in the aqueous phase. The fourth power dependence of log E on log T T A has already been established by H ~ A N and co-workers ~l°,xx~and therefore the value of p can be taken as zero. In Fig. 2 is shown the plot of log E 0 vs. ~9~R. E. CONNICKand W. H. McVEY,J. A. Chem. Soc. 71, 3182 (1949). tle~ E. H. HUrrMANand C. J. BEAUFArr,J. A. Chem. Soc. 71, 3179 (1949). txl~ E. H. HUFFMAN,G. M. IDDINGS,R. N. OSBORNEand G. V. SnAUMOFF,J. A. Chem. Soc. 77, 881 (1955).
R.G. DESHPANDE,P. K. KHOPKAR,C. L. RAO and H. D. SHARMA
2174
log [H +] for perchlorate medium. It is seen that up to 1.5 M [H+] the curve has a slope of --3 indicating that the species in solution has an average charge of + 3 and above 1"5 M [H +] the slope is - - 4 showing that hafnium (IV) exists as species with a charge of + 4 . Thus, in 2M HC104, the equilibrium can be represented as follows provided activity coefficients of the reacting species do not vary considerably, H f 4+ + 4HT ~ HfT 4 + 4H +
(3)
which gives the fourth power dependence of E o on H + ion concentration. At concentration 10-4 M of hafnium in 1.5 M HC104, probably species of the type Hf(OH) ~are present in solution, while at higher acidities H f 4+ species are present if the assumptions connected with TTA method hold good as far as activity coefficients of the reacting species are concerned. Furthermore, the distribution coefficients in the experiments carried out at 2 M acidity did not change when the concentration of H f 4+ was TABLE 1 .--SOLVENT EXTRACTION DATA FOR THE DETERMINATION OF STABILITY CONSTANTS OF H f 4+
Conc. HSO4- ion (M)
Eo/E
Conc. NOn- ion (M)
0.01 0'02 0"03 0.04 0"05 0"06 0"07 0"08 0.09 0'10 0.12 0.15
1.67 2-75 3.67 5.30 6.62 9"22 11"02 12"85 14'59 18"01 22.66 34.86
0.1 0'2 0.3 0.4 0"5 0.6 0.7 0'8 0"9 1.0 . .
Conc. C1- ion (M)
Eo/E 1.13 1'12 1.25 1.34 1"41 1"49 1"52 1'60 1'72 1-86 . .
. .
0.1 0.2 0-3 0.4 0.5 0.6 0'8 0"9 . . . .
Conc. HF (M)
Eo/E 1.06 1'15 1.28 1.35 1"47 1'64 1'87 2.00 . .
. . . .
1 × 10-4 5 × 10-4 1 × 10-a 5 × 10-8 ----. . . .
Eo/E 18"52 116.3 238.1 666.7 -----
varied from 10-7 M to 1.6 × 10-3 M but thereafter they decreased rapidly at higher concentrations, the value of distribution coefficient being 10 4- 1 at the former concentrations and 1.5 at 10-8 M Hf(IV). Similarly at 1.4 M acidity up to a concentration of 6.65 × 10-4 M Hf(IV) essentially the distribution coefficients remained the same but at higher concentration they decreased showing that at 10-4 M (concentration of H f in the present studies) essentially monomeric species of H f 4+ and Hf(OH) a+ are present at these acidities. These results may be compared to those of CONNICK and McVEY (9) who reported by similar extraction studies that at tracer concentrations in 2 M HCIO4, zirconium (IV) exists chiefly in the form of the monomer Zr4+; and in the range 0.2-2-0 M HC104 the composition of zirconium (IV) ions correspond to the formula Zr(OH) 3+. According to LARSEN and WANG/7) zirconium (IV) species at 10-4 M also exists as Zr 4+ ion in 2 M HC104. (ii) Anion eomplexing. The complexing behaviour of hafnium (IV) with sulphate, nitrate, chloride and fluoride ions was studied by TTA method. All the experiments were conducted at constant ionic strength/, = 2 and constant acidity of 2 M, the
The aqueous chemistry of hafnium (IV)
2175
