Jan., 1962
FORMATION CONSTANTS OF TANTALUM FLUORIDE SYSTEM
significance. Toward this end extensive studies of the reaction behavior in the remaining tantalate systems have been initiated. Acknowledgments.-The author wishes to thank
21
Dr. F. H o h b e r g for invaluable contributions to the ideas discussed in this and earlier publications, M. Witzen for assisting with X-ray analysis and B. Agule for the preparation of samples.
THE FORMATION CONSTANTS OF THE TANTALUM FLUORJDE SYSTEM. I. POTENTIOMETRIC AND ANION EXCHANGE STUDIES-EVIDENCE FOR SPECIES OF COORDINATION NUMBER NINE1v2 BYLOUISP. VARGAAND HARRY FREUND~ Department of Chemistry, Oregon State University, CorvalZis, Oregon, and the U.S. Bureau of Mines, Albany, Oregon Received Mag 8g, I961
Potential meanurements with the quinhydrone-calomel cell on perchloric acid solutions containing Ta(V) and hydrofluoric acid were interpreted in terms of the species TaFe-, TaFT-; TaF8--- and TaF9----. When conditions were defined where the concentrations of hydrolytic, polynuclear and weak acid species of the tantalum fluoride system were negligible, an analytical expreaision for the average ligand number, Z, in terms of the experimental hydrogen ion concentrations allowed calculation of the formation curve from fi = 6 to 9. The distribution of trace concentrations of TaFs- between the perchlorate form of an anion-exchange resin and 1M erchloric acid quantitatively indicated the presence of TaF4+and TaFs. When combined with the potentiometric data a pull sigmoid-shaped formation curve was obtained between the average ligand numbers 4 and 9 suggesting that simple mononuclear species outside these limits were not present. Ranges of values for the stepwise formation constants 4, ks, k7, les and kg at 25 were calculated by the ligand number method using a digital computer.
There is considerable qualitative evidence in the literature for the existence of a series of tantalum fluoride complexes of the type TaF,(5-n) but no studies have described the stepwise formation of these complexes and their simultaneous existence at equilibrium. Solvent extraction distribution data,4 chromatography on cellulo~e,~anion-exchange distribution,6 X-ray studies on cryslals,7 and tantalum electrode potential studies discussed in a paper to follow*all suggest unhydrolyzed species of one or more varieties at moderate and high acidities. It was the purpose of this study to establish the acid, metal and fluoride ion concentration ranges in which only unmixed mononuclear tantalum fluoride species existed and to calculate the stepwise formation constants of the system. Methodis for determining the mixed hydrolytic polymers of metals in this region of the periodic table are under study and will be presented upon satisfactory completion. Potentiometric H+Ion Measurements. Theory. -Several reviews have appeared in recent years which adequately discuss the general methods for studying complex formationg and the compilations (1) Abstracted in part from the Ph.D. thesis of Louis P. Vargac Oregon State University, June, 1960. (2) Presented at the Symposium on the Determination of Consecutive Formation Conatants, N.W. Regional Meeting Am. Chem. SOC., Richland, Wash., June 17, 1960. (3) To whom oommunications should be addressed. (4) J. R. Werning, K. B. Higbie, J. T. Grace, B. F. Speece and H. L. Gilbert, Ind. Eng. Chsm., 46,644 (1954); R. A. Focs and H. A. Wilhelm, U.S. Atomic Energy Comm., ISC-694pp. 31-32 (1054). ( 5 ) F. H. Burstall, et al., J . Chem. SOC.,1497 (1952). (6) K. A. Kraus and G. E. Moore, J . Am. Chem. Soc.. 7 3 , 13, 2900 (1951); J. P. Faris, Anal. Chem., 38, 620 (1960). (7) J. L. Hoard and W. J. Martin, J . Am. Chem. Soe., 61, 1252 (1939); J. .L. Hoard, W. J. Martin, M. E. Smith and J. F. Whitney, ibid., 76,3820 (1954). (8) L. P. Varga and H. Freund, J . Phys. Chem., 66,187 (1962). (9) J. C. Sullivan and J. C. Hindman, J . Am. Chem. Soc., 74, 6091 (1952); L. G. Sillen, J . Inorg. & Nuclear Chem., 8,176 (1958); R. 9. Tobias, J . Chsm. Edw., 85,592 (1958); H. M. N. H. Irving, Chapterin “International Conference on Codrdination Chemistry,” The Chemical
of stability constants by Bjerrum, Schwarzenbach and Sillen’O give numerous references to work in the field. I t is found that the question of what species exist in solution cannot be separated from the calculation of the stability Constants. When the species have been determined in a logical manner the calculation of the constants is straightforward. The procedure in this investigation was to determine the concentration ranges of metal and hydrogen ion which gave values of 0, 1, 0, respectively, to the parameters p , 9, r in the general reaction for complex formation in the tantalum fluoride system rH+
+ pTaV -+ p O H - + jF-
= H,Ta,(OH),F,
(1)
The several concentration formation constants at 25” may be written
where j , p , q and r may each have a range of integral values. So that the activity coefficients of all species remained approximately constant over the concentration ranges studied, a constant perchlorate ion concentration of 1 M was maintained. If the total analytical concentrations of metal, CM,and ligand CA, are known and allowed to vary independently and if the complex species under investigation are relatively stable, then an independent measurement of the free ligand concentration, ( A ) , allows a complete study to be made of the system. Experimental values of the average ligand num’ber, a, as defined by Bjerrurn’l Society, London, 1959 (Special publication no. 13); F. J. C. Rossotti and H. S. Rossotti, “The Determination of Stability Constants,” McGraw-Hill Book Co., New York, N. Y., 1961. (10) J. Bjerrum, G. Schwarzenbach and L. G. Sillen, “Stability Constants,” I. Organic ligands, The Chemical Soaiety, London, 1957 (Speoial publioation no. 6); 11. Inorganic ligands, 1958 (Special publication no. 7). (11) J. Bjerrum. “Metal Ammine Formation in Aqueous Solution,” P. Haase and son, Copenhagen, 1941.
