NOTES
2360
Acknowledgment. The generous support in the form of a fellowship to Ismail Y. Ahmed from the National Science Foundation administered by the American Friends of the Middle East is gratefully acknowledged.
Results and Discussion The vapor was found to contain only the species PbCI2, PbBr2, and PbClBr (identified as positively charged ions) ; hence the discrepancy in vapor pressure measurements is explicable not by the formation of PbCla. PbBrz but by the equilibrium PbC12
The Formation of Lead(I1) Chloride Bromide
+ PbBr2 = 2PbClBr
Table I gives a summary of the mass spectral data (listed in order of measurement) using 20-ev electron energy and photomultiplier amplification. The formation constant of PbClBr is given in terms of the partial pressures by
(PbClBr) in the Vapor Phase by H. Bloom and J. W. Hastie Chemistry Department, The University of Tasmnia, Hobart, Australia (Received October $8,1966)
PPbClBr2
Kp =
PPbClgPbBrn
From the measurement, by transpiration, of partial vapor pressures of PbCl2 and PbBr2 above molten mixtures of the two salts at 770°, Greiner and Jellinek' found that the apparent activities of PbBr2 were slightly lower than Raoult's law values over the whole composition range, but that those of PbCl2 were higher than the Raoult's law values from 0 to 0.7 mole fraction of PbCI2. These observations were contrary to the Gibbs-Duhem relation and also to the results of Salstrom and Hildebrand,2 whose activity values of PbBr2 from measurement of the emf's of formation cells were considerably lower than those reported by Greiner and Jellinek. To account for the discrepancies, Greiner and Jellinek suggested a vapor phase equilibrium PbC12
Its heat of formation (per 2 moles) is
AH =
Experimental Section Using a quadrupole mass spectrometer, details of which will be published separately, the mass spectra and ionization characteristics of vapors above an equimolar PbC12 PbBr2 mixture were investigated between 421 and 495'. The melt was contained in a silica crucible within a silver Knudsen cell and heated in a furnace in the chamber of the mass spectrometer. A shutter was used to eliminate background ions. Temperature was measured by a Pt vs. Pt 13% Rh thermocouple and a Leeds and Northrup millivolt potentiometer.
+
+
The Journal of Physical Chemistry
- AH(v,PbCld
where AH[v,PbClBr), etc., are the heats of vaporization of PbCIBr, etc., and are obtainable from the slopes of the graphs of log P vs. 1/T for each species or, in the present investigation, from the graphs of log I+T us. 1/T. Table I : Ion Current us. Temperature Data I +T for the vapor speoieaa
Temp,
+ PbBr2 = PbCI2.PbBr2
This equilibrium would cause the apparent vapor pressures of both components and therefore the derived activities to be higher than the real values, but only in the case of PbC12 would apparent activities exceed the Raoult's law values. The present investigation relates to a mass spectrometric study to identify the vapor phase species.
-
~ A H ( v , P ~ c ~ B ~AH(v,PbBrr) )
a
OC
PbCl+
PbBr +
495 486 480 450 454 461 475 466 441 421
200 133 143 37 59 90.5 129 72.2 34.3 19.3
720 460 450 150 210 310 500 300
.-. ... *
PbClBr
+
55.6 42.5 39.6 14 19 29.4 39.8 26.3 13.1 5.1
PbBrr+
175 118 131 37 55 83.4 121 71.2 37.2 26.9
Ion current in arbitrary units; T in "K.
Ion currents for PbCl2f could not be determined accurately owing to interference by an intense PbBr+ ion close in mass number to PbCl2; hence AH(,,PbClr) was assumed to be equal to A H ( v , P b B r t ) and equal to the heats of vaporization for the two pure salts, which have been found by direct measurement3 to be the same within experimental error (32 f 2 kcal mole-'). These assumptions are reasonable in view of the lack (1) B. Greiner and K. Jellinek, 2.Physik. Chem. (Leipaig), 165, 97 (1933). (2) E. J. Salstrom and J. H. Hildebrand, J. Am. Chem. Soc., 5 2 , 4641 (1930). . . (3) H. Bloom and J. W. Hastie, unpublished results.
