Shock Waves in Chemical Kinetics Citation Britton, John Doyle (1955) Shock Waves in Chemical Kinetics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Y16V-VY27. https://resolver.caltech.edu/CaltechETD:etd-11262003-143942 Abstract NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. The rates of dissociation of I[subscript 2] in N[subscript 2] and CO[subscript 2], and Br[subscript 2] in A were measured at temperatures around 1300[degrees]K by heating room temperature mixtures by means of shock waves and observing the subsequent reactions. The rates of recombination of both I[subscript 2] and Br[subscript 2] were found to decrease with increasing temperature. The results, combined with room temperature measurements seemed to be best expressed in the form K[subscript R] = A exp([...]/RT). Attempts to measure the efficiency of I[subscript 2] or Br[subscript 2] molecules as third bodies for the recombination gave only rather wide limits to the possible values. The experiments also showed that CO[subscript 2] is vibrationally relaxed at high temperatures in a time short compared to the reaction time of 20-200 microseconds. It was not possible to decide whether or not N[subscript 2] is vibrationally relaxed at this temperature in this short time. Extinction coefficients of I[subscript 2] and Br[subscript 2] were measured as a function of the temperature. They appeared to be dependent on the inert gas. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Chemistry and Mathematics) Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Minor Option: Mathematics Thesis Availability: Public (worldwide access) Research Advisor(s): Davidson, Norman R. Thesis Committee: Unknown, Unknown Defense Date: 1 January 1955 Record Number: CaltechETD:etd-11262003-143942 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-11262003-143942 DOI: 10.7907/Y16V-VY27 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 4670 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 26 Nov 2003 Last Modified: 10 Jul 2023 17:33 Thesis Files Preview PDF (Britton_jd_1955.pdf) - Final Version See Usage Policy. 3MB Repository Staff Only: item control page

SHOCK WAVES IN CHEMICAL KINETICS Thesis by Jonn Doyle Britton In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1955 Acknowledgements I would like to thank Professor Norman Davidson for supervising what was an extremely pleasant and instructive period of time. I would also like to thank the many faculty members, employees, and fellow students who were ever ready with aid and advice. . The receipt of assistantships or fellowships from the California Institute, &. I. du Pont de Nemours and Co., Ine., and the National Science Foundation is gratefully acknowledged. The research was supported by the Office of Naval Research. Abstract The rates of dissociation of Ig in No and COs, and Bro in A were measured at temperatures around 1300°K by heating room temperature mixtures by means of shock waves and observing the subsequent reactions. The rates of recombination of both I, and Bro were found to decrease with increasing temperature. The results, combined with room temperature measurements seemed to be best expressed in the form kp = A exp(E/RT). Attempts to measure the efficiency of Ip or Bry molecules as third bodies for 7 the recombination gave only rather wide limits to the. possible values. . a _ The experiments also showed that COp is vibrationally relaxed at high temperatures in a time short compared to the reaction time of 20-200 microseconds. It was not > possible to decide whether or not No is vibrationally relaxed at this temperature in this short time. Extinction coefficients of Ip and Br, were measured as a function of the temperature. They appeared to be depersent on the inert gas. Table of Contents Introduction Shock Wave Behavior The Shock Tube The Apparatus and the Experimental Procedure Extinction Coefficients of Ip Extinction Coefficients of Bre The Dissociation Reactions Kinetics. of Ip Dissociation Kinetics of Bro Dissociation Discussion Appendix A Definition of Symbols Appendix B Shock Wave fquations Appendix © Calculation of High Temperature Extinction Coefficients Appendix D Kinetics of the Dissociation of a Diatomic Gas in a Shock Tube Propositions ® Ow MD FH 18 26 30 35 41 . 45 49 52 58 59 66 Introduction A shock wave is a steep fronted pressure wave. It pro- vides a means by which gases can be compressed and heated in a time of the order of a few collision times for the molecules. Thus it is possible to heat a gas to a non-equilibrium situa- tion if the gas is one that can undergo some reaction at higher temperatures. The heating that takes place represents a change in the translational energy of the gas. Molecular rotation is excited nearly as fast as the translation, that is, in the front of the shock wave itself, and too fast to be de- tected by the means described below. The excitation of vibra- tional energy, also referred to as vibrational relaxation, sometimes occurs nearly as fast as rotational excitation and therefore too fast to detect, and sometimes occurs too slowly to detect, and of course at all rates between. A chemical re- action, in which the molecular species change, is also possi- ple, and may occur at a rate anywhere from too slow to be measured to too fast to be measured. If it is possible to follow some characteristic of the gas behind a shock wave as a function of the time then it may be possible to study the kinetics of a reaction occurring in the gas. The first chemical reaction to be studied by this method was the dissociation of Ng04, into NOg (1), which occurs at a measurable rate near room temperature. It was studied by fol- lowing the change in the color of the gas. At the wavelength of light used the color was due to NOg and therefore provided a direct means of following the NOp concentration. As the 2 second test of the method it was decided to study the rate of dissociation of Ip into atoms (2). This reaction is essen~ tially the game as the No0,-N0, reaction axcept that it occurs at higher temperatures, around 1300°K. It was of additional interest because the rate of recombination of I atoms into molecules had been studied at room temperature by flash pho- tolysis techniques, and the high temperature results would provide an extension of this work. After the work on Ip was well under way it was decided to study the dissociation of Bro as well. This thesis describes some of the work done to date on T,, and Bro dissociation. 2 Shock Wave Behavior From the equations of state for a particular gas and the assumption of conservation of mass, momentum, and energy across a shock wave the conditions in a shock wave can be cal-~ culated. The equations describing the behavior of a shock wave have been derived in the literature a number of times, but they are rederived here (Appendix B) in a form more con- venient for calculations. The derivation is in the spirit of the treatment by Dbring (3). | The number of parameters required to describe a shock wave and the physical restrictions on these parameters are such that if any one parameter is determined and the initial conditions are known then all the parameters of the shock wave are determined. The parameter that is measured in order to determine the behavior behind the shock wave is the velocity. D If there is a reaction behind the shock front then the condi- tions are determined for any given amount of reaction. They are not known for a particular point behind the shock front becausé to know this one would need to know the rate of the reaction. Measuring the rate of a reaction behind a -shock wave involves measuring the change in some property of the gas as a function of distance (and also therefore of time) behind the shock wave, and comparing this “ts the calculated change in this property as a function of the amount of reaction. The behavior of various properties of certain gases is shown, semi-quantitatively as a function of distance behind the shock wave, in figure 1. It can be seen from these curves that pressure would be a poor parameter to measure in any case. Density would be rather good if vibrational relaxation or the dissociation of pure I, were being studied. It is also appar- ent that the dissociation of pure Ig in a shock wave is highly non-isothermal, and that in order to approximate isothermal conditions it is best to use a large percentage of inert gas to act as a heat capacity buffer. In this case the density also changes little and Ip concentration is a much better pa- rameter to measure. This is what is done. Te Shock Tube The shock tube is a device for producing uniform shock waves. In its simplest form it consists of a tube which can | be separated into two sections by an easily ruptured diaphragm. Into one section gas at high pressure, called the driving gas, is introduced. Into the other section the gaseous reaction 4 , Figure 1 Behavior Behind the Shock 1200Fr 600r - — 1200 vibration + or 600b Tyeact ien L 100¢ percent dissociation> . of I, os =4 [xlO q, 1 ~ concentration moles pcr liter oO & A CO; ae 1% I, . . 