摘要:

DISCUSSIONS OF THE FARADAY SOCIETY No. 17, 1954 THE STUDY OF FAST REACTIONS THE FARADAY SOCIETY Agents for the Society’s Publications : The Aberdeen University Press Ltd. 6 Upper Kirkgate AberdeenThe Faraday Society reserves the copyright of all Communications published in the " Discussions '' PUBLISHED . . 1954 PRINTED IN GREAT BRITAIN AT THE UNIVERSITY PRESS ABERDEENA GENERAL DISCUSSION ON THE STUDY OF FAST REACTIONS A GENERAL DISCUSSION on The Study of Fast Reactions was held in the Depart- ment of Chemistry, Birmingham University (by kind permission of the Vice- Chancellor) on the 7th, 8th and 9th April, 1954. The President, Prof. R. G. W. Norrish, Sc.D., F.R.I.C., F.R.S., was in the Chair and about 250 members and visitors were present. Among the distinguished overseas members and visitors welcomed by the President were the following :- Mr.J. Adam (Brussels), Dr. and Mrs. E. J. Arlman (Amsterdam), Mr. T. Bak (Copcnhagen), Prof. E. Barany (Uppsala), Prof. S. H. Bauer (Cornell University), Dr. S. A. Bernhard (U.S.A.), Dr. Britton Chance (University of Pennsylvania), Prof. N. Davidson (California Institute of Technology), Prof. P. Delahay (Louisiana State University), Dr. and Mrs. M. Eigen (Gottingen), Dr. F. Hageman (Amsterdam), Prof. H. S. Johnston (Stanford University), Dr. Y . Haven (Eindhoven), Dr. T. Iredale (Australia), Dr. C. Jouwersma (Eindhoven), Prof. W. Jost (Darmstadt), Dr. F. Kaufman (U.S.A.), Prof. G. B. Kistiakowsky (Harvard University), Prof. I. M. Kolthoff (Uni- versity of Minnesota), Dr. G. F.Lanzl (Wilmington, Del.), Dr. J. E. LuValle (Arlington, Mass.), Dr. R. A. Ogg (Stanford University), Dr. R. G. Pearson (Northwestern University), Dr. D. C. Pepper (Dublin), Dr. G. Salomon (The Hague), Dr. M. Sangster (Amsterdam), Dr. R. Schlogl (Gottingen), Dr. K. E. Schulcr (The Johns Hopkins University), Dr. J. J. van Deemter (Amsterdam), Prof. T. Vermeulen (University of California) and Dr. Voetelink (Oklahoma). 3A GENERAL DISCUSSION ON THE STUDY OF FAST REACTIONS A GENERAL DISCUSSION on The Study of Fast Reactions was held in the Depart- ment of Chemistry, Birmingham University (by kind permission of the Vice- Chancellor) on the 7th, 8th and 9th April, 1954. The President, Prof. R. G. W. Norrish, Sc.D., F.R.I.C., F.R.S., was in the Chair and about 250 members and visitors were present.Among the distinguished overseas members and visitors welcomed by the President were the following :- Mr. J. Adam (Brussels), Dr. and Mrs. E. J. Arlman (Amsterdam), Mr. T. Bak (Copcnhagen), Prof. E. Barany (Uppsala), Prof. S. H. Bauer (Cornell University), Dr. S. A. Bernhard (U.S.A.), Dr. Britton Chance (University of Pennsylvania), Prof. N. Davidson (California Institute of Technology), Prof. P. Delahay (Louisiana State University), Dr. and Mrs. M. Eigen (Gottingen), Dr. F. Hageman (Amsterdam), Prof. H. S. Johnston (Stanford University), Dr. Y . Haven (Eindhoven), Dr. T. Iredale (Australia), Dr. C. Jouwersma (Eindhoven), Prof. W. Jost (Darmstadt), Dr. F. Kaufman (U.S.A.), Prof. G. B. Kistiakowsky (Harvard University), Prof. I. M.Kolthoff (Uni- versity of Minnesota), Dr. G. F. Lanzl (Wilmington, Del.), Dr. J. E. LuValle (Arlington, Mass.), Dr. R. A. Ogg (Stanford University), Dr. R. G. Pearson (Northwestern University), Dr. D. C. Pepper (Dublin), Dr. G. Salomon (The Hague), Dr. M. Sangster (Amsterdam), Dr. R. Schlogl (Gottingen), Dr. K. E. Schulcr (The Johns Hopkins University), Dr. J. J. van Deemter (Amsterdam), Prof. T. Vermeulen (University of California) and Dr. Voetelink (Oklahoma). 3CONTENTS A. GAS REACTIONS- Introductory Paper. By H. W. Melville . Photoelectric Methods for following Fast Gas-Phase Reactions. By Harold S. Johnston . A Thermal Method of Investigating Fast Gas-Phase Reactions. Part I. -The Mercury Photo-sensitized Decomposition of Ethylene. By A. B. Callear and James C .Robb . The Temperature Pattern Method in the Study of Fast Chemical Reactions. By David Garvin, Vincent P. Guinn and G. B. Kistiakowsky . The Application of Flash Techniques to the Study of Fast Reactions. By R. G. W. Norrish and G. Porter . Reactions of Atomic Oxygen with Molecular Oxygen. By Richard A. Ogg, Jr. and William T. Sutphen . A Mechanical Method for the Activation of Fast Reactions. By T. H. Bull and P. B. Moon . Shock Waves in Chemical Kinetics. The Rate of Dissociation of Molecular Iodine. By Doyle Britton, Norman Davidson and Garry Schott . Relaxation Techniques for Fast Reactions. A Study of the Dis- sociation of Nitrogen Tetroxide. By S. H. Bauer and M. R. Gustavson . GENERAL DrscussroN.-Dr. H. 0. Pritchard, Mr. R. G. Sowden, Dr. A. F.Trotman-Dickenson, Prof. S. H. Bauer, Prof. G. B. Kistiakowsky, Mr. A. R. Callear, Dr. J. C. Robb, Mr. C. R. Patrick, Dr. R. A. Ogg, Jr., Dr. A. D. Walsh, Dr. G. Porter, Dr. N. Davidson, Mr. R. R. Baldwin, Prof. A. R. Ubbelohde, Dr. A. J. B. Robertson, Dr. R. A. Ogg, Dr. J. Weiss, Mr. M. W. Windsor, Mr. J. Dewing, Dr. K. E. Russell, Dr. D. Britton, Mr. G. Boocock, Dr. J. J. Long, Dr. K. W. Sykes, Miss Christie, Prof. R. W. G. Norrish, Dr. K. G. Dcnbigh, Dr. G. Salomon, Dr. Y . Haven, Dr. M. Eigcn, Mr. M. Sangster, Dr. James E. LuValle . B. SOLUTION REACTIONS- Introductory Paper. By R. P. Bell . PAGE 9 14 21 32 40 47 54 58 69 90 114 Rapid Rcactions in Biology. By*F. J. W. Roughton . . 116 56 CONTENTS PAC+$ Regeneration and Recirculation of Reactants in the Rapid-Flow Apparatus.Part 1.-Design Criteria. By Britton Chancc . . 120 Part 2.-Practical Designs. By Britton Chancc and Victor Legallais 123 The Application of Photoelectric Spectrophotometry to thc Constant Flow Method. By K. DaIziel . . 128 A Semi-Automatic Apparatus for the Photometric Measurement of the Rates of Fast Reactions. By E. F. Caldin and F. W. Trowse. 133 Stopped-Flow Apparatus for the Study of Rapid Reactions. By Q. H. Gibson . . 137 A Quenching Method for Studying Rapid Reactions. By B. R. W. Pinsent . . 140 The Measurement of the Rate of Rapid Reactions by a Thermal Method. By L. Pearson, B. R. W. Pinsent and F. W. Roughton . 141 The Capacity Flow Method in Chemical Kinetics. By K. G. Denbigh and F. M. Page . . 145 Developments in the Thermal Maximum Method for Reaction Veloci- By R.P. Bell, V. Gold, J. Hilton and M. H. Rand ties in Solution. 151 Applicability of Megacycle Frequency Oscillator Circuits to Reaction Rate Measurement. By Philip J. Elving . . 156 The Use of Rotating and Stationary Electrodes for Fast Reactions. By I. M. Kolthoff and W. L. Reynolds . . 167 A Photoelectric Rccording Interferometer. By G. M. Burnett, P. J. Deas and H. W. Melville . . 173 Studies of thc Triplet State in Fluid Solvents. By George Portcr and Maurice W. Windsor . . 178 Rates of Ion Recombination in Solution by a Radio-Frequency Dis- persion Method. By Ralph G. Pearson . . 187 Methods for Investigation of Tonic Reactions in Aqueous Solutions with Half Times as short as 10-9 sec. Application to Neutralization and Hydrolysis Reactions. By M. Eigen . . 194 Applications of Voltammetry at Constant Current in Chemical Kinetics. By Paul Delahay . . 205 Study of Ultrarapid Reactions in Nuclear Magnetic Resonance Spectra. By Richard A. Ogg, Jr. . . 215CONTENTS 7 PAGE GENERAL DIscussIoN.-Dr. F. W. Trowse, Prof. F. J. W. Roughton, Dr. H. Gutfreund, Mr. R. P. Bell, Dr. James E. LuValle, Dr. R. G. Pearson, Dr. Y. Haven, Dr. Britton Chance, Dr. K. G. Denbigh, Mr. F. M. Page, Mr. F. Goodridge, Prof. S. H. Bauer, Dr. V. Gold, Dr. N. Uri, Prof. I. M. Kolthoff, Dr. G. Porter, Dr. F. J. Wright, Dr. J. Weiss, Prof. P. Delahay, Dr. G. Salomon, Dr. M. Eigen, Dr. R. A. Ogg, Jr. . . 220 Author Index . . 234 Reviews of Books . . 235

