Sept,., 1962
ELECTROMOTIVE STUDIESIK ~IOLTEIU BISMUTH-BISMIUTH TRIBROMIDE SOLUTIONS 1,587
ELECTROMOTIVE FORCE, POLAROGRAPHIC, AKD CHRONOPOTENTIOMETRIC STUDIES I N MOLTEN BISRIUTH-BISMUTH TRIBROMIDE SOLUTIOSS' BY L. E. TOPOL AXD R. A. OSTERYOUNG Atomics International, A Division of North American Aviation, Inc., Canoga Park, California Received November 21, 1061
E.m.f. and polarographic measurements on cells of the type C, Bi(N1),BiRr3(l - A'l)iiBiBra(l - SP)> Si(,\)), C where to about 0.08, w r e made a t 220, 235, 250, 275, 300, and 325 . In add]tion, a chronopotentiometric study was performedon a cell containing -Ir?'sof 0.0027 to 0,0210 a t 285-290' and S 2 = 0.0027, O.OO:U, and 0.0128 a t 240". The e.m.f. and polarography results were similar to those found in thc Bi-BiCl, system. The e.m.F. data were consistent with the reaction 4BiBr = BirBrt and the equilibrium constant, K N , can he expressed as log K N = (2.83 =t 0.83)(10a/TOK. - 1.852) 3.98 k 0.25 for N B , $060-
l
’
+A
d o
‘
+60
’ do
’
do
TIME (seconds).
Fig. 2.-Chronopotentiogram-potential time. 10.0
325
TOC. 275
300
of Bi-BiBrd melt us.
250 235 226
40
1
r 2,0--
0.6
j4L i
l
LOG K,=
(2.83 i 0.83)(&-1.85:
AH”=-129 r 3 8 kcal
-RT E =: -In nF‘ 0 , L I I I I [Bi+“(a) ] [Bi+(1) ] [BiBra(1)](2’3)t +’ [BiBr(1)] 24 1600 1700 I800 1900 2000 2100 [Ri+3(l)][Bi+(2)][BiBr,(2)](a’3)t’+8[BiR~(2)]2t’+ IO~TOK, Fig. 3.-Effect of temperature on equilibrium constant for (6) the reaction 4BiBr = (BiBr)4. 2RT [BiBrs(1) [BiBr(1)1” and the concentration of Bi(2) is greater than = E n , t . - --In Bi(1). Thus, the difference between E,.t. and the nF [BiBr3(2)](l’a)t’ts [ B i B r ( 2 ) F measured E depends on the ratios of both the Bi(7) Br3 and BiBr activities raised to the appropriate where t + 3 and t’+3 are the transference numbers of powers. NOW,[BiBr(2)] > [BiBr(l)], [BiBr3(2)]< Bi+3in the two half-cells, t+ and t’+ those for Bi+, [BiBra(l)],t’+ > t+! and t’+3 < , t + 3 , so that the two En.t,the e.m.f. of the cell without transference, ratios in the logarithm of eq. 7 act in opposite directions and no definite conclusion can be (4) S. J. Yosim, L. D. Ransom, R. A. Sallach, and L. E. Topol, @
J Phys. C‘hem., 66, 28 (1962). ( 5 ) D. Cubicciotti and F. J. Keneshea, Jr., ibid., 62. 999 (1958). (6) J. D. Corbett, abtd., 62, 1149 (1958). (7) H. A. Levy, 1\1. A. Bredlg, M. D. Danford, and P. Agron, ibid., 64, 19.59 (1960). (8) C. R. Boston and G. P. Smith, ORNL-2988, July, 1960, pp. 9-16. (9) C. R. Boston and G. P. Smith, $bstracts of the XVIIIth International Congress of Pure and Applied Chemistry, llontreal, Canada, August, 1961, R3-13, p. 184.
(10) For the cell:
Bi(2), BiBra(2)11 BiBr3(1),Bi( 1)
the simple electrode rcactlou is
+ Bi+3(1) = Bi+3(2) + B i + ( l ) given bv Z/d’+~Bi+3(2) + 2t’+BiC(2)+ 2r1 - i+3 - t + ) Br-(1) = ?/d+3B1+3(1)+ 2t+Bi+(1) + 2(1 - t’+3 - t +)Br-(2) Bi+(2)
whereas the transference expression
IS
Combining terms of these two equations, one gets the total cell reaction for which eq. 6 holds.
I,. E. TOPOL ASD R. A. OSTERYOUSG
1590
100
-
0''l.600
325
300
I
I
1.700
T"C. 275250 235 226
m-
I
1.800
1.900
2,000
-.
of the limiting current constant with temperature.