99% A I, The I, ts assumed \ to relax vibrat ionally in the shock front. Th The changes shown are those dug to dissociatian | i <— distance behind shock ( qualitative) 5 mixture, at low pressure, is introduced. To produce a shock wave the diaphragm is ruptured and the high pressure driving gas allowed to expand. This compresses the low pressure gas and drives it down the tube. The steep pressure front of this moving compresséd gas is the shock wave. It is steep fronted because the gas behind it is heated when it is compressed, and any pressure increments travel to the shock front at the speed of sound in the heated gas plus the speed of the gas moving behind the shock wave. This speed is always greater than the speed of the shock wave itself, so that any pressure incre- ments catch up with the shock front eventually. A shock tube and the pressure configurations in the shock tube at several times during the course of the shock wave are shown in figure Qe The Apparatus and the Experimental Procedure The shock tube and the various detecting and measuring arrangements are shown schematically in figure 2. Figures 3ab and 4ab are photographs of the apparatus from various angles. They will be referred to as the different features of the ap- paratus are discussed. The tube was of uniform 15 cm inside diameter. Two sec- tions for the driving gas were available, one 182 cm long, and the other 51 cm long. The driving section was connected to a manifold through which the tube could be evacuated and filled with any desired driving gas and the pressure measured. The driving section was mounted on rollers so that it could be moved away from the low pressure section to allow the mounting 6 Figure (4 Diagram of the Apparatus Pressure Profiles in a Shock Tube tO vacuum | {une lights O O O oO Driving gas reaction mixture | : L_ ‘ diaphragm [ photomultipliars © ; O i | ampli- ompl- fier : fier oscilloscepe oscilloscope ae FF c $ cf 4 i¢ ié 4 delay | al delay | T| trigeer | | trigger | eon off« timer . initial pressure configeration in shock tuba —7 pressure configuration at time. & after breaking © diaphragm =} Nee at time 2T , : ex Shee’ front Cc} | boundary between driving and driven gas 3a View from south, same orientation as figure 2 3b View from north, showing vacuum line and high pressure end 4a View from east, showing low pressure end, light sources, and iodine saturator 4b View from west above, looking down towards low pressure end, showing optical bench and light arrangement 9 of the diaphragm. All this can be seen in figures 3a and 3b. The diaphragms were sheets of cellulose acetate of thick- nesses from 0,003 in. to 0.050 in, They were clamped between the driving section and the low pressure section in a device which allowed them to be broken by @ needle if necessary. There is a certain amount of turbulence at the first due to the breaking of the diaphragm. Presumably if the diaphragm broke poorly, that is, slowly or into large fragments, there could be so much turbulence that the region behind the shock would not be uniform when the shock passed the observation stations. It was observed that even when the diaphragms were broken at one-half their spontaneous breaking pressure there was no evidence that the shocks were any different from the usual ones. “However, looking through a fifteen centimeter light path one might not see turbulence if it were on a very small scale or confined to a small layer near the walle. ‘The low pressure section was 292 cm long. . It consisted of a 140 cm aluminum section next to the high pressure end and a 152 em section of Pyrex pipe through which observations were made. Two different methods were used to fill the low pres- sure section with the reaction mixture. For mixtures inciud- ing I, the inert gas was flowed through a 15 cm tube filled | with Ip erystals, which was held at a fixed temperature. This device can be seen in figure 4a. It determined the pressure of I, and the pressure of the total mixture was measured as the gas flowed out of the shock tube. The flow was from right to left in figure 2, and served to sweep the tube free of 10 other gases as well as saturate with In. For mixtures involv- ing Bre the mixture was made up in bulbs on the vacuum line and stored. The tube was evacuated until just before the shock was to be run and then filled to the desired pressure with the mixture. The low pressure section could be evacuated to less than 1 micron pressure, and leaked or degassed at about 0.1 micron per minute. The arrangement used to study any reactions behind the shock wave was to observe the colored gases spectrophotometri- cally at various points along the shock tube. Light from a 500 watt tungsten projection lamp operated at 120 volts d.c., or from a Hanovia medium pressure ee mercury arc, Se 5051, was used. The light from the source, 17 cm from the tube, was passed through a slit 1 om from the tube, through the tube, through another slit 1 cm from the tube, through another slit 16 em from the tube, and onto the photomultiplier, 9 cm fur- ther on. The photomultipliers were RCA 93l's.. The light arrangement can be seen in figure 4b. Filters were used to limit the light present. they will be discussed more fully in the sections on extinction coefficients. . A simple optical bench was constructed in order to align the lights, slits, photomultipliers, and tube as well as pos- sible. The following tolerances were acheived. The distance between successive slits was 10.000 t 0.005 em. The distances between any particular set of pairs of slits on the three dif- ferent slit systems was the same to 0.0005 cm. The slits were perpendicular to the axis of the tube to within an angle of 5'. 11 The plane containing the successive slits was parallel to the axis of the tube to within an angle of 10'. The inside and outside diameters of the tube were measured at various points along the tube. These measurements are shown in figure 5. The walls of the tube are uniform but the diameter varies by about 0.1 cm in 100 em. The maximum angular variation in the “@iameters 1s about 15'. These alignments were made because some results from early experiments seemed to indicate a lack of alignment and hence a loss of resolving time. This was indicated by the time it took the steep front of the shock wave to rise its full height on the oscilloscope trace. If one observed the passage of a shock front at 100 em/msec velocity past a 0.10 em slit system, through which, by perfect alignment, a sheet of light 0.10 cm thick were passing parallel to the shock front, it would take the shock front 1 microsecond to rise to its full height. Some experiments showed a time of rise of 5-7 microseconds. The optical system described was construct- ed in which, with the limits of error given, and the arrange-~ ment of slits, lights, and photomultipliers described, the same shock should have a rise time of less than 3 microseconds. The long times of rise still occurred in some of the shocks. ‘This indicated either that the shock fronts were curved or that they were not normal to the walls of the tube. In figure 7b an oscilloscope trace displaying this slow rise is repro- duced. As indicated in figure 2 signals from the photomultipli- 2 ee ee ee ee eee oT APYDWIeID Dpisus e + 009 e e 4 e @ oe °¢ 41799 S45 | Jo uoryisod AY seuss SY OIUPLSIP e e e e | 4 ADL WUEID DPIs4no e e e e . | e mus —09'9 °° 6. | 1 aqot y20US Dut ; 1 o Ayiwosodiy DANS) Jo Kynus0fiun S 14 ll 1%99 13 ers at either end went to a timer, a Potter Model 456 1.6 Megacycle Counter Chronograph. This determined the time for the shock to pass between these two stations to an accuracy of 0.63 microseconds. The signal from the initial station also served to begin the oscilloscope sweeps. . Signals from the two middle photomultipliers were dis- played directly on two different oscilloscopes. That two oscilloscopes were avallable made it possible to observe the shock wave at two different wavelengths of light or at two different writing rates on the oscilloscopes. The time scale was put on the oscilloscope by putting a signal from a 100 ke crystal controlled oscillator onto an intensifying electrode in the cathode ray tube, and blanking 1 microsecond of the sweep in every 10. Vertical deflection calibrations were put on with a battery and a Helipot precision potentiometer. The oscilloscope traces were photographed, and measurements made on enlarged projections from the negatives. | Figures 6ab, Yab, and 8ab show various types of oscillo- scope traces. Figure 6a is the record of a shock wave in a COo-Ip mixture at a temperature low enough that no reaction takes place. Figure 7a shows the dissociation of Bre proceed- ing at a measurable rate. Figures 8a and 8b show the same shock wave recorded at two different writing rates on the two oscilloscopes. In figure 8b the reaction can be seen to pro- ceed up to the cold front, that is, the boundary between the driving gas and the driven gas, at which point there is a sudden decrease in the Bro concentration. 