F. J. KENESHEA, JR.,AND DANIELCUBICCIOTTI
1472
T (OK.)
Vol. 63
TABLE I1 THERMODYNAMICS OF THE BUTADIENE-VIN YLCYCLOHEXENE EQUILIBRIUM 298.1 300 400 500 600 700 800
900
1000
(a) Free energies of formation (kcal./mole) Butadiene" Vinylcyclohexene
36.01 46.18
36.07 46.07
39.46 57.20
43.05 68.82
46.78 80.70
50.60 92.76
(b) Equilibrium free energy changes (kcal./mole) Thermodynamic data -25.84 -26.07 -21.72 -17.28 -12.86 - 8.44 Reaction rate' data ..... ..... ..... . . . . . ( - 3.2) ( - 1 . 9 ) See ref. 8. Values in brackets are extrapolated values.
54.48 104.92 -4.04 -0.6
58.40 117.17
62.36 129.43
0.37
4.71 2.0
0.7
Q
-18.3 e.u. per g. mole per cc. if the transmission from assumptions to distinguish conclusively becoefficient is assumed to be unity. The entropy of tween the two possibilities,10 the close agreement reaction A S for this process a t 600'K. may be com- above between the entropy change for the reaction puted from the value for butadiene,8 84.36 e.u., and and entropy of activation makes the assumption of a vinylcyclohexane, 124.75 e.u., both at 1atmosphere, highly circumscribed transition state, rather similar using the Sackur Tetrode equation to correct these in structure to the product molecule, L e . , cyclic, a values to volume concentration units. The above very probable one. The question still remains open value for vinylcyclohexene was calculated by the whether the transition state in this process is a dimethod of group equations. This computation radical or simply a polarized molecular state. Acknowledgments.-One of us (G.J.J.) wishes to gives, as the entropy change for the dimerization of butadiene a t 600'K., the value of -21.2 e.u./per cc. thank Hervey H. Voge, Emeryville, Calif., and per g. mole of butadiene. Whereas the calculations Yukio Mikawa, Tokyo, Japan, for directing atbased on statistical thermodynamics for the entro- tention to the need for revision and correction of the pies of activation assuming both linear and a cyclic earlier calculations. transition state complexes were not sufficiently free (10) A. Wassermann, J . Chem. Soc., 612 (1942).
VOLUME EFFECTS ON MIXING I N THE LIQUID Bi-BiIa SYSTEM' BY F. J. KENESHEA, JR.,AND DANIEL CUBICCIOTTI Stanford Research Institute, Menlo Park, California Received Februaru 86, 1969
Volume effects on mixing in the liquid Bi-BiL system have been determined by measurements of the density as a function of temperature. The total volume of the system decreases on mixing. The partial molar volume of BiI3 differs only slightly from the molar volume of the pure salt while the partial molar volume of the bismuth is much less than the molar volume of pure bismuth. These volume effects are analogous to the changes found previously for the bismuth-chloride and bismuthbromide systems and are interpreted in terms of the same model of an interstitial type of solution. The experimental values in all three halide systems are in fair agreement with an expression derived from the model which relates the partial molar volume of the bismuth with the halide ion radius.
Introduction In an effort to gain some knowledge concerning the nature of metal-salt solutions we have previously studied the volume effects in the Bi-BiCl3 and the Bi-BiBrs systems.2 As a continuation of this work we have measured the volume changes in the Bi-BiI, system. Bismuth has been shown3 to exhibit appreciable solubility in BiI,, analogous to the Bi-BiCla and Bi-BiBra systems. There is some evidence for the formation of solid BiI. In the temperature range 406-500' and up to about 50 mole % bismuth, one liquid phase is obtained. Solutions of Bi-BiI, in this range have been investigated in the present study. (1) This work was made possible by the financial support of the Research Division of the United States Atomic Energy Cammission. (2) F. J. Keneshea, Jr., and D. Cubicciotti, THIS JOURNAL, 62, 843 (1958); 63, 1112 (1959). (3) (a) L. Marino and R. Becarelli. Atli Accad. Lincei, 8 1 [51, 695 (1912); (b) h. 6. Van Klooster, Z . anorg. Chem., SO, 104 (1913); (c) G. G. Urazov and M. A. Sokolova, Akad. Nauk. SSSR.,Insl. Obshch. Neorg. K h i m . , Sektor Fiz-Khim. Anal., Izueat., 25, 117 (1954).