0000-
I
2u 7 0 0 0 1 a p.
(which is greater than one) will be much greater than the ratio of log [RiBr] (which is less than one). Since In [BiBr(l)] is always negative (activity is less than unity), the valuc of expression 8 is posiii\re, and En,t.is g r a t e r than the measured E . If this is true, i.e., if Bi+ carries an important fraction of the current, then the results from the e.m.f. data would be shifted in the direction of higher polymer formation, e.g., (BiBr)a rather than trimers. An attempt to measure roughly the Bi+ transference number in BiBra was made employing a six-compartment cell. Four compartments were joined in a row by means of ultra-fine glass frits, and two reference half-cells consisting of known quantities of Bi and BiBrp were joined to the second and third compartments. The first and fourth compartments were utilized as the cathode and anode, respectively. Compartment 2, the half-cell adjoining the cathode, contained a small amount of Bi, e.g., 0.1 mole %, while compartment 3, that between 2 and the anode, contained a larger amount of metal, e.g., in one case 1% and in the other 10%. After a known amount of current was passed between l and 4, the increase in Bi + concentrations in half-cell 2 was determined from the e.m.f. change, i.e.
2.1
IOYT'K
Fig. 4.-Variation
as Henry's law has been shown to hold for dilute Bi concentrations, and the [BiBr8]ratio before and after electrolysis is essentially constant. Thus, 1+, the mean transference number of Bi+ between the concentrations in compartments 2 and 3, could be calculated with the relation
6000&
E
g 5oooL
SLOPE = 2 76, 0-62 x IO"
Vol. 60
cmysec
1+ =
L!
-
5 4000-
g. equiv. Bi+ gained in 2 g. equiv. current passed
(10)
T'alues of t+ of about 0.007 and 0.07-0.08 thus were found a t 280" when compartment 3 contained W 1.0 and 10.0 mole % Bi, respectively. Although 3 2oooc I these t+ values are for large concentration differences, 2c I O O O F it is interesting to note that the Bi+ appears to L L d carry an amount of current directly proportional O h k h O 600 d o lob0 1200 14b0 1600 le00 200022002400 to its concentration. This transference behavior, CONCENTRATION 8 i (microequlvalents). if true, would confirm the assumption above that Fig. 5.-Average i ~ ' ' 2 us. concentration of bismuth. the log expression in eq. 7 is positive, and if large drawn. However, since the change in the BiBr3 enough, pentamers rather than tetramers may ratio as well as the difference in Bi+3 transference indeed be present. numbers should be much less than that for BiBr €3. Polarography.-The polarographic behavior for the concentrations in question, it would appear, found in this system suggests that (a) the electrode as a first approximation, that the logarithm of the reactions involved probably are reversible as the BiBr3 ratio can be neglected. If this assumption current-voltage curve crossed the zero current is made, then the logarithm expression in (7) is axis a t maximum slope, and (b) the dissolved metal positive. This may be seen more readily by writing yields a species that is subject to oxidation. From the relation 2RT [BiBr(l)]'+ 2RY' = --(t+) hi [RiBr(l)] In i l = LAC (11) nF [BiBr(2)It'+ n F where il is the measured limiting current, A the t'+ 111 [BiBr(2)] electrode area, and C the formal concentration of {I - t+ In [BiBro]) (*) bismuth calculated from the weight and density" W
2 3000b LT
c
~
Kow, generally the value in the braces will be negative as the ratio of transference numbers
(11)
F. J. Keneshea, Jr., and D. Cnblcomtti, J . Phvs. Chem., 63,
1112 (1959).
Sept ., 1962
PEROXIDE DECOMPOSITION AND CAGEEFFECT
of BiBr3 in the compartment, values of the limiting current constant 7c were determined. These values in units of microamperes/microequiralent/ ~ m . ~ / m mare . ~very slightly lower than those reported for Bi-BiCL2 As discussed previously2 a plot of log k 11s. 1/ T should yield the activation energy of the limiting process. Such a plot is shown in Fig. 4, and a least squares treatment results in an activation energy for the currentlimiting process of 5.1 f 0.9 kcal., about the same as that found in the chloride (5.8 1.1kcal.).2 C, Chronopotentiometry.-To check the applicability of the basic equation of chronopotentiome try12
i7
‘/t
__
C
-
a1/2nFD1/Z
~0
(12)
Y
where i is the current density, r the transition time, and C and D the bulk concentration and the diffusion coefficient of the electroactive species, respectively, various relations were examined. Plots of log 7 us. log i a t constant C yielded lines of slope which varied from -1.90 to -2.30, but most of the slopes were close to the theoretical value of -2.0. However, a t constant concentration, the transition time constant ir1/2/C was not independent of C but varied from 3.5 to 2.9 a t 285” and from 2.7 to 2.2 a t 240” as the concentration of metal increased. Further, the transition time con(12) P. Dplahay, “New Instrumental Methods in Electrochemist r v , ” Interaciencp Publishers, Ino., Neu York, N.Y . , 1954, Chap. 8.