6a 6b 14 Figure 6 Shock wave in COp (0.45% I Temperature 736°K assuming CO, relaxed. rahees concentration 2.14 x 10“°mole/fiter. Compression ratio 5.83. The spike at the left side of the picture is related to the timing, and can be ignored. Shock wave in CO, (1. 21% Io) showing vibrational relaxation of COs. Temperature 573°K before relaxation, 500°K after. Initial concentration 0.615 mole/liter. Compression ratio 3.63-3.73 (final). 7a 15 Figure 7 Shock wave in A (1% Bro). Temperature 1490°K before reaction, about 1412°K after. Note sharp rise of signal at front of shock wave, about 2 microseconds. Shock in A (10% Br,). Temperature 2130°%K before reaction. flote slow rise of signal at front of shock wave, about 7 microseconds, when 2 to 3 would be expected. This suggests curved shock front, or plane front not perpendicular to the walls of the tube. 16 Figure 8 Sa Shock wave into A (10% Brg). Initial temperature 1767°K. Writing rate of oscilloscope 20 micro- seconds per centimeter. 8b Same shock wave as 8a. Writing rate of oscillo- scope 100 microseconds per centimeter. Note cold front about 350 microseconds after shock front. 17 The inert gases used were Linde Air Products Co. argon, said to be better than 99.8% pure, Linde pure dry nitrogen, gaia to be 99.90% pure, and carbon dioxide supplied by Pure Carbonics Incorporated and said to be 99.5% pure, with impuri- ties air and water. The I, used was ‘Baker's Analyzed! Rea- gent. The Br, was Merck Reagent Grade. Both were used with- ‘out further purification. | . . In the Ip experiments the inert gas flowed through a regulator at a few pounds pressure above atmospheric, through a flowmeter at the rate of about 500 ec/min, through a needle valve where the pressure dropped to the experimental value, over the I,, and through the shock tube. The gas mixture entered the shock tube at the downstream end and left near the diaphragm where it went to a glass vacuum apparatus in which the pressure could be measured on a dibutyl-phthalate manom- eter. It left the vacuum line through a needle valve and went to a pump. The two needle valves were the only significant constrictions in the system. Since there were no important constrictions between the two needle valves the pressure in the whole system could be assumed uniform, and a measurement .of the pressure in the manometer on the glass vacuum line was @ correct measubement of the pressure of the gas flowing | through the shock tube. In the Bre experiments Bro was put into evacuated bulbs to the desired pressure which was measured on the dibutyl- phthalate manometer. Inert gas then was added to give that total pressure which gave the desired percentage of Bp The 18 . gases: were allowed to stand and mix overnight. The mixture was fed into the evacuated tube through the opening near the ‘membrane one or two minutes before the shock was run. @xtinction Coefficients of is The light used was of two kinds. One was that from a 500 watt tungsten bulb operated at 120 volts and filtered through a combination of filters that gave the transmitted light curve shown in figure 9a. The other was that from a Hg are filtered through a combination of filters that gave the transmitted light curve shown in figure 9b. Both curves were determined using a grating monochromator and the same photomultiplier used in the experiments. The filters used in 9a were a Bausch and Lomb 486 mp interference filter and a Corning no. 3385 sharp cut filter. The filters used in 9b were a Bausch and Lomb 436 ma interference filter and a Corning no. 3389. sharp cut filter. The tungsten lamp arrangement essentially gave light with a wavelength of 487 mu. The Hg arc gave a wave» length of 4356 mp. _ The room temperature extinction coeffictent for the tung- sten lamp arrangement was determined from very strong shock waves in Ip mixtures. If the shock wave was so strong that all the Ig dissociated then the change in photocurrent ob- served was that due to the initial absorption by the Ip. These experiments gave a value of 450 + 20 fore. The extinc- tion coefficient € 1s defined by log (I/I,) = - «cl, where I and Ip are the transmitted and incident light respectively, ¢ is the concentration in moles per liter of the absorbing (9 Figure 9g Light Used to Detect I, 9a light from tungsten lamp and filters €» 408 equvelent to A= 487 my less than 0.2% -_ —»p of peak 450 500 §50 aN (rp) 9b light from Hg arc and filters €-=29 A= 436 less than 0.2% 400 450 A (mp) 20 . | species, and I is the path length in centimeters. Combining the light transmission curves for the filters and light with the measured extinction coefficients of Ip (4) the value E€= 408 was found for the tungsten light arrangement. This value was believed to be the more accurate one and was used for calculations. For the Hg arc (436 mp) the room temperature extinction coefficient was taken as 29 from the measured values indicated (4). From the measured velocity of the shock wave and a knowl- edge of the initial conditions the extinction coefficient of Ip just behind the shock front can be calculated for every shock, whether or not there is a subsequent reaction. These calculations are outlined in Appendix C._ _ Figure 10 shows € versus T for shocks in No-Ip mixtures, where No is assumed to be unrelaxed vibrationally. Figure 11 shows the same for No assumed to be relaxed. Figure 12 shows the results from experiments in CO9-Ip mixtures assuming both relaxed and unrelaxed C0Oe. - Curves were drawn through the experimental extinction coefficient points by eye. All the curves so obtained are shown together on figure 15. Relaxed and unrelaxed No and CO. are compared with A, He, and relaxed and unrelaxed 02, these latter through the courtesy of G. Schott (5). The N5 and A were measured at both 487 mp and 436 mp, the COg only at 487 mp. Because some filters were changed in an attempt to in- crease the signal to noise ratio in the photomultiplier output 21 Figure 10 400Fr e @ | A = 487 mp so00or e f 200) Extinction ee 6 Coefficients of I, in Nz N, assumed vibrationally unrelaxed 300 500 {9000 {s00 22 Figure iI Extinction Coefficients ee of I, in Nz N. assumed vibrationally relaxed 400 A=2487 mu R Love) } e e 200F 100 1900 T *K 1soo 23 Fipure 12 Extinction - Coefficients of I, in COZ 600} ° - CO, assumed vibrationally unrelaxad 500 E 400 assumed . P vibrationally relased e 300 r mn a 7 A 2 _A. rn 2 __ A. a. a r > 300 500 [000 1500 24 L unrelaxed COs . . Figure 13 Extinction Coefficients of I, in. various pases 400-- A» 484 Mp ' relaxed COz y relaxed\ Neo } 300r i, A L He rN E aa A 484 unvelared J @ relaxed 200F unrelaxed Ne Tele) 25 the He and Op were measured at what was effectively 484 mp rather than 487 mpe On looking at the curves it is apparent that, except for CO-, no decision can be made as to whether the gases with vi- brational degrees of freedom are relaxed or unrelaxed. At 487 mp the difference between the results in A and those in No, calculated assuming either relaxed or unrelaxed No, seems to be larger than experimental if one looks at the scatter of the experimental points. At 456 mp the A and either No agree with- in experimental error in the region from 1000°K to 1500°%K where both were measured. a . _ The comparison of the CO curves with those of N, and A makes it seem clear that COo is relaxed vibrationally. This 1s substantiated by the fact that the shock into COp at the lowest temperature used seems to show a relaxation. This is — shown in figure 6b, which should be contrasted with figure 6a, which is typical of the results in hotter COp shocks. The relaxation of COs has been measured in a shock