SHOCK WAVES IN CHEMICAL KINETICS THE RATE OF DISSOCIATION OF MOLECULAR IODINE BY DOYLE BRITTON, NORMAN DAVIDSON AND GARRY SCHOTT Gates and Crellin Laboratories of Chemistry, California Institute of Technology, Pasadena, California Received 18th February, 1954 Inert gas + ca. 1 % 12 mixtures have been rapidly heated to temperatures of 1060"- 1860" K by passage of a shock wave and the rate of the dissociation reaction, kD M + I2 + M + I -I- I, kR measured photoelectrically. The reaction times were of the order of 30-300 psec. The experimental results for the rate constants for recombination are given by loglo k, (mole-2 1.2 sec-1) = 8-87 - 1-90 (f 0.14) loglo (T/lOOo), (argon) ; loglo k, = 8.85 - 1-91 (f 0.29) loglo (T/lOOO), (N2, assumed to be vibrationally unexcited); loglo kR = 9.01 - 1.44 (f 0.32) loglo (T/lOOO), (N2 assumed to be vibrationally excited).Comparison of the average high temperature results with those obtained at room temperature by flash photolysis confirms the negative temperature coefficient for kR but suggests the relation, k, z= AIT1.5. The high temperature values for kD for argon fit the equation, kD = 1-5 x 107 Tf(U/RT)2*8 exp (- U/RT) mole-1 1. sec-1, where U = mold energy of dissociation of 12 at 0" K. The extinction coefficients of 12 at 490 mp and 436 mp were measured as a function of temperature ; as expected, the former decreased with temperature and the latter increased. The rate data do not reveal whether the nitrogen is vibrationally un- excited or excited during the time period of the experiments; the extinction coefficient data favour the former possibility.A shock wave is a positive pressure wave with the shape of a step-function which moves through a gas with a velocity which is greater than the velocity of sound in the unshocked gas, and therefore which is of the order of, or for strong shocks somewhat greater than, the mean molecular velocity. The shock front is a few mean free paths thick, so that, as the shock passes through a particular mole- cule, the translational and rotational energy of the latter is increased in a time of the order of a few collision times. A shock wave is, therefore, the most rapid method of directly transmitting translational energy to an element of a gas. The number of collisions required to readjust the vibrational energy varies with the nature of the gas.The rates of chemical reactions in the heated gases behind a shock can be most conveniently studied with the plane, uniform waves generated in a shock tube.le2 Fig. 1 illustrates the basic features of this instrument. The left-hand chamber contains a " driving " gas B at a high pressure ; the right-hand chamber contains the gas which is to be shocked, A, at a lower pressure. When the diaphragm D breaks, the gas A is subjected to a compressional pressure wave. The propa- gation of the various pressure disturbances in the tube is represented in the sequence of pressure profiles in the lower half of the figure. Irregularities caused by the breaking process are smoothed out by the time the pressure wave has propagated downstream a few (3-20) tube diameters and a shock wave S is formed.The uniform pressure behind the shock front characterizes the case in which gas A undergoes no chemical reaction after being shocked. At the same time, B expands 58DOYLE BRITTON, NORMAN DAVIDSON A N D GARRY SCHOTT 59 and pushes on A, so that an expansion wave propagates to the left through B. D' is the boundary between expanded cold B and heated compressed A. In practice the shock front S is well formed but the boundary D' is not. For a given initial pressure ratio between chambers B and A the greater the velocity of sound or the molecular velocity of the driving gas B, the greater is the shock strength. It is therefore advantageous for the generation of strong shocks to use hydrogen or helium as B.It is easy to compute that the limiting enthalpy increase per mole ( WA g) of gas A in a shock tube configuration for infinite bursting pressure ratio is 2( WA/ WB)~J~TB/(YB - 1)2, where W refers to molecular weight, yB is the heat capacity ratio, and TB is the initial temperature of gas B.3 A light beam and a photomultiplier-oscilloscope combination can be used to observe the initial compression and any subsequent chemical changes provided a reacting component of gas A is coloured. The temperature and density changes across the shock can be computed from the velocity of the shock wave using the quantitative relations described subsequently. ko vacuum L - / L-2 f - 3 ---- 0 0 0 Time - 2 D, 5 FIG. 1 .