DOYLE BRITTOSAKD ROGER11.COLE
1302
n1.6826We computed the standard deviation in the heat content, from their published data, with thc use of Birge’s eq. 40. This was done in the range of the observations (up to -lOOO°K.) and also a t (26) Douglas, et aL , use t h e average deviation, a measure of spread which 18 frouned on b y statisticians. See W. J. Youden, “Statistical Methods for Chemists ” John Wiley a n d Sons, I n c , New York, N. Y., f 9 5 1 , p 8.
Vol. 65
1100 and 12OO0I3. It was found that the error in the function was nearly constant in the range of observation and that it went up, from that constant value, by a factor of two a t llOO°K. and a factor of five a t 12OOOK. We applied these factors to the uncertainties given by Evans, et u Z . , ~ in the liquid free energy function in the extrapolated region.
SHOCK WAVES I N CHEMICAL KINETICS: THE HYDROGEK-BROXIKE REACTIOS BY D O ~ LBRITTO\ E 4x1)ROGER 11.C,C.LE School qf Cheniislrg, University o j Minnesota, Minneapolis, Minnesolts Received December 6 , 1960
The reaction between Hp and Brz to form HBr has been studied between 1300 and 17OO0K.in a shock tube. The rate of tjhe reaction Br H? + HBr H has been directly determined for Hz and D2. The rate of the reaction Br HBr + BrZ H has been directly determined. The relative rates of the reactions H HBr + H? Br and H Br2 -L HBr Br have been determined independently from the forward and reverse reaction data. All of these results are in general agreement -with the predictions which could be made from the low temperature results of earlier workers. As a necessary preliminary t o the preceding the efficiency of HBr as a third body for the reromhination of Br atoms was detprmined, and found to be slightly greater than the efficiency of argon.
+
+
+
+
Introduction The reaction between H2 and Brz is the classic example of a chain reaction. It has been studied here by shock wave techniques both to extend the temperature range over which the rate constants have been determined experimentally and to further test the shock tube method. This reaction has been well reviewed, for example by Pease’ and by Campbell and Fristrom,2and only those pieces of earlier work which are of specific interest will be mentioned below. The simple reactions which occur in the hydrogen-bromine system, and which are of importance, :ire3 Br2 + M = 2Br + BI (1) Br H
+ HP HBr + H + Brz = HBr + Br 5
(2) (3)
Reactions 2 and 3 are the propagation reactions, and if it is assumed that the steady-state approximation can be applied to the H atom concentration then Reaction 1 is t,he source of the bromine atoms. At low temperat,ures or a t large relat,ive Hz and Brz concentrations the reverse reaction can be ignored and equation 4 ca.n be rearranged to d(HBr) _ _ _ _ _dt 1
2kdBr)(Hz)
+ kz,(HBr)/kdBrd
(5)
At’ low temperatures the Br atoms maintain equilibrium with the molecules and (1) R. N. Pease, “Equilibrium a n d Kinetics of G a s Reactions,“ Princeton University Press, Princeton, N. J., 1942, pp. 112-121. (2) E. S. Campbell a n d R. M. Fristrom, Chem. Revs., 68, 173 (1958). (3) T h e following notation ail1 be used: Ki is t h e equilibrium constant for reaction 1,i) a s written; kif is the rate constant for t h e forward reaction in equation (i); ki, is the rate constant for t h e reverse reaction, Ail concentrations will be expressed in moles/liter a n d all times in seconds unless otherwise noted. T h e units of t h e equilibrium and rate constants will be the appropriate combinations of moles/liter a n d swonds.
+
(Br)
=
+
+
+
[KI(Br2)]’/2
If the correct assumptions are made that reaction 1 can be either ignored or studied independently arid that all of the equilibrium constants for the various reactions are known, then two kinetic constants need to be determined to characterize the entire reaction. These t’ivo constants have genand the ratio l ~ ~ f i h - 2 ~ . erally been k2f(orh-~~K1”2) We have re-examined the data of Bodenstein and Lind,4 who reportb ksf/k2r = 10 without giving any error estimate nor any clear indication how the value was determined, and we find a temperature independent value of 10.2 2.4. If their experiments with excess H,, which yield a ratio 12.3 =t 1.5, are compared with their experiments with excess Brl, which yield a ratio 6.9 f 0.8, it is clear that some unknown systematic error is present. The value of Bodenstein and Jung6 of 8.4 h 0.6 seems therefore to be the better value, although the error estimate is optimistic. Fortunately an uncertainty of 2OY0 in the value of this ratio only lead? to a 3% uncertainty in the value of 122f.7 The data of Bodenstein and Lind were calculated using 8.4 and more modern values of KI8 to obtain the parameters given later in Table IV. The other results a t lo^ temperature.. were ohRI. Bodenstein and S. C . Lind, 2. physik. Chem., 57, 68 (1906). (5) T h e units used in this paper are not t h e same a s those used b y Bodenstein a n d Lind. I n all cases where comparisons are made their values have been converted t o t h e present units. Similarly, some of the rate constants differ b y factors of two from those given here since t,hey were differently defined. (13) 31. Bodenstein a n d G. Jung, 2. phgsik. Chem., 1’21,127 (1926). (7) Campbell and Fristromz make a mistake on this point in their review paper. Both Bodenstein a n d Lind, a n d Bach, Bonhoeffer and hloelwyn-Hughes calculate values of kafKi”sK2 from their experimental d a t a assuming t h a t k3f/k2r = 10. This value of 10 should therefore be used t o convert their results t o values of k2f. Campbell and Fristrom used t h e value of 8.4 t o make this conversion, with t h e result that their Table 9 has values for k2i (kaf in their notation) which are too large b y about 15%. (8) National Bureau of Standards, “Selected Values of Chemical Therrnod,vnamic Properties,” Series 111, Washington, 1948, 1954. (4)
IS CHERIICAL KISETIC