tube using an interferometer to follow density changes (6). These measure- ments indicate that in all the COp experiments the vibrational relaxation time would be a few microseconds or less, agreeing with the above conclusion that the CO, is relaxed. The relax- | ation time for COs estimated in the one case where it was ob- served in the Ip experiments agreed fairly well with that cal- culated from the reported results from the interferometer method. The Oo results when compared with the He results would 26 -geem to show that the Op is vibrationally unexcited, but the differences are not enough to be sure of this. The rate con- stants measured for Op as the third body seem to indicate that the Op is relaxed, and this is probably the more conclusive evidence. _ Allowing for the change in wavelength, the He and A re- sults agree fairly well, although the scatter in the points _ for He is quite large. The experiments in He were more uncer- tain than the others due to non-uniform conditions behind the shock wave, probably: due to cooling to the walls (5). _ That the extinction coefficient of a colored gas, when measured in the continuous region of the spectrum, should change with the addition of. a foreign gas is not expected. However the phenomenon is known in the case of Br, and it 2 should not seem unreasonable here. to find a small effect. The difference between the values measured in A and those measured in No in these experiments are nevertheless so large at low temperatures as to suggest that there is some systematic error in the shock wave measurements. Careful static measurements of the extinction coefficient of Ip at and near room tempera- ture, that is, 300 to 400°K, in various inert gases would be interesting to decide this point. If the difference between “A and Np as foreign gases is really as great as the results of the shock tube experiments indicate it should be readily measurable. Sxtinction Coefficients of Bro In the experiments with Bry several different combina- 27 “tions of lights and filters were used. Two were the same combinations used with I, and shown in figure 9. A third was the Hg are with a Corning no. 5543 wide band pass filter and a Corning no. 5060 sharp cut filter. This combination let through the 436 my Hg line and some of the 406 mp Hg line, as 1s shown in figure l4a. A fourth combination, shown in figure l4b, was the tungsten light with a Corning 436 mp interference filter and a Corning no. 3060 sharp cut filter. The extinction coefficient of pure Br, vapor has been measured as a function of wavelength (7), and, using these measurements, one can assign extinction coefficients to the light combinations shown. In the experiments with Bro it was possible to measure the extinction coefficient approximately in each experiment. This was because the tube was filled in about a minute and the change in photocurrent could be meas- ured with some confidence since the argtt rate of the photo- multipliers was low. The results of these measurements are given in table 1. It should be noted that the Bre concentra- tion is approximately the same in every experiment, so that the higher the percentage of Bre. the lower the total concen- tration of all gases. The results in table 1 would then indicate that a pressure effect 1s very likely present. That the extinction coefficient of Bro is affected by the presence of foreign gas, even in the continuum, is a known phenomenon (8). No measurements appear to have been made in argon but measurements in all other gases studied showed an increase in the extinction coefficient with increasing amount 23 Figure 14 Ls ght Used to Det ect Br i4da light from Hg arc and filters © _ \ Ji 400 450 A (mp) l4b light from tung stem lamp and filters 400. "450 A mpl ‘Room Temperature Extinction Coefficients of Bro light = -shown in figure wave length (approx) € in pure Bro from reference 7 % Bre in mixtdre ‘OQ ®*€ VY HE 10 ‘80 100 153 146 158 9a 436 mp 134 it I+ oo © . 29 Table l 9b 14a 487 436 + 406 89 138 € 154+ 12 105 + 9 121 t11 90 +4 147 £6 137 +7 133 +5 14b 435 135 156 £13 i+. 153 144 133 i+ oO i+ on no. typical of conc. runs moles/1. 11 8 9 5 2.6x107° 3.0 1.6 1-0 0.42 0.08 0.04 50 of foreign gas. This is what is found here. A few measure- ments were made in a Cary Recording Spactrophotometer of the ‘extinction coefficient of Br, in 10% Bro - 90% A mixtures at various total pressures. In these experiments the extinction coefficient of Br, was found to fall with increasing concen- tration. This was an unsatisfactory point at which to leave this question, but since the measurement of extinction coeffi- cients was not the primary purpose of these experiments no further work was done. It is clear that this is a problem in which more experimental data would be welcome. | It was decided to use the measured set of extinction coefficients in the calculations. At low fractions of Br, in 2 the mixtures it does not matter much which extinction coeffi- cients were used, but at higher fractions it can make a great difference in the rate constant. This will be gone into more fully in the section on kinetics. The measured values of the extinction coefficients of Brp are shown in figures 15 and 16. For comparison, values deter- mined up to 900°K (7) in a conventional manner for pure Bry are shown also. The temperature dependence found here agrees with this earlier work as well as can be expected in view of the fact that pressure effects have shifted the values of the extinction coefficients. The Dissociation Reactions The dissociation of diatomic molecules into atoms re- quires that some otherwise non-reacting atom or molecule collide with the diatomic molecule and transfer sufficient ai . i 0002 oost » ooo! 00s OQo0E qT Y Ul T Tt T t t ¥ T T T T r T T T 4 ¥9 8 -%Y W 7 09 Z o e ; ow ug wand Yur 4B Ke a . -ZUvUADANSeBUs 4DDAIp a et . v 4 . e v *% «6 . fe! Ww reb ~ y v 0 GG ®oanos 4481) Sf 70! Me aa 0002 oos! Q00} - 00S ooe tT v T ¥ T —T t ¥ T T T t v T T T T 4 09 %9o ° e ( £ 2>Uur4rJ24) “vy 5 a e v ug sand VW “Gq YZ? e va a 2UPUPanseDuUs eo” «Uf v @ v G $>?4!P + 901 e e Vv nugeh - e v v § . PG 2noes 3431) J oF! ova Z 4g jo ] S}uU DIDI} }D0-) 100139417 XF CG} a40814 | 32 000? oos\ -. 4 000! aos ooe Li Li T t Ly T t T “=? — —T T ee ¥ t ¥ if S4tun 3 OY “ PArmuMep preidsip 7001-05 stiun 3 OZ v 7 a P4aPmMumop y Ww v a 109 prreidsip ~%o} vv Vy ¥ ; a , y } @ ® vv wu 4q@ ~~! e °, e e 00! # ( 2 22urvA25J04) z ad wu Sb ~ ¥ $.u pup nse aus p>BAIp G pl} wv24unos 2435} obi 0002 005! Mt c001 90 ooe ¥ T T T “er T T ¥ —T T T ¥ —_— T syiun >) OOr _ PAPMuUMOp p22edsip 7, O001-OS ao @ = # a 409 Spun > OF Psemumop Vv Vv P prreidsip =» of Yv v a 4 v ; e e ° ® @e 4 zt _) vursuge%i © ® Se FY Qo! (2 224249324) die gop +4 Huw Qcp eV tag aund 4 e bl 2>unes 2481 SZUBWIBZANSP BU = ZIDAIP Zaq Jo Or! $3 2191JJ204 , 40139UIAXZ 9g) 24n8s4 oD ‘energy to it to allow it to dissociate. The equation describing this reaction is | M+Xp —-M+X+X , : where M is the atom or molecule with sufficient energy to dissociate the X5 molecule. The recombination of the two atoms into a molecule is described by the reverse of the reaction above M+X+X—>M+X 2. In this reaction M has the role of taking off the excess energy liberated in the recombination. In this reaction M is called the third body, and in the following pages it will be referred to as such whether recombination or disso- ciation is being considered. — The kinetics of the dissociation and recombination can be described by the equation . — A(Kg) = = ky(Xy)(M) + (x), where (M) represents the total concentration of third bodies. (All concentrations will be given in moles per liter and all times in seconds.) The two rate constants kp and Kp are re- lated by k, = kK, where K is the equilibrium constant for the reaction Kinetics of io Dissociation On fifty-one oscilloscope traces taken of forty shock waves it was possible to measure the rate of dissociation of Ip in the presence of No. These covered a temperature range | 34 from 1100 to 1740°K if the No is assumed unrelaxed, or from 1060 to 1610°K if the Np is assumed relaxed. The total concentrations of gas used varied from about 0.4 x 107° to 2.0 x 1079 moles per liter, and the Ip percentage varied from about 0.4 to 2 percent. Rate constants were calculated either by using an integrated rate expression or by measuring the initial slope of the trace, both as explained in Appendix D. The results were substantially the same by either method of calculation. The rate constants so measured were converted to rate constants for recombination, Kp. The values of kp obtained are plotted in figures 17 and 18 as log kp versus log T. They could just as well have been plotted as log kp versus 1/T. The points are so scattered that which of these two forms gives the better straight line could not be determined. Figure 17 shows the points assuming the No to be unrelaxed, figure 18 assuming it to be relaxed. The straight lines drawn on the two figures were fitted by least squares to the points shown. The points were weighted depending on the smoothness of the curves, the value of the extinction coefficient found, that is, how well the extinction coefficient agreed with that obtained from an average of all the data, and similiar | considerations. The equations for these straight lines are log kp = 8.835 - 1.651 (40.242) log(T/1000) log k, = 9.007 - 1.376 (£0.267) log(T/1000) for unrelaxed and relaxed No respectively. The errors given 35 T CK >| 000 \yaele) 14900 : 1600 1890 Fipure 17 Recombination Rate Constants r I, in N. Nz assumed unrelaxed™ 9.0} 4.0 «10? 