--(a) Schematic diagram of apparatus. By driving gas ; D, diaphragm ; A, driven gas (inert gas + iodine mixture) ; L, lights ; PM, photomultipliers.(6) initial pressure configuration in the tube. (c) and (d) pressure configurations after diaphragm bursts. S, shock front; D', boundary between expanded, cold B, and compressed, hot A. The time resolution in this method is related to the time for the shock wave to move through the light beam. For a 1 mm beam and a shock of velocity 105 cm/sec (typical of the experiments reported here), this is 1p sec. The gas behind the shock wave is flowing downstream (to the right in fig. 1) so that at a time T after the shock wave passes the observer at PM-2, the gas at PM-2 has come from farther upstream and has therefore been heated for a time considerably longer than r. Because of this feature, the true time resolution is that computed above multiplied by a factor equal to the compression ratio across the shock and is 3-7 psec for our typical experiments.The measurement, in this laboratory, of the rate of dissociation of N2O4 behind a (weak) shock wave at final temperatures of - 20" to 28" C has previously been described.4 We report here a study of the rate of dissociation of iodine, M + I2 -+ M + I + I, where M is an inert gas (nitrogen or argon), in the tem- perature range 1060-1860" K. This reaction is of kinetic interest because it is a simple dissociation process and because its rate is known at room temperature from the flash photoIysis measurements of the reverse process.5 Because of its kinetic and experimental simplicity it is well suited for an initial investigation of the use of strong shock waves in high temperature kinetic studies.A problem of interest in the nitrogen investigations was whether the vibrational degree of60 SHOCK WAVES freedom of N2 became excited during the short time of the experiment (ca. 4 x 105 collision times) or whether the N2 behaved as a rigid dwnbbeli. Other investigations of elementary processes by means of shock waves include the study of the structure of the shock front itself and the rate of equilibration between translational and rotational energy,6 and the measurement of vibrational equilibration times.7 METHODS EXPERIMENTATION.-The driving section of the shock tube was a 180 cm Iength of 15 cm diameter steel pipe. The shock wave section consisted of a 140 cm length of 15 cni aluminium pipe and a 150 cm length of 15 cm Pyrex pipe.Cellulose acetate diaphragms were clamped between the steel and the aluminium sections. The shock wave chamber could be evacuated to 1 p pressure and degassed or leaked at a rate less than 0 1 p./min. The spontaneous bursting pressures of the membranes are not very reproducible ( f 20 %). Some typical values are : 0.005 in., 1-7 atm ; 0.0075 in, 2.2 atm ; 0.010 in,, 2.1-2.7 atm ; 0.015 in., 3.5-4-1 atm. Depending on the experiment, the membranes were allowed to break spontaneously or were induced to break at a slightly lower pressure with a needle. Good shocks were obtained even when the membranes were broken at one-half their spontaneous breaking pressures. The inert gases used were Linde Air Products Co.argon, stated by the supplier to bc better than 99.8 % pure (with the principal impurity nitrogen), and Linde pure dry nitrogen, stated to be 99.90 % pure. In many of the experiments, the N2 was passed through a 150 cm column of Drierite ; within the rather large cxperimental error, this did not affect the results. These gases were allowed to flow from the cylinder at a regulated pressure of a few psi and at a rate of ca. 500 cm3/min through a flowmeter and then a needle valve across which the prcssure dropped to that of the experiment, and then through a 1 cm diameter U-tube packed with a 30cm length of C.P. iodine. The gas mixture entcred the shock tube at the downstream end, flowed through the tube, and then out via a needle valve to a trap at - 80" and a pump.The only significant constrictions were the needle valves ; and the flowing gas between them was at a constant pressure. The total pressure was measured with a dibutyl phthalate manometer and the iodine partial pressure computed from the temperature