ISSN:0366-9033    

DOI:10.1039/DF9541700001

出版商:RSC    

年代:1954

数据来源: RSC

摘要:

A. GAS REACTIONS XNTRODUCTORY PAPER BY H. W. MELVILLE In this Discussion on fast reactions it has been convenient to divide the proceedings into two parts, namely, one dealing with gas-phase reactions, and the other with reactions in the liquid phase. In some cases the basic methods of approach are similar in principle but there are considerable differences which soon define the development of methods according to whether the gas or liquid phase is being studied. For example, diffusion coefficients in the gas phase at 1 atm are a thousand times greater than those in the liquid phase, and hence diffusion processes are not so likely to control reactivity in the gas phase. Again, three- body collisions are much rarer in the gas phase and their frequency is under control simply by changing the total pressure, whereas in the liquid phase it is difficult to say whether or not three-body processes come into operation in certain types of bimolecular reactions.Similarly, the kinetic theory of gases can provide immense help in calculating frequencies of collisions and distribution of energy along the molecules in gaseous systems, whereas in the liquid phase the kinetic theory of gases is virtually applied to a system which does not approximate to a dilute gas and may in some cases approximate to a solid. Since the discussion on the gas phase is not concerned with ionic processes, the entities to be considered are normal and excited molecules, atoms, and radicals of all energy contents. In studying fast reactions there are perhaps two general lines of approach which determine the nature of the method to be used.Some reactants when brought together react directly without requiring appreciable activation energy, and hence the dynamics of the reaction can only be studied by inventing rapid methods for following the extent of conversion in short intcrvals of time. In the second type, reactions occur at what might be called normal rates (excepting explosions, for the moment) but active intermediaries-atoms or radicals-control the speed even though their concentration is minute. The reactions of these intermediates with molecules and with themselves are fast and it is therefore necessary that the chemistry of the reaction must be elucidated and the velocity coefficients of the relevant processes measured accurately. In a general way these two classes divide themselves naturally into non-chain and chain types, though there may be intermediate types so that the discrimination should not be too precisely defined.NON-CHAIN PROCESSES Such processes may be followed statically or dynamically, but there is an intermediate technique-the stopped-flow technique. In the static method there are two difficult problems to be solved. The first is to initiate reaction, either by mixing and admission of the gases to the reaction vessel or alternatively by sufficiently rapid heating of the mixture to the reaction temperature in the vessel itself. The speed of mixing in a vessel of reasonable dimensions put a very definite limit to thc minimum half-life that can be measured in this way, though of course this can be considerably cut down by working at low enough pressures. Similarly, the raising of a mass of gas to reaction temperature imposes a limit (probably of a second) if the conventional method of admitting the gas to the heated reaction vessel is used.Fortunately this latter difficulty can now be 910 INTRODUCTION overcome to some extent by momentary heating of the gas by a shock wave produced by apparatus easily capable of being attached to a normal reaction system. The time of heating can bc cut down to a figure as low as a few micro- seconds, so there is ample time to follow the chemical events that succeed the passage of the shock wave. Another method of shock heating may be achieved by the use of flash methods provided that the radiation is used simply to heat the system by the degradation of absorbed electronic energy and not at all by photolytic action.Provided the above-mentioned conditions are fulfilled the second major problem is to follow the extent of chemical change down to time intervals as low as 10-5 sec. Spectrophotometric methods would appear to be most suitable using radiation in the visible and ultra-violet. These are to a large extent facilitated by the use of photomultiplier cells in conjunction with amplifiers and suitable recorders, when high sensitivity and high speed of response may be achieved. The limitation here is probably in sensitivity since not all systems, especially the simpler ones, absorb strongly or selectively enough in the ultra-violet to make the method uni- versally useful. This is due to the fact that simple molecules naturally absorb at wavelengths about 2000A and less, and therefore the multiplier cells in the reaction systems are insensitive to variations in the extinction coefficients at these short Wavelengths.At present, therefore, it would appear that the chemical system has to fit the photometric devices in order that these reactions can be followed. The more highly selective infra-red absorption method is unfortunately limited partly by the speed of response of detectors and the limits of sensitivity of fast- recording detectors such as photoconductive cells. Current improvements in detectors, especially with a view to extending their wavelength range, may bring the infra-red method more into use, but the most useful range of infra-red spectrum is out of reach at present with really fast recording detector systems.Of the remainder of other physical methods that might be employed, it is usually not difficult to convert the physical change into an electrical change of current or voltage which may be amplified and displayed, in times required for fast reactions. The real difficulty is the non-selective character of most methods, though if the chemistry is simple enough this may not be a serious disadvantage provided a change of temperature does not introduce additional complications. Gas-phase interferometry, for example, would appear to provide sufficient sensitivity but in fact even with long tubes of lOOcm, the change in the position of interference fringes is disappointingly small when chemical change occurs.It makes it very difficult, therefore, to apply this attractive technique even though the problem of recording the movement of interference fringes is one that can be solved by photo- electric and photographic means. Manometric methods so useful in many gas- phase reactions suffer as yet from lack of sensitivity and speed of response. For example, if the goal were sensitivity to lO-5mm in a time of lO-3sec, there is yet to be designed a manometer that would meet both these rather stringent requirements. With flow systems, matters are in some respects simpler. It is easy to achieve flow rates of 102 cmlsec and above and hence resolution so far as the time element is concerned is not too difficult.The real problem is to measure the extent of chemical change in different parts of the flow system, either by sampling and im- mediate quenching of the system or by observing the concentration of reactants or products along the line of flow. One of the most accurate general methods consists in allowing one gas to diffuse into another in a flow system as is done in the reaction between sodium atoms and halogen compounds. Determination of the spatial distribution of sodium atoms by fluorescence or by absorption of D radiation provides along with flow data and diffusion coefficients the necessary information. But this is a highly specialized and limited techniquc and it is of interest to find that Kistiakowsky and his co-workers have made the approach more general by measuring the extent of an exothermic reaction in differentH .W . MELVILLE 11 parts of such a system, in this case between boron trifluoride and amines, by means of a minute exploring thermocouple which indicates the point-to-poin t variation of temperature in the flowing gases. Since the reaction concerns only molecules, and since it is likely that the junction comes into thermal equilibrium with the gases, the method should give reliable results in these particular cases. For flow systems involving atoms or radicals considerable complications arise. Precise knowledge about the effectiveness with which atoms and radicals affect the temperature of the detecting element, apart altogether from the general rise in the temperature of the system as a whole, must be forthcoming.There is, therefore, a great need for physical analytical methods that would permit of an exploration of