Experimental As in the previous experiments, the densities of the liquid Bi-BiIa mixtures were determined by a pycnometric method. In general, the procedures were the same as those used for the chloride and bromide experiments.* The BiIs &as prepared by reaction of reagent grade BiZ03 with aqueous HI followed by eva oration of the water under a nitrogen stream. The crude &I3 thus obtained was distilled twice under n stream of dry h.2. The product from the second distillation was ground in a mortar and stored in a desiccator. Two separate preparations of Bi13 were made. They gave bismuth analyses ot 35.32 and 35.20% compared to the theoretical amount for bisniuth of 35.44Tob. As it had previously been found in vapor pressure measurements on the Bi-BiI3 system4 that BiIa tends to decompose to yield free 1 2 when heated, it was thought that a small amount of free It might be present ill the distilled BiIa. To test for the presence of any free 12, duplicate samples of BiI, were dissolved under a nitrogen atmosphere in oxygen-free KI solution acidified with HCl and immediately titrated with NazS20ssolution. The results showed less than 0.03% .I$ to be present in the BiIa. The melting point of the 1311, used ranged from 405.9 to 406.6°.4 (4) D. Cubicciotti and F. ,J. Kenesliea, Jr., THWJOURNAL, 63, 295 (1959).
Sept., 1959
VOLUMEEFFECTB ON MIXING IN LIQUIDBISMUTH-BISMUTH TRIIODIDE SYSTEM
1473
In the experiment successive portions of the BiI3 were melted under N2 in a weighed pycnometer. When the proper volume was obtained the pycnometer and contents were again weighed and the weight of the Ai13 obtained by difference. A. weighed amount of bismuth was then added and the pycnometer wan sealed under vacuum. The density measurements were then made as in previous experiments.2
Results The densities of seven Bi-Bib solutions, ranging in compositioii from pure Bi13to 0.34 mole fraction of bismuth, are shown as a function of temperature in Fig. 1. The least squares equations obtained from the data are given in Table I. From the TABLE I DENSITY EQUATIONS Mole fraction Bi
p = u U
- bl
FOR
Bi-BiTa MIXTURES Standard error, g./cc.
(g./cc.)
b X 103
Exptl. temp. range, "C.
0.003 425-492 2.22 5.558 0" ,002 434-494 5.523 2.09 0,0190 ,002 423-489 5.597 2.16 ,0450 .OOl 452490 5.664 2.10 .0927 ,002 436-494 5.761 2.02 ,1708 ,002 420-494 5.821 1.85 .2313 .002 414-494 6.013 1.72 .3443 a Two different preparations of pure BiIa were measured and the average density taken. I n the range of temperatures investigated the samples differed by less than 0.3% in their densities. (Both data are plotted in Fig. 1.)
4
4.2 400
420
440 460 480 500 520 Temp., "C. Fig. l.--l)ensity of Bi-BiI:, mixtures. Numbers on curves indicate mole fraction Bi. 8 e
.
---------
experimental densities the molar volumes were calculated and plotted as a function of composition for temperatures of 420, 460 and 500". From these curves the partial molar volumes were calculated as previously described2 and are listed in Table I1 for several compositions.