LOUISP. VARGAAND HARRY FREUND
22 a
= CA
- (A) CM
(3)
were determined by calculating (A) from potentiometric H+ ion measurements. The quantity ( A )in the hydrofluoric acid system is given by ( A ) = (F-)
+ (HF) + Z(HFz-1
(4)
For the calculation of ( A ) it was determined first that the value of r in equation 1 was zero. With no weak acids other than HF present the sum of the stoichiometric perchloric and hydrofluoric acid concentrations, CH, is given by CH = (H")
+ (HF) + (HFz-1
(5)
The dissociation constants of hydrofluoric acid which Ahrland and co-workers12 determined a t (Clod-) = 1.0 M are the values used here after correction to 25'
(7)
From equations 3, 4, 5 , 6 and 7 a close approximation to the fluoride ion concentration is
which when substituted back into equation 3 and solved for gives this quantity in terms of experimental Hf ion concentrations and the stoichiometric concentrations of total ligand, metal and acid, CA, CM and CH, respectively,
j=1 p = o q=1
Equation 12 indicates a powerful method for studying the complex system. Experimental values for calculated from equation 9, when plotted against free ligand concentration, can be interpreted by equation 12. Perturbations brought about in the formation curve by varying the metal and acid concentrations indicate the dependence of fi upon metal and acid concentrations. I n these studies it was determined from the analyses of 12 formation curves1 that p , q = 0, 1 up to a tantalum concentration of 2.0 mM if CH/CM were greater than 150. Under these conditions equation 12 reduced to the familar (12) S. Ahrland, R. Larsson and K. Rosengren, Act4 C h e q . Scqnd.,
io, 705 (1956).
Vol. 66 j(F-)iKj 3=1
the form used in calculation of the constants of the system.
Experimental Reagent grade hydrofluoric and perchloric acids were standardized with carbonate-free sodium hydroxide using, respectively, phenolphthalein and a-naphthophthalein indicators. All vessels in contact with fluoride containing solutions during make-up and storage were of polyethylene. Standard solutions of sodium perchlorate were made by neutralizing aliquots of standard perchloric acid with sodium hydroxide to pH 6.8 using a glass electrode. Potassium heptafluorotantalate, KzTaF7, was prepared by the method of Brauer's from tantalum metal which contained less than 0.001% Cu, 0.001 to 0.01% Fe, 0.001 to 0.01% Mn, 0.01 to 0.1% Nb, 0.01 to 0.1% Ni, 0.001 to 0.01% Si, 0.001 to 0.01% T i and 0.001 to 0.01 % V. Analysis of the salt for tantalum by the method of Hague and MachlanI4 and for fluoride by the method of Willard and Winter and Armstrongls showed the fluoride:tantalum ratio to be 7.03. For solution make-up purposes the composition of the salt was taken as K2TaF7. Titration vessels were of polyethylene or polystyrene, and the buret used in the titrations was constructed entirely of polystyrene. A bright platinum electrode was used as the quinhydrone indicator electrode. The calomel reference electrode was separated from the titration vessel by a salt bridge containing saturated sodium chloride. Liquid junction between the calomel electrode and the salt bridge was through a half-inch length of Corning no. 7930 porous glass rod. The end of the salt bridge which contacted the fluoride-containing solutions in the titration vessel was constructed of polyethylene with an asbestos fiber wick junction sealed into the polyethylene tubing. The calomel electrode, most of the bridge solution and the titration vessel were kept partly submerged in a water-bath at 25 =!= 0.1". A Leeds and Northrup type K-2 potentiometer was used with an Eppley standard cell and a General Electric mirror galvanometer with a sensitivity of about 0.001 microampere per mm. of scale division. For each titration the initial known volume of cell solution contained perchloric acid equal to CH molar, sufficient sodium perchlorate so that (C104-) = 1.0 molar and was saturated with quinhydrone. Potential measurements of this quinhydrone-calomel cell were taken to establish the initial diffusion potential, Ed, in the absence of hydrofluoric acid and tantalum. Sufficient K2TaF7then was added to the cell solution to bring the total metal concentration to the value CM molar for the particular run. Potentiometric titration of this cell solution was made using a titrant solution containing hydrofluoric acid and perchloric acid such that the sum of the concentrations was CE molar. Thus CH was constant in the solution being measured for the entire course of the titration. The titrant also contained CJI molar KsTaF, to maintain CW constant during the titration. The perchlorate ion