concentration either of products or reactants in this type of inter- diffusing flow sys tem. Many of the virtues of both static and flow methods may be combined in the so-called stopped-flow technique in which flow is suddenly arrested in a selected part of the apparatus after mixing has occurred and the change in concentration followed by suitable detecting devices both sensitive in extent of reaction and in time. REACTIONS INVOLVING ATOMS AND RADICALS These reactions probably form the largest class of gas-phase reactions and there is no doubt that all gaseous oxidations whether slow or explosive, thermal and photochemical decomposition of organic molecules at elevated temperatures, addition polymerization, reactions of halogens with organic molecules and many others proceed through the intermediary of atoms and radicals (in subsequent discussion, radicals will include atoms).When this was suspected, much experi- mental work was concerned with studying individual radical molecule interactions, usually in a flow system, in order to measure velocity coefficients of such reactions to get some idea of their kinetics. It is no easy task to generate radicals at a known concentration, to mix them with the chosen molecules and then to measure the concentration of radicals or products along the reaction tube. Much of the earlier work was concerned with atomic hydrogen, oxygen, methyl and other simple alkyl radicals but the above-mentioned measurements could not be made with sufficient precision to get accurate values of velocity coefficients and complete knowledge about the chemistry of these radical-radical reactions.There is now, however, another approach to this kind of problem. The ordinary flow method consists essentially of a source of radicals and a sink, usually a liquid-air trap, separated by a space into which molecules may be injected. The same state of affairs may be set up in a static system in which transport of radicals occurs by diffusion. To simplify the system it is convenient to arrange for one-dimensional diffusion by constructing the reaction vessel in the form of a flat box with the distance between the sides small compared with the other two dimensions. The source of radicals must then be the photodecomposition of molecules and the sink a layer of molybdenum of tungsten oxide.From extinction coefficients and the geometry of the system the distribution of radicals may be calculated. On introducing suitable molecules the radical concentration is altered and by suitable analytical devices the number of molecules changed may be calculated and therefore the absolute velocity coefficients of the radical-molecule reactions computed. The resulting radicals are also absorbed by the oxide and the system is therefore a particularly simple one as far as the chemistry is concerned. A more direct approach consists in exploring the spatial distribution of radical concentrations in such a one-dimensional system, but it is not easy to devise a probe that is only affected by radicals and unaffected by any thermal effects that may occur as a result of reaction.In the complex reactions mentioned above, the investigation of the fast reactions occurring between the radicals and molecules simply reduces to a problem of determining the radical concentration and the rate of accumulation of products12 INTRODUCTION in the system. Therefore, if two or more radicals are concerned in the process, the only disadvantage is that that step which is rate-controlling and involving radicals can be investigated by thc methods existing at present. It is feasibl:: to arrange the kinetics of the reaction so that the different types of rate-determining step may be brought into operation and therefore it is possible to get a more detailed picture of all the types of radical reactions that occur in such systems.Un- fortunately these radical concentrations are usually so low that the concentrations cannot be directly measured except in one particular case. When the reaction can be initiated photochemically by the flash technique, the radical concentration becomes so high that not only can the concentration of a variety of radicals be detcrmined simultaneously by flash spectrophotometry, but the variation of the concentration with time may be displayed by suitable recording devices. In order that this technique may be applied, it is essential that the radical concentra- tion should be an appreciable fraction of the total molecule concentration. Another generalized method of approach consists in extracting from the reaction system a sample of all the entities present and directing them into the ionization chamber of a mass spectrometer where the presence of radicals can often be detected and their nature determined by the fact that the ionization potentials of radicals are rather smaller than that of the molecules from which they are derived.While this is an attractive and direct technique, the difficulty is to design reaction systems in the more complicated reactions which would be capable of projecting into an ionization chamber a representative sample of the entities present at any point in the reaction volume. In more normal reactions radical concentrations may be a million-fold less than the molecule concentration and therefore the spectroscopic, and even the mass spectroscopic method, becomes inapplicable.In addition the lower con- centration of radicals alters the character of the overall reaction. The only method, therefore, is an indirect one. In order to compute the radical concentration it is necessary to know the rate of production and rate of removal. Rate of production may often be calculated from the thermal or photochemical decomposition of molecules. Rate of removal can only be measured in photochemical reactions. In these cases when the radicals disappear two at a time, the sector method can be used effectively, but unfortunately the kinetics of the majority of gas-phase radical processes seem to indicate that radicals usually disappear by first-order process such as wall combination, and the sector technique is therefore useless.An alternative method, which has been successfully applied to liquid-phase re- actions consists in following the non-steady state of these reactions either at the beginning or at the end of the reaction when the source of radical production is suddenly cut off, as, for example, in the photochcmical reaction. These methods are applicable to first- and second-order of removal of radicals. Essential features of the method are high sensitivity to reaction and sufficient resolving power in time. In the liquid phase, high time resolution is not always required, but in the gas phase a much higher resolving power will probably be necessary. So far these methods have not been applied to gas-phase reactions for the simple reason that the physical conditions needed for the operation of the non-steady statc technique cannot easily be complied with.The study of the non-steady statc of gas-phase reactions with suitable techniques would resolve these problems and it is to be hoped that this method may eventually be applied so that a much more detailed understanding of gas-phase processes can be obtained in this way. The methods mentioned above are concerned with investigating the overall kinetics of various types of chemical reactions, but there is another general problem of great interest in gas kinetics, and that is the more detailed analysis of molecular dynamics, in order to investigate how the speed and activation of energy of molecules affects reactivity and problems of that kind. Some time ago, molec- ular beam techniques were applicd to problems of this kind and in this discussion there is a paper on the mechanical activation of molecules, with a view to gettingH . W. MELVILLE 13 some understanding of the more detailed mechanism of effective chemical collisions. There is still much to be done here though the development of suitable techniques is an obstacle of considerable magnitude to be overcome and results often are not sufficiently precise to give as much information as would be desired. But this is a field of enquiry which may extend owing to the development of highly specialized and sensitive techniques in other fields. With this tremendous wealth of methods of approach to all sorts of chemical reactions in course of active development, it is to be hoped that they will be exploited to the full and reveal new knowledge about the kinetics of gas-phase reactions which have hitherto been withheld owing to the limitations of the methods currently available.

ISSN:0366-9033    

DOI:10.1039/DF9541700009

出版商:RSC    

年代:1954

数据来源: RSC

摘要:

PHOTOELECTRIC lMETHODS FOR FOLLOWING FAST GAS-PHASE REACTIONS BY HAROLD S . JOHNSTON Department of Chemistry, Stanford University, Stanford, California Received 26th January, 1954 Several similar systems are described which, by photoelectric and oscilloscopic methods, directly follow fast gas-phase reactions over a wide range of pressure and temperature. The guiding principle behind the development of these methods was that reaction should be followed at constant temperature and at constant volume, so that results may be compared directly with those obtained by regular means. The fact that a reaction is fast makes difficult the requirement of constant temperature for gases. For this and other reasons, rates’ successfully measured by these methods have had half-lives no shorter than 0.1 sec and usually from 0.1 to 1 or more sec.Oxides of nitrogen, ozone, and fluorine are typical of the substances whose rates have been followed by these methods. Fast gas-phase reactions are interesting in providing extreme cases for testing theories of reaction rates against experiment. For unimolecular reactions it is of great interest to study the effect of foreign gas pressure on the first-order rate constant from the high-pressure limit to the low-pressure limit. Since this takes a range of 105 or 106 in total pressure and since there is a range of 103 or more in the rate constant at one temperature, one needs a fast reaction method at high pressures in order not to have to wait unduly for the reaction to go at low pressures. With these purposes behind our studies, we have attempted to retain conditions such that results can be compared directly with rates measured by regular, slower means, that is, the reaction must be carried out at constant temperature and constant volume. For the sake of studying unimolecular reactions we have been interested in measuring rates over wide ranges of pressure and temperature.In the study of fast gas-phase reactions at constant volume and constant tem- perature, there are two easily differentiated tasks. First, one must rapidly prepare the reaction system, that is, bring up (or down) to temperature, mix, and isolate the reactants. Secondly, one needs a fast sensitive method of following the reaction after the system is prepared. The first task requires a different treatment for different pressure regions, and several systems will be described later.The second task is easily solved by a light absorption method which is essentially the same for each kinetic system, and it will be described first. A PHOTOELECTRIC METHOD FOR FOLLOWING REACTANT OR PRODUCT A schematic diagram of the photoelectric method is given in fig. 1. A light source suitably filtered and chopped, is focused through a reaction tube or bulb on to an electron- multiplying photoelectric tube (RCA 931A, 1P22, or 1P28). The output of the photo- electric tube is put across the vertical deflection plate of an oscilloscope (Dumont 208, 247, 304 or 322). The oscilloscope is set to give a single sweep, and the beam is focused off the screen. The operator opens the shutter of a camera (35 mm or 5 by 7 in view camera) focused on the oscilloscope screen, and at the same time he makes an action which simultaneously prepares the reaction mixture and initiates a single sweep of the oscilloscope.This action is to close or open a stopcock of some sort (stainless steel plunger, coupled stainless steel needle valves, 4- or 6-way glass stopcock) and to make an electrical contact in the sweep circuit of the oscilloscope. The camera records the path of the beam as it moves once across the screen, the vertical amplitude giving the 14HAROLD S. JOHNSTON 15 concentration of some reactant or product and interruption of the beam by the rotating sector giving a time scale along the horizontal axis. The procedure is carried out on an evacuated cell to give an incident-light intensity (corrections must be applied for non- linearity of the oscilloscope screen), and the cell is calibrated by measuring light intensity when it is filled with a known pressure of a given substance.The important characteristic of a light source for this method is that it does not vary in intensity at a rate comparable to the chopping rate, 0.01 to 1 sec usually. A slow C I I ~ H O D E UAY OSCILLOSCOPE S\R'CI- ,,UP',13 HrACl10N MOTOR AND LlGKi CELL BULB CHOPPER fly& GLASS FIUERS OR QUARTZ YONOCHROMATOR ! CAMERA t 1 JF I"" INITIATES I"". BY OPERAT'JR FOR TIME EXPOSURE ACTION -------9 - FIG. 1.-Schematic diagram of optical system for recording rate of fast reaction. steady drift over a long period of time is much less serious than short-term fluctuations. At present we prefer a tungsten bulb operated from a large storage battery for visible light, and for ultra-violet radiation the hydrogen arc or mercury arc used with the Beckman DU spectrophotometer.We have always used photomultiplier tubes because they are both very fast in response and sensitive to small signals. The sensitivity is important in reducing the danger of photo-chemical action by the measuring light. If the half-life is as long as 3 sec, the output of the phototube is sent to a fast-responding electronic voltmeter, and readings are taken visually with the services of two operators when necessary. The Voltmeter has much better resolution and linearity than the oscilloscope, and when it can be used it is preferred.This general system has been used by us for several different reactions, and the components differed from one study to another. Table 1 gives a summary of the various components used and references. TABLE COMPONENTS OF OPTICAL SYSTEM USED FOR DIFFERENT REACTIONS light source filter substance followed reaction ref. 120 V d.c. glass NO2 from tungsten 4300 to 4700A 2N02 + 0 3 = N205 -t 0 2 2 tungsten 3389 and 51 13 4100 to 4600 A 2N02Cl= 2N02 + Cl2 4 AH4 mercury Corning NO2 at 4358 8, NO + N205 = 3N02 5 6 V d.c. Corning : NO2 from 2HN03 = 2N02 + H20 + 4 0 2 3 arc 3389 add 5113 2N0 + 0 2 = 2N02 6 7 8 9 2N02C1= 2N02 + Cl2 10 low-pressure chemical 0 3 at 2537 A NO + 0 3 = NO2 3- 0 2 11 mercury arc solutions hydrogen arc Beckman quartz HNO3 at 2HN03 = 2NO2 + H20 + Q02 3 monochromator 2100 A N204 at N2O4 = 2N02 12 2100 A N2O5 = 2N02 + 4-02 2N02 + F2 = 2N02F N02Cl+ NO = NO2 + NOCl REACTION CELLS WHICH TRAP A SAMPLE OF FLOWING GAS.-FlOWing gases may be rapidly mixed in a Hartridge and Roughton 1 type mixing chanber.For the liquid phase one can measure the rate of a fast reaction from the steady-state structure of a continuously flowing system. For gas-phase reactions the pressure drop due to flow, the mole number change (if any) due to the reaction, and the thermal effects due to the heat of reaction make it difficult to follow reactions in this way and to have the results strictly comparable to the conditions of constant volume and constant temperature. However, if a sample16 PHOTOELECTRIC METHODS of mixed, but not completely reacted, gases is isolated in a fixed volume and if the subse- quent changes with time are followed, one gets away from some of the difficulties inherent in the flow method.If a positive closure is made on both sides of a reaction cell, the condition of constant volume is easily met. If both reactants are pre-heated (or pre-cooled) before mixing, uncertainties in temperature are reduced. If the reaction is highly exothermic, the reactants must be diluted with a great excess of inert gas in order to main- tain constant temperature. If the reaction is a decomposition at high temperature, it may be rapidly and sharply brought up to temperature by mixing with a great excess of pre-heated inert gas. An example of this type of system, suitable for use from 50 to 800 mm, is shown in fig.2. The two reactants and the diluent gas are stored in 3-1. flasks, and their partial I2 LITER VACUUM RESERVOIR FIG. 2.