of the saturator (measured to O*lOo) and vapour pressure data.8 The shock tube was isolated just before breaking the membrane, by closing wide- bore stopcocks lubricated with Silicone grease. Observations were made with light beams defined by 2.5 cm by 1 mm slits on both sides of the shock tube. The light sources were 500 W tungsten projection lamps operated from a d.c. generator. Obscrvations with A = 436 mp were made with a Hanovia medium pressure d.c. mercury arc, Sc 5031. Schlieren and total internal reflection at the shock front can bend a light ray several degrees. It is therefore necessary to use a well-collimated sheet of light if the sharp change in density at the shock front is to be observed.The four slit system indicated in fig. 1 achieved this end. The transmitted light was passed through suitable filters and the intensity changes measured with RCA 93 1 photomultipliers and a Tektronix 512 oscilloscope. Typical operating conditions were 80 V/dynode, 100 p A output current, and electronics rise time about 1 psec. The signal/noise ratio is limited by the intensity of the light sources and was about 50. Three or four light beams were used, each one being 10.0 or 20-0 cm downstream from the preceding one, and the first one being 240 cm (16 tube diameters) from the membrane.Several slightly different systems for obtaining data were used. The one used for most of the experiments is illustrated in fig. 2. The amplified signal from the first photo- multiplier, PM-1, triggers a univibrator trigger circuit when the shock wave passes this station. This triggers two delay circuits, The delayed output of one of these triggers a single horizontal sweep of the oscilloscope at a suitable time (30-150psec) later. The delay time of the second circuit is accurately known from careful calibrations ( f 1 psec) and this output pulse is mixed into the vertical amplifier system. Its position on the trace essentially gives the time that the shock wave passes PM-1. The particular oscillo- scope used is provided with a difference amplifier and the difference in photocurrent between PM-2 and PM-3 is recorded as the vertical deflection.Until the shock wave reaches station 3, this is essentially the photoelectric record of the change in iodine concentration at station 2. From the record one can measure the average velocity between stations 1 and 2 and between 2 and 3. The pictures also contain vertical calibrationA B 3 c C FIG. 3.-Oscillograph records of photocurrent for typical experiments. A, signal from delay circuit 2, related to arrival of shock wave at PM--1 ; B, compression as shock front passes PM-2 (increasing photocurrent from this station deflects the trace down) ; C, compression as shock front passes PM-3 (end of experiment). The small pips are lop sec timing markers.The smooth horizontal traces are evenly spaced voltage calibrations. Photograph a b C C1 4 S argon 2.27 x 10-3 mole/]. 0-484 x 10-2 1.OOO x 105 cmlsec 3.10 1195" K 0.79 3.27 1172" K nitrogen 1 -65 0.524 1 ~429 * 4.65 1276 0.90 4.73 1253 argon 1.75 0.623 1.136 3.26 4-97 1216 1455 0.82 0.97 5-03 3.46 1195 1422 t Subscripts zero refer to conditions immediately behind the shock front. refer to equilibrium with respect to iodine dissociation. * calculations made assuming N2 to be not vibrationally excited. -f calculations made assuming N2 to be vibrationally excited. Subscripts [To face page 60 3 aFIG. 4.-(a) Shock wave heating an argon + iodine mixture to 953" K, where the rate of dissociation is negligible ; (6) shock wave heating an argon + iodine mixture to 2100" K, where the dissociation is complete and rapid.The subsequent decrease in photocurrent is attributed to cooling at the walls. [To face page 61DOYLE BRITTON, NORMAN DAVIDSON AND GARRY SCHOTT 61 marks applied with a precision potentiometer (Helipot) and time markers on the sweep from a 100 kc crystal controlled oscillator. An improved procedure has been to measure the time for the shock to travel between stations 1 and 3 or 4 with a Potter Model 456 1.6 Megacycle Counter Chronograph which is a time interval meter that can be triggered on and off by univibrator voltage pulses from the photoelectric stations. Two oscilloscopes are available and two independent photoelectric records can be made from PM-2 and PM-3. The time scales of the two sweeps can be interrelated so that the average velocities between all the successive stations are known.CALCULATIONS.