concentration was 1.0 M as in the initial cell solution. To correct for the change in the diffusion potential as the hydrogen ion Concentration changed during the course of a titration, diffusion potential curves were p1otted.l These plots were obtained from titrations made in the absence of tantalum and HF. Increments of 1 M perchloric acid were added to 1 Jl sodium perchlorate over the same hydrogen ion concentration range covered in an actual titration. The difference between the hydrogen ion concentration as calculated from the dilution factor assuming volumes were additive and that calculated from the Kernst equation was assigned to the correction term Ed. From the titration data taken on solutions containing hydrofluoric acid and (13) G. Brauer (ed.) "Handhuoh der praparativen anorganisohen Chemie," Ferdinand, Stuttgart, 1954, p. 198. (14) J. L. Hague and L. A. Machlan, J . Research Natl. Bur. Standards, 62,53 (1959). (15) H. H. Willard and 0. B. Winter, I n d . Eng. Chem., Anal. Bd. b, 7 (1933); W.D.Armetrong, ibid., 8,384 (1936).
Jan., 1962
FORMATION COKSTASTSOF TAXTALUM FLUORIDE SYSTEM
23
LOUISP. VARGAAND HARRY FREUND
24
Vol. 66
TABLE I1 FLUORIDE ION CONCENTRATIONS AT HALF-INTECRAL VALUES
n.'
10.)
10-4
Fluor d e Ion Niolorify
Fig. 1.-The formation curve of the tantalum fluoride system. The experimental fluoride ion concentrations and their standard deviations at half-integral a's are given by -0-. The full drawn curve was calculated from the average formation constants and the dashed curves were calculated from the standard deviation limits. tantalum, corrected values for the hydrogen ion concentrations were calculated.
CH/CM 151 161 151 151 152 152 162 162 175 200 200
Fluoride ion molarity-n = 7.6 9.0 x 10-4 10 x 10-4 2 . 6 x 10-4 5.1 x 10-4 10-4 4 . 7 5 ~10-4 10-4 6.25 x 10-4 5 . 1 x 10-4 5 . 6 x 10-4
iii = 6 . 5 2.6 x 1 0 - 4 3.5 x 10-4
1.8 1.45
2.5 2.5
x x
X 10-4
x
10-4
a09
Means Stand. dev. of means
7.0 6.4
200
250
7.0 X 10-4
x x
i = 8 5
0.7
x IO-'
0.7
x
10-8
2.6 X 10-1 1.15 X 10-8
10-4
10-4
4 . 4 6 ~io-' 2.67 X 10-4
6.0 x 10-4 6.23 X 10-4
2.16 X 10-8 0.8 x 10-8 1.35 X 10-8
f O . 3 8 X 10-4
f 0 . 5 8 X 10-4
f 0 . 3 4 X IO-S
metal concentrations were used so that low loading of the resin was maintained, the concentration of Results of the Potentiometric Titrations.the ligand in the resin phase remained constant at Fourteen formation curves which were thought to the exchange capacity of the resin. The resin phase represent the simple mononuclear tantalum fluoride activity coefficients could be assumed constant system were calculated from the titration data by over the ligand concentration range studied or a equations 9 and 8. Representative data given in small correction determined. When strong comTable I have been presented in full in ref. 1. The plexes were under study it was assumed usually molar ratio CH/CM ranged from about 151 to 309 that the outer phase activity coefficients were in the 14 runs. The average ligand numbers constant over the small ligand concentration range went from about 5.5 to 9 in the fluoride ion concen- required to study the system. Distribution studies tration range of 1 X lowKto 5 X loFa M. The under such conditions allowed quantitative calculafluoride ion concentrations a t half-integral f i tion of the stability constants of the system. It values of 6.5, 7.5 and 8.5 which were read from the is interesting to note that distribution data may be formation curves plotted in ref. 1 are given in interpreted easily when the ligand form of the resin Table 11. The mean fluoride ion concentrations is used even if more than one anionic species simulfor the 14 formation curves at each half-integral B taneously sorb on the resin. When relatively value given in Table I1 are indicated in Fig. 1 weak complexes were under study, however, the along with the standard deviations of the means. required large variation of ligand concentration As shown below these values were used to deter- in the outer phase necessitated, for quantitative mine, in part, the formation constants of the system work, extensive and sometimes unreliable determinations of outer phase activity coefficients. from equation 13. The conditions whereby the neutral salt form It did not appear desirabIe to use the potentiometric data below B = 6.5 for quantitative pur- of an anion-exchange resin may be used to study poses. The decrease of f i in this region of lorn ex- complex systems quantitatively when a high concess fluoride ion as the fluoride concentration stant neutral salt concentration was maintaiid increased suggested the possibility of hydrolysis in the outer phase