NOTES
2078 (This minimization demand is not equivalent to that imposed by eq 2; however, t o the extent that F , in the neighborhood of the minimum, approaches a quadratic form, the results will be identical.) The values of Al? and k cannot be found directly by standard leastsquares calculations, because eq 4 leads t o terms higher than quadratic in the arguments AH and K of the function F. Therefore, we search for the minimum by an iterative method, which consists of guessing a pair of values AH and K , approximating the function F ( A H , 1/K) in the neighborhood of this point by a quadratic expression G(AH, 1/K) having the same numerical values for its first and second derivatives as F ( A H , l/K), computing the minimum of G by solving two linear equations in two unknowns, and using the roots as a new guess for the next iteration. This procedure was programmed in FORTRAN IV and run on a UNIVAC I11 computer. The data analysis for the thermometric titration curves was based on formulas 32, 33, 36, and 38 of ref 1, and, as far as could be verified from Table I of ref 1, the calculated heats of reaction as a function of titrant added were identical. For each run, the final averaged AH and K values given by Hansen4 were used as starting values for the calculations. Indicating the present method as method I1 and that of ref 1as method I, we compiled the results of both procedures in Table I. For each experimental point, the value of Qio - Qro was calculated by substituting the AH and K values found. For these differences two statistics were determined, viz., the mean &" - &" value and the standard deviation g, both of which are included in Table I. It appears that the two methods of calculation give significantly differing results, although they originate from the same experimental data. For method I, the mean &" - Qa values are considerably larger than for method 11, as are their standard deviations. Therefore, it can be concluded that the iterative method is to be preferred for this type of calculations. The experiments of ref 4, performed with a titrant concentration of 0.991 M were not included in the comparison because the value for +T, the apparent molar enthalpy of the reacting species in the titrant, quoted in ref 4, seemed to be erroneous. We recalculated these experiments, using a corrected value of &. The final results obtained by means of method 11, including this correction, are AH = -5.41 f 0.04 kcal/mol and pK = 1.930 f 0.005 with 21 degrees of freedom. The values seem to be in better agreement with the literature values compiled in Table I11 of ref 2 than those obtained with method I.
Convergence The Of the calculations cited above 'Onverged within three Or four iteration steps when the AH and K values obtained by method I were used as startThe Journal of Physical Chemistry
ing values. However, the calculations turned out to be rather critical with respect to the initial values chosen for AH and K. Starting values deviating more than about 15% from the final values sometimes gave rise to strong fluctuations in the calculations and to large negative K values, which are physically meaningless. However, in view of the very strong correlation which turned out to exist between AH and K , this behavior was in agreement with expectation; the calculated correlation coefficients varied between 0.989 and 0.9997. This may, indeed, cause the successive values in the sequence of iterations to follow a rather erratic path. A cursory look at the surface P ( A H , 1/K) revealed that, in accordance with the strong correlation mentioned, the contour lines were very thin and possibly somewhat bended ellipses. This may give rise to wild excursions in the iterative procedure if AH and K are not close to Al? and k. The strong correlation between A€? and k may well be visualized also chemically; e.g., formula 4 allows the correction for too high values of Qo by lowering either AH or K . Summarizing, we may conclude that only the iterative procedure is capable of fully utilizing the high precision obtainable with the apparatuslts described by Izatt, Christensen, and coworkers. The two-point procedure may serve to compute the necessary starting values. (8)J. J. Christensen, R. M. Izatt, and L. D. Hansen, Rev. Sci. Instr., 779 (1965).
86,
Mass S p e c t r u m and Molecular Energetics of Krypton Difluoridel*
by P. A. Sessalb and H. A. RilcGee, Jr. School of Chemical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30338 (Received November 14,1068)
The possible existence of fluorides or oxides of He, Ne, Ar, and Kr has been discussed by many investigators, and all suggested experiments have involved cryogenic considerations for an enhanced stability. A number of properties including the positive ion mass spectrum2 of gaseous krypton fluoride have been reported, and although the compound was once reported to be KrF4,a (1) (a) Research sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, U. 8. Air Force, under Grant AF-AFOSR-1308-67, (b) NDEA Predoctoral Fellow in chemical engineering. (2) E. N. Sloth and M. H. Studier, Science, 141,528 (1963). (3) A. v. Grosse, A, D, Kirshenbaum, A. G, Streng, and Le V. streng, ibid., 139, 1047 (1963).