-Fig. 3 and 4 show some typical oscilloscope records for shock waves heating inert gas -I- iodine mixtures (cu. 1 % 12). When the shock passes through the light beam, the light transmission abruptly decreases because of the compression and then gradually increases as the iodine molecules dissociate into an equilibrium mixture of atoms and molecules. Quantitative interpretation requires a knowledge of the conditions of the heated gas, specifically of its temperature and density and of the extinction coefficient of molecular iodine at the high temperature. As the endothermic dissociation reaction occurs, the gas mixture cools and compresses somewhat. The photoelectric curve of light trans- mission as a function of time, after the initial step due to the shock compression, results P"' 7 1 L I I 1 FIG.2.-Block diagram of the recording system. Circuits enclosed by the dotted line are part of the oscilloscope. from a combination of (a) a decrease in iodine molecule concentration due to dissoci- ation, (6) an increase in iodine molecule concentration due to compression, and (c) a change in extinction coefficient due to the change in temperature. Fortunately, effect (a) is much larger than (b) or (c). The kinetics are complicated by the following factors. As the molecular iodine dissociates, the reverse recombination reaction I + I + M -> 12 -i- M must also be considered. Since the gas behind the shock is flowing downstream, a transformation from laboratory time to the time that molecules in the light beam have been heated is introduced. The rate constant for dissociation is a function of tem- perature and therefore changes as the reaction proceeds.It is the object of this section to outline the calculational procedure for making all these corrections. Because the iodine is highly diluted with inert gas (ca. 1 : 100) the changes in density, temperature, and extinction coefficient are small and the corrections are readily made. The legends to fig. 3 give typical examples of the changes. For a perfect gas of constant heat capacity, the temperature and density of the gas just behind the shock can be expressed as simple closed functions of the initial conditions and the velocity of the shock wave.9 For a general fluid, a numerical solution of the following equations is required : (d, d3 -- +p2 1 HZ - W - PI) - + -- , ____- where subscripts 1 and 2 refer to conditions in the unshocked and shocked gas, re- spectively, W =; mean molecular weight of the unshocked gas, H = enthalpy per W g of gas, P = pressure, D = density, and s L-: shock velocity.The enthalpy is a function of P2 and 0 2 (for a perfect gas with variable heat capacity it is a function of P2/D2, that is,62 SHOCK WAVES of the temperature). For a given s the above equatioiis can be solved. For a shock wave propagating at a constant velocity down a tube of uniform cross-section, these equations apply to the properties of the fluid at any point behind the shock. In particular, for a reacting gas, the enthalpy can be expressed as a function of temperature and of a reaction variable (which in the present instance is a, the degree of dissociation).For a given shock (fixed s), the pressure, density and temperature can therefore be determined as functions of a. Let T = (P2/P1), 8 = (7'2/7'1), A = (&/&), U = molal energy of dissociation of 12 gas at 0" K, fi =r 2[(H - Ho)/RT] - 1, + = mole fraction 12 in the initial gas. The quanti' @ is related to an effective heat capacity for the gas. Superscripts M, 12, and I refer t, .nert gas, iodine molccules, and iodine atoms. The perfect gas law is, Eqn. (1) and (2) become : T = (1 + +)A8. =: (1 - +)(by+ - ST") + $([(I - a)& + 2~p:ie - B? -I- ~ ~ ( u I R T ~ ) } -f- (1 -1 &)(d/T), (3) RT1 (r - 1) s 2 r.