D
TABLE I1 PARTIAL MOLARVOLUMES IN Bi-BiL MIXTURES Mole fraction Bi 0
0.10 t o 0 . 2 0 0.30
420' 127.9 f 0 1 127.0 i . 2 125.0 1 .8
Fisira, cc. 460°
500'
130 0 f 0 . 1 129.G 1 . 2 127.0 f . 8
132.7 1 0 . 1 132.0 f . 2 129.5 f .8
-
0
0.10 t o 0 . 2 0 0.30 1.00
2 1 3 8.8 f 2.8 13.3 i 2.2 21.22 f 0.02
"si, 1 5.9 13.1 21.33
cc. 1 3
f 2.8 f 2.2 f 0.02
-5 f3 5.2 1 2 . 8 11.5 1 2 . 2 21.45 0.02
- 100
I
I
I
0.1 0.2 0.3 0.4 0.5 Mole fraction bismuth. Fig. 2.-Expansivity of Bi-BiIs mixtures a t 500'. 0
tion, v ~ decreases i with increasing temperature and in very dilute solutions becomes negative a t As in the chloride and bromide systems, a de- higher tem eratures. This trend toward negative crease in the total volume occurs when bismuth is values of ?i ~i was noticed also for the chloride and mixed with BiI3. This decrease amounts to about bromide systems. The expansivity, l / V ( b V / b T ) , of the iodide 0% a t a bismuth mole fraction of 0.35 and a temperature of 500°, which is about the same solutions also shows the same general behavior as decrease found in the bromide system a t a bismuth the chloride and bromide solutions. The tots mole fraction of 0.4 and a temperature of 400'. expansivity, l / P ( d P / d T ) (Fig. 2) show negative The partial molar volumes in the iodide system deviations from the ideal value. This negative exhibit the same behavior as in the other halide, deviation is again due to the behavior of the bissystems. The partial molar volume of Bi13, muth in the solution as can be seen from the conv ~ i l varies ~ , by only 2% up to 0.3 mole fraction trib_utio_nsof the bismuth and Bi13 expansivities, of bismuth, indicating that the Bi13 behaves l / V ( d V / W ) , to the total expansivity in Fig. 2. almost ideally in this composition range. The These curves indicate that the Bi13 expansivity in partial molar volume of BiI, increases with in- the solution is fairly constant, reflecting the almost creasing temperature (Table 11). The partial ideal behavior of the BiL, while the bismuth exmolar volume of bismuth, VB~,in dilute solutions pansivity is negative, due to the decrease of v ~ i is much less than the molar volume of pure bismuth with increasing temperature. The expressions and approaches the value for bismuth with in- relating the various expansivities have been decreasing concentration. For a given concentra- veloped in previous reports.2
*
F. J. KENESHEA, JR.,AND DANIEL CUBICCIOTTI
1474
Discussion Since the results found for the iodide system are similar to those of the other halide systems, the model previously suggested is also applied here. I n this model the bismuth species from the added bismuth metal enter empty octahedral holes in the liquid halide quasi-lattice. Thus, there is a net decrease in volume on mixing bismuth with the bismuth halide because the bismuth occupies holes already present in the salt. With an increase in temperature the lattice expands and allows the added bismuth to be more rekdily accommodated; hence there is a decrease in V B ~with an increase in temperature. At bismuth concentrations approac_hing zero the very small and negative values for VBi suggest that the added bismuth enters an empty hole and also causes a contraction of the bismuth and halogen species in the vicinity of the hole. At higher concentrations, where the added bismuth enters holes which are very near one another, it might be expected that this contraction would be essentially cancelled because of competition for the same surrounding halides. I n this case, the volume effects are due mainly to the changes produced by inserting the added bismuth into the empty octahedral holes. Thus the volume change is roughly the difference between the volume of the bismuth species added to a hole and the volume of the hole. For a mole of added bismuth this may be expressed by the equation FBi
= v*Bi
- Vhole
(1)
Vol. 63
