[CONTRIBUTION FROM THE OAK
RIDGENATIONAL LABORATORY, CHEMISTRY
DIVISION]
Hydrolytic Behavior of Metal Ions. VIII. Ultracentrifugation of Bismuth(II1) in Perchlorate Solution1t2 BY ROBERT W. HOLMBERG, KURTA. KRAUSAND
JAMES
S. JOHNSON
RECEIVED MAY 17, 1956 Equilibrium ultracentrifugations of bismuth(II1) perchlorate solutions were carried out as a function of acidity, of supporting electrolyte (NaClOa) concentration and of bismuth concentration. Over a range of acidity (ca. 0 01 to 0.1 Af H30+ ) where bismuth is considerably hydrolyzed (hydroxyl number n = ca. 2 ) a monodisperse hydrolytic polymer of degree of polymerization N = 5 or 6 was found. This polymer appears to be appreciably complexed by perchlorate ions.
Early investigators3 of the hydrolysis of bismuth in aqueous solutions tended to describe their results in terms of the monomeric ions Bi(OH)++ and BiO+. More recently evidence has been proposed for the existence of hydrolytic polymers4J even in the early stages of hydrolysis. Graner and SillCns investigated the hydrolytic equilibria in bismuth-perchlorate solutions by potentiometric methods in which both the hydrogen and bismuth ion concentrations were measured. They found reproducible and steady potentials, which indicated that the system is reversible and amenable to interpretation by equilibrium considerations. Their results showed that the unhydrolyzed ion Bi+3 is predominant in solutions of acidity greater than ca. 0.5 M. Below this acidity, hydrolysis dependent upon bismuth concentration was found. They interpreted their results in terms of the successive formation of polymeric particles of the general formula BiNO$ ? ', with the average degree of polymerization N (the number of bismuth atoms per polymer particle) rapidly imreasing with Bi(II1) concentration and $H.7 Souchay and Peschanskia investigated bismuthperchlorate solutions by a photographic ultraviolet light absorption technique under conditions similar to those of GranQ and Sill6n. They interpreted their data using only the equilibrium
+
AVBi+3 NH2O
+ 2NH+
(BiO)N+AV
(1)
inconsistent with that of the other workers, since Swinehart and Garrett worked in a different medium and a t lower Bi(II1) concentrations. Procedures have been outlined recently for the determination of molecular weights in charged systems by equilibrium ultracentrifugation.?a> lo,l This technique has been applied here in an attempt to resolve the divergent opinions regarding Bi(TI1) hydrolysis. Experimental Equilibrium ultracentrifugations were carried out, as previously described,'* in a Specialized Instrument Corporation Model E ultracentrifuge using a Philpot-Svensson optical system. X quantity 2 proportional t o the gradient of the refractive index with radius of rotation x is measured for two runs: a "polymer run" containing both bismuth and supporting electrolyte and a "background run" containing only supporting electrolyte. The difference between these values of 2 is designated by Z* and measured in cm. This quantity forms the basis of the interpretations. Bismuth oxyperchlorate solutions of known acidity were prepared by dissolving bismuth oxide in a known amount of The dissolution, often slow, perchloric acid (ca. 6 was usually complete after overnight digestion at ca. 100". Sodium perchlorate was prepared by neutralizing sodium hydroxide with perchloric acid and then filtering t o remove insoluble impurities. All chemicals were reagent grade and were used without further purification. Densities of solutions containing bismuth oxyperchlorate dissolved in sodium perchlorate-perchloric acid mixtures were measured pycnometrically a t 25.0" in the Bi(II1) and acid concentration ranges of interest ( M Bi(II1) < 0.1, M HClOa < 0.15). Apparent molal volumes 4" for the component BiOC104 were computed. It mas found that 4" was sufficiently independent of bismuth concentration to equatc with the partial molal volume P with negligible g r o r to the ultracentrifugation results. The change of I/BiOC!O, with HC1O4 concentration was similarly small. Acidities were determined (25.0') potentiometrically using a glasscalomel electrode assembly with a vibrating reed electrometer . I 3
