THEKINETICS OF CIF AT HIGHTEMPERATURES
3939
18, we suggest that this model too, properly considered, leads to the equilibrium relation at low flow rates. To put our criticism another way, Ackers, like Verhoff and Sylvester, identifies KGPCwith a sieve constant; and this is what is basically at issue. As eq 22 shows, P, defined by eq 16 is indeed (almost) the sieve constant; but as eq 21 shows, it is incorrect to equate P , with KGPC. According to the form of eq 13, any first-order hydrodynamic contribution to KGPCcould only increase it since the sieve constant is between zero and unity on the basis of any of the models we have discussed-even though the effect of relative flow velocities of particles and carrier fluid increases the sieve constant in the flow models and decreases it in the restricted-diffusion model. These contrary effects on transport of suspended particles through narrow tubes obviously prompt a question as to which kind of model might be the more realistic. Reasonably, both effects might be included; indeed R e n k i ~suggested ~ ~ ~ that the sieve constant should be q”[1 ( 2 r / a ) - (r/a)2]. However, it would be outside the ambit of this paper to delve further into the difficult problem of the actual behavior of suspensions flowing through small channels. 43 44 49
+
Unlike the hydrodynamic contribution to Kapci true nonequilibrium effects in partitioning, as expressed by the idealized stochastic theory, do not affectthe average elution volume for a solute; but according to eq 2 they tend to shift the maximum of the peak toward a smaller volume. The preponderance of evidence is that nonequilibrium has only a minor effect on elution peak maxima in ordinary columns, but under certain experimental conditions nonequilibrium behavior of the qualitative character predicted by the stochastic theory can become p r ~ m i n e n t . ~ l -The ~ ~ corollary of the insensitivity of mean and most probable elution volumes to flow and nonequilibrium phenomena is that detailed study can most profitable be directed toward the shape and breadth of peaks, on which both classes of phenomena will have more direct effects. There is the interesting consideration, pointed out by Guttman and DiI\Qarzi0,3~ that flow and diffusion tend to compensate: mass flow through pores will clear them of solute in a finite time and thus act to counter the skewing and tailing of peaks characteristic of diffusion-limited transport. (49) See, for example, a review by H. L.Goldsmith and S.G. Mason in “Rheology: Theory and Applications,” Vol. 4, F. R. Eirich, Ed., Academic Press, New York, N. Y . , 1967, Chapter 2 .
The Kinetics of Chlorine Fluoride at High Temperatures by J. A. Blauer, W. C. Solomon,* and V. S. Engleman Technology Division, A i r Force Rocket Propulsion Laboratory, Edwards, California OS6RS
(Received April $0, 1971)
Publication costs assisted by the A i r Force Rocket Propulsion Laboratory
Two-body emission from chlorine atoms has been used to follow the thermal decomposition of ClF occurring behind incident shock waves in the temperature range of 1700-2200°K. The initial reaction rates were interM = C1 F M and may be expreted in terms of the bimolecular rate constant for the reaction C1F pressed in the form &[initial] = 1014.6*00.a exp(-61,300 =t3000/RT) cc/mol-sec. However, if the competing exchange reaction C1 ClF = Clz F is very fast, then the rate expression for CIF M = C1 F M becomes IC3 = 1014J 0.4 exp(-57,500 + 3000/RT) cc/mol-sec. The latter value for ha is in better agreement with all of the available data.
+
+
+ *
+
Introduction Although there have been theoretical predictions concerning the behavior of the C1F system,*S2 there are currently few actual rate data available. Global rates for the reaction occurring between Clz and Fzhave been r e p ~ r t e d ;however, ~ no attempt was made to attribute experimental significance to the rates of individual reaction steps. The present shock tube study is the third in a series of kinetic measurements on the
+ +
+
+
related systems C1F5, ClF,, and ClF being conducted in these lab~ratories.~J (1) S. W. Benson and C. R. Haugen, J . Amer. Chem. SOC.,87, 4036
(1965). (2) R. M. Noyes, {bid., 88,4311 (1966). (3) E. A. Fletcher and B. E. Dahneke, ibid., 91, 1603 (1969). (4) J. A. Blauer, H. G. McMath, and F. C. Jaye, J . Phys. Chem., 73, 2683 (1969). (5) J. A. Blauer, H. G. McMath, F. C. Jaye, and V. S. Engleman, ibid., 74, 1183 (1970).