-Reaction system for intermediate pressures and near room temperature. pressures are known by synthesis. TO carry out a run, one evacuates the reservoir, re- action cell, through the second 4-way stopcock up to the first 4-way stopcock. A reading of lo, the initial light intensity, is taken. Then the first 4-way stopcock is opened, and the reactants flow through the heating coils, mixing chamber, reaction cell, and the constricting capillary into the vacuum reservoir. After 2 or 3 sec of such flow, during which a steady state is attained, stopcock 2 is rapidly closed, and this makes an electrical contact leading to a single sweep of the oscilloscope and a recording of a run, The total pressure in the 3-1.flasks is read before and after each run. The pressure drop due to flow from the storage bulbs to the reaction cell must be calibrated ; by use of large-bore stopcocks this pressure drop can be held to 1 % or less. If one channel of the second STEEL SLIPRIFJ G, GLASS ,,GOLD SOLDER STAINLESS STEEL FIG. 3.-Reaction cell for high pressures, temperatures up to 180" C. 4-way stopcock cuts off slightly before the other, it is essential that the first line to close be on the exit side, otherwise serious error can arise from partial evacuation of the reaction cell during the closing of the stopcock. The reaction cell of a high pressure apparatus is shown in fig. 3. The body is nickel, the windows are glass fused to a Covar rim (specially made by Stupakopf Ceramic Co., Latrobe, Pennsylvania), and the Covar rim is clamped tightly against a gold gasket.The windows are coated with magnesium fluoride for protection against fluorine. Teflon- packed needle-valves of nickel or stainless steel are used. Up to this time, this system has been used only up to 180" C ; in the past we have had highly unsatisfactory service from such systems when made of stainless steel and used at 400" C . At 200" C nickel seems to be far superior to stainless steel for the handling of corrosive substances.HAROLD S . JOHNSTON 17 Temperature uniformity in these systems is attained by enclosing them in massive castings of aluminium. Various modifications of this system have been made for different reactions, and different combinations of components are listed in table 2.The system which can measure the shortest half-life is that using a very short cell and a steel plunger as a stop-gate. Wayne and Yost 13 measured half-lives as low as 0.01 sec by this method. The system using the steel plunger gives results with a rather high experimental error, and the other systems with longer light paths, leak-proof stopcocks, and reduced trouble from vibra- tions give more precise results. By virtue of the longer light path these systems can measure an equally large second-order rate constant as the plunger device, even though it follows a longer half-life in doing so. TABLE 2.-cOMPONENTS OF FLOW SYSTEM USED FOR VARIOUS REACTIONS reaction cells ref. cut-off device total dimensions mm -- reaction carrier pressure mm material gas dilasr$.length body window NO + N2O5 I NO2Cl (decomp.) HNO3 (decomp .) N02Clf NO 0 2 760 N2 200to 700 {arious 50 to 700 7000 40,000 N2 2000 to N2 1000 to Nz 760 N2 300-700 2 37 glass glass st. st. plunger 2 8 100 st. st. quartz coupledneedle 1 1 8 105 glass glass 4-way stopcock 15 valves 10 100 st. st. glass coupledneedle 15 20 100 nickel glass- needle valves 4 Covar rim 20 48 glass quartz 6-way stopcock 3 valves 8 100 quartz quartz 4-way stopcock 9 BIG BULB METHOD OF STUDYING FAST REACTIONS A separate, though prior, development of a photoelectric method for following fast gas-phase reactions was carried out by Smith and Daniels,*4 who initiated reaction by shooting reactants into a 3-1. bulb or into cylinders of different sizes.Big bulbs have a great advantage in that surface effects are minimized, and they are ideal for studying reactions at low pressure. In the systems we have used, a half-life of 1 sec is about the fastest rate which can be followed. However, the long light path available in the large bulbs makes it possible to measure second-order rate constants almost as big as those found by the flow method. One example of a big bulb reaction system will be described in detail. It is based on a 144-1. Vycor bulb (Vycor is the trade name of the special Corning glass which is 96 % silica; it is made over a period of several months by leaching out substances other than silica after the glass is formed, and then it is heat-treated again).In the autumn of 1950 we asked Corning Glass Works if they could make a Vycor flask 22-1. or larger. For moxe than a year they tried and repeatedly failed to make a 33-1. bulb. Finally they tried the next smaller size utilizing standard moulds, and after 6 months’ of work and one failure, they completed and delivered a 144-1. Vycor flask equipped with outlet tube 1 cm in internal diameter and with a graded seal to Pyrex. The entire reaction system is shown in fig. 4. The flask is enclosed in two close-fitting silver hemispheres of 0.040 in. thickness, and this is wrapped with asbestos. This unit sits in sand inside a welded aluminium can 1 ft. 3 in. diameter, 1 ft. 3 in. high, & in. wall thickness ; the metal is 2 S alloy, that is, virtually pure aluminium.The can is wrapped with asbestos and wound closely and uniformly on all sides with a 14-ohm Chrome1 A heating coil, controlled by a Powerstat variable tiansfoxmer operated from 208-V, 60-cycle a.c. supplied by a Stabiline Electro- mechanical Voltage Regulator (Superior Electric Co., Bristol, Conn.) The can is placed on fire bricks inside an outer welded aluminium can 2 ft. 4 in. high, 2 ft. 4 in. diameter, and fi in. wall thickness. The space between the inner and outer cans is filled with 6in. of Santocel-A insulation (Monsanto Chemical Co., Merrimac Division, Boston,18 PHOTOELECTRIC METHODS Mass.). The Vycor bulb could be taken up to 800" C, but the present system is limited by the melting point of aluminium and we have not gone above 625" C.Temperature is measured by one Pt-Ir thermocouple and four chromel-alumel thermocouples. The e.m.f. is read on a Leeds and Northrup type K potentiometer. At 600" C temperature varies IF from point to point over the silver shell and at any one point it drifts 4" from time to time depending on room temperature. Lengths of quartz tubing lead through lin. holes in the side of the cans, ending with quartz windows inside the inner can. Holes are provided on the silver shell for the light beams. Two of these light paths are arranged at right-angles to each other, so that it is possible to follow the reaction by two different wavelengths at once. The Vycor flask mounted in this way transmits ultra-violet radiation above 2350 A. The Pyrex system of gas pipettes a and b in fig.4, Bourdon gauge, storage bulb d, and vacuum lines are all of the usual sort. The optical system differs from the general one described above only in that it has a second phototube which measures the incident light. The output of the two beams is presented at once on the Dumont 322 dual-beam oscilloscope. n MERCURY MANOME T€R DRY AIR VACUUM LIGHT L-- IMSULATlOk i l__ll__-_l_- PHOT~TUEE FIG. 4.