They stated they could not experimentally distinguish between the degrees of polymerization AT of 4, 5 or 6, but preferred N = 4. Swinehart and Garrettg described the solubility of BiOru'O3 in dilute HN03 solutions on the basis of an equilibrium between solid BiON08 and unhyResults and Discussion drolyzed Bi+3 even a t acidities where other inGranCr and SillCn6 showed that for 0.05 M Bi vestigators found appreciable hydrolysis of the ions (111) in 3 . A 1 perchlorate, hydrolysis begins near in solution. This interpretation is not necessarily 0.5 A 1 H+. The hydroxyl number nI4 rises with (1) This document is based on work performed for t h e U. S. Atomic decreasing acidity but near 0.1 A ' H + tends to Energy Commission a t t h e Oak Ridge National Laboratory. (2) Previous papers: (a) VI, J. S. Johnson and K. A. Kraus, THIS level a t n = ca. 2 . Their data were extended in this Laboratory to lower acidities with the followJ O U R N A L , 78, 3937 (1950); (b) VII, K. A. Kraus, "Hydrolytic Behavior of t h e Heavy Elements," Proceedings of the International Coning results for 0.05 d.I Bi(II1) in 3 M NaC104: ference on the Peaceful Uses of Atomic Energy, Vol. 7, p. 245, Session 0.025 M H', w = 2.01 i- 0.02; 0.050 M H+, TZ = 10B.1, P/731, United Nations (1956). (3) See, for example, (a) D. F. Smith, THISJOURNAL,45, 300 (1933); (b) E . H. Swift, ibid., 46, 371 (1923). (-1) A. Holmqvist, Svensk K e m . Tidskr., 48, 106 (1936). 1 3 ) If.Prytz and P. Nagel, 2 . Q n 0 7 g . allgem. Chem., 227, 65 (1936). ((,) F. Graner a n d L. G. Sillen, Acta Chem. Scand., 1, G31 (1947). ( 7 ) See also (a) L. G. Sillen, ibid., 8, 299, 318 (1954); (b) S. Hietanen and L. G. Sillen, ibid., 8, 1607 (1954). ( 8 ) P.Souchay and D. Peschanski, Bull. soc. chim. France, 16, 439 I 1 9-18). (9) D. F. Swinehart and A. B. Garrett. THISJ O U R N A L ) 73, 507 ( I !3.5 1 ) ,
(IO) J. S. Johnson, K . A. Kraus and G. Scatchard. J. Phys. t h e n . , 68, 1034 (1954). (11) J . S. Johnson, K . A. K r a u s and R. W. Holmberg, THISJOLJRN A L , 78, 26 (1956). (12) J. S. Johnson, K . .4.Kraus and T. F. Young, ibid., 76, 1430 (1954). (13) K . A. Kraus, R. W. Holmberg a n d C. J. Borkowski, Anal Chem., 22, 341 (1950). (14) n is defined a s t h e average number of hydroxides per metal ion. For its computation from measured acidities, see e g., K. 4 . Kraus and R . W. Holmberg, J . Phys. Chem., 68, 325 (193iii.
Nov. 5, iS5G
ULTRACENTRIFUGSTION OF
Bi(lI1)
IN PERCHLORATE SOLUTION
5507
1.99; 0.101 M H+, n = 1.95. For 0.05 M Bi(111) in 1 M KaC104: 0.025 M H+, n = 2.00. The lack of dependence of n on acidity over a considerable acid range strongly suggests the existence of hydrolytic species of the general formula (Bi0)k" a t low acidities, though the formula BiNONfT1+ -with N large-as proposed by Graner and SillCn6 is also consistent. Ultracentrifugations were carried out under a variety of conditions of bismuth concentration, supporting electrolyte concentration and acidity (see Table I). I n most experiments the acidity was such as to correspond to hydroxyl numbers n of ca. 2.0; the main exception was expt. 16 where n was ca. 1.6. One run was made a t low temperature (0.8') ; all others were near room temperature. Slthough centrifugation equilibrium was attained in approximately 3 days, the centrifugations usually were continued for 2 or 3 days longer. TABLE I ULTRACENTRIFUGATION OF BISMUTH( 111) IN PERCHLORATE SOLUTION Expt. no. and conditionsa
--Initial BiOClOh
molarities---XaC10d HC104h
Temp., SeC
(18
'C.