The Journal of Physical Chemistry, Val. 76, No. $6,1971
J. A. BLAUER, W. C, SoLowm, AND 1 7 , 5. ENGLEMAN
3940 We have selected an experimental procedure which is based upon a measurement of the intensity of the two-body emission from C1 atoms behind incident shock waves. Our use of 5000 A as the point of observation is based upon the results of Carabetta and t Palmer.6 They found that at the latter wavelength r" the emission intensity is independent of temperature k! and linearly dependent on the square of the C1-atom concentration,
1
~
'
0.1 VOLT
T
Experimental Section The shock tube and associated apparatus have been described adequately elsewhere.' In the present instance, spectral isolation was by m a n s of a Beckman DU monochromator, and detection of radiation was accomplished with a 1P2S photomultiplier tube. Gaseous C1F having a purity of 98.0% was purchased from Ozark-Mahoning Co. and was further purified by trap-to-trap distillation at - 100". High-purity CIS and HF (ea. 99.5% min) were purchased from Matheson and were treated by cooling to -loo", followed by removal of all permanent gases in vucuo. Argon having a minimum stated purity of 99.9% was also purchased from Matheson and was used without further purification. Chlorine trifluoride having a minimum purity of 98% was purchased from RIatheson, The gas was further purified by forming the KF complex, KCIFI, at ambient temperatures. The pure ClFa was recovered by vacuum distillation at 200". The purity of the C1F5 used in these experiments was the same as that discussed in our previous paper.5 After a gaseous mixture with argon had been prepared, its CIF, Fz, and Clz contents were determined by measuring the optjcal densities at 2600, 2850, and 3250 A, respectively. A solution of the resulting three simultaneous equations gave the initial concentrations of the aforementioned species. The CIFa and ClFs concentrations were obtained from pressure measurements.
Results and Discussion A typical emission trace is shown in Figure 1. It may be seen that after 150 ,usee of test time drift due to nonidealities appeared in some traces making it necessary to estimate the equilibrium intensity as early as possible (ea. -100-150 psec). In accordance with the results of Carabetta,e the C1-atom concentration was related to the emission intensity, I , by means of the expression, [Cl] = A(I)"*. Here, A is the proportionality constant which was evaluated from the equilibrium conditions. Values of A = [Cl]equi~/(I)l'z for binary mixes of C1F in Ar were normalized to a standard value obtained for a binary mixture of C12in Ar. Both of the above-mentioned values of A were acquired on the same day. The results are found in Table I . It is seen that even over a factor of 50 variation in the value for [ClIequilthese proportionality constants showed The Journal of Physical Chemistry, Vol. 75, No. 26,1071
TIME
____C
Figure 1. Emission trace for test no. 22, 0.1 V/ordinate division, 10 Fsec and 50 gsec/abscissa division, 2.0% ClF in Ar. Incident shock temperature and pressure at the front of 1878°K and 22.7 atm, respectively. The arrows show the extrapolated point of shock incidence and direction of increasing intensity.