408 ; 2 8.8} e 10.6 log ke 4 Ke &.6 + 40,4 ast e e°? § e Jo.2 82 . | i. L i rs ] s " i 3.0 3. 3.2 36 TK \ooo0 1200 14900 1600 {e900 9.2 T T T ms ¥ ¥ Tv e q e e e e se 8 9.0F 41.0 % 10? 40.8 asr 4 0.6 log kj 4 Kp %e 8.6} ® 40.4 e e - 84} Figure is Recombination Rate Constants L in N. 40.2, N2 assumed relaxed 8.2 2 2 2 oa | 4 1... t . 4-4 a 4 i. ry 3.0 3.1 3.2 log T ay are probable errors, calculated according to Margenau and Murphy (9). The probable errors in log kp at the centers of the range covered are 0.012 (T= 1344) and 0.013 (T=1274) respectively. 7 | The corresponding ‘equations for log kp versus 1/t are log kp = 7.752 + 1053 (#449)/r and log ky = 8.138 + 925 (#543)/T _ for unrelaxed and relaxed No respectively. The probable errors in log k, at the centers of the range covered are 0,004 (T=1335) and 0.005 (T=1267) respectively. If one converts the slopes in this formulation to energy units one finds 4.81 + 2.05 and 4.25 + 2.48 kilocalories per mole respectively. _ . . - In CO, only two experiments yielded rate constants. These were the following: T= 1077 kp = 1.85 x 10° a 1137 1.50 CO, assumed relaxed, 1559 2:85 x 10° . _ 1666— Be 50 C05 assumed unrelaxed. Looking at these and comparing them with the No results which are of the order of 10? 4 appears clear that C05 is relaxed, in agreement with the conclusion from extinction coefficients. The rate of recombination of I atoms into molecules in various inert gases has been measured at room temperature by — a flash photolysis technique by a nimber of experimenters (10, 11, 12, 13, 14). Although recent work indicates that the older values for rate constants are too high only one of the earlier reports gives rate constants for the gases studied here. Accordingly this work (12) is used for comparison. 38 The high temperature results for the Ig dissociation in Ne and CO. have been described. Other work in this laboratory has yielded similYar results for A, 09, and He (5). These results are all collected in figures 19 and 20. These show 293°K (room temperature) and 400°K results from flash photol- ysis, and the high temperature shock wave results. Figure 19 combines these on a plot of log Kp versus log T.. Figure 20 shows log kp versus 1/T. Since the slopes of the results at high temperatures are all quite uncertain only a single point is used to represent each set of shock wave results for a particular inert gas. . _ _ From these two figures it appears that plotting log Kp versus 1/f seems to fit the data over the entire measured range better. If one accepts this as the correct representa- tion then it would appear very likely that No is vibrationally unrelaxed at high temperatures. The previous conclusion that COp is relaxed is supported. No decision can be made for Oo, but judging from the slopes of the other lines relaxed Op is possibly more likely. Although the He results give a good straight line it should be remembered that there was some un- certainty as to the correctness of the high temperature points. Recent flash photolysis results (14, 15) have indicated that Ig molecules are themselves exceptionally efficient as third bodies. One result (14) gives Ip as 285 times more efficient than A. An attempt was made to determine this ratio at high temperatures by plotting the percent deviation of Kp from the smoothed curve values against the percent Ip for each {0.0 9.5 log ky 9.0 8S 39 Figure 19 I, Recombination Rate Constants log ka versus log T Various inert gases CO, Nz relaxed aA en unrelaxed O2 relaxed He QO Oz unrelaxed 40 Figure 20 I, Recombination g CO, Rate Constants log Ka versus + 10.0 Various inert gases - oO @ N, : A 95 He CO, log kp i 3.0 b> Nz relaxed s r adA r @ O, relaxed Nz 8.5 unre faxed He unrela xed l . i Fi k . .003 .002 7 .00} T i i i aie 298 400 T °K 1000 ZO0O — 41 shock. Ideally this would give a straight line, the slope of which would be the ratio. Actually the scatter of the results was $0 great that no reliable value could be measured. That the ratio is probably between O and 30 is all that could be concluded. Similiar attempts to measure this ratio in A led to the conclusion that I, is less than 25 times as efficient as A (5). Kinetics of Bro Dissociation ~ On sixty-two oscilloscope traces from forty-two shocks it was possible to measure the rate of dissociation of Bro in A. The percentage of Br, varied from one to ten. The one percent Bre results are the only ones that are regarded as very reliable since the correction terms become quite large and uncertain as the percentage of Bro increases, The results in one percent Bry were obtained over a temperature range from 1380 to 1771°K. These are shown, along with a straight line fitted through them by least squares in figure 21. Also shown in figure 21 are the results from two, four, six, and ten percent mixtures. The total concentration of gas before the shock was of the order of 2.8 x 107% moles per liter in the one percent mixtures and proportionately less with the larger . percentages of Bry The larger percentages of Bro were used in an effort to . measure the rate constant for Bro as the third body. However, as is shown in Appendix D, the rate constants depend quite markedly on the value of ae /aT, which from figure 16 can be seen to be uncertain by a factor of two at least. Because of 42 Fipure 21 Recombination Rate Constants 90F Br in A Qo A 8.8, ; Ls A @ @ a S86F log Kyl Oo fe) 8.4 fe} fe) fo] 0° fe] B.2/ @ i% Bin A A 2% 4 Gg 4% o 6% . Oo 10% 2 o a a ry . a s + I rt ~. a a. A. 2 4 a s f a s o 3.2 log T 3.3 4 a s a i rn i a 1400 \7o0o 2000 43 this, in the ten percent Pro experiments the rate constants were uncertain by a factor of about two. Considering all the data as in the case of Ip it appears that Br is between 0 2 and 8 times mere effective as a third body for the recombina- tion. The only value given for this ratio at room temperature is >14 (16), and this is fairly uncertain. _ | A more accurate estimate of this ratio could probably be determined in the same manner as was attempted above except that C0, should be used as the inert gas. The heat capacity of COp at high temperatures is over twice that of A so that the temperature change in a one percent Bro shock wave in COo is less than half that in a one percent Bro shock in A. This makes the correction terms correspondingly less and therefore the uncertainty caused by the uncertainty in aé/aT less im- portant. Determination of the rate constant at one particular temperature in one percent and five percent Bre shocks should then allow the measurement of the relative efficiency of Bro and C0, as third bodies. It would also be better to observe the reaction with light around 487 mp where d€/dT is less than at 456 mp. . Figure 22 shows the room temperature value (13) combined with the shock wave value on two plots. One is log kp versus log T and the other log kp versus 1/f. That the measured high temperature slope agrees better with the 1/T plot is probably meaningless. No intermediate point is available here to compare the two methods of plotting the results. The high temperature results for Bro can be represented by the equations a4 r Figure 22 Br, Recombination 9.4 } Rate Constants in @argen 9.2 F f log Kq versus log T 9.0 F log Kr q 8.8 Ff a.6f } 4 1 r 1 1 l 2 4 4. 2.9 log T 3.0 9.4 7 loo ka versus _L X0F ® R Tr log kp &.aF &.6F 003 ,002 .oo| ar [ «45 log kp =. 8.631 - 0. 524 (£1. 