1 .oo 0.010 0.101 8 . 6 30.4 c - 3 0,020 1 .oo ,025 ,092 7 . 9 30.4 2d C-3 ,050 1.00 ,100 ,093 7 . 9 26.9 .C50 3 B-2 1 .oo ,100 ,091 7 . 7 2 6 . 5 ,050 4a B-2 1.oo ,100 ,096 7 . 5 0 . 8 ,050 4b B-2 1 . 0 0 ,036 080 7 . 6 2 6 . 7 E-1 ,070 5d 1 .oo ,050 085 7 . 3 3 1 . 4 6 B-3 ,100 . 006e .145 7 . 5 2 9 . 9 ,0063" 3 . 0 0 7 A-4 2.97 ,013 .157 8 . 1 30.1 8 A-4 ,026 ,050 2.99 9 B-2 ,025 .OS6 7 . 3 28.4 lad E-1 .050 2.99 .025 .081 7.7 26.7 11 B-4 ,050 3.00 ,025 .144 7 . 4 28.7 12d D-1 .050 3.00 ,067 ,082 7 . 9 28.1 13 B-2 ,048 2.97 ,083 ,088 7 . 4 27.9 3.00 .090 7 . 6 26.4 14 B-2 ,050 ,087 3.00 .140 .050 ,076 7 . 3 2 8 . 1 15d D-1 .050 2.77 .180 ,130 6 . 8 33.2 16 B-4 a Bar Angle: A, 35'; B, 45'; C, 50'; D, 55". E , 60'. Approximate speed of rotation (r.p.m.): 1, 16,930; 2, 17,960; 3, 18,030; 4, 23,130. * Molarity of HClOd in excess of the component BiOClOd. For all solutions n = cu. 2; hence the stoichiometric HClOd concentration is approximately equal to the hydrogen ion concentration. The listed values of S, were used t o compute Fig. 1. Experiments carried out in cells with 30 mm. light path; all others in 12 mm. cells. a Initial Bi(II1) concentration 0.025 M . Most of Bi(II1) precipitated during run. It is assumed that the HC104 concentration did not change as a result of the precipitation. Remaining Bi( 111) concentration determined polarographically. I d
Graphs of log Z*/x vs. x2 were made for all experiments. In all cases, approximately straight lines were obtained; ;.e., Se = d In (Z*/x)/d(x2) is nearly independent of x2, suggesting that the systems are monodisperse.15 This behavior is demonstrated in Fig. 1 in which the experimental data are presented as deviation functions (log ( Z * / x ) S e x2/2.303) plotted against x2. The average slopes (15) T h e term "monodisperse" will be used here t o imply t h a t the polymeric component occurs principally in t h e form of a species with a definite degree of polymerization. In general, however, the method is not sufficiently sensitive t o permit unambiguous exclusion of small concentrations of other polymeric aggregates, particularly with similar degrees of polymerization.
Fig. 1.-Test of constancy of S. (experiment numbers indicated refer to conditions listed in Table I).
S, listed in Table I were used to compute these functions. Table I also includes values of a e = lo6 SeT/w2; i.e., values of the slope S e adjusted so that experiments performed at different angular velocities w and temperatures T are comparable. Over the entire range of conditions investigated n e averaged 7.6 with a maximum deviation of 13%. Such constancy suggests monodispersity. At constant NaC104 concentration, a e decreases somewhat with Bi(II1) concentration (expt. 1-6), but this is expected for a charged monodisperse system (see eq. 2). An increase in ae would be expected for a polydisperse system with concentration dependent degree of polymerization.11 No appreciable dependence of ae on temperature (expt. 4a and 4b) or angular velocity (expt. 10 and 11) was found. Experiments 10 to 16 were carried out a t the same bismuth and sodium perchlorate concentrations but a t different acidities ( M HCI04 from 0.025 to 0.18). With the exception of expt. 16, the values of ae fall in a narrow range and show no trend with acidity. In expt. 16 the acidity was highest of the series and for it the hydroxyl numb,== n = 1.6 (interpolated from the data of GranCr and SillCn)6 is significantly below the value Of 2*o to the Others. Hence, for this experiment, a lower degree of polymerization might
5308
R.iJ’. HOLMBERG, k.A. KRAUSAXD JAMES S . JOHNSON
