1178
CHARLES
R.BOSTONAND G. P E D R O SMITH
Vol. 66
SPECTRA OF DILUTE SOLUTIOSS OF BISMUTH METAL IS MOLTEN BISMUTH TRIHALIDES. I. EVIDENCE FOR TWO SOLUTE SPECIES IS THE SYSTEM BISMUTH-BIShIUTH TRICHLORIDE’ BY CHARLES R.BOSTOX AKD G. PEDRO SNITH Metallurgy Division, Oak Ridge A’ational Laboratory,2 Oak Ridge, Temessee Reeeivsd Januarg 18, 1962
Solute bismuth metal in chloride-rich melts of the system Bi-BiCl3 is found to be partitioned into two chemical species which obey the law of additive absorbances. ilbsorption spectra from 450 to 750 mp are reported for molten Bi-BiClr mixtures 0.0027 to 0.7 AI in solute bismuth metal a t path lengths as short as 24 p and a t temperatures of 264, 350, and 433”. The spectrum consists of an intense, broad band with a maximum near 560 m p . Large apparent deviations from Beer’s law are found a t all wave lengths. These spectra have the characteristics expected for solutions with two light-absorbing solute species. Phenomenological equations are derived which describe the spectra of solutions consisting of any given number of solute species derived from a common substance, modified for high-temperature work10 was used to make the Introduction spectral measurements. Fused silica cell-insert combinaThe molecular constitution of the liquid phases tions were used to provide path lengths from 24 to 500 P . of bismuth-bismuth trihalide and related metal- Cells were loaded with weighed amounts (10-12 g.) of Bimetal salt systems is an unsolved problem which c13 in the drybox and held under a flow of argon durin spectral measurements. Melt composition was change$ has attracted much recent research and debate, between spectral scans by adding bismuth metal through the Much of this work is reviewed elsewhere.3-5 top of the cell while keeping a stream of argon passing over It usually is assumed that bismuth metal dissolves the melt. The possibility that atmospheric contamination signifiin halide-rich melts to form a single solute species, cantly influenced the spectra was excluded by the results However, some ~ o r k e r sassert ~ , ~ that there are two of measurements on two Bi-BiC& mixtures which were or more solute species which are in equilibrium. sealed in optical cells under 1/3 atni. of argon. The spectra No specific solute species has been demonstrated of these sealed mixtures were quantitatively like the spectra with stoppered cells. to exist in the halide-rich melts. The species which obtained Nomenclature and Units.-All of the melts to be conhave been postulated include such diverse entities sidered lie at the BiCla-rich end of the Bi-BiCla binary sysas bismuth atoms,7 polymers of bismuth atoms,B tem. Accordingly, pure BiC13will be referred to as the solmonovalent bismuth ions and their p~lymers,~Agvent and the amount of bismuth in excess of that in pure and “ions plus electrons.”* The research reported BiCla will be referred to as solute bismuth. The concentration of solute bismuth in moles per liter of melt is calculated here provides spectrophotometric evidence which from the composition by weight on the basis of the density clearly favors a two-species model for chloride- measurements of Keneshea and Cubicciotti,7 and is denoted J I f . This is a “formal” measure of solute concentration rich melts of bismuth in bismuth trichloride.
Experimental Materials.-Bismuth trichloride was prepared by direct reaction between bismuth metal and chlorine gas. The product was purified by distillation under chlorine followed by purging chlorine from the melt with argon. Analysis of the salt showed 33.68 wt. % ’ C1 as compared with the theoretical value of 33.73%. This material m-as extremely sensitive to air contamination. Therefore, all handling, including analytical weighing, was performed in a vacuum-type drybox filled with high-purity nitrogen. Bismuth metal, used as a solute, was deoxidized by bubbling hydrogen through molten, reagent-grade metal held on a sintered glass disk. The oxide-free metal was filtered through the sintered disk into a glass tube, sealed off under vacuum, and later opened in the drybox where the metal ingot was broken up in a mortar and placed in a weighing bottle. Measurements.-A Cary Model l l M S spectrophotometer (1) A preliminary report of this study was presented a t the 137th National Meeting of the American Chemical Society, Cleveland, Ohio, .4prll, 1960. A final report was presented a t the XVIIIth International Congress of Pure and Applied Chemistry, Montreal, Canada, August, 1961. (2) Operated for the U. S. Atomic Energy Commission by the Union Carbide Corporation. 13) D. Cubiociotti, J . Chem. Educ., 37,540 (1960). (4) 6 . J. Yosim, A. J. Darnoll, W. Gehman, and S. ’VC’ Mayer, J . Phys. Chem., 63,230 (1959). ( 5 ) N. H. Nachtrieb, %bid.,66, 1163 (1962). (6) M. A. Bredig, ibid., 63, 978 (1959). (7) T. K. Keneshea, Jr., and D. Cubicciotti, t32d., 62, 843 (1958); 63, 1112, 1472 (1959). (8) J. D. Corbett, ibid., 62, 1149 (1958). (9) 1,. E. Topol, 9. J. Yosim, and R. A. Osteryoung, %bid.,65, 1511 (1961).