little drift. Similarly, although the F-atom concentrations vary over a factor of 20, their presence had only a slight effect upon the emission intensity. These observations precluded any significant contribution to the radiancy from such two-body processes as
+ F = C1F + hv F + F = Fz + h~
C1
(1)
(2)
and demonstrated conclusively that the emission intensity was a true measure of the C1-atom concentration. This conclusion has been further corroborated by the data obtained with ClF, and CIFj (see Table 1 p 9
Resort is made to the method of initial slopes to estimate the rate constants for the processes
+ 11= ci + F + n4 ci, + n1 = ci + c i + M
CIF
(3)
(4)
It is found that plots of (1)'" us. time are linear over at least 50% of the reaction, making the evaluation of initial rates from the first 10% of the reaction profile a relatively simple process. The point of shock incidence is found by extrapolating these plots to zero intensity. Density corrections are made in the manner outlined by Palmer.1o The resulting experimental rate constants are found in Table I and plotted as func( 6 ) R. A . Carabetta and H. B. Palmer, J . Chem. Phys., 46, 1333
(1967). (7) J. A. Blauer and W.C. Solomon, J . Phys. Chem., 72,2307 (1968). ( 8 ) It has been reported@that the emission intensity from shockheated HF* is altered in the presence of C1 atoms. Experiments (see Table I) with C1-HF mixtures seen herein show no such behavior for the radiancy from the two-body recombination of C1 atoms. Similarly, the presence of HF has no effect upon the dissociation rate of Cln; see Figure 2. (9) J. A. Blauer, V. S.Engleman, and W.C. Solomon, 13th International Symposium on Combustion, Salt Lake City, Utah, 1970, p 109. (10) H. B. Palmer and D. F. Hornig, J.Chem. Phys., 26,98 (1957).
THEKINETICSOF CIF AT
HIGHTEMPERATURES
3941
Table I: Initial Reaction Rate Data (Arlo X lo*, Test
Tat OK
mol/co
17 18 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 3ad 39 40 41 42 43d 44 46 47 49 a 50" 51a 54 57 59* 67
1779 1692 2176 1924 1878 1796 1676 2196 2236 1786 1810 2167 2145 1902 2042 2274 1986 1951 1768 1759 1921 1916 1834 1776 1559 1750 1757 1912 2133 1718 2047 2150 1847 2248 1938 2540
0.143 0.141 0.039 0.146 0.144 0.114 0.094 0.039 0.040 0.076 0.071 0.038 0.046 0,056 0.018 0.061 0.098 0.099 0.094 0,095 0.071 0.070 0 089 0.095 0.111 0.094 0.094 0.130 0.024 0.154 0,093 0.057 0.114 0,101 0.077 0.051
... ...
0.288 0.079
0 296 0.294 0.232 0.191
I
0.079 0 * 082
. . I
...
0.399 0.373 0.205
*..
...
...
0.094 0.296
...
...
0.096
... *.. ... ...
...
...
0.124 0.112 0.074 0.036
... ,
I
.
0.048 0.092 0,123
... 0.100 0.046
...
0.242 0,334 0.060 0.314 0,189 0.115
...
0.668 0 114
...
0.233 0.206
I , .
... ... , . I
...
...
I
. I .
... ... ... ... ...
I , .
...
0.156
...
0.104
... .
I
.
... I . .
...
...
... ... ...
... I
0.047 0.633 0.441 0.296
... ...
0.664
...
0.91 1.00 1.02 1.26 1.03 1.12 1.20 0.98 1.00 1.26 1.13 1.00 1.03 1.03 1.12 0.99 1.08 1.02 1.06 1.06 0.99 1.01 0.99 0.98 1.02 1.01 0.95 1.11 .
.
I
... 0.93 1.10 1.00 1.00 1.04 1.08
k X 10-7, oo/mol-sea
0.91 1.4 38 3.2 2.2 1.4 0.26 32 51 1.o 1.3 18 28 2.7 15 62 10 9.9 3.1 3.2 9.1 12 6.3 4.9 0.65 3.3 0.80 4.1 24 0.47 8.9 21 5.5 72 4.5 245
[(Cl)/z/i], refers to measurements made with a binary mixture of Contains 2.0% HF.
f
3000/RT)
cc/mol-sec 1013.3 * o . 2 (exp(-46,450 + 1500/RT)
cc/mol-sec The latter expression is in good agreement with the earlier findings of CarabettaJ6 Thiel," and Jacobs.I2 The use o f the above expression as an estimate of the rate constant for reaction 3 is clouded by the possible occurrence of the two exchange reactions. =
0,085
[(cl)/,/T]/
I (C1)/ d i I * C
' Binary mix of CIFa and Ar.
k3[initial] = 1014* 0.3 (exp(-61,300
+ C1 Clz + F ClF + F = C1 + Fz
(Flequii x 106, mol/oa
0.125 0.201 0.203 0.192 0.195 0.145 0.146 0,181 0.193 0 226 0.195