ionic strength being maintained constant by the addition of perchloric acid, so as to minimize the change in the activity coefficients of the anionic species. The concentrations of HSO4-, HF, NOa- and C1- have been used for the calculation of stability constants (vide Table 1). The stability constants flj were calculated from the extraction data obtained at various concentrations of ligands using the method of DAY and STOUGHTON (12) c o n s i d e r i n g the following equilibrium M ~" + j A -'~ ~ MA +(4-"~) MA + (4--n./) fl,. = [Ma+][A_,q~ where [A] = j = n = The fl~ values
(4)
(5)
concentration of ligand number of ligands attached to the metal ions charge of the ligand. were determined for the following equilibria from the experimental data: H f a+ + HSO 4- ~- HfSO4 ~+ + H + H f 4+ + 2HSO4- ~-- Hf(SO4)2 + 2H + H f 4+ q- C1- ~ HfCI 3+ H f 4+ q- 2C1- ~ HfClz~+ H f 4+ + NO 3- ~-- HfNO33+ H f 4+ + H F ,~- H f F 3+ + H +
(6) (7) (8) (9) (1(3) (11)
Table 1 gives the extraction data for the various systems studied from which the various stability constants have been evaluated; and Table 2 gives the values of the stability constants of H f 4+ with sulphate, chloride, fluoride and nitrate ions, and the values for both H f 4+ and Zr 4+ reported by other workers.(e,3,4,5,%13,14,TM As seen from Table 2, the first and second stability constants for hafnium complexes are generally lower than those for zirconium; this is expected as the ionic radius for Zr 4+ is smaller than that for H f 4+. The lower values of fll and fl~ for sulphate complexes of hafnium compared to those for zirconium are also consistent with the observed elution characteristics of hafnium and zirconium from the cation exchange columns with sulphuric acid. In the case of nitrate complexes our lower value of fl~ (0.8) for H f 4+ appears to be reasonable compared to 8.2 for the same ion reported by PROKI-IOROVAand BV,~ZHNnVA(3) who used the tributyl phosphate (TBP) solvent extraction method. The TBP solvent extraction method is found to give higher values for the stability constants if [TBP] alone is used in the calculation as against [HNOa-TBP]. t16) The values for the stability constants of fluoride and chloride complexes obtained by us using T T A method are in general agreement with those reported by other workers, although the fluoride system has not been studied very exhaustively in the present studies. (12~R. A. DAY and R. W. SxooG~rroN,J. A. Chem. Soc. 72, 5662 (1950). ~13~I. N. MAROV,Candidate's thesis, Vernadski Institute of Geochemistry and Analytical Chemistry, Moscow, 1961 (as cited in Reference 1). (14JA. S. SOLOVKIN,Zh. Neorff, Khim. 2, 611 (1957). ~13~S. ARm.ANt)and D. KAPaViDS,B. NOV.EN,Acta Chem. Scand. 17, 411 (1963). ~18~T. S. LAXMINARAYANAN,S. K. PATmand H. D. SHARMA,J. Inorg. Nucl. Chem. 26, 1001 (1964).
Fluoride
Nitrate
Sulphate
Ligand
-
0.7
-
0.8 -
42 x104 _
4
2
2
2 2 2 2 4 4
2
4-
3
-
-
2.33
2
-
110 -
B1
___----92
-
-
z -
-
0.48
-
o-90 2.18 0.6 8,2
0.95 24
-
_
1.87 x 104
--_---__-_
-
-
108
5x108 -
-
/%
x
3.6
_
108
0.12 3.21
0.55 1.0
0.12 1.18
-
_
2.12 x103 _
Ba
Hafnium
z 0.19 -
0.01 ;25
_
10’4
x
x
10”
1,95
1
3.35
1
I 0.03 119
0,08 0.05
_
_
_
81 -
Others
x
I 10’6
q
121
-
-z
_
_
-
85
x
10’8
2.31
z
6;s
z -
-1
_
_
f%
x 105
-
3.2 x 10’0
-
1.32 x 10’0
0x6 0.14
0.92 2.0 O-88 -
6.3x 106
0.12 z
_ 2.4 x 104 3.48 x 108 5.0 x104
pa -
0.95 1
x 102
4.6 x 102 4.66 x 10=
/?I -
/!& -
-
-
s.a x 10’8
-
-
OTOl 0.05 32
-
_ 2.4 x104 3.92 x106
Zirconium
OF Hf4+ AND ZI?+ BY SOME INORGANIC LIGANDS
-
/%
110
TABLE 2.-COMPLEXING
Ba
This work
2
2 2
Ionic strength ,u
-
-
-
-
-
15-
0.08 -
-
-
-
_ -
/Y4 -
extraction
Ion exchange
TI’A extraction and Potentiometry.