which may or may not equal the molar concentrations of the atomic, molecular, or ionic species in which the solute bismuth exists in the solution. The absorbance A of a solution is defined in the usual way as log [I(solv)/l(soln)]. I n practice, the absorption ?f the solvent and the solution were measured separately with an air reference as functions of wave length using the same cell under the same conditions. Then the absorbance of the solution was calculated by subtraction. The data were recorded as binary numbers punched into paper tape by means of high-precision recording devices. Calculations including the above subtraction were done by a digital computer which read directIy the paper-tape output of the spectrophotometer. I n the recording operation, absorbance values were sampled a t 1-mp intervals. The extinction coefficient (molar absorptivity) E of a single solute species is defined in the usual way by the relation E = A/bM a-here rl and M are the absorbance and molarity, respectively, ascribed to a specified species and b is the path length in em. The formal extinction coefficient E f of a solution (which may contain several species) is defined by the relation ef = A/bMf, where A is the experimentally measured absorbance of the solution. It may be helpful to know that the composition in mole % ’ of solute bismuth metal is about 8 to 10 times Aff. The exact relation depends, of course, on the temperature and the exact i%ffvalue.
Results The bismuth trichloride solvent was essentially transparent a t wave lengths between 500 and 750 mp but a steeply rising absorption edge occurred below 500 mp which gave a short wave length cutoff. Figure 1 shows the position of this edge a t temperatures and path lengths frequently used (10) C. R. Boston and G . P. Smith, ibid., 62, 409 (1958).
June, 1962
SPECTRA O F DILUTE
SOLUTIONS O F
in this research. From considerations of signalto-noise ratio, it was concluded that no useful absorbance values could be determined below 400 mp. The limiting wave length for precise measurement varied between about 420 and 500 mp depending on the conditions of measurement. With long path lengths (small M f ) a t 433", the limit for precise measurement was about 500 mp, while, with short path lengths (large Md at 264', the limit was about 420 mfi. Typical spectra for different concentrations of bismuth a t different temperatures are shown in Fig. 2 in terms of q as functions of wave length. The shaded strip a t 264' is a region within which lie the spectra for all solutions from 0.0141 Mf down to the lowest concentration measured, 0.0027 Mf. At low concentrations, a strong band is found. The band maximum occurs a t a wave length of about 560 mp for 264' and at a somewhat longer wave length for higher temperatures. The band is skewed toward longer wave lengths and a t 433' has a slight shoulder near 610 mp so that, it may be a composite of absorptions due to more than one electronic transition. The most striking feature of the spectra is the manner in which the band diminishes with increasing &f*until it is almost indistinguishable against the background of a diffuse absorption edge which rises very slowly with shortening wave length. Figure 3 shows the manner in which A/b varies with fWf for a wave length near the band maximum for each temperature studied. At quite low concentrations these curves are linear but beyond this brief low-concentration range the departures from linearity are very large. The linear range at 264' is defined by seven spectra with Mf values from 0.00273 through 0.0141 mole/l. of solute bismuth. The slope, which equals ef over the linear range, has a value of 5820 l./mole-cm. At 350' the linear range, with a slope of 4200, is defined, by six spectra with M i from 0.00965 through 0.0562 mole/l. .4t 433" the linear range is not accurately defined. The shaded strip in Fig. 2 for 264' includes all of those spectra which lie in the linear range of A/b us. Mr. There is no trend with increasing Mt for the spectra within this strip. Consequently, the strip indicates the precision within which 9 is known for. the linear range and, likewise, the precision within which A / b us. ;Cff is linear at wave lengths other than that chosen for Fig. 3. h similar shaded strip could be drawn about the lowest-concentration spectrum at the other two temperatures. Discussion For solutions with a single solute species, Beer's law usually is obeyed, that is, A / b is proportional to the solute concentration and the molar extinction coefficient r varies with wave length but not concentration. However, for solutions of bismuth metal in fused bismuth trichloride, it is evident from Fig. 2 and 3 that Beer's law is not even approximately obeyed save a t the lowest concentralions. We shall show that these very large departures from Beer's law can be accounted for in a quantitative way if one assumes that the
BISMUTH IS
IFUSED
1179
BiC13
25
20
15
3 -
0,
IO
05
0 350
400
450
500
550
600
h(rnp),
Fig. 1.-Typical abscrption spectra of pure molten BiCla plus the silica cell. Spectra A, B, and C are for a path length of 0.00276 cm. and temperatures of 264, 350, and 433", respectively. Spectrum I3 is for a path length of 0.0501 cm. and a temperature of 350".