- W (1 - (l/A). (4) With these equations and thermodynamic tables,lo numerical values for T, A and s as functions of 8 and a can be calculated for an assumed value of $. These can be graphed so as to show the variation of A and 0 with a at particular values of s. The character- istics of the shock wave were computed for + = 0 and, as a function of a, for + = 0.01, and it was shown by a few additional calculations that for the range of + used (+ < 0*025), a linear extrapolation or interpolation was satisfactory. Two separate sets of calculations for nitrogen were made assuming : (a) that HF - H Y = (7/2)R(T2 - TI), i.e. that during the time of the experiment the N2 remained vibrationally unexcited, and (b) using the thermal equilibrium values for H F .If the velocity of the flowing gas behind the shock is v, conservation of mass in steady- state flow requires A == s/(s - v). The transformation between " molecule " time t and laboratory time 7 is then readily shown to be dt = AdT. For the chemical reaction, M I- I2 + M 1- I + I, the rate equation is - [3(12)/3t]~ = k,(M)(I2) - kR(M)(f)2; kR = k,/K, where K is the equilibrium constant (dimensions, moles/l.) for the chemical equation above. The rate equation can be transformed to ( 5 ) where c1 total concentration of unshocked gas (mole/l.). The quantity A changed at most by 10 % from a =--: 0 to a = 1, whereas K changed typically by 50 %, but both A3 and KIA were, to a satisfactory approximation, linear functions of a. This makes it possible to integrate eqn.(5). drjdr = kRA3[(qK(l - .)/A) - 4+c12a2], where d l n K d l n A 3 d I n k d l n A 3d In A C Y - v'=dr---- da 4 da da ' do: * Subscript zero refers to conditions just behind the shock wave at a = 0.DOYLE BRITTON, NORMAN DAVIDSON AND GARRY SCHOTT 63 On the oscilloscope records one determines a at various points in time behind the shock. This involves knowing the density as a function of r (from measured velocity), the initial concentration, and the extinction coefficient of 12 as a function of temperature (i.e. a). These values of a at times T are inserted in eqn. (6) and the indicated function plotted against 7. The slope of this plot gives k, and k , =: k,K. The basic assumption here is that k, is temperature independent and k, has the same temperature dependence as K.The results of the experiments show this is not so but correcting for this effect would change the individual k,'s by less than 5 % and the temperature dependence not at all. It may be mentioned that for cases where at equilibrium a =. 95 z, the effect of the back reaction can be neglected and a simpler integrated rate equation used. RESULTS AND DISCUSSION DISSIPATIVE EEFFCTS Other workers have observed, by means of flash interferograms or Schlieren pictures, that the shock waves generated in shock tubes are planar and normal to the tube walls.2 In most of our experiments when the light beam was properly aligned and collimated, the abrupt decrease in photocurrent as the shock wave passed the light beam occurred in 1-2 psec, indicating that the shock front was well formed, plane, and perpendicular to the tube axis.Fig. 4a shows a shock wave heating an argon + iodine mixture to 953" K where the rate of dissociation is negligible. The photocurrent is constant to rf: 1 % for 220 psec of laboratory time (600 psec molecule time) indicating that there is no appreciable cooling and compression at the walls. Fig. 4b shows a shock wave heating an argon + iodine mixture to 2100" K where the dissociation occurs in about 20p sec. The photocurrent then corresponds to 100 % transmission. There is a subsequent slow decrease in photocurrent which, we surmise, is due to re-association in a cooled layer next to the walls. In this case there is a decrease in transmission of about 5 % over a period of about 70 psec (laboratory time), which means that a layer of gas about 1/40 the diameter of the tube (i.e., 0.4 cm) has cooled to below 1100" K where the re-association becomes large.It was noted that, as expected, this cooling effect was greater at low gas densities. A rough estimate of the rate of cooling may be made as follows. The thermal conductivity 11 of argon at 1500" is about 1.1 x 10-4 cal cm-1 sec-1 and the heat diffusivity at a concentration of 3 x 10-6 moles/cm3 (the concentration of the shocked gas for fig. 4b) is about 12 cni2 sec-1. Therefore in 240 psec (mole- cule time for this experimcnt), the mcan diffusion distance (2 IN),, is calculated as 0.08 cm, compared to the 0.40 cm which is the crude observation. If gas in a cylinder is uniformly heated to a temperature above that of the wall and if a con- centric ring of gas at the wall, dr thick, cools by conduction so completely that it effectively contracts to a much smaller volumc, the gas in the middle of the cylinder will expand outward adiabatically and therefore cool.The magnitude of this cooling effect is (dT/T) = 2(y - 