have not been defined previously. occurring even though the free H+ ion concentra- It will be shown below that for systems of strong tions were a t a maximum in this portion of the complexes where only one anionic species is sorbed titration. Release of hydrogen ions by hydrolysis by the resin over a given ligand concentration would appear as release of hydrogen ions from HF range the distribution data may be used t o calcuin the process of complex formation in the theoreti- late the formation constants of the complex species cal treatment outlined here. In addition, the rela- in the outer phase. These constants, valid for the tive high acidity a t the beginning of a titration solution medium used, are comparable then with made small differences in H+ ion concentrations those obtained by other methods in this medium. difficult to measure and the data were scattered. At radioactive trace concentrations of tantalum in For the low a region the distribution of trace levels 1 M perchloric acid polynuclear and hydrolytic of anionic tantalum fluoride complexes between species were assumed absent. By comparison molar HClO, containing known HF concentrations with the acid and metal concentrations considered and an anion-exchange resin was used to deduce the adequate in the potentiometric studies, this assumption appeared justified. formation curve as shown in the next section. For the case of a positive metal ion 11of charge rn Anion-exchange Distribution. Theory.-In the and a negative monovalent ligand A, the expression past, quantitative studies on complex ions using (16) K. A. Kraus and F. Nelson, "Proo. Intern. Con:. Peaceful Uses anion-exchange resins usually have employed the Energy," Vol. 7, Geneva, 1956, p. 113, 131; S. Fronaeus, ligand form of the anion resin without maintaining Atomic Svsnsk Kern. Tidskr., 65, 1 (1953); V. V. Somin and V. V. Sinkovskii, a constant ionic strength with NaC104 or other Zhur. A'eorg. Kham., 1, 2316 (1956) (U. S. Atomic Energy Comm. neutral salt in the outer phase.16 When trace Transl. no. 3212); Y. Marous, J. Inorg. & Nuclear Chrm., 12,287(1960)
FORMATION CONSTANTS OF TAXTALUM FLUORIDE SYSTEM
Jan., 1062
for the anion-exchange equilibrium based on the law of rnass action may be written ( j- m ) RC10.j f MAi = RMAj
+ ( j - m)C101-,
j>m
(14)
for the case where the perchlorate form of the resin is used. The resin is designated by R and j is the generalized ligand number of the complex. The concentration equilibrium constant for exchange is
and the concentration formation constant of the j complex in the solution phase, Kj, is
A t constant perchlorate concentration in the outer phase, low loading of the resin by the complex species and by the ligand, consideration of equations 11, 15 and 16 shows that the distribution ratio, 4, of the metal species between the resin and solution phase is
for the case where more than one complex species is sorbed by the resin. The constant Lj* in equation 17 represents the term
. (RC104)i-“
Lj* = LjKj
(ClOn-)i-”
Equation 17 is considerably complicated by the dependence of C$ on a different combined exchange equilibrium constant for each species sorbed by the resin. Xf the special case of only one complex species being sorbed is considered, the summation sign in the numerator of equation 17 may be omitted. Then differentiation of C$ with respect to (A) ,and substitution of the expression for ft from equation 13 gives This relation was given by Bjerrumll for the degree of formation function and has been used in various partition studies. If the value of j is known, the ligand number of the species actually sorbed by the resin, equation 19 may be used to derive the formation curve of a system from the slopes of the log C$ vs. log (A) plot. Since in the case of tantalum the ligand number for the neutral species was linown to be 5, measurement of the first significant uptake of the metal complex species by the anion resin from low ligand concentrations to higher concentrations may be interpreted in terms of j = m 1 = 6, Experimental
+
The anion-exchange resin used was Bio-Rad Laboratories AR grade Dowex 1 X 8, 100-200 mesh, C1- form, capacity 3.2 meq. per dry gram. Batches of resin were prepared by repeated washing with 1 M perchloric acid until no chloride test was obtained with dilute silver nitrate. The resin bhen was washed thoroughly with distilled water and dried ah 85” for 12 hours. Radioactive Ta,-l82 produced at Oak Ridge National Laboratory was received in the form of tantalate in 1.4 N KOH solution. The solution concentration was 0.435 mg. Ta per ml. and the specific activity was 7494 mc. per gram.