reasonably be expected. In expt. 7, most of the bismuth precipitated during centrifugation. It is interesting to note that a e was about the same for this experiment as for the others, though the final concentration of Bi(II1) was much lower. The distribution of a polymeric electrolyte PX, in a centrifugal field depends upon the charge of its ions as well as its molecular weight. These quantities may be determined from centrifugations in the presence of a supporting electrolyte BX for systems for which species activity coeflicients, specific refractive index increments, partial specific volumes g, solutioii density p , weight average degree of polymerization iV or Swand charge of the polymeric ion z may be assumed constant.2a.1u.11For purposes of computation the polymer component (component 2 ) is defined as PX, - (212) BX and is considered to be tilade up of N or ATw monomer units, each containing one metal atom (-ITwis a weight average for a polydisperse system). We have assigned the formula BiOClOd(zf/2)NaC104 to the monomer unit where z’ is the charge per monomer unit. This is equivalent to the assumption that the polymeric ion, except for complexing by Clod-ions, has the formula (BiO)$”. Since most of the experiments were carried out a t a hydroxyl number n = en. 2, such an assignment appears justified. Small deviations in the degree of hydrolysis would not significantly affect the calculated values of :V.” The values of ae may be used to estimate the degree of polyincrization :2‘and the charge per monomer unit z’ = z ‘Swith the equation”
where c2’ is the concentration of component 2 expressed as monomer (c2’ = cBi(III)), c3 is the concentration of the supporting electrolyte B X (component 3 ) and .\/Cyeo is the limit of .\/(y, a t L ~ ’ / c S = 0. Initial concentrations c? and c3 were used together with the tabulated values of a e (Table I) since these concentrations occur a t equilibrium near the center of the cells where S e and hence [Ye apply. In the derivation of eq. 2 the sedimentation of the supporting electrolyte is assumed negligible compared to that of the polymer. In the present work u = d In cald(x2)16was ea. 3% of S = d In c2’ld(x2)which is always larger than S, (see eq. 6), and hence this assumption appears justified here. X plot of 1 /.\/ai z’s. c2’ ’i3should give a straight line of positive slope for a charged rnonodisperse poly2/2.\/Z&0) and meric system. Frotii the slope (1q7~’ intercept ( I /&ro) of such a plot, :V and z’ may be evaluated by a short iteration using the relations
and
M2’is ihe formula weight of the monomer unit, R the gas constant and go the partial specific volume of the-monomer unit (here 2’2 = (VBiOClO, (2’ ’2) VNacio4)/Af2’). The value ?BiOCIO, = 50 was (I(!) Values of u were estimated using eq. 18, reference 10
Vol. 7s
determined in 1 AI NaC104 and wss assumed to hold in 3 A l NaC104. Values of VN~CIO,= 45.6 and 48.4 for 1 A I NaC104 and 3 A I NaC104 solutions were taken from the Iiterature.“ The average values of the solution densities p = 1.09 (observed for 0.05 M BiOC104-1 111 NaC104) and 1.23 (observed for 0.05 M BiOC104 - 3 M NaCIOd) were used for 1 M and 3 Jf NaC104 solutions irrespective of the bismuth concentration. Plots of l/.\/Cy; us. c~’/c3 are shown in Fig. 2. The points for the 1 AI NaC104 experiments fall approximately on a straight line. From the slope 0.46 and the intercept 0.33, values N = G.2 and z’ = 0.G7 are obtained. The small range of the data for the 3 Af NaCI04 solutions precludes an unambiguous evaluation of N and z‘. X line with a slope that corresponds to the z’ = 0.67 found for the 1 M NaClO1 series has been arbitrarily drawn through the points for the experiments in 3 ,If NaC104. Since as much or more perchlorate complexing would be expected in 3 M NaC104, this line represents an upper limit to the expected slope. From the slope and intercept of this line N = 5.4 is obtained. If a lower value for z’ is chosen, a lower value of N results (e.g., for z’ = 0, A7 = 4.8). The points for the 3 A I NaC104 solutions are significantly higher than those for the 1 series. The reason for this divergence is not clear, although i t was also found in another system.” Presumably, some of the restrictions on which this method is based do not apply strictly. The assumption that species activity coefficients are constant is the most suspect. Another method of estimating At and Z’ makes use of the equations (eq. 1 and 11 of reference 11) N =
SIAz’ 1-
^126