187) log 1000/t or log kp = 8.300 + 357 (4803)/T ‘The probable. errors in log k, in the center of the range covered are 0.049 (T = 1595) and 0.049 (T =1590) respectively. The latter slope is equivalent to an energy of 1.63 + 3.67 kilocalorties per mole. Discussion ; The experiments described here are a more stringent test of the shock tube in chemical kinetics than the N04 experi- ments previously described (1). They point up the advantages of the shock tube quite clearly but they also point up some serious deficiencies. The advantages are that very fast reac- tions can be studied, that high temperatures can be readily attained for kinetic measurements in a region where even static measurements are troublesome by ordinary means, and that one is more or less assured of a homogeneous reaction. The disadvantages are in some respects necessary consequences of the advantages. Because an essential assumption of the shock wave method 1s that in the short time available the walls do not interact with the shocked gas the reactions which are to be studied must be fast reactions. This limits the . range of pressure and temperature over which a particular reaction can be studied. Also since the temperature of the walls is not directly related to the temperature of the gas the behavior of the gas is governed by purely hydrodynamical considerations and if any reaction takes place it does so in a highly non-isothermal medium. When working in temperature 46 ranges far above room temperature the need for essentially static data, such as extinction coefficients or equilibrium constants, to more accuracy than that attainable by the shock wave method, is often felt, and the data are found to be un- available. At temperatures high enough the cooling effect of the walls does become important and limits still further the time in which observations can be made. Finally the electron- ic and photometric devices with which measurements are made are being used at their limits because the resolving times required are so small. Some of these problems are unavoidable. Some problems, like the electronic and photometric equipment, and the lack of high temperature static data can and will become less serious with time. | The results recorded here are interesting in that they confirm earlier conclusions that the rate of recombination of I atoms decreases with increasing temperature, and extend these earlier conclusions to considerably higher temperatures. Such behavior can be interpreted as meaning that the kinetic energies of two I atoms must be below the average kinetic energy at a particular temperature for recombination to take place. The question of how this temperature dependence should be described, as log kp versus log T, or as log Kp | versus 1/T, is an interesting one. If the 1/1 description is correct, as the overall survey of the existing data would indicate, then it would appear that an energy is associated with the recombination. One is left with the pleasantest of speculations to account for this energy. Unfortunately shock | 47 waves alone cannot give results precise enough to determine if this 1/T representation is right, at least not in the present, or in an immediately forseen future apparatus. The shock wave points do provide an extension to flash photolysis results which could and should be obtained up to about 800% to decide this point. a Table 2 shows the equations obtained by combining the room temperature points with the high temperature points for both methods of expression. If the form k,= AT™ 4s correct one might expect that n is the same for any third body. That n varies considerably is perhaps another argument for the form Kp=A exp(@/RT). Comparison of the results for Br, and Ip in A show that the recombination rates are about the same, and have about the same temperature dependence, even though the dissociation rates are quite different. It would be interesting and quite readily possible to measure the rate of dissociation and recombination of Cl. It would be interesting to measure the rate of dissociation and recombination of Fp. - In doing future work elther with Bre and Ip and other inert gases, or with Clo and Fo in any inert gases, it seems clear that it is not worth trying to cover a large range of temperature, but rather to do enough runs at one temperature to have some confidence in the average, and to cover a range of temperatures by combining shock tube and flash photolysis measurements. 48 Table 2 Recombination Rate Constants between Room and High Tempsrature Unrelaxed No-Ip k, = 4454x10°(1/300)"**75 or = 1.57x108exp(1.95/R7) Relaxed No-Ip 2214x100 4..41x10°(1/300) 71°25 4.28x10°exp(1.37/RT) Relaxed CO0p-I,, | . 13.0 x10°(t/300)7+*76 6.37x10° exp(1.78/RT) A-Ip oo ao | . 3.52x109(t/300)"~* 2.44x10 exp(1.57/RT) He-I, oo. . 1.65210" (1/300) 7294 1.28x10°exp (1.51/RT) Relaxed Op-Ip 7 3 3 6 .42x10° (7/300) 2°" 1.71x10 exp(2.14/RT) Unrelaxed Op-Iy - <2 41 ; 8 6 .36x10° (7/300) 5.71x10 exp(2.78/RT) Ig-l, oo 2.97 9 between 8.50x10"7(t/300)7 ° 2.78x10° exp(3.36/RT) and 8.05x10'* (1/300) 6 3.50x10 exp(5.90/RT) A-Br,, . 2.5 x18°(t/300)7++49 8 exp(1.45/RT) 49 Appendix A Definition of symbols a velocity of sommd = pypati”% in em/msec where given ) S| numerically fA concentration of atoms of dissociating gas moles/liter om degree of dissociation B bursting pressure ratio = Ps P, 6 enthalpy function = 2H-!] c total concentration {formal) moles/liter D density & a specific variation in some parameter with respect tog, for example 61T = Tly.00, — Tle=o AV shock density ratio = D2 D, E specific internal energy E° molar internal energy E molar extinction coefficient (decadic) liter/mole em mole fraction of reacting gas referred to no dissociation ¥Y heat capacity ratio = Cp Cy H specific enthalpy H° molar enthalpy H. molar enthalpy at absolute zero le 50 light intensity incident light intensity. concentration of inert gas moles/liter specific reaction rate concentrations in moles/liter . . times in seconds equilibrium constant = A* moles/liter M , L equilibrium constant = Pa | (atmospheres )* ) (Raye _ (kappa) dimensionless molar enthalpy function = H-H.- RT length of light path natural logarithm base 10 logarithm concentration of molecules of dissociating gas moles/liter pressure © shock pressure ratio = Pr JP, gas constant in whatever units are convenient shock velocity in em/msec where given numerically time temperature apparent time in shock wave SL. © shock temperature ratio = Ta Ty “u velocity of gas relative to shock front Ll4 molar heat of dissociation (one mole of molecules) LJ; molar heat of tonization (one mole of atoms) v cold front velocity in em/msec where given numerically V specific volume W molecular weight Wa mean molecular weight for ~ dissociation W mean molecular weight a =0O Subscripts o initial value that is at tor t= 0 co equilibrium value that is at t or 4 = oo ; vefers to conditions before the shock wave 2 refers to conditions behind the shock wave refers to conditions in the undisturbed driving gas » refers to values at a particular a refers to atoms (if on & refers to atoms as estan , body m refers to molecules (if on & molecules as third body) x refers to inert gas (if on fe inert gas as third body) po on refers to dissociation R on fe refers to recombination 52 Appendix B Shock Wave Equations The equations to be used for shock waves in which disso- clation or ionization occur will be developed. The develop- ment wlll be based on a stationary shock wave in a tube of uniform area. The transformation to a shock wave moving into a gas which is stationary in the laboratory system is straight- forward, and involves only the two relations u,=s and u,=s-v. For a stationary shock wave the following equations hold: (1) Du, =D ,u. conservation of mass (2) PB+Du?* = P+ Diu,” conservation of momentum (3a) —, + Boy ut = E,+ P, +u.* conservation of energy (3b) H, + us = H, + ut 2 Zz From these one obtains (42) Ha- H = +(P,-P) (V+) = _ tL (4b) =t PV (T-1) 01+) (4c) =i RE (q- as From (1) and (2) and the velocity transformations one obtains (5) os = E m-1\]2 er (R=) rN H can most easily be defined relative to absolute zero so that (7) H= Ho He RT _ gp RT RT Ww WwW 53 For a partially dissociated gas (8) H = (1-o)s4, BY + 2x RT + « Us The perfect gas law, which is assumed throughout, has the following form (9) l= (ite) AO | Writing a terms of (7) and (8), and equating tt to (4), (10) H,- H, = (1a) Rn Rie + 20 Man RT + Ua Us — 39, RT RT, =4 RE (1-1) (1+) Solving this and substituting (9) (ute) Th = O[(1-%)(2Ha_o1) + Ze (Zax N] — (23m -1) ox LI b+ 9 + RT + (Ita) Oo Making the substitution @=2x-| = - ~ u S (llb) T= © (( &) Bria +20 Br | Cm + tan + (ite) 2 Equations (11b), (9), (5), and (6) are used to calculate be- havior in the shock wave. Some special cases of (1lb) are of interest. For a pure gas with no dissociation (llc) TT= OBnr — Be +2 For a monotomic gas (no electronic excitation) (lla) Th= 4( 0-1) + & _For a linear rigid rotor Qe) Ths 6(O-1) + & 4 For a non-linear rigid rotor (lif) TtT= T(@-1) + & TT 54 The same development for the case of a mixture of two- gases, one inert and one dissociating, is also of interest. (12) He = (1) stgRT + @[0-«) ta RT +200 #aRT ta dy | 1+ pa (13a) We = (\- ¢) Wr + (1-0) Wa + 6% Wa ] lt ge (13d) = Wr + 6(Wr -We) | + po (13c) = _W Lt oa (148) H = _H® Wa (14o) = (I) a RT + @ [ (1) ot BT +20 Mp RT + a] w Ww w w (15) H.