25
About 60 days elapsed from the assay date to date of first use to allow for decay of the 5.2 day Ta-183. The isotope was characterized by 0-absorption and decay measurements using standard techniques. Due to the appearance of some solids in the Oak Ridge tantalate solution, the solution, which was about 1 ml. in volume, was treated with 1.0 ml. of standard 9.91 M HF. Effervescence occurred, undoubtedly due to carbonates, leaving a clear solution. From 25 to 40 microliters of this solution was used in each equilibration mixture. Reagent grade hydrofluoric and perchloric acids were used for solution make-up. The perchloric acid was standardized against sodium hydroxide and solutions containing fluoride were standardized against thorium nitrate.’ The total HF concentrations of the various solutions used are listed in Table 111. The final perchloric acid concentm tion of all solutions was 1.O M
.
TABLEI11 ANIONEXCHANGE DISTRIBUTION AS A FUNCTION OF FLUORIDE IONCONCENTRATION All solutions were 1.0 molar in perchloric acid
0.0184 ,0290 .0396 .0715 .1141 .211 .211 .396 .409 .694 .694 .707 .992 .991 1.004 1.995 1.98 1.98 1.98 0.0178 .0326 .0656 .I483
,.. “.. % . .
,.. *,.
0.3076 I . .
(1 .O)
(1.0) (1 . O ) (1.0) (1.0) 1 .o (1.0)
-4.706 -4.509 -4.374 -4.117 -3.914 -3.648 -3.627 -3.375 -3.361 -3.140 -3.140 -3.128 -3.011 -3.023 -2.989 -2.752 -2.742 -2.772 -2.772
1 .o 1.o (1.02) .3064 1.02 1.01 .3067 ... (1.08) 1.11 .3043 ,3059 1.04 ,3025 1.19 * 301 1 1.15 ,3014 1.24 .3014 1.24 (Quin-satd. cal.) 0.45138 1.00 -4.721 .45131 1.GO -4.458 ,45283 1.06 -4.180 .45152 1.01 -3.805 .3048 .3068
...
-0.0542 ,1193 ,2263 .4814 .5418 .683 .8102 .736 .771 * 753 .735 .709 .725 .800 .644 .616 .637 .737 ,615 -0.1896 .0445 .5328 .6i17
All of the anion-exchange equilibrations were made with 0.100 g. of the Dowex 1 resin and 15 ml. of solution. The equilibrations were carried out by stirring the solution and resin mixtures in polyethylene centrifuge tubes while immersed in a water-bath a t 25’ except for the last four equilibrations, which were made by shaking the mixtures in 50-ml. polyethylene bottles. Contact times were mostly in the range of 3 to 4 hours but were nearly 4 days for the last four equilibrations without appreciable difference in uptake noted, so that 3 hours was assumed to be sufficient contact time. After equilibration the resin-solution mixtures were centrifuged, the solution decanted off and saved for assay, and then the resin was washed rapidly into a filter crucible and repeatedly washed with small portions of distilled water. The resin then was air dried and transferred to tared stainless steel cups in preparation for radioactive assay. The resin samples were weighed and the resin count rate then was corrected to 0.100 g. of resin. Assay of the solutions was made by counting 0.100-ml. aliquots of the solutions on copper planchets after drying under a heat lamp. Duplicate planchets were prepared from each solution assayed. A Tracerlab G.M. tube type TGC-2 was used for the radioactivity measurements. The detector was used with an Atomic Instrument Co. “Multiscaler” model 105. Counting times varied considerably but the total count
26
LOUISP.
$-
I
./-/
v-./. 50
45
VARGA AND
i I
1
40
35
-30
25
Log i f ~ m o i o r l
Fig. 2.-The anion-exchange distribution of tantalum fluoride complexes. cp = counts per min. per g. resin/counts per min. per ml. solution. The curve follows the least squares equation log cp = -4.6021 - 3.2244 log(F-) -0.4837 log(F-) 2. taken on the planchets, when feasible, was kept above 10,000 to reduce the random counting error below 1%. Duplicate counts were taken in some cases to improve reliability. The count rates (see ref. 1) were corrected for background, for daily randomness by a RaD-E reference standard and for radioactive decay. Dead-time corrections were made on all count rates above 10,000 counts/min. Since count rates for resin and solution were in units of c./m. per 0.1 g. and c./m. per 0.1 ml., respectively, the ratio of experimental resin activity to solution activity gave 9 directly in units of ml./g. in Table 111. Hydrogen ion concentrations were obtained from hydrogen electrode-N calomel electrode potential measurements on most of the solutions after equilibration and from quinhydrone-satd. calomel measurements on the last four solutions. From the stoichiometric HF concentrations and the experimental H + ion concentrations, fluoride ion concentrations of Table 111were calculated by the relation (HF)stoic. (F-) = (20) 2 1 - (HF)stolc. K, KaP
+ +
Results of the Anion-exchange Studies.-The logarithms of the distribution ratios and fluoride ion concentrations, log and log (F-), of Table I11 were plotted in Fig. 2. A least squares analysis of the data gave the equation for the curve drawn in Fig. 2 log P, = -4.6021-3.2244
Vol. 66
The maximum in the distribution ratio shown in Fig. 2 suggests that the resin was showing some selectivity to an anionic species of low charge. Resin selectivity may be related to ionic radii considerations and by Donnan membrane equilibria to resin and solution phase activity coefficients" in effect in the 1 M perchlorate medium used in these studies. Results of the Combined Data.-The fluoride io: concentrations a t half-integral f i values from the potentiometric and anion-exchange distribution studies are given in Table IV. The data of Table IV are plotted in Fig. 1 and the standard deviation TABLE IV FLUORIDE IONCOSCEKTRATIONS AT HALF-INTEGRAL E VALUE?