4
3 v '
2 1
6
5 4
3 2 I -
I
1
'450
500
550
6D0 h (.mpi).
650
750
700
-
Fig. S.-Typical spectra of molten Bi-BiCla mixtures in terms of er vs. X with Mr values as follows: a t 264", A = 0.0027 to 0.0141, B = 0.0341, C = 0.113, and D 0.696; at 350°, A = 0.0485, B = 0.148, C = 0.280, and D = 0.679; a n d a t 433", A = 0.0099, B = 0.106, C = 0.213, a n d D = 0.464.
solute bismuth metal is partitioned between two solute species each of which individually obeys
1180
CHARLES
R. BOSTOSS X D G. PEDRO SMITH
of X, and X m . At a given temperature, the quantit>iesA and ef are?of course, functions of wave length and concentration while En and em are functions of wave length alone. Equations 1 and 2 may be combined to eliminate one concentration variable. Inasmuch as we have no direct way of measuring separately the two terms on the right-hand side of eq. 2, we shall recast this equation into a form in which en and em are replaced by the formal extinction coefficients Ef of two solutions which we can measure and which we shall call "reference" solutions. In choosing reference solutions we require only that the algebraic difference between their formal extinction coefficients be significantly larger than experimental errors over most of the wave length range. Designate quantities pertaining to the two reference solutions by the subscripts 1 and 2 and quantities pertaining to any other solution by the subscript 0. From eq. 2 we have
a
b
Vol. 66
+ + +
(A/bh = Mfoafo = MnoEn MmEm (3a) (A/b)l = Mflefl = M n l t n ikfm~~m (3b) (A/b)z = M ~ Z E = ~MZ n2en Mm~ern (3c) Define two parameters y and 6 by the equations
6
4
Mno = Y M n 1 + SMn2 Mmo = Y M ~ I 6Mmz
(48) (4b)
+
2
Algebraic manipulation of ey. 3 and 4 leads to Mtom = YMfieri
(A/b)o
0
81
I
+ 6Mrzerz
(5)
Using eq. 1 and 4 , the parameter 6 may be eliminated by the relation 6 =
(MfO/MfZ)- Y(MfdMf2)
(6)
The parameter y may be expressed in terms of concentration variables by solving eq. 4 to give Y = (MmoMn2
- MnoMmz)/(Mm&fn2
- MrJ4'mz)
(7)
Upon substituting eq. 6 and 7 into eq. 5 and rearranging, we obtain I I$
0 3 0
I
I
!
,
!
'
I
O (
0 2
0 3
0 4
0 5
0 6
0.7
I
'-
~
Mf '
Fig. 3.-Beer's law plots for all values of Mi and for A / b near the band maximum. At 264 and 350°, A / b .was determined a t 560 mp while a t 433' A / b was determined at 570 mp.
(tfo
-
Erz)
= (efi
- efz) YMfdMto
(8)
Equation 8 may be somewhat generalized to give (efo
-
€fl)
=
(Ef2
- Ef3) razlY13ZMf2Mfa/(MfOMfl)
(9)
where the subscripts 0, 1, 2, and 3 designate any four solutions, none of which need be regarded as references, and where Yijk
= (MmxMnk
- AfniMmk)/(Mmjivnk
- MnjMmk)
(10) Beer's law, that is, a two-species solution with additive absorbances. Since we have no a priori We shall generally use these equations in the logaway of knowing the molar extinction coefficients of rithmic forms these postulated species, we shall recast the log(ato - E f 2 ) = log(Ef1 - Ef2) log(YMfl/Mfo) (11) phenomenological law of additive absorbances into log(er0 - E f d = log(ef2 - Ef3) 10gr (12) a form which does not contain these coefficients. Let us suppose that the solute bismuth dissolves where f is the collection of concentration terms in in or reacts with the fused bismuth trichloride eq. 9. Equations 8, 9, 11, and 12 are alternative desolvent to form two molecular species Xn and X m . scriptions of the behavior of an isothermal family of Conservation of mass requires that spectra of solutions of two light-absorbing species in Mr = DnMn 4- DmMm (1) equilibrium which obey the law of additive absorbwhere M , and M , are, respectively, the molar con- ances. They will be referred to as the two-species centrations of X, and X,, and where D, and D m are model. I n principle, €,/Onand em/Dm constitute the numbers of moles of solute bismuth required the envelopes or extremes of an isothermal family, to form one mole, respectively, of X, and of X m . and all possible spectra of mixtures, that is, all The law of additive absorbances may be written EL, lie intermediate to these extremes. A / b = erMt = enMn e m M m (2) There are two simple properties of the twowhere and em are the molar extinction coefficients species model which may be deduced from the
+
+
+
COMPOUND REPETITION ISTHE SYSTEM LizO-'V20s
June, 1962