-H. = (1-6) (#r, RG — x, RY) + é[ (1-«) Ynz 22 Ro + 2a War RY pal - of RT| ew OED (eg) In this case the perfect gas law becomes (6) Te = (1+ %%) AO Solving (15) and substituting (16) (17a) Tl = (1-6)(B,.eE -~Bx,) + 6 $[u-«) Bn2 +2 Bar }O -Bni + af + (lta) @ = (6x28 - Gx.) + > [ (Brio 62.) 0 — (Bram Bx] + Ox [ (26a.-@n2) O +2, U4 | + (1+ dx) @ (17b) 55 In the same manner one may find the expression for a mix- ture of an inert gas and a gas partially dissociated which dissociates further in the shock. This is probably the most. complicated system in which any useful kineticscould be done. (18) T= Avge (B229-Fe0) + PSL) Bm + 2°26 m2 | © - ~ m1 Cir 1 Us \ 2 [a Bear + 2exGai] +2 (on-0%) Fe + (es) S Finally, for a mixture of an inert gas and an ionizing monatomic gas Qe) TE= (1-6) (re -6x) + 6 f4[Cised 0 =1] Qo Ui ash + (1400) 2 This assumes that a gas of ions behaves as a perfect gas. In all of the last three cases the proper mean molecular weight, W, (see (13)), must be used in (5) when calculating the velocity. | For cases where @ is large the calculations for the shock behavior are best utilized by plotting lines of equal a, equal S, and equal v on a diagram of TT versus Tz for a given qT, ’ usually 300°K,. wand plotting lines of equal a on ab versus S$ _plot. A particular shock wave will follow along a line of constant shock velocity, S , provided that the gas comes to % The final parameters are related to a given final temper= ature and are insensitive to’ the initial temperature being changed by about one percent, to the accuracy required in these experiments. 56 | its high temperature equilibrium before the cold front. In the case where > is small (of the order of 0.01) the simplest procedure is to solve for the behavior as a function of temperature for the pure inert gas, and for the mixture with m= 0.01 and &= 0.00, 0.50, and 1.00. From these. two sets of data calculate (20a) 6T = Weszo.o: - Tlheeo (20b) SQ = Agszoo - Agzo (20c) Sv = Vesa. —- vo=o (20a) as‘ = S'p20.01 — s'g=o where s'is defined as the velocity which the gas would have had had it had a molecular weight W,rather thanW, that is In a given shock s is measured and @ is calculated from the original conditions. From these s' is calculated, and then Sg=0 is calculated. (22) Sg=0 > s - © 6&s' ; o.al Sp=o is the velocity a shock wave in pure gas would have had if this same temperature had been produced. From Sg=o and the careful calculations for the pure gas the temperature can be found. Since &'s have been calculated for several o's (and are approximately linear in®) the temperature for any o along the course of the reaction behind the shock can be found. Knowing the temperature at any & along the shock the true A, etc. can be calculated, (23) Ag = Deeg + 2 5A ote s 57 since the &'s are given as functions of the temperature. In mixtures of iodine and nitrogen sample calculations have shown that the B's are linear in @, up to at least b= 0.068, to the accuracy required for these experiments. . To use the observed density changes as a function of time to study the kinetics of a reaction it must be realized that there Is an apparent time contraction in the moving shock wave. Consider a shock wave traveling a distance dx. The shock wave requires at snock= SX% to reach x + dx from x. The moving gas 3 . s—_ v—- x X+dx requires dt,.,3= ax to reach x + dx from x. However, the Vv rea observed time after the shock front reaches x + dx that the gas which was shocked at x reaches x + dx is at wpserved = os - ox = Gtresi - Itynoope Recalling equation (6) and eliminating dx, one obtains (24) at = at ° A or real observed dt = AdTt The relation between the original pressure in the low pressure side of the shock tube and that in the high pressure side to the characteristics of the shock wave is given by “ Vz ram | - (Ey | This has been repeatedly derived in the literature (17). This is not an experimentally fxact formula since the mechanical process of breaking a membrane is not perfect, but it is useful for estimating the correct initial conditions to obtain a desired shock. 58 Appendix C Calculation of High Temperature Extinction Coefficients __. The measurement of extinction coefficients at high temperatures is quite direct. The fraction by which the transmitted Light decreases across the shock front, 2, As measured from the oscilloscope trace. The fraction of the incident light that was transmit ted by the colored gas before the shock was run, » is calculated from a knowledge of € at room temperature and the initial concentration of colored gas, that is, lop & = -e€,c,2 OR - The shock parameters are determined from a measurement of the velocity of the shock so that A is known. Then Ack ts cf S&F If a reaction occurs in the gas the trace can be extrapolated visually to the initial value except in very hot shocks where the reaction is very fast and €, cannot be measured. 59 Appendix D Kinetics of the Dissociation of a Diatomic Gas | in a Shock Tube In a mixture of a dissociating diatomic gas and an inert gas the dissociation is governed by the following differential equation, which is for constant volume. (1) ~ oft { = Ron, MM + Ron MA + for MI at th » ~(fen AM +Ran PA + Rez AT) From a consideration of thermodynamic equilibrium it holds that for any third vdody _ ot (2) Ko = ee. Combining (1) and (2) and factoring (3) 2m] = (KM- AY) (Ran M Ren + Ker T) If c, is the original total formal concentration of gas, and c the total formal concentration in the shocked gas, then (4a) c= AC, (4b) M= (lI-«) $a,4 (4c) A= @xpoaA (44) I= (1-6) A (5) ~3ft | = 9G A dx A Substituting (4) and (5) in (3) (6) se - [ kK Ac, (1-e) —46(Oayur] ° ((2Rea- Rendo> + hend +( 1-9) Rex | At this point the photo_metric equations will be introduced. (7) E Cay, 2 = — log -E- 60° 7 where Cats is the concentration of the absorbing species. In the case of iodine or bromine, where molecules are the absorb- ing species, Cabs = M=(1-a)pAqso that (8) (p—e paceR = logs Taking derivatives of both sides of (8) (9a) pac,eL [' - (1-ai) (dnd + dine) | da da . d_log i/i. In the case where the atoms are the absorbing species this becomes (9v) 2deAc, Es [1 +o (did + dine) | de __d Jog ivin It can be seen from these that the case where the atoms are the absorbing species is the more desirable, because the change. in light absorption due to the density increase with dissociation and that due to dissociation enhance each other. Equations (6) and (8) are now combined and the correction for the apparent time contraction is introduced (10) 5 [(2 kena ~feen\t + Ren] + I- -o) erg = aP l d log t/to + 1 [i — (1-2) (ayn4 a ane) If & can be determined at each point on the curve of loge £ - the equilibrium constants can be determined, since in any shock once s is known « is known as a function of T, and A, K, and € are assumed to be known as functions of T beforehand, and hence also of x. This expression is valid in any case, but in cases where @ is small changes in A, K, and € can be approximated as linear functions of «% and an expression formed 61 which can be integrated. In the case where pis large equation (10) would have to be used since A, is, and € could not be approximated by linear expressions. If this were the case fexx would probably be known, so that &,,and Ram alone would need to be determined. The above method requires that & be known at each point, but if A, K, and € are known as functions of &, then given the shock velocity the value of log£ for a given « could be calculated, and all that need be determined experimentally is the time dependence of loge. To determine the values of é and fearas functions of temperature experiments where @ is small (about: 0.01) must be carried out. In this case t is plotted versus T and extrapo- lated to zero time. From this one can calculate ( legit). (11) Nog ten - (l-a) SE (log tlls)eno Ate Et= 0 For small P the changes in A and € can be approximated as linear with«, that is (12) A = Arse ( 1+ diA oynere ding is assumed constant € = €,. d iné,, \w dine t=o ( i+ ia. ot) here diné€ is assumed constant : “ , so that (13) tsp S/t. tri. = (l-« [+ AlnA & ; d Ine ; (\eq Cfin)y ng r¢ AM ) (V4 42 a ) This can be solved for a& by successive approximations. Equation (10) now becomes (14) Rp, = dlogific to . dc MER T weac, (l-a) — £€pAc,) a] ! . —_ ~ dindA d Ine | Cti-e) ( ae + qos 62 which can be solved as before. If it is desired to integrate it is better to go back to equation (6) which becomes (allow- ing for the time cerrection also) (15) e = hex A [reac (ie) - +g acya J An (16) i} a 3 dt kar & 4 [ec k K (l-a) — 4(c,)* a* | Using equations (12) and a similiar expression for IK, and making certain approximations by the binomial expansion, (16) becomes 7) dt = far AS (14 $0) ES $<. ( Lena i-x) — 4( $c)" ] > where 4 ~ SdindA . Ax i dink ~dinA _ B dink d ind Ax Adc 4 aw da Let €= 4GGAe and (17) can be written (18a) Ao _ We OS Chaya) (1 - Ci-n ya - CS¥m)ar] Raz St Integrating and rearranging this (18b) —] \ \ — flim) : (1-2) (i-7) (\-3 - . 