Pauling's crystal radii5), in agreement with the relationship shown in equation 2. The agreement is well within experimental error, both a t 400 and a t 250". (The data for the iodide system were obtained by linear extrapolation of the experimental densities (Table I), a super-cooled liquid being assumed a t 250O.) Extrapolation of the curve for 250" discussed above yields a value for V*B~in equation 2 of about 16 cc., which is rather close to the value of 14.2 cc. that one would calculate for V * B i if the added bismuth species were atoms (taking 'TBi = 1.78 However, roughly the same value would be possible for V*B~if the added bismuth reacts with the solvent to yield a monohalide (e.g., Bi l/z Bi13 = 3/2 BiI), with Bi+ instead of atoms entering the holes. I n this case the volume change associated with a mole of Bi+ would be smaller than that of bismuth atoms (since r B i + < r B i ) but there is also a volume increase due to the change of '/z mole of Bifa to Bi+. It has been suggestede that for the Bi-BiCl3 system, results of cryoscopic7 and vapor pressures measurements may be interpreted in terms of the formation of an ideal solution of BiC4 and Bi4C14. I n view of the more recent value for the heat of fusion of BiC139a better interpretation would be the formation of BipClz instead of the tetramer. It is of interest to calculate, from the known molar volume of these solutioiq2 the apparent molar volume of the BizClz
+
@BizClr
= P/ZBiaCIz
- (TBiCLa/ZBi~CIz)~BBiCla
where V B ~is the partial molar volume of bismuth where z = mole fraction. At 250" this volume i 0.050) in cc., V*Bi is the volume in cc. of a mole of added varies from -9 CC.a t ~ B i & l=~ 0 . 0 3 9 ( ~ ~ = bismuth species, without specifying the nature of to 5 CC. a t xBizClr = 0 . 1 7 7 ( ~ ~=i 0.200). (The these species and Vhole is the volume in cc. of a mole corresponding values for BipBrz(2500) are - 21 of empty octahedral holes. Equation 1 holds only and 1 cc.; for Biz12(4200)they are -34 and -10 for V*Bi > Vliole; if V*Bi < Vhole then VBi should be cc.) At higher temperatures $C is smaller. For an zero for the simple model used here. The volume ideal solution the apparent volume of each comof a hole can be approximated by the volume of a ponent should be constant and equal to the molar sphere which can be accommodated by the hole, volume of the pure component. The large change assuming contact of the halide ions, i e . , 4 / 3 ~ in 9 and the small, even negative, values calculated ( ~ ' 2 . 1 )A.3 ~ ~per ~ ~hole or 0 . 1 7 9 ~cc.~ per ~ mole of for this quantity thus do not appear to be consistent holes, where rx is the radius of the halide ion in A. with the assumption of an ideal mixture of bismuth trihalide and dimeric bismuth monohalide. Equation 1 then becomes Acknowledgments.-The authors are indebted to V B ~= V * B ~- 0 . 1 7 9 ~ ~ ~ (2) Dr. C. M. Kelley for many helpful discussions and I n the range of concentrations where equation 2 to Mr. W. Robbins for assistance in the experimenis expected to hold both V*B~and rx (at constant tal work. temperature) may be assumed to be independent (5) L. Pauling, "Nature of the Chemical Bond," Cornell Univ. Press, of X B ~ , the mole fraction of bismuth, and from Ithaca, N. Y.,1948,P . 340. equation 2 we 5nd that ( b v B i / b x B i ) T = 0. (6) J. D. Corbett, THISJOURNAL, 62, 1149 (1958). Experimentally, b V B i / b x B i = 0 in all three halide (7) S. W. hiayer, S. J. Yosiin and A. J. Darnell, Ahstpacts of Paperh, solutions a t bismuth mole fractions of 0.1 to 0.2. ACS Meeting, New York, N. Y . ,Sept. 1957,Abstract NO. 71,p . 28s. (8) D. Cubicciotti, F. J. Keneshea, Jr., and C. 51. KellPy, T H I B For these concentrations it is possible to fit a JOURNAL. 62, 463 (1958). straight line with a slops equal to 0.179 to the ex(9) L. E.Topol and S. W. illeyer, Abstracts of Papers, ACS hleotperimental data when V B is~ plotted vs. rx3 (using ing. Chicago, Ill,, Sept. 1958,Abstract No. 29. P . 14s.