1591
stant was not independent of i but increased somewhat with decreasing i. This behavior has been found in practically every chronopotentiometric study to date13 and suggests that semiinfinite linear diffusion is not the only means of mass transfer of the electroactive species to the electrode surface. However, the solid electrode used was sealed in glass and mounted horizontally to achieve near-optimum conditions. l 3 Similar electrode geometries have been used in other fused salt studies.I4j16 ,illthough the diffusion coefficients may not be very meaningful, plots of the average i r 1 / 2 for each concentration os. C for all the runs did result in straight lines a t each temperature, as demonstrated in Fig. 5. From the slopes of these two lines and eq. 12, diffusion constants for Bi+ of aboiit 0.62 X and 0.30 X cm.2/sec. a t 285 and 240°, respectively, and an activation energy for diffusion of about 7.3 kcal. were calculated. This value for the activation energy of diffusion is in fair agreement with that found polarographically. (It is assumed that the current-limiting process in the polarography is diffusion controlled.) A41thoughtheoretically, chronopotentiometry should give a more direct determination of diffusion parameters than does voltammetry a t solid electrodes, experimentally, ideal conditions are more difficult to achieve. (13) A. J. Bard, Anal. Chem., 33, 11 (1961). (14) H. A. Laitinen and W.S.Ferguson, i h i d . , 29, 4 (1967). (15) H. A. Laitinen and H. C . Gaur, Ana2. Chim. Acta, 18, 1 (1968)
PEROXIDE DECO;CiIPOSITION AND CAGE EFFECT BY Mi. BRAUIV,~ L. RAJBESBACH, AND F. R. EIRICH Institute of Polymer Research, Polytechnic Institute of Brooklyn, Brooklyn, N . Y . Recezced Januargi 6 , 1961
After assuming that the lifetime of the acetoxy radical is of the same order as the [‘lifetime” of a “geminate diffusive combination” reaction (cage) and assuming that ethane results from the geminate combination of methyl radicals, it is possible to rel?te the amount of ethane formed to microscopic diffusion parameters and the lifetime of the acetoxy radical, while assuming “free” diffusion of the radical pairs. The calculations lead to results consistent with these assumptions. The rate constant for the decarboxylation of the acetoxy radical was calculated to be k = 1.6 x
[email protected], a t 60°, and the activation energy, 6.6 kcal./mole. In order to evaluate the possibility of the reaction scheme involving the geminate combination of a methyl radical with an acetoxy radical to explain the “cage” methyl acetate experimentally obscrved, a calculation was carried out assuming this mechanism. The ratio of cage methyl acetate to cage ethane was thus calculated and it agreed remarkably well with the experimentally observed ratio.
If two free radicals (fragments) formed by the decomposition of the Same molecule become initially separated by an average distance of a t least several molecular diameters, the surrounding liquid can then be considered as a continuum and interactioiis between the two fragments can be neglected. In other words, the fragments can be treated as if they were undergoing random displacements. The probability that they meet again, i.e., that “geminate diffusive combination” occurs, can be evaluated as a function of their initjal separation. Two methyl radikals, for example, formed by a two-step thermal decomposition of a diacetyl peroxide molecule, apparently satisfy this condition. It will be shown (1) Taken in part from a thesis to be submitted in partial fulfillment of the reqriireinents for the Ph.D., by this author.
that it is possible to calculate the extent of radical combination (ethane formation) as a function of the viscosity of the hydrocarbon solvent medium and of the lifetime of the intermediate acetoxy radical, while treating the fragments as undergoing free diffusion and justifiably neglecting proximity effects normally encountered in cage (re)combination problems.2 The latter is a particularly significant point since cage (re)combination problems invariably involve (a) neglecting the effect of the primary cage, although the radical pair immediately subsequent to formation is still caged in by the surrounding solvent molecules, and (b) assuming that the radicals undergo free diffusion after escaping the primary cage and are separated by ( 2 ) R. M. Noyes, 2. Elektrochenz., 64, 153 (1900).