1) (dr/r). Taking dr = 0.20 cm as a compromise between the experimental and theoretical values for the thickness of the cooled layer, the computed value dT/Tfor the main body of gas is 0.03. Experiments at the higher temperatures were done at low gas densities to increase the reaction time; nevertheless, the rate of dissociation was so fast that a slope like that of fig. 4b and a cooling like that computed above are not serious. In experiments at lower temperature, the gas density was higher and cooling less important.The kinetic results did not show any anomalies or variations with pressure that could be attributed to cooling effects. The evidence is, therefore, that cooling effects due to the walls were not large enough seriously to affect the kinetic results of this investigation. It should be emphasized that there is no satisfactory experimental or theoretical treatment of dissipative phenomena in a shock tube; the problem is quite complicated because it involves both heat con- ductivity and viscosity effects. It is probable that these dissipative effects will be64 SHOCK WAVES limiting factors in the quantitative study of reaction rates at still higher tempera- tures by the shock tube method.In almost all of the experiments, the two average velocities measured with three photoelectric stations at 10 or 20 cm intervals agreed to 14 %. The apparent acceleration was sometimes positive and sometimes negative. It is not known to what extent this change in velocity is due to experimental error in measuring the oscilloscope records or to a lack of reproducibility in the delay time of the cali- brated delay circuit, rather than to a real change in strength of the shock wave. A few experiments were discarded because the velocity change between successive stations was as high as 4 % The temperature of the reacting gas is calculated from the shock velocity and is approximately proportional to the square of the velocity, so that a 1 % uncertainty in velocity corresponds to a 2 % uncertainty in temperature. At 1500" K, the corresponding uncertainty in the rate constant for dissociation is f 26 %, which is about the same as the mean deviation of the results. EXTINCTION COEFFICIENTS Most of the observations were made with the light from a 500-W tungsten filament projection bulb with the colour temperature defined by operation at 120 V.The light filters were a Bausch and Lomb interference filter with a measured maximum transmission of 36 % at 487 mp, a half width of 8 mp and a trans- mission of the order of &l % through the rest of the spectrum, and a Corning no. 3385 sharp cut filter with a transmission of 50 % at 487 mp, of 37 % at 481 mp, and which was opaque to bluer light. The detector was an RCA 931 photomultiplier.The molar extinction coefficient of 12 at room temperature, E = loglo (lo/l)/cZ mole-1 1. cm-1, for this particular optical system, was found to be 450 -& 20, by measuring the photocurrent in front of and behind shocks of sufficient strength to dissociate more than 99 % of the 12 present in an argon 1 % I2 mixture, as in fig 46. This value is the same as that at 490 mp as measured in a Beckman spectrophotometer12 and we take 490 mp as the effective wave length of the light. In previous experiments using the interference filter without the cut-off filter, lower values of E were observed because of a greater contribution from blue Iight.5~ For some shocks in nitrogen, E at 436 mp was measured using a mercury arc, a 436 mp interference filter, and a Corning no.3389 sharp cut filter which was down to 37 % transmission at 436 mp. The value of 30 for E at room temperature was taken from spectrophotometer experiments. The high temperature extinction coefficients were found by extrapolating the photocurrent records back to zero time visually, and computing the concentration of 12 just behind the shock from the compression ratio which is calculated from the shock velocity. Curve A of fig. 5 displays the results in argon for 490 mp and fig. 6 gives the results in N2 at 436 mp. As expected in view of the potential curves and by analogy with the other halogens,l3 the extinction coefficient at 490 mp falls with temperature because the extinction coefficient of the zeroth vibrational state is greater than that of the higher vibrational states at this wavelength, and the ex- tinction coefficient at 436 mp rises