TTA extraction
TTA extraction
TTA extraction Ion exchange TTA extraction ‘ITA extraction Ion exchange TBP extraction
TTA extraction TTA extraction Ion exchange TTA extraction Ion exchange TBP extraction
Ion exchange
Ion exchange
=A
TT’A extraction
TTA extraction
Method
(15)
(4)
(9)
-
(9)
(9) (2) (14)
(15)
(13)
(9)
(5)
-
Reference
The aqueous chemistry of hafnium (IV)
2177
(b) Diffusion experiments The quantity of hafnium, adsorbed on the resin at any time t, is related to the diffusion coefficient in the resin phase, by the relationship(m Q' - 6 J ( - ~ ) Q o - - Q ° Q ~ r Q~o
(12)
where
D -----diffusion coefficient, r = radius of the resin bead Q0 = original amount of hafnium Qt and Qo~ = amount of hafnium taken up at time t and at equilibrium respectively. This relationship is valid only if the particle diffusion is the controlling mechanism as against the film diffusion. (17) The diffusion experiments suggest the former mechanism as indicated by the linear relationship observed between Qt/Q~o and ~/t for the perchlorate system, shown as a typical case in Fig. 3. 1'0 0
0'9
0'8 P
0'7 ~0'6 0"5 0"4 0'3 0'2 0"1 I
0
I
2
I
1
4
I
I
6
I
I
8
I
vT
I
10
I
I
12
I
l
lk
I
I
16
I
18
FIo. 3.--Uptake of hafnium (IV) with time [Hf] = 0.0019 M [HC104] = 1-0 M The values of D calculated from the data given in Tables 3, 4 and 5 show that D increases with acid concentration in all the cases. When log D is plotted against log M, M being the molarity of the various acids, linear plots are obtained as shown in Fig. 4, except in the case of the HNO3 system where corrections have been applied for the ~a~)T. R. E. KRESSMANand J. A. KITCm,rER, Disc. FaradaySoc. 7, 90 (1949).
2178
R. G. DF..SI"IPANDE,P. K. K.HOPKAR,C. L. RAO and H. D. SHARMA TABLE 3.--DIFFUSIONOF Hf (IV) IN HC1 IN ZEOKARB-225(H+ FORM)
No. 1 2 3 4 5 6 7 8
[Hf] = 0'001 M Conc. (M) D x 101°(cm2/sec) 0"73 0"88 1"09 1"35 1"65 2"01 2"37 3"09
0"53 1"45 6"96 32"24 73"31 190'30 424"80 1550"00
incomplete dissociation o f the acid as given by HESFORD a n d McKAY. cls) D can be expressed b y the relationship
D = Do M~
(13)
where D, D O = diffusion coefficients at acid molarities M a n d 1 respectively, a n d n = c o n s t a n t (slope of the line). TABLE 4.--DIFFUSIONOF Hf (IV) IN HNO8 IN ZEOKARB-225(H+ FORM)
No. 1 2 3 4 5 6
[Hf] = 0"0012 M Conc. (M) D × 101°(cm~/sec) 0"89 1"18 1'45 1"9 2"3 2"8
0'19 0"75 6"30 96-87 201"0 351'8
I n T a b l e 6 are given the values o f D o a n d n for the various systems. It is seen that the values o f n range f r o m 5.2 to 6.6, while D Ovalues differ by a large factor, between 3.98 × 10 -1° for HC1 system a n d 4 × 10-12 for H C 1 0 4 system. D values were also d e t e r m i n e d for h a f n i u m (IV) in 1 M HNO8 with varying fluoride c o n c e n t r a t i o n as presented in T a b l e 7. TABLE 5.--DIFFUSIONOF Hf (IV) IN HC104 IN ZEOKARB-225(H + fORM)
No. 1 2 3 4
[I-If] = 0.0019 M Conc. (M) D × 101°(cm~/sec) 1"0 2.0 3.0 4"0
0.04 10.74 76"21 456-2
~18)E. HESFORDand H. A. C. McKAY, Transaction of Faraday Soc. 54, 573 (1958).
The aqueous chemistry of hafnium (IV)
2179
Effect of size and shape of the ion The diffusion of a spherical particle in a cylindrical pore is retarded due to friction with the pore walls o f t h e ion exchange resin. The reduction in the mobility is expressed by a drag factor F in the FAXEN equation.ttg) F -~ I - - 2.104 ~ + 2.09 (r~p)' -- 0.95 (r. I
I' \rpl
rp
(14)
where r I = diameter of the diffusing species, rp = pore diameter. A large variation of r i has to be assumed, in order to explain the large variation in the diffusion coefficients. As r~ is not likely to vary to such an extent in the range of acidities above 1-5 M, the above relation does not satisfactorily explain the present
10
z
1
I
0"1
I
I
IIIill
I
I
I
1
~ttll[
I
10
I
i
iiii1|
I
D X 1010 100
i
i
iiii1|
1
t
t
, LII
1000
FIG 4.--Variation of diffusion coefficient of hafnium (IV) with acid molarity. A HC104 system × HC1 system © HNO3 system • HNO8 system (corrected; see text) experimental observations. It m a y be emphasised that none of the theoretical relations which have so far been developed seem to explain the experimental results. (~°) TABLE 6 System
n
Do × 101°(cm~/sec)
HC1 HNO8 HCIO4
5-2 6"6 6"6
3"98 0"35 0'04
(19)H. FAXEN,Ann.Physik, 68, 89 (1922). (~o)F. HELEFERICH,Ion Exchange,p. 303. McGraw-Hill, New York (1962).