Noms
2079
-ELECTRODE IAI
12
10
A IK~F'I
I
2.0
U
Figure 1. Electric discharge apparatus for the synthesis of krypton diEuoride.
more recent studies'-' confirm the structure to be linear, symmetric KrFz. No other compounds of the above four noble gases are now known. I n this investigation krypton difluoride was prepared using a cryo-quenched electric discharge apparatus, and the product was then subjected to a mass spectral and energetic analysis using a Bendix Model 14-107 timeofflight mass spectrometer. Analysis was made without prior warm-up using a cryogenic inlet arrangement similar in basic design principles to apparatus developed earlier in this laboratory? Initial syntheses were performed in a Pyrex discharge reactor,a but low yields and the formation of undesirable SiF4 led to the design of the metal reactor shown in Figure 1. Discharge occurs between the stainless steel high-voltage electrode (A) and the grounded brass walls of the reactor (B). The enlarged cross section (C) prevents the discharge from occurring near the Teflon tube electrical insulator and vacuum seal (D). An arc near the Teflon results in its rapid erosion in the concentrated fluorine environment of the reactor. One opening (E) serves alternately as the reactant gas inlet and reactor pump-out, while the other (F) leads through a valve to the ionization chamber of the mass spectrometer. The ionizing electron beam m&es grazing tangential contact with the mass spectrometer inlet port at the opposite end of this latter passageway which is maintained a t the same temperature as is the reactor over its entire length of about 75 cm. Typical reaction conditions giving optimum yield with the reactor immersed in liquid Nz (- 196") were 4-20 Torr, 20-30 mA, and 5 M 1 0 0 0 V ac. Since the vapor pressure of Kr at - 196' is about 2 Tori-, an excess of Kr was added so that the actual gas
2.1
22
I
--
II A ~-AV 15.76 -2.08 = 13.68
I
1.3 2.4 VOLTAGE DIFFERENCE, lev)
L 2.5
Figure 2. Determination of A(KrF+, KrF,) from ionization efficiency data using the extrapolated voltage difference method. Argon serves as the energy standard.
phase composition was dependent on total reactor pressure. Additional Kr and FPwere separately added, as determined from monitoring the mass spectrum of the reacting gases and from the reduction in reactor pressure as both reaction and condensation of the excess Kr occurred. An average reactant composition of K v F 2 of 1:5 was maintained. After reaction for 6 hr, unreacted Kr and FZwere pumped away and the products were analyzed during a controlled warm-up from - 150" to room temperature. Similar synthesis operations as well as a wide variety of rf excitation and quench experiments with Ar-O*, Ar-Fz, and KFOZ systems have all failed to give any evidence of reaction. During the warm-up, the positive ion mass spectrum of krypton difluoride appeared at -80" and yielded Kr+ and KrF+ ions, as has been previously reported,% and F+ions. However, the typical ratio of KrF+/Krf of 1:3 that was observed here appears to be considerably higher than earlier reported from standard room temperature inlet procedures. The absence of Fz+in the spectrum suggests that if KrF2 is thermally decomposing a t -8O", the mechanism would have to involve the (4) J. J. Turner and G . C. Pimentel. Science, 140,974 (1963). (5) F. Schreiner, J. G . Malm. and J. C. Hindman. J . A m . Chem. Soc., 87.25 (1965). (6) H. H. Clawen, G . L. Goodman, J. G . Malm. and F. Sohrsiner, J . Chem.Phvs.. 42, 1229 (1965). (7) W. Harshbanper, R. K. Bohn. and S. H. Bauer, J . Amer. C h . Soc., 89.6466 (1967).
&.
(8)H. A. MeGee. Jr., T. J. Malone, and W. J. Martin. Sci. Imtmm.. 37, 561 (1966). The newer meohmioal design used here will be degoribed hy J. K. Holzhsuer and H. A. MeGee, Jr., Anal. Chem., m press.