with temperature, because the reverse is the case.Fig. 5 also shows the absorption coefficients at 490 mp measured in nitrogen experiments and computed assuming that the nitrogen behind the shock is not vibrationally excited (curve B) and is vibrationally excited (curve C). The ex- perimental points are shown for curve B and the scatter of the points is about the same for the other curves. The wave length 490 mp is beyond the convergence limit of the discrete spectrum of 12, and the absorption coefficient should be in- dependent of inert gas. Curves A and B coiiicide within the limit of experimental error but curves A and C (vibrationally excited N2) do not. This suggests thatDOYLE RRITTON, NORMAN DAVIDSON AND G A K R Y SCI-IOTT 65 the nitrogen is not vibrationally excited fot at least 25 psec (typically 4 X 104 nitrogen-nitrogen collisions) after being shocked, but, in view of the rather large experimental error, this conclusion is only a tentative one.€ - 50 400 800 /ZOO /600 Gmperuture "K FIG. 5.-Extinction coefficients for 12 at 490:mp. A, argon ; B, N2 assumed vibrationally unexcited ; C, N2 assumed vibrationally excited. The experimental points for curve B only are shown. - - 0 1 l l l l l l l l l I 1 1 1 FIG. 6.-Extiiiction coefficients for 12 at 436 mp in N2. B, assumed unexcited, points shown ; C assumed cxcitcd. KINETICS Fig. 7 shows the results of this investigation plotted as loglo kR against loglo T for argon, nitrogen assumed to be vibrationally unexcited, and nitrogen assumed excited.Parameters for straight line plots of the results have been found by least squares (using for convenience the erroneous assumption that the temperatures are known with certainty) : loglo kR (moles-2 1.2 sec--2) == -- 1.90 (& 0.14))loglo (7'/1000) -I- 8.87 (argon), loglo kR = - 1.91 (& 0-29) loglo (T/lOOO) -t 8.85 (N2 unexcited), loglo k , -- - 1.44 (& 0.32) loglo (T/lOOO) -I- 9.01 (N2 excited), where the indicated uncertainties are probable errors. Thc mean deviations of the experimental rate constants from the calculated curves are -I: 11 % (argon), 4 22 % (nitrogen-excited or unexcited). We cannot at present evaluate all the sources of experimental error. As noted previously, there is an uncertainty of the order of 26 % in the rate constants due to possible errors in the measurement of shock velocity.It appears that there are also significant errors in reading the oscillograph records and in making the elaborate calculations involved in inter- preting the data. We do not know why the nitrogen results show greater scatter than the argon results. Over a threefold variation in total pressure at a fixed C66 SHOCK WAVES temperature, the rate showed the expected first-order dependence on inert gas concentration. Fig. 8 shows the results of this investigation at 1060-1860" K and of the various flash photolysis measuremcnts of kR, mainly at room tempcrature,s as a loglo k FIG. 7.-Recombination rate constants. FIG. 8.-Recombination rate constants.Iysis results. Points are the low-temperature flash-photo- Heavy lines are the results of this research. The light lines go through the average room temperature results and the average high temperature rcsults. against loglo T plot. In spite of the present experimental uncertainties both at high and low tcmperaturcs, it is clear that k, decreases quite significantIy withDOYLE BRITTON, NORMAN DAVIDSON AND GARRY SCHOTT 67 temperature. The slope of a straight line through the average of the room tem- perature argon results and an average high temperature argon result is 1.49 i.e., kR = A/T1*49, as compared to a slope of 1.90 for the high temperature results above. It is possible but by no means certain that this change in slope is real. The slopes of the loglo k against loglo T plots through the room temperature and the average high temperature results for nitrogen are 1.59 (unexcited), 1-26 (excited).The temperature coefficients of kR obtained at Manchester by flash photolysis 56 at 293" and 400" K are larger than those reported here and correspond to n = 3-0 for an assumed power law dependence, kR = A/Tn. It is most probable that the conflicting result obtained in Pasadena5c by flash lamp experiments that kR for neopentane is constant from 298" to 473" K is wrong. A curve going through both the Manchester and the shock wave points is irregular and bumpy in an implausible way ; probably one set of data or the other are wrong in so far as the temperature coefficients are concerned. The shock wave experiments cannot be extended to lower temperatures because the rate of dissociation is too slow ; further careful flash lamp experiments over a range of temperatures will be of great interest. FIG.9.