-
Souroe
Snion ex. Anion ex. Potentionietric Potentiometric Potentiometric
(FG,,
4.5 3.5 6.5 7.5 85
Standard deviation Absolute %
1.32 X lod6 0.12 X lod5 9 . 1 1.41 x 10-4 .13 X low4 9 . 2 14.2 2.67 X loe4 .38 X 6.23 X IOe4 .56 X lod4 9 . 0 1 35 X .34 X 25
limits of the experimental fluoride ion concentrations are indicated. These results were found for molar ratios C H / C ~greater ~ than 150 from the potentiometric data and for trace tantalum concentrations in 1 perchloric acid from the anionexchange data. Calculations.-On the basis of the species TaF4+, TaF6, TaF6-, TaF,--, TaFs--- and TaF9---- only existing a t equilibrium in the conceiytration range studied in this investigation we may define the over-all formation constant as
+ F-
l?aF4+
log (F-) -0.4837 log (F-)' (211
Differentiation of equation 21 with respect to log (F-) gives
'
HARRY XREUND
log = -3.2244 d log (F-)
- 0.9674 log (F-)
(22)
from which t'he value of log (F-) at any value of A may be calculated from equation 19. Accordingly, log (3'-) = -4.88 and -3.85 when d log $/d log (F-) is 1.5 and 0.5, respectidy. Therefore, (F-) was found t o be 1.32 X and 1.41 X M when + =i4.5 and 5.5, respectively, assuming that i = 6. These values are shown in Fig. 1 and they will be combined with the potentiometric data to calculate several constants of the system. If TaF6- is being sorbed in the range where fi = 5, then the presence of TaF4 must be inferred in this region also. For quantitative interpretation of the anion-exchange data the assumption was made that only TaF6- was exchanged by the resin in appreciable concentration up to ? = i 5.5, where the slope of the curve of Fig. 2 is 0.5. At higher fluoride ion concentrations, the potentiometric (E+)studies indicate that the concentration of TaFF-- mould rise gradually.
Tafff
+ 5F-
=
TaFg----,
09
= rTaF4+) ( T a F ----) (F-)5
The average ligand number becomes from equation 12 '
+ XTaFs) -I- 6(TaFs) +
4(TlzF4)
(TaFT)
+ (TaFd + (TaF9) (24)
From equation 13 this may be rearranged to P5(5-ii)(F-) Ps (6 - E ) (F-1' + PT (7 - E ) (F-)3 0s (8
+
- Ej
+
(F-)4 6s (9
- E ) (F-)5 = E - 4
+
(25)
in terms of the over-all formation constants Pj from the equations of (23). As sugges1,ed by Sullivan and Hindmang the simultaneous equations of the form of equation 25 were solved by taking (F-) values a t half-integral values of A. An ALWXC 111-E electronic digital computer was used to make the required calcula(17) J. E. Salmon, Rev. Pure and A p p l . Chem. (AuStTalW), YB, 2 5 (1956).
Jan., 1962
FORMATION CONSTANTS OF TANTALUM FLUORIDE SYSTEM
tions in the series of 5 X 5 determinants which were programed. Substituting the data of Table I V into the matrix for equation 25, it was found that positive consstants were obtained only when the fluoride ion concentrations were adjusted to give a smooth sigmoid curve between a values of 4 and 9. The experimental values of the fluoride ion concentrations for fi = 4.5, 5.5, 7.5 and 8.5 were held fixed in these calculations. A smooth curve could be drawn through these points as may be seen on inspection of Fig. 1. By iteration procedures the fluoride ion concentration range a t a = 6.5 which gave positive formation constants was found to be (3.52 f 0.32) X M . Solution of the system using this value a t f i = 6.5 yielded the following average values of the over-all formation constants : 65 = 6.47 x io4, p6 = 2.67 x lo8, p7 = 5.86 x pS = 5.50 X loT4and pg = 2.05 X 10l8. These constants were used to calculate the relative concentrations of the individual species as shown in Fig. 3. The over-all formation constants a t the f limits of the fluoride ion concentrations were calculated similarly to give the standard deviation range of the constants. From the relations k5 = p5, k5k6 = p6, k5k6k7 = p7, ksk6k7k8 = p8 and k5kak7ksk9 = pg the stepwise formation constants of tantalum fluoride were calculated from the over-all formation constants shown above. These stepwise constants, shown in Table V, apply to a 1 molar perchlorate ion medium a t 25’.