Volume 75, Number 6 June lgS9
NOTES
2080 formation of a nonvolatile compound with some reactor material. The appearance potentials of Kr+ and KrF+ were measured from -75 to -50" using an extrapolated difference method involving plots of the ion intensity us. the difference in ionizing electron energy for the unknown ion and some convenient standard ion that is necessary to produce equivalent ion intensities.9 A typical such manipulation of the ionization efficiency data on KrF+ appears in Figure 2. Eleven measurements were made on both 84Kr+ and 84KrF+ using argon as the standard, I(Ar) = 16.76 eV, and the results were A(Kr+, KrF2) = 13.21 0.25 eV, and A(KrF+, KrFJ = 13.71 f 0.20 eV. Possible processes for the formation of Kr+ from KrF2 involve the formation of two F atoms, two Fatoms, and one F and one F- atom, or an F2 molecule. The merits of each of these four processes were explored using D,,(Kr-F) = 11.7 kcal/mol, 0.51 eV, as calculated from the calorimetrically determined AHr(KrF2),'0 I(Kr) = 14.00 eV, EA(F) = 3.57 eV, and AHf(F) = 0.82 eV. The latter of these four processes, Le. KrFz e +Kr+ Fz 2e (1)
+
+ +
yields a predicted A(Kr+) of 13.4 eV which is in best agreement with experiment. If reaction of KrF2 with reactor material were occurring at these low temperatures, as discussed above, then A(Kr+) would equal I(Kr), which is not the case. Similarly KrF+ can be formed with either an F atom or an F- ion. Neither of these processes can be verified since the ionization potential of the KrF radical is unknown, and there is no reason to believe that D,,(Kr-F) closely equals D(KrF-F). If one makes this assumption, however, F atom formation implies I(KrF) = 13.20 eV while F- ion formation suggests I(KrF) = 16.77 eV. Instrumental deficiencies prohibited a study of the negative ion spectrum. (9) J. vi'. Warren and C. A, McDowell, D ~ S C ~ L S SFaraday ~ O ? L S SOC., 10, 53 (1951). (10) S. R. Gunn, J. Phus. Chem., 71,2934 (1967).
Isomerization of n-Hexyl Radicals in the Gas Phase
by IC W. Watkins and L. A. Ostreko
Gordon and ?tIcYesby2 found evidence for n-pentyl radical isomerization at 300" by observing the products propene and ethyl radical presumably from sec-pentyl radical decomposition. Quantitative kinetic data on radical isomerizations are lacking. Recently, Endrenyi and LeRoy3 have reported kinetic parameters for the intramolecular 1-4 hydrogen atom migration in npentyl radical. n-Pentyl radicals were produced by the addition of n-propyl radicals to ethylene. The n-propyl radicals resulted from the addition of methyl radicals to ethylene. The detection of isohexane in the products was taken as evidence that some n-pentyl radicals had isomerized to sec-pentyl. sec-Pentyl radicals on combination with a methyl radical gave isohexane. The rate constant reported for the 1-4 intramolecular hydrogen atom migration was k = 1.4 X lo7 exp( - 10.8 X 103/RT) sec-'. I n the course of a similar study of the kinetics of the addition of ethyl radicals to ethylene we have found evidence for the isomerization of n-hexyl radical to sec-hexyl radical. The rate constant for the unimolecular isomerization is similar to that reported for n-pentyl radical isomerization. Experimental Section Azoethane was prepared by the method of Leitch4 and stored in the vapor phase in a blackened bulb. All gas handling was performed with a conventional vacuum system. Aeoethane and ethylene were measured separately for each run. Azoethane at a conmol ~ m was - ~ photolyzed centration of about 0.5 X mol ern+ of ethylene. in the presence of about 2 x Unfiltered light from a Hanovia 550-W high-pressure mercury arc lamp was used for the irradiation. The reaction vessel was a 10.0-cc Pyrex cylinder. The amount of azoethane consumed was usually between 15 and 25%, and the ethylene consumed was always less than 1% of the initial ethylene. After an irradiation time of either 4 or 8 min the entire reactant-product mixture was analyzed by gas chromatography, using a 6-ft silica gel column and a flame ionization detector, Quantitative determinations were based on calibrations of peak areas using measured amounts of certain hydrocarbon standards. The use of hydrocarbon standards containing varying numbers of carbon atoms showed that the response (peak area) per mole of hydrocarbon was directly proportional to the number of carbon atoms per molecule.
Department of Chemistry, Colorado State Uniaersity, Fort Collins, Colorado 80621 (ReceQed November 21, 1988)
Results and Rate Constant Calculation Reactions 1-16 were proposed to explain the observed products.
The isomerization of long-chain alkyl radicals via intramolecular hydrogen atom migration was first proposed by Kossiakoff and Rice' to explain the products observed from the decomposition of hydrocarbons.
(1) A. Kossiakoff and F. 0. Rice, J . Amer. Chem. Soc., 65, 590 (1943). (2) A. S. Gordon and J. R. McNesby, J . Chem. Phys., 31, 853 (1959). (3) L. Endrenyi and D. J. LeRoy, J . Phys. Chem., 70, 4081 (1966). (4) R. Renaud and L. C. Leitch, Can. J . Chem., 32, 545 (1954).
The Journal of Physical Chemistry