-Reaction system for low pressures, temperature up to 600" C. a and b, calibrated gas pipettes ; c, 14h-1. Vycor flask ; d, storage bulb ; 1-7, high vacuum stopcocks greased with polychloro-trifluoro ethylene ; 3, stopcock with 8-mm opening. A second example of the big bulb system will be mentioned briefly. It consists of a 50-1. Pyrex bulb with two quartz windows protruding 7 cm inside it.These windows are fused to a 12-mm quartz tube which connects through a graded seal to the body of the Pyrex flask. It was necessary to have these windows protrude inside the flask instead of outside in order not to have 14 cm of optical path through the reaction mixture with a very non-representative surface to volume ratio. This flask is transparent to radiation above 2000 A. It is mounted inside two large concentric steel cans with 5 in. of Santocel-A insulation between them. Heating wires are uniformly spaced inside the inner can and control is obtained by a second small on-and-off heater at the bottom. The air is vigorously stirred by a large blower mounted inside the inner can and connected by a long shaft to a motor outside. The top of this furnace is removable and replaceable by a large copper can which can be filled with a coolant.This system has been operated from Several other big bulb systems have been used, some successfully and some un- successfully. A 2-1. Vycor bulb is set up very much the same as the 144-1. bulb, except it has only one light path. A 22-1. reaction bulb and its pipette system has been described eIsewhere.5 A 34-1. stainless steel bulb was rejected as useless after it was found that it could not be protected against fluorine at moderately high temperatures, and that the fluorinated surface adsorbed nitrogen dioxide very strongly. A summary of rate studies of fast reactions which we have made by the big bulb method is given in table 3. The study of the decomposition of nitrogen tetroxide, mentioned in table 3, is very frag- mentary, representing so far only a couple of rate measurements at - 50" C and at 0.1 mm total pressure.- 50" C UP to 250" C.HAROLD S. JOHNSTON 19 TABLE 3.-D"ACTIONS STUDIED IN VARIOUS BIG BULBS useful temp. range reactions O C bulb material Pyrex 25 to 100 NO 3- NzOs NO + N02Cl 2N02 + F2 Pyrex with -50 to 250 NO2Cl (decomp.) N2O4 (decomp. at quartz windows - 50") Vycor 25 to 600 HNO3 (decomp.) Vycor 25 to 600 HNO3 (decomp.) volume of bulb, 1. 22 50 2 14.Q ref. 5 9 8 10 12 16 3 RATE OF MIXING, HEATING, AND ISOLATING REACTION MIXTURE If the integrated rate expression is known for a reaction, a suitable plot can be made against time such that extrapolation to zero gives the effective time of mixing and flowing into the cell.Plots of this sort have been published for nitrogen dioxide and ozone,2 delay time 0.03 sec, and for nitric oxide and ozone,ll 0-07 sec. The steady-state temper- ature of the reaction cell of the flow method has been measured by small thermocouples. Based on these studies we use 70 cm of 8 mm glass tubing for a pre-heat coil for each re- actant, and it appears that highly exothermic reactions in 8-mm tubes gives a temperature rise of only about + of that expected from adiabatic conditions. For the big bulbs a direct measure can be made between the time the stopcock starts to turn and the time for a stable gas, such as bromine, to reach a steady concentration inside the flask ; for the 14i-1. flask these times are 0.2 to 0.4 sec. The time for a gas IN THE PRESENCE OF 37 MM OF NITROGEN .I .2 .3 R .S .6 7 .8 .S 1 .0 1.1 I2 13 1.4 15 1.6 I7 IS 19 SECONDS FIG. 5.Time to flow in and heat up to 603" C. Straight line is plot of integrated rate expression for decomposition of nitrogen dioxide. to heat up in the big bulb can be estimated by measuring the initial rate constant for the well-known bimolecular decomposition of nitrogen dioxide.17 The apparent decrease in the rate of this reaction with increase in the pressure of inert gas is interpreted as a failure of the gas to reach the bulb temperature as fast as it flows in. Fig. 5 gives an example of a calibration of this sort in the 14i-1. flask, and it also indicates a time of about 0.2 sec for the gas to flow in. These calibrations are not completed, but it appears that 2 mm of nitrogen dioxide and 20 mm of argon reaches bulb temperature at 450' C as fast as it can flow in.Twice this amount of each gas appears to reach a temperature about 4" C too low upon flowing in, and the gas does not pick up the remaining few degrees in the 1 to 10 sec during which a fast reaction might be followed. This feature of a steady but incorrect temperature over the course of a reaction can be a serious and easily over- looked source of error. In using big bulbs for fast reactions one must take care to go to20 PHOTOELECTRIC METHODS low enough pressures or go to small enough bulbs so that serious temperature gradients are not set up because of the heat of reaction18 HANDLING CORROSIVE GASES Corrosive gases can be handled rapidly and conveniently by means of high-vacuum hollow-bore glass stopcocks greased with polychloro-trifluoro-ethylene stopcock grease.Though corrosive gases do not seem to react with this grease, the less volatile ones such as nitric acid and nitrogen dioxide arc quite noticeably soluble in it. Also the grease itself has a considerable vapour pressure. Some of these gases are best handled in a metal vacuum system with Teffon-packed needle valves, and junction to glass is made by Covar- to-glass graded seals. For certain cases it is desirable to protect the Covar with a film of polychloro-triff uoro-ethylene (Kel-F dispcrsion, The M. W. Kellogg Co., Jersey City, New Jersey). FUTURE WORK As these methods have been used by us in the past, the precision of the rate constants measured has varied from fair to poor.Some progress has been made recently in separating, identifying, and removing sources of error, and this pro- gramme is our principal goal so far as methods are concerned. As a summary of the work done so far on these methods and as a map for future extensions, a graphical outline is given in fig. 6 of the regions of pressure I I I I I I 1 FIG. 6.-Temperature and regions within which these have been used to study actions. pressure methods fast re- TEMPERATURE *C and temperature at which rate measurements or calibrations have been made. Rate studies under way at present make interesting the closing of the gap between 10 mm and 1 atm below 500" C. It seems that apparatus could readily be designed and built to fill in most of the area in fig. 6, perhaps excepting the upper right-hand corner.We know of no method to measure fast reactions at very high pressure and very high temperature. Another line of development under way at present is to modify the materials so that these methods can be used with fluorine and its compounds. It is a pleasure to acknowledge the contribution of Prof. Don M. Yost to the conception of these methods and this field of research. Especial thanks are expressed to Dr. Robert L. Mills who designed and built systems for all pressures, to Mr. Daniel Devor who designed and put together most of our recent apparatus for low pressures, and to all the co-workers who have used and improved on these systems. Much of this work could not have been done without the support of The M. W. Kellogg Co., Special Projects Department; the United States Office of Naval Research; and the Naval Ordnance Test Station, Inyokern. We are grateful to Corning Glass Works for the development of the big Vycor bulb, to the Reynolds Metal Co. for generous samples of aluminium, and to the Shell Oil Co. and American Cyanamid Co. for fellowships.HAROLD S. JOHNSTON 21 1 Hartridge and Roughton, Proc. Camb. Phil. Soc., 1926, 3, 450. 2 Johnston and Yost, J. Chem. Physics, 1949, 17, 386. 3 Johnston, Foering and Thompson, J. Physic. Chem., 1953, 57, 390. 4 Casalleto, work in progress. 5 Wilson and Johnston, J. Amer. Chem. Soc., 1953, 75, 5763; also 1953, 75, 1567; 6 Johnston and Slentz, J . Amer. Chem. SOC., 1951, 73, 2947. 7 Johnston and Tao, J. Amer. Chem. SOC., 1951, 73, 2948. 8 Perrine and Johnston, J. Chem. Physics, 1953, 21, 2202. 9 Freiling, Johnston and Ogg, J. Chem. Physics, 1952, 20, 327. 10 Cordes, work in progress. 11 Johnston and Crosby, J. Chem. Physics, 1951, 19, 799 ; 1954, to be published. 12 Herschbach, work in progress. 13 Wayne and Yost, J . Chem. Physics, 1951, 19, 41. 14 Smith and Daniels, J. Amer. Chem. Soc., 1947, 69, 1735. 15 Mills and Johnston, J. Arner. Chem. SOC., 1951, 73, 938. 16 White, Thesis (Stanford Univ., 1953). 17 Bodenstein and Ramstetter, 2. physik. Chem., 1922, 100, 106. 18 Benson, J. Chem. Physics, 1954, 22, 46. 1951,73,4782.