above equations and which serve as tests of the compliance of real solutions. First, if two spectra intersect a t any point in the cf - X plane, then all spectra intersect at this same point. This is the familiar isosbestic point which has long been used as a test of the two-species model. Unfortunately, the spectral range in our measurements is not wide enough to include an isosbestic point. Second, according to eq. 12 log (eti - tfj) is, to within an additive constant, an invariant function of wave length for every pair of spectra, q i and E f j . This function is singular at isosbestic points and, hence, is of no practical value for wave length regions where the e~ curves come close together. For this reason, the above two properties are complementary tests of Compliance. In the research described here, there are no isosbestic points and, hence, this conventional test is of no aid. For this reason, the second test was developed. The extent to which the above compliance tests are unique Tor the two-species model may be ascertained by examining the N-species model. The above procedure for deriving the two-species model is easily generalizod for N species in terms of N reference solutions and gives
.v
( ~ / b ) o.= M f o e i o =
yinffjefj
(13)
3-1
where Jffj and cfj are the Mf and tf of the j-th reference solution and yj is one of N parameters which are functions of the concentrations of the N species. Any one and only one yj may be eliminated by the relation
1181
By substituting the conditions of the compliance tests for the two-species model (for example, cfl = efz = . . . = cf. a t an isosbestic point) into eq. 13 and combining with eq. 14, it may be shown that the multispecies models ( N > 2 ) mill not, in general, accord with these tests and that an "accidental" accord is possible only for certain unique situations. The situations which give log(efi cfj) an invariant shape for N greater than two are sufficiently unique so that we regard them as implausible. It may be worth noting that the equations derived above apply to any solution of two solutes which are in equilibrium or which may be derived in principle from a common substance. The experimental spectra at each temperature were tested by computing log(cfi - q j ) over the full wave length range for many pairs of cf functions, and then verifying that the shapes of the resultant curves were essentially the same. Conclusion The data presented here provide substantial evidence that, in dilute solutions of bismuth metal in fused BiC13, the solute exists as two light-absorbing species. Acknowledgment.-The authors are indebted to Dr. L. C. Howiclr, University of Arkansas, who assisted with evaluating the computer results, to Mr. W. M. Ewing who assisted in experimental phases of the research, to Mr. D. E. LaValle who supplied the bismuth trichloride, and t o Dr. M. A. Bredig who encouraged this research in many ways.
CONPOUND REPETITIOK I N OXIDE-OXIDE INTERACTIONS : THE SYSTEM Li20-V205 BY ARXOLD REISMAN ASD JOAN MINEO 7'. J . Watson Research Center of International Business Machines, Yorktown Heights, N . Y . Received I"ebruaTy 8. 1962
Previous work on compound repetition in oxide-oxide interactions has been extended with studies of the system LiaOV2O6. It has been found that crystallization from the melt occurs metastably in the high vanadium pentoxide portions of the system with the resultant exclusion of a stable phase, 2NagO.l7V~Ob,which melts incongruently a t 621'. The phase 2 N a ~ 0 . 5 V ~has O ~ been found to melt congruently at; 603' in the metastable equilibria and incongruently a t 601' in the stable solid-liquid equilibria. A compound having the composition NazO.VZ05 melts incongruently a t 6 1 6 O , while another This phase exhibits three crystallographic compound having the composition 3ru'az0.V& melts congruently a t 1152 inversions, a t 724, 773, and 1152'. The results of the present work are compared with other reported data on the system LigO-Srz05 and are used as a basis for prediction of compound repetition in the system NazO-V20r.
.
Introduction The topic of compound repetition in oxide systems has been the subject of previous reports.l+ Studies of the system L~zO-VZO~, together with future work on other alkali vanadates, are intended to provide further data on which to evaluate the ideas discussed previously.' Based on the results of an incomplete examina(1) A. Reisman, J . Phys. Chem., 66, 15 (1962). (2) A. Reisman and J. hlineo, ibid., 66, 996 (1961). (3) A. Reisrnen and E'. Holtaberg, ibid., 64, 748 (1960); J . Am. Ciiem. SOC.,80, 6503 (1958).
tion of the solid-liquid equilibria in the system L~zO-VZOS, Canneri4 concluded the existence of two lithium vanadates, LinO ~VZOSand 2 L i ~ .0V Z O ~ . More recently, Kohlmuller and Martin15employing differential thermal, X-ray, and dilatometric techniques, detected three compounds in the system. These were identified as the 1:3, 1:1, and 3 :1 salts, the latter exhibiting two phase inversions. Although the discrepancies evident in the above (4) G. Canneri, Gazz. chinz. ital., 68, 6 (1928). ( 5 ) R. Kohlmuller and J. Martin, Bull. S O C . chim. France, 4 , 748 (1961).