56 0) AY 7 = xt ern) (I~ v) _ 7 mt item) bar “em \n [ l- (t-»)a — ($+) at] 1+ fa = Ret + constant 63 Expressing (18b) in terms of the equi librium rg Xe = ~Li-m) | yp Wig atsen) 2($+77) Cry if €+n=0 hey = <5 2( 6+) — JCi-n)- (18¢) 4 KeAtC, ; [is ue] \ scp eter” ~p°-faxy] in Xa — _ s (i-n ) +. C87) (tm +2) (S+m) ~S*- SC I-) In [ (og —ee) [O11 HE+) ec -a)]}" {> = Re T + constant T+ Yo : The above equation was rather tedious to use and it was found that a measurement of the initial slope of the reaction gave satisfactory results more readily. The calculations based on the initial slope were made as follows; For &=o0 equation (6) becomes (19) det = WAC. ( fam + (I) fear )_ Let k = © kro + (-O) Rex then (19) can be written (20) KR = Aa I at WAC, = Pe | log Csin At { dA_ log </ie kK A*c, Aa Recall (8) log i = — EAGARCI-a) which becomes, upon differentiation with respect to (21) A leg “ia _ -146 lo | ; = _ = | c Ac ( I S& ) e+ | Q “Sz, tr —..— is plotted versus t the slope is _—! id ‘lop ihis log the P t P ¢ leg thay dt 64 so that (22) Fe = slope x C1 aq Chie) - QW A* c, = _ slope \ intercept QwWwaArc, _ The derivatives needed above can be found by different- lating equations (16), (17), and (5) from Appendix B to obtain the results . : 2u (23) 49. ~$eS(a-2) #64 2+) 26 me Fm) + zvs | (1b CAE) + (8-248) [ (1-6) Gra.t Mel-woFme 426A) 24 _ — ( da = $F ACA I\(((26a1-Grr) + Lud | EP e tlaiPant tain sam @ dAe€nommator gs is determined experimentally from the € versus T curves and (25) de = dé Tt do S Ac ol z A o (1) (2) (3) (4) (5) (6) (7) (8) (9) (20) (11) (12) (13) (14) (as) (16) (17) (18) 65 References Tucker Carrington and Norman Davidson, Journal of Physical Chemistry (1953), 57, 418. Doyle Britton, Norman Davidson, and Garry Schott, - Discussions of the Faraday Society (1954), no.17, 58. OW. Dbring, Annalen der Physik (1949), 6. 5, 133. W. B. DeMore and N. Davidson, private communication. Garry Schott, private communication. Baward F. Smiley and Ernst H. Winkler, Journal of Chemical Physics (1954), 22, 2018. A. P. Acton, R. G. Aicken and‘N. 8: Bayliss, Journal of Chemical Physics (1936), 4, 474. N.S. Bayliss and A. L. G. Rees, Transactions of the Faraday Society (1939), 35, 792. Henry Margenau and George Mosely Murphy, "The Mathema-" tics of Chemistry and Physics," New York, 1943, (Pe 502. M. I. Christie, R. G. W. Norrish, and G. Porter, Proceedings of the Royal Society (1952), A 216, 152. Royal Marshall and’Norman Davidson, Journal of Chemical Physics (1953), 21, 659. K. #. Russell and J. Simons, Proceedings of the Royal Society (1953), A 217, 271, Robert L. Strong and John £€.° Willard, Abstracts of Papers Presented at New York, N. Y., Sept. 12 to Sept. 17, 1954, American Chemical Society Meeting, p. 26R. M. Christie, R. G. W. Norrish and’G. Porter, Discussions of the Faraday Society (1954), 17, 107. Don L. Bunker, private communication. — B®. Rabinowitch and W. C. Wood, Transactions of the Faraday Society (1936), 32, 907. W. Payman and W. C.F. Shepherd, ‘Proceedings of the Royal Society (1946), A i186, 293. National Bureau of Standards, "Selected Values of Chemical Thermodynamic Properties, Series III," Washington, D. C., 1954, 6 Propositions 1. It is suggested that the kinetics of the decompo- ‘sition of the carbonyl halides be studied using the shock wave technique. : 2. - Certain disubstituted compounds of ferrocene have been prepared which are thought to be substituted on opposite rings as far apart as possible (1). (a) It is suggested that a determination of the space group of one of these crystalline compounds might confirm this conclusion by showing that a center of symmetry is: required in the molecule. oO 9 (b)° It is suggested that if ferrocene diacetic acid be prepared, from this compound it might be possible to obtain information about the location of the groups or the energy of rotation of one ring with bespect to the. other by a study of the formation of the acid anhydride. (1) R.°B. Woodward, M. Rosenblum, and M. C. Whiting, J.A.C.S., 74, 3458 (1952). “S$. It is suggested that the structures of fifth. group pseudohalides be determined with the end of explaining the unusual behavior of some of these compounds. In particular ~ the structures of the triisocyanates of phosphorus, antimony, and arsenic (1, 2) and of phosphorus tri- and pentacyanide (3) should be determined. From a consideration of possible resonance forms it is suggested that these molecules might be planar, as compared to the phosphorus trihalides which are pyramidal. . (1) G. S. Forbes and H. H. Anderson, J. A.C. S.,. 62, 761 (1940). (2) H.H. Anderson, J.A.C.S., 64; 1757 (1942), (3) H. Gall and J. Schuppen, Ber, 63B, 482 (1950). 4 Light rare earth sulfates crystallize as ennea- hydrates, while heavy rare earth sulfates crystallize as — octahydrates, the change presumably because the heavy rare earth ilons cannot support the coordination number of twelve which is required for one half the metal ions in the ennea- hydrate structure (1). The other half of the metal ions in this structure have nine fold coordination. . It is suggested that the compound LaY(SO )5°9He O should be prepared if possible, and examined to see te the znetal ions are ordered between the two different crystallographic positions. (1) &. B. Hunt Jr., R. &. Rundle, and A. J. Stosick, Acta Cryste, 7%, 106 (1954). 5. PBre is) strongly colored in solution, and in 0.01 F solution in cel, only about one third dissociated. Because of the strong célor it might be suspected that there is a molecular compound of some sort rather than molecular PBr, It is suggested that this could be determined by finding 67 the position of the phosphorus K absorption edge in this solution. (1) Ae T. Popov and N. &. Skelly, J. A.C. S., 6, 5916 (1954) 6. It is suggested that the compound 1,2,5,6-cyclo- octatetraene should be prepared if possible. Tt would offer an interesting example for the study of pi bond interaction ~ in a non-conjugated’ system. It would have three more or less strain free isomers, d, 1, and meso which would differ by rotation around one or two” ‘double bonds and which therefore would be sepgrable isomers. Te It is suggested that the decouposition. ¢ of 1, 2-dilodo-~ ethane should be studied by the shock tube method. “This reaction has been studied at low temperatures (1) and the high temperature results would provide knowledge of 4 unimolechlar reaction over a large temperature range. (1) L. B. Arnold and G. B. Kistiakowsky, J. Chem. PhYS«, 1, 166 (1933). 8. It has been shown by radioactive exchange studies that exchanges rapidly with equatopial Cl and slowly with apteat Cl in Pols (1). ' It is- suggested that the following exchange reactions be studied, Fo-PF,, Clo-PF2Clo, Bg FEstt in the same manner, (1) 3.3. Downs Bnd R. E. Jofinson, *AG.S., 77, 2008 (1955). 9. It is suggested that benzene hexacarboxylic acid (mellitte acid) is a compound which might be completely intramolecularly hydrogen bonded, and that these might be symmetric hydrogen bonds. Crystal structure studies by x-ray and neutron diffraction should be made to determine whether this is so. 10. The arguments of Perros et al. (1) that PrF, should be stable are incorrect. A correct argument says that the free energy of the reaction PrF5(,) + 2F2(¢) > PYF ate) equals - ad 24 keal/mole. All attempts to fluorinate PrP, have been unsuccessful, but it is suggested that it might be possible to make +4 Pr in a fluoride by fluorinating solid solutions of PrFs in COP a. : (1) T° P. Perfos, T. R. Munson, and C. R. Naeser, J. Chem Bduc.e, 30, 402 (1953).