27
Fig. 3.-The distribution of tantalum between the various complexes as a function of fluoride ion concentration.
anionic species are enlarged compared to the species in a crystal. This may take place by competitive attraction of the fluoride ions of the complex by sodium ions and by the positive dipoles of the mater molecuies. In a comparable easel3 a decrease in the stability of the cadmium chloride complexes as the salt medium was changed from RbCl to LiCl showed that the stronger the electrostatic field of the cation, the more it weakened and so lengthened the bond between the central and coordinating ions. If the TaFg---- ion indicated in these studies actually exits it may be assumed to have a radius ratio of a t least 0.732, which is required for stability of the group. Confirmatory evidence for the existence of TaF9---- from tantalum electrode potential measurements is given in a TABLE V THESTEPWIajE FORXATION CONSTANTS O F THE TANTALUMfollowing paper.* Solvent extraction studies to be presented at a later date should give further 17LUORIDE SYSTEM information on this point. Average One standard deviation limits ( 5 . 7 to 7.3) x 104 The nature of the bonding in complexes of this k5 6.47 x 104 IC6 4.13 X 108 ( 3 . 7 to 4.9) x 103 type has been discussed by DuffeyZ0in connection ki 2.20 x 103 (0.64 to 4.1) X lo3 with OsFg-. In complexes where the central metal has no unshared electrons, the usual spd hybridizaks 9.39 x 102 102 to 5 x 103 k.9 3.73 x 10s 103 t o 4 x 104 tion gives a maximum covalence of 9. However, KimballZ1points out that bonds of this nature may a One standard deviation of the measured fluoride ion concentrations. be so ionic that the directed nature of covalent bonds and the covalency rules may not apply. Discussion A distinguishing feature of the tantalum fluoride Inspection of Fig. 1 shows that the formation system, shown clearly in Fig. 3, is the high relative function of the simple mononuclear tantalum fluo- concentration of t)he solvated neutral TaF6 species ride complexes exhibits a full sigmoid shaped curve throughout almost the entire fluoride concentrabetween the average ligand numbers of 4 and 9. tion range studied. The high extractability of These results indicate strongly that fluoride ligand tantalum from acid fluoride media into organic numbers below 4 will not be found in the unmixed ketones4 is due likely to a high relative concentrafluoride complexes because of the increased ability tion of this TaF6 species over a wide acid, metal of OH- to compete with F- in complex formation and fluoride concentration range. when the fluoride ion concentration becomes small. It must be recognized that the method for asLigand numbers above 9 are unlikely because of signing a measure of confidence to the calculated radius ratio considerations. Paulingl* gives the minimum radius ratio for stability of the poly- constants was, of necessity, arbitrary due to the hedron of coordination number 9 as 0.732. This two entirely different types of experiments combined t o calculate the one set of results. In addicompares with 0.643 for the radius ratio of TaFs--from the X-ray data of Hoard.’ In a crystal such as tion, the ranges of values given for the calculated K&Fe illustrated by Paulingls, each K+ ion is constants still are highly dependent on the correctsurrounded by twelve F- ions and the ability of the ness of the several assumptions made in the treatK + ions to attract F- ions away from Si+4 is se- ment of the data. The ranges of values given in verely limiteid. It is reasonable to assume that in (19) Ya. A. Fialkov and V. B. Spivakovskii, Buss. J. Inorg. Chem., aqueous soluiions containing M sodium perchlorate 4, 675 (1959).
(18) L. Paulinp, “The Nature of the Chemical Bond,” Cornell Univ. Press, Ithaart, N. Y., 1948, p. 382.
(20) G. H. Duffey, J . Chem. Phys., 19, 553 (1951). (21) G. E. Rimball, abid., 8, 188 (1940).
28
S. J. YOSIM,L. D. RANSOM, R. A. SALLACH AND L. E. TOPOL
Table V for the stepwise formation constants appear large but they only reflect the extreme sensitivity of polvnomials such as equation 25 to small changes in the experimental ligand concentration. In terms of the formation function the range of constants listed describes the complex system over a quite narrow band indicated by the pair of broken lines in Fig. 1. Acknowledgments.-This work was made possible through a fellowship authorized in a cooperative agreement between the U.S. Bureau of
Vol. 66
Mines, Albany, Oregon and Oregon State University. Assisting in some of the analyses were Howard F. Griffin and personnel of the spectrographic laboratory at the Bureau of Mines. Assistance in the statistical treatment of data was given by Dr. R. G. Petersen of Oregon State University and computer programing assistance was given by Robert N. Brenne. Research paper No. 412, Oregon State University, School of Science, Department of Chemistry.