2180
R.G. DESHPANDE,P. K. KHOPKAR,C. L. RAO and H. D. SrIAman
In an attempt to explain the particularly large variations of D over a small acid range we have applied the Stokes' equation RT
D -- - -
67rNrlrs
(15)
R ----gas constant T = absolute temperature N = Avagadro number ~/= viscosity of the medium rs = Stokes' radius of the ion Assuming that the Stokes' equation for diffusion is applicable to the hafnium (IV) systems studied, the variation of D by a large factor (108 to 104), when acid strength changes from 1 to 4 M cannot be explained in terms of the variation of rs (it has
TABLE 7.--EFFECT OF ANION COMPLEXING SV H F ON DIFFUSION OF H f ( I V ) INTO CATION EXCHANGE RESIN
[HNOs] = [HF](M) D
1.0 M ×
0.00 5 × 10 -4
101°(cm2/sec) 18.00
30.8 28.0 164.5 173.7
5 × 10-3 1.25 × 10-2 2.5 x 10-2
already been shown from the TTA solvent extraction data that in > 1.5 M HC10 4 solution hafnium (IV) exists as unhydrolysed H f 4+ species). The viscosity of the medium is also not likely to vary by a significant factor over the small acid range (1 to 4 M). However, when diffusion of ions in the capillary pores of the ion exchange resin is considered, a drag similar to the viscous flow of liquids, may be experienced by the ions inside the resin pores. It may not be irrelevant to consider this in view of the fact that the fixed charges on the resin will certainly have a large number of oriented water dipoles. Similarly H f 4+ ion has a hydration sheath and therefore while passing through such a pore, it will encounter certain resistance. The size of the capillary and the size of the hydrated ion are an important factor in explaining the variation of diffusion coefficients of hafnium (IV) through the ion exchanger. This may be represented as inversely proportional to the fourth power of(rp -- rs) in place of the viscosity ~ in the Stokes' equation. The Equation (15) can thus be represented as D -- RT(rp -6¢rNrs
rs) 4
(16)
so that
(17)
The aqueous chemistry of hafnium (IV)
2181
where D x and D~ are the diffusion coefficients of any two ions having (rs)~ and (rs)y as Stokes' radii. The results of SOLDANOt21~ on the diffusion coefficients for Na +, Zn 2+, ya+ ions and LAGOS and KITCHNERt22~ for Na +, Cs+, Ag + and Ca ~ suggest that the above relationship is approximately valid. It may be emphasized that the effects of the medium on the resin matrix which in turn is heterogeneous, cannot be neglected and this simple relationship cannot alone account for the complicated phenomenon. A systematic study is necessary to test the validity of the relationship. Large changes in D values were also observed by LISTER and MCDONALD(s~ for zirconium (IV) system which cannot possibly be accounted for by hydrolytic polymerisation alone.
Effect of valence and chemical nature of the species From the experiments it is clearly seen that at comparable acidities D in C1- > D in NO3- > D in C104- ions. The chloride and nitrate ions are known to complex Hf 4+ ions as shown earlier. It is also known that the equilibrium distribution coefficient in ion exchange resin for any metal ion is higher compared to its charged ion complex, e.g. Ko for Eu 3+ is ver ymuch higher as compared to 1(,ofor EuCI2+.c~a~ This may be explained on the basis that the diffusing species in the pores may be a complex ion of rs (eft), lower than that of the hydrated radius of the uncomplexed ion; but it would seem that predominantly the latter is taken up in the resin phase by excluding the ligand. The increase in D can be attributed to lower values of rs (eft) of the complex. This has been shown by the experiments with fluoride ion (Table 7) in low concentration which brings about a reduction in the size of the hydration sheath of the species present, resulting in high D values. A linear relationship between log D and log M is obtained in the present studies (Fig. 4). This behaviour is different from the observations on a similar study of zirconium (IV) ts~ where a plateau was obtained between certain molarities of nitric acid. Similar evidence of a polymerization plateau indicating low molecular weight species has been obtained for zirconium (IV) and hafnium (IV). t6~ Present results show that the size of the ion increases gradually, and therefore indicating continuous polymerization, thus supporting the hypothesis of SILLEN, (24) which has further been substantiated by the experiments of LARSENtT) and COW,rICK and McVEY. t°) Acknowledgements---The authors are thankful to D r K. A. KRAUS for his valuable comments and to SHRI S. K. PATIL for his help in calculations. i~1) B. A. SOLDANO, A/D/. N.Y. Acad. Sci. 57, 116 (1953). Iz2~ A. E. LAGOS and J. A. KITCI-~R, Trans. Faraday Soe. 56, 1245 (1960). ~8~ H. IRVlNO and P. K. KHOPKAR, J. Inorg. Nucl. Chem. 26, 1561 (1964). t24) F. GARNER and L. G. SILLEN, Acta Chim. Scand. 1, 631 (1947).