ISSN:0366-9033    

DOI:10.1039/DF9541700014

出版商:RSC    

年代:1954

数据来源: RSC

摘要:

HAROLD S . JOHNSTON 21 A THERMAL METHOD OF INVESTIGATING FAST GAS-PHASE REACTIONS PART I.-THE MERCURY PHOTO-SENSITIZED DECOMPOSITION OF ETHYLENE BY A. B. CALLEAR AND JAMES C. ROBB Dept. of Chemistry, The University, Birmingham, 15 Received 22nd December, 1953 This paper describes a method of measuring rates of chemical reactions in the gas phase which occur so quickly as to render inadequate any conventional experimental method based, for example, on pressure mcasuremcnts. The mercury photo-sensitized decomposition of ethylene has been investigated by this method and shown to occur by a mechanism somewhat simpler than that which has been previously proposed. INTRODUCTION The stationary temperature which a reacting gaseous system attains is obviously some measure of the rate of reaction.In photochemical reactions, this temperature is usually less than about 0.1" C above ambient, but it has proved possible to measure rapidly the steady temperature with a reasonably high precision. In a study of the mercury photo-sensitized decomposition of ethylene, investigation is complicated by the products of reaction, hydrogen and acetylene. The hydrogen produced quenches the excited mercury atoms, so forming hydrogen atoms which then hydrogenate the ethylene to ethane and butane. As will be seen later, pressure measurements, which can be made only by allowing a significant fraction of re- action to occur, may be ambiguous, especially at low pressures of ethylene. This thermal method allows measurements of rate of reaction to be made accurately when only an insignificant amount of reaction has taken place, thus removing the necessity for considering the secondary reactions of the products.The major features of the mercury photo-sensitized decomposition of ethylene are well established. (1) The overall process can be written C2& + Hg3P1 --f C2H2 + H2 + Hgl&22 THERMAL METHOD The rate of decomposition of ethylene decreases with increasing pressure (for a constant quantum input of 2537A radiation) and this has been attributed to the formation of an excited molecule C2H4* in the initial step, which can either decom- pose or be deactivated by suitable gas-phase collision. The complete reaction sequence would then be represented by (2) C2H4* -+ C2H2 + H2 (3) C2H4* + M +- C2H4 + M (4) C2H4 + Hg3P1 --f c2&* + HgWo Leroy and Steacie 1 concluded that for a constant quantum input, the dependence of rate of decomposition on total ethylene pressure is rate = A/(l + BP) where A and B are constants and P is the total pressure of ethylene. This leads to a bimolecular deactivation process.Darwent2 showed that the results of Leroy and Steacie were in better agreement with the relationship rate = A(l + BP2) (which would imply a three-body deactivation process) although in a subsequent publication3 he put forward a more complex mechanism involving a partial heterogeneous decomposition of the excited ethylene molecules. The main evidence for this suggestion is the variation of rate with mercury-vapour pressure. He found that lowering of the mercury-vapour pressure caused a decrease in the rate of reaction although the absorption of 2537A radiation was complete, and con- cluded that at the low mercury-vapour pressures, the excited ethylene molecules, produced farther from the vessel walls, had less chance of undergoing hetero- geneous decomposition.Further, Leroy and Steacie 1 found a maximum rate of reaction at about 10 mm pressure of ethylene and suggested that the fall-off in rate below this pressure was due to lack of quenching of Hg* by ethylene. Darwent 3 points out that the measured quenching cross-section of ethylene for Hg* is such that no fall-off in quenching should occur at 10 mm pressure and suggests that the fall-off in rate is accounted for by the deactivation of metastable mercury atoms (Hg3Po) on the walls of the vessel.He assumes that ( 5 ) is slow compared with reaction (2). C2H4 + Hg3Po + c2H4* + HglSo THEORETICAL CONSIDERATIONS The thermal conductivity of most simple gases is independent of pressure if the mean free path is small compared with the distance the heat is conducted. If a thin wire in a gas is maintained initially at constant temperature, the heat loss at low pressures falls off due to the appearance of a temperature discontinuity at the gas-solid interface. At any fixed pressure, the heat loss is proportional to the temperature of the wire, until at high temperatures convection occurs. The temperature differences attained in the gas phase in the investigation of this photo- chemical reaction are about 3 x 10-1" C , with a quantum input of about 1014 quantalcrnz sec.The platinum filament used to measure the temperature changes is maintained at about 0.5" C above the temperature of the thermostatted reaction vessel. In the reaction system and conditions considered here, heat is trans- ferred by conduction solely up to pressures of the order of 200 mm. Fig. 1 shows the absorption of light in a semi-infinite reaction vessel, bounded by a plane transparent window. The vessel contains mercury vapour and a gas which can quench excited mercury atoms. The absorption of light will be ex- ponential and I = I0 exp (- kx),A . B. CALLEAR AND JAMES C. ROBB 23 where k is the extinction coefficient, I is the light intensity per unit area at a point distant x from the window, and I0 is the incident light intensity per unit area.Between x and co the amount of energy appearing in the gas as heat is Iohv exp (- kx). When thermal equilibrium is attained, all the heat must be conducted back to the plane window, maintained at constant temperature. The thermal conductivity K FIG. 1.-Variation of light intensity and temperature in a semi-infinite reaction vessel. is related to the temperature gradient d0/dx and the amount of heat Q conducted per unit area by the relation The amount of energy conducted through unit area distant x from the window is Iohv exp (- kx) per unit area. It follows that Q = - Kdekdx. Kd0ldx = Iohv exp (- kx), whence where A0 is the difference in temperature between the window and a point x. Thus A0 is proportional to the energy input to the gas and inversely proportional to the thermal conductivity of the gas.When 2537A radiation is being absorbed by mercury vapour at its vapour pressure at 30" C, A0 becomes almost constant for x greater than 5 mm. In the practical case, this idealized state of affairs will not be realized since the finite geometry of the reaction vessel will impose disturbances on such a tem- perature distribution. In another paper 4 it has been demonstrated experimentally that for a system of finite size, the temperature difference between any point in the vessel and the walls is proportional to the heat input. A0 = Iohv[l - exp (- kx)]/Kk, EXPERIMENTAL APPARATUS REACTION vmEL.-The Pyrex reaction vessel A (fig. 2) has an upper ground flange to which is fixed a quartz window B. The resistance thermometer D, a platinum wire 10-2 mm diameter, is held in position parallel to B and 7 mm below it, by two thin platinum supports C.Electrical contact is made through the base of the reaction vessel by tungsten seals and finally by insulated connections, through the thermostatting liquid. The vessel is connected t o the high-vacuum line by a side tube E. The flange on the thermostat lid limits the light input and serves as a 4-cm diameter stop. The resistance of D is about 60 ohms a t room temperature. THERMosTAT.-The thermostat consists of a lagged rectangular tank, 15 in. X 11 in. and 14 in. deep, fitted with a close-fitting lid with a circular hole in the centre. The thermistor F forms one arm of an a.c. bridge network and controls the temperature to 10-3" C.Insulated heating wire is stretched near the inside of the bottom of the tank. The thermostatting liquid, a solution of sodium chloride in water, is stirred vigorously through the bottom of the tank. The level of the liquid is maintained constant and above the level of the flange on the lid to prevent ripples forming on the liquid surface through which the light passes.24 THERMAL METHOD ULTRA-VIOLET LAm.-The lamp G is of the low-pressure mercury discharge type in the form of a U cooled by circulating water at 25 5 0.5" C. The lamp is supplied by a Tinsley a.c. stabilizer and a transformer. The u.-v. radiation (2537A) is admitted to the reaction vessel by opening a Pyrex shutter H. MEASUREMENT OF TEMPERATURE.-The platinum wire in the reaction vessel forms onc arm of a d.c.bridge network. The off-balance signal is amplified and displayed on an oscilloscope screen.4 This signal is then reduced to zero by varying the e.m.f. across the bridge. If the u.-v. is admitted to the reaction vessel, the oscilloscope trace is de- E flectcd. With about 30 mm of C02 in the system, the half-life time of the temperature rise in the gas is about 1 sec. This enables one to discriminate the slight rise in temperature of the vessel and supports of half-life time of 1 min. MANOMETER.-A modified Pear- son differential manometer was used, having a sensitivity factor 5 of 200. The best performance was obtained using a platinum electrode with a sharp point, to detect theposi- tion of the mercury surface. Repro- ducibility was improved by sparking the electrode with a Tesla coil dis- charge before use.Electrical con- tact was observed using a triode valve circuit, the mercury contact applying a negative bias to the grid. PREPARATION OF GASES.-The inert gases were supplied spectroscopically pure by the British Oxygen Company. The carbon dioxide was obtained pure by distillation and fractionation of the solid. It was dried over phosphorus pentoxide. The ethylene was obtained from a cylinder supplied by the British Oxygen Company. It was purified by repeated distillation and fractionation. r'"-*->q --L FIG. 2.-Reaction system. RESULTS The data presented herc have been measured at 32" C unless otherwise stated. ARGON.