NOTES
2361
of strong interactions in the liquid mixtures, as evidenced by the not too far from ideal activity values determined by Salstrom and Hildebrand and by the simple phase diagram for the ~ y s t e m . ~The equality of slopes of log I + T against 1/T for PbCl+ and PbBr+ supports the assumption. From the mass spectral data, AH(v,PbClBr) = 31 f 2 kcal, hence AH = 1 3 kcal/mole for PbClBr. The ratio PPbBrS/PPbClBr = I+PbBm/l+PbClBr Was found to be 3.15 f 0.4 from our ion current results. This may be compared with a value of 3.43 from the vapor pressure results of Greiner and Jellinek, corrected for the partial pressure of PbClBr by using Salstrom and Hildebrand’s results for the activity of PbBrz at 450’. (The temperature difference has only a minor effect on activity.) The partial pressures of PbBrz, PbCl2,and PbClBr of the equimolar mixture for use in the equilibrium constant expression were calculated as follows. P P b B r l was obtained from the activity measurements of Salstrom and Hildebrand together with the measured valuea of vapor pressure of pure PbBrz at the same temperature. PPbC12 was obtained likewise by using the Gibbs-Duhem calculation of the activity of PbClz and the vapor pressure3 of pure PbCl2. The partial pressure of PbClBr was then obtained by combining these “true” partial pressure results with the apparent pressures of Greiner and Jellinek. The value of K p is 0.38 at 700’ (neglecting change of activity with change of temperature) and the corresponding AQ for the reaction is 1 kcal/mole of PbCIBr.
*
Acknowkdgment. We wish to thank Dr. A. L. G. Rees and Dr. J. D. Morrison of the Division of Chemical Physics, C.S.I.R.O., Melbourne, for use of the mass spectrometer and the Australian Research Grants Committee for financial support. (4) K. Monkemeyer, Neues Juhrb. Mineral., 2 2 , 1 (1906).
Pressure and Viscosity Effects on the
Recombination of t-Butoxy Radicals from Di-t-butyl Peroxide’ by Cheves Walling and Harold P. Waits Department of Chemistry, Columbia University, New York,New York 10097 (Received January $0, 1967)
The cage effect (recombination of radicals produced in pairs in close proximity to one another) often deter-
mines the efficiency of radical production in homolytic scission reactions, as counted by scavengers or by the initiation of chain processes. When recombination regenerates the original radical source, the cage effect may also affect its measured rate of dissociation leading to a decrease in rate with increasing solvent viscosity. In 1959, Walling and Metzger2 reported a study of the effect of pressure on the rate of decomposition of di-2-butyl peroxide and noted that AV varied significantly with solvent and since the larger values were observed in toluene and cyclohexene which are readily attacked by 2-butoxy radicals, they suggested that the differences arose from competition between t-butoxy radical recombination and attack on solvent, both within the solvent cage. This proposal can now be reevaluated in the light of new data on cage effects and alkoxy radical chemistry. Significant cage recombination of acetoxy radicals from acetyl peroxide was deduced by Braun, Rajbenbach, and Eirich3 from the dependence of both decomposition rate and products on solvent viscosity and has been confirmed by Taylor and Martin4 by 0l8 labeling experiments. More pertinent here, extensive recombination of t-butoxy radicals from di-t-butyl peroxalate in viscous solvents has been detected by Hiatt and T r a y l ~ r . ~ Finally, concentration levels at which scavenger reactions can compete with cage recombination of radicals from azo-l-cyanocyclohexane have been determined by Waits and Hammond,s with results indicating directly that cage reactions must occur within a very small number of diffusive displacements.
*
Cage recombination of t-butoxy radicals from di-tbutyl peroxide itself is best examined by kinetic measurements, since isotopic scrambling is inapplicable and scavengers suitable for use at high levels at the necessary temperatures are not known. Early work has shown that the decomposition rate is remarkably solvent independent (except in systems in which induced decomposition gives high rates) Very recently, a detailed study by Huyse? has shown that, while
.’
(1) Support of this work by a grant from the National Science Foundation is gratefully acknowledged. (2) C. Walling and G. Metrger, J . Am. Chem. Soc., 81, 5365 (1959). (3) W. Braun, L. Rajbenbach, and F. R. Eirich, J . Phys. Chem., 66, 1591 (1962). (4) J. W. Taylor and J. C. Martin, J . Am. Chem. SOC.,88, 3650 (1966). (5) R. Hiatt and T . G. Traylor, ibid., 87, 3766 (1965). (6) H.P.Waits and G. 8. Hammond, ibid., 86, 1911 (1964). (7) C. Walling, “Free Radicals in Solution,” John Wiley and Sons, Inc., New York, N . Y., 1957,p 469. (8) E. S. Huyser, private communication.
Volume 71, Number 7 June 1067