THE BISMUTH-BISMUTH TRIBROMIDE AND BISMUTH-BISMUTH TRIIODIDE SYSTEMS BY S.J. YOSIM, L. D. RANSOM, R. A. SALLACH AND L. E.TOPOL Atomics 3nternationa1, A Division of North American Aviation, Inc., Canoga Park, California Recebed June 3, 1961
The phase diagrams of the Bi-BiBs and Bi-Bi18 systems have been determined. The experimental techniques included sampling a t temperature, visual observations, conventional thermal analyses and differential thermal analyses. The consolute temperatures (538' at 62 mole yoBi and 458' a t 78 mole YoBj for the BiBrs and Bi18 systems, respectively) are considerably lower than that of the BiCl, system (780' at 51 mole % Si). The freezing point depressions of the metal-rich and salt-rich regions were analyzed. The salts dissolved in molten bismuth were found to have a cryoscopic number of 3. As in the BiC18 case, this effect can be explained by dissociation of BiXa solute or by reaction of BiXa with Bi to form the monohalide. I n the case of the salt-rich regions the data did not fit a curve corresponding to one single mechanism over the entire liquidus.
Introduction In a previous report2 the phase diagram of the Bi-BiCl, system was described. A retrograde solubility was found, and the two components became completely miscible at 780O. In order to see the effect of varying the anion on the miscibility gap, the liquid-liquid regions of the Bi-BiBr3 and the Bi-BiIs systems were determined. Since there are considerable discrepancies in the liquid-solid portions of the phase diagram of the Bi-BiB1.s system3-6 and the Bi-BiIa system,6-8 these regions were investigated also. Finally, the freezing point depressions of the bismuth trihalide by bismuth and those of bismuth metal by the salts were examined in order to see what could be learned about the species in these solutions. Experimental Materials.-The purification of bismuth is described elsewhere.2 Bismuth tribromide and bismuth triiodide were synthesized by direct combination of the elements. I n the BiBrs case, the molten bismuth was exposed to bromine vapor supplied by a bromine reservoir. The starting materials were contained in a sealed, evacuated Vycor system. (1) This work was supported by the Research Division of the U. 8. Atomic Energy Commission. I t has been presented in part before the Division of Physical Chemistry at the National Meeting of the A.C.S. in New York, September, 1960. (2) S. J. Yosim, A. J. Darnell, W. G. Gehman and 5. W. Mayer, J . Phys. Chem., 6 3 , 230 (1959). (3) B. G. Eggink, 2. physil. Chsm., 6 4 , 449 (1908). (4) L Marino and R. Becarelli, Atti accad. naz. Lincei. 2 4 , 625 (1915);26, io5 (1916);as, 171 (1916). (5) G. G. Urazov and M. A. Sokolova, Akad. Nauk; X.S.X.R., Inst. Gen. Inorg. Chsm., 24, 151 (1964). (6) L. Rlarino and R. Becarelli, Atti accad. naz. Lincei, 21, 695 (1912). (7) H. S. van Klooster, 2.uanorg. aEZgsm. Chem., 80, 104 (1913). (8) G. G. Urazov and M. A. Sokolova, Akad. Nauk S.S.S.R., I n a l . Cfen.Inorg. Chem., 26, 117 (1964).
I n the case of the iodide, finely ground bismuth metal was intimately mixed with a slight excess of iodine and the mixture was heated in a sealed, evacuated Pyrex tube at 175"for 24 hr. Both salts were sublimed under reduced pressure after the excess halogen was removed from them. The melting points of the bromide and iodide were 218.5 and 407.7", respectively. Chemical analysis of the bromide showed a 46.5 wt. % bismuth as compared to 46.57% theoretical, while that of the iodide showed a 35.9 wt. % ' bismuth as compared to 35.44% theoretical. Experimental Methods and Procedure.-The techniques used in this work have been described p r e v i o u ~ l y . ~The ~~ miscibility gaps were studied by decanting the salt-rich hase at tern erature, by differential thermal analyses and gy the visuafmethod. The solid-liquid equilibrium curve between the salt-rich eutectic and the base of the miscibility gap in the Bi-BiBr3 case was determined by decantation. All other transitions involving the solid phases were determined by conventional thermal analysis or by differential thermal analysis.
Results
(A) The Bi-BiBra System.-The
phase diagram of the Bi-BiBr3 system under its own pressure is shown in Fig. 1. The consolute temperature was found to be 538', considerably lower than that of the Bi-BiC13 system (780O). A plot of the mean values of the bismuth metal compositions of the two conjugate solutions vs. temperature was linear and the composition corresponding to the consolute temperature was 62 mole yoBi. Just as in the BiBiC13 case,2 a retrograde solubility was observed in the salt-rich region (from 57 mole % at 294' to 45% at 430') while the solubility of the salt in the metal continues to increase with increasing temperature. The results of the liqiud-solid portion of the system are compared in Table I with the results re(9) L. E. Topol and A. L. Landis, J . Am. Chem. SOC.,82, 6291 (1960).