-Temperature dependence of the rate constant (inert gas, argon) and thc equilib- rium constant for I2 dissociation. It is of interest to consider the temperature coefficient of kD, the rate constant for dissociation. Fig. 9 displays the temperature dependence of log kD f U12.303 RT for argon and log K + U/2*303 AT, where U = 35,544 cal. The former, of course, decreases more rapidly with temperature; the high temperature data fit the equation although the room temperature results fall considerably below this. In conclusion then, the main results of thc present investigation is to provide additional evidence that kR decreases with temperature, and that this dependence can be approximated by kR == 4T1.5.The physical significance of this result is that the average kinetic energy in a system undergoing a recombining three-body collisioii is less than the average kinetic energy of all three-body collisions. By microscopic reversibility, in a dissociating collision between an inert gas molecule and an iodine molecule, the resulting iodine atoms and inert gas molecule have less than the average kinetic energy as they fly apart. The rate constant for dis- sociation can be described by the equation, kD = (A/TF3) eXp (- U/RT), kD == 1.50 x 107 Tf (U/RT)2'83 exp (- U/RT) moles-1 1. sec--l.68 S HO C I< WAVES The “collision theory ” interpretation of this kind of a rate expression is that several degrees of freedom other than translation along the line of centres contri- bute energy to the dissociation process.It is to be noted that in the rate constants which have been used for making calculations about H2 + Br2 flames, it has been assumed that the rate constant for recombination is a constant and that the pre-exponential factor for kD increases with temperature. 14 The kinetic results for nitrogen do not reveal whether or not it remains vibra- tionally unexcited during the time of an experiment (typically, about 4 x 105 nitrogen-nitrogen collisions and 4 x 103 nitrogen-iodine collisions). The extinc- tion coefficient measurements make it appear probable, but not certain, that for the first 104 collisions the nitrogen remains unexcited. It is of course conceivable that the nitrogen relaxed vibrationally during the course of the iodine dissociation reaction. This would make the measured values of kR too low. With the present limited experimental accuracy there is no possibility of recognizing such a pheno- menon. It may be recalled that impact tube measurements 15 indicate that vibra- tional equilibration requires at least 107 nitrogen-nitrogen collisions at 600”-700” K, whereas ca. 3 x 104 collisions between N2 and H20 are required for vibrational adjustment of the N2. We are grateful to the O.N.R. for its support of this research. One of us (D. B.) is the recipient of a fellowship from Du Pont, Co. 1 Payman and Shepherd, Proc. Roy. SOC. A , 1949,186,293. 2 Bleakney, Weimer and Fletcher, Rev. Sci. Instr., 1949, 20, 807. 3 Resler, Lin and Kantrowitz, J. Appl. Physics, 1952, 23, 1390. 4 Carrington and Davidson, J. Physic. Chem., 1953, 57, 418. 5 (a) Christie, Norrish and Porter, Proc. Roy. SOC. A , 1953, 216, 152. (h) Russell (c) Marshall and Davidson, J . and Simons, Proc. Roy. SOC. A , 1953, 217, 271. Chem. Physics, 1953, 21, 659. 6 Greene and Hornig, J , Chem. Physics, 1953, 21, 617. 7 Schwartz, Slawsky and Herzfeld, J. Chem. Physics, 1952, 20, 1591. 8 Giauque, J. Amer. Chern. SOC., 1931, 53, 510. 9 ref. 1, p. 313 or any standard treatise on gas dynamics. 10 Selected Values of Chemical Thermodynamic Properties (National Bureau of 11 Tables of Thermal Properties of Gases (National Bureau of Standards, Washington, 12 DeMore and Davidson, private communication. 13 (a) Acton, Aickin and Bayliss, J. Chem. Physics, 1936, 4, 476. 14 Cooley and Anderson, Ind. Eng. Chern., 1952, 44, 1402. 15 Huber and Kantrowitz, J. Clzem. Physics, 1947, 15, 275. Standards, Washington, series 111, 1947). 1951), table 19.42. (b) Gibson, Rice and Bayliss, Physic. 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