-cUrVC A, fig. 3, demonstrates how the measured temperature varies with argon pressure, when a constant intensity of 2537A radiation is admitted to the reaction vessel.Argon is a very inefficient quencher of Hg* and the temperature measured by the wire arises largely from radiation falling directly on to it. The sharp rise in tem- perature at low pressures is due to thermal conduction from the wire decreasing rapidly due to the temperature discontinuity, while the slight rise at higher pressures is attributed to quenching of the Hg* by small traces of impurity in the argon. CARBON ~ ~ o x r ~ ~ . - C u r v e B, fig. 3, shows the variation in temperature with pressure for constant light input. Carbon dioxide quenches Hg* fairly efficiently and the fall-off in temperature bclow about 50 mm pressure is attributcd to decreased quenching of Hg* while above 50 mm, quenching is almost complete.That this fall-off is not due to thermal conductivity changes of the system can be demonstrated by using a mixture of argon and C02. The high argon content of the mixtures maintains the thermal conductivity of the system constant while the temperatures can be measured down to low C02 partial pressures. Curves C and D, fig. 4, are obtained for such mixtures containing respectively 14 % and 5.2 % C02. To compare the temperatures measured in C and D with those in curve B, it is necessary to correct those temperatures obtained in the C02 + argon mixtures, to the equivalent in CO2. This is easily done since the thermal conductivities of argon and C02 are known and have been measured in this apparatus.4 This cor- rection puts thc curves B, C and D on the same temperature scale so that the hcat pro- duced in the system is proportional to the measured temperature.Plotting the adjusted curves C and D, together with curve B against the partial pressure of C02, producesA . B . CALLEAR A N D JAMES C . ROBB 25 one common smooth curve. This shows that the fall-off in temperature at low C02 pressure is not a function of the thermal conductivity, but solely due to decreased quench- ing of Hg" by C02. Further, the coincidence of these curves leads to the conclusion that the wire is not affected by diffusion of excited atoms and molecules since the variation 14 __o_ T +--- 6 A FIG. 3.-Variation of temperature in reaction vessel as a function of pressure : (A) argon; (B) carbon dioxide.in diffusion constant would in this case show temperature changes with alteration of pressure and composition of the gas mixture. The form of the curve for the fall-off in quenching a t low pressures is the same for a number of gases investigated. For C02, quenching in the reaction system falls off to 50 % at a C02 pressure of 0.73 mm. ETHYLENE.-when ethylene in the presence of mercury vapour is irradiated with light of wavelength 2537 A, the curves obtained for the temperature of the gas as a function of pressure are more complex since in this case it is necessary to take into account the energetics of the decomposition reaction. Fig. 5 shows four curves, E, F, G and H, obtained in this way. The gas compositions are respectively 100 % ethylene, 10-4 % ethylene, 1.07 % ethylene, and 0.09 % ethylene respectively, argon again being the diluent to maintain the thermal conductivities constant for each run over the pressure range Eta/ Pressure (nrm Uy ) /uo -2 5u I .___-----I--- FIG.4.Variation of heat appearing in the reaction vessel as a function of total pressure : (C) argon 86 %; carbon dioxide 14 %; (D) argon 94.8 %; carbon dioxide 5.2 %. involved, The curves are plotted as heat liberated in the gas in arbitrary units as a function of pressure. The heat liberated is obtained by multiplying the temperature observed by the thermal conductivity of the gas mixture. For the curves G and H, where the ethylene concentration is low, the Hg* is still quenched solely by ethylene. Since the excited ethylene molecules so produced are deactivated only by collision with argon, then on either curve, for a constant total pressure,26 THERMAL METHOD the ratio of the number of ethylene molecules decomposing to the number being de- activated is constant.It is possible to estimate the fall-off in quenching as follows. Suppose a point P is chosen on curve H and at that total pressure the corresponding point on curve G is Q. Assuming that at P, quenching is 50 %, then from the form of the curve obtained in fig. 3 for C02, which is generally applicable to the fall-off in quenching by any gas, and knowing the ethylene pressures at P and Q, it is possible to calculate the per cent. quenching which should be occurring at point Q. It is then easy to calculate the heats which would be measured if quenching were 100 % at P and at Q.These shoiild both give the same value. Failure to obtain the same value means that the assumption of 50 % quenching at P is incorrect and another point is chosen and the process is repeated. FIG. 5.-Variation of heat appearing in the reaction vessel as a function of total pressure : (E) pure ethylene ; (F) argon 89.6 %; ethylene 10.4 %; (G) argon 98-93 % ; ethylene 1.07 "/o ; (H) argon 99.91 % ; ethylene 0-090 % By trial, or by a graphical method, the point P can be found which corresponds to 50 % quenching. The method can be repeated for various quenching pcrcentages and table 1 gives the information obtained. It is seen that quenching of Hg* by ethylene is 50 % at an ethylene pressure of 0.050 mm. Leroy and Steacie concluded that quenching in their experiments dropped to 50 % at about 1 mm pressure compared with 89 % quenching at 1 mm pressure in thesc experiments.If the Hg* reradiates its cnergy, and imprisonment of this radiation does not occur, the fraction of the total radiation which is quenched is ~ / ( t + r), where r is the average lifetime of Hg* and t is the average time between collisions for Hg* and ethylene molecules. At 1 mm pressure of ethylene both t and are about 10-7 sec, leading to a value of 50 % quenching. An approximate pressure of C2H4 % radiation graphical treatment of the imprisonment cffect which occurs in practice, leads to this formula being modified to 67/(f i- 67), for a system of the dimensions used hcre. This gives a value of about 86 % quenching at 1 mm.The value of 89 % quenching found experimentally a t 1 mm is in good agreement with the lifetime of Hg*. The curve E obtained for pure ethylene can be corrected for fall-off in quenching and assumes the form shown in fig. 6, curve J. From 1-5 mm pressure the heat liberated in the gas is practically constant. The shape of this curve is described qualitatively as follows. At suficicntly high pressures, practically all the CzH4* formed is deactivated by collision, so that nearly all the radiation entering the system will appear as heat in the gas. As thc pressure is reduced, decomposition of C2H4* will become more significant and a fraction of the energy is absorbed as a result of the chemistry which occurs. Thus the heat liberated in the system will decrease.At low enough pressures, nearly all the CzH4* will decompose. An einstein of 2537 8, is equivalent to an energy of 112.2 kcal. The heat of the reaction TABLE 1 rnrn Hg quenched 4 3 2 1 0.50 0.050 g8*0 96*7 93*5 88.5 81.0 50.O c2H4 -> C2H2 + H2A . B . CALLEAR AND JAMES C . ROBB is calculated to be - 41.71 kcal/mole from the following data : 6 heat of combustion of H2 f; 68-32 kcal/mole at 25^ C to liquid water, 9, 3, C2H4 = 337.23 ,, 9 , ,, Y > 9 , C2H2 = 310.62 ,, Y, 9 , 27 In curve J, the heat liberated is still rising slightly at 150 mm pressure with pressure increase. The curve is asymptotic to a value obtained when all the energy entering the system is appearing as heat. This value was obtained by replacing the ethylene by COz, measuring the heat appearing in the system, and correcting with the thermal conductivities of ethylene and C02, since the quantum input is the same in both cases.This value is marked at Y. The heat measured at low pressure is marked at Z. If the zero on the heat axis is V, then YV is a measure of the quantum input and ZV should correspond to the energy entering the system less the energy of reaction, if each quantum of radiation at low pressure decomposes one molecule of ethylene. Thus for 100 % primary quantum efficiency, YZ corresponds to the heat of reaction, - 41-71 kcal/mole and YV to the energy in an einstein of radiation, 112.2 kcal so that YZ/YV should be 0.37. The value measured is actually 0.36, in agreement with a primary quantum efficiency of 0.97. FIG. 6.-Variation of heat appearing in the reaction vessel for pure ethylene, after correction for fall-off in quenching.EFFECT OF INERT cAsm.-Curve F, fig. 5, can be corrected for fall-off in quenching and gives the dotted line. It will be seen that the heat measured at low pressures in this case is about 10.4 arbitrary units compared with 10.2 measured in pure ethylene, curve J, fig. 6. This close agreement supports the validity of the method. Curves such as F, with added inert gas can give information on the deactivation of C2H4* by collision with the inert gas molecules. For any point X on a curve such as J, it can be seen that XZ is a measure of the number of C2H4* being deactivated. One can deduce the percentage deactiva- tion at any pressure. Table 2 shows the percentage of C2H4* being deactivated at 50 pressure of inert gas.TABLE 2 He 10 Kr 23 A 29 c2H4 63.4 deactivation gas yo deactivation deactivation gas yo deactivation CONCLUSIONS DRAWN FROM THE ABOVE EXPERIMENTS mm (i) The observations are in agreement with a primary quantum yield close to unity. This is not in agreement with the observations of Leroy and Steacie 1 and Darwent 3 who find a yield of 0.37 at about 10 mm pressure of ethylene. (ii) The information presented here demonstrates that at pressures above 1 mm, quenching of Hg* by ethylene is virtually complete, while Leroy and Steacie 1 found about 50 % quenching at 1 mm.28 THERMAL METHOD (iii) Darwent has put forward a complicated mechanism whereby C2H4* partly decomposes on the vessel wails. If this was the case, at low pressures of ethylene, curve J would show a marked decrease in the heat appearing in the gas, due to energy being transported to the walls of the vessel.His main experimental justification for this mechan- ism lies in his observations that the rate of photolysis decreased with decreasing mercury vapour pressure. Points (ii) and (iii) have been further investigated by carrying out the photolysis of ethylene and measuring the rate of reaction by manometric methods. MANOMETRIC RESULTS RATE OF REACTION AS A FUNCTION OF ETHYLENE PREssuRE.-In fig. 7 are shown measure- ments at 20" C of pressure as a function of time as the photodecomposition proceeds. The initial increase in pressure arises from the decomposition of ethylene to acetylene and hydrogen and the subsequent decrease in pressure arises when the hydrogen itself reacts to give atoms and hydrogenation of the ethylene occurs.A cursory inspection of these curves would lead one to the belief that the initial rates of decomposition are quite strongly pressure dependent, but this is not the case. The complication of subsequent hydrogenation becomes important quite early on in the reaction. Fig. 8 shows the initial rates of pressure rise measured with the sensitive manometer over the first minute of reaction, when the extent of reaction is so small that the amount of hydrogen produced is sufficiently FIG. 7.-The pressure increase during the photolysis of ethylene, at different total pressures, carried out at 20" C. (1) 6.5 mm Hg pressure (3) 3.0 mm Hg pressure (2) 4.7 mm Hg pressure (4) 1.7 mm Hg pressure.small not to quench a significant amount of Hg*. Now it is clearly seen that the rate of decomposition is practically constant, falling off by only a few per cent. at 1 mm pressure. The rate of decomposition as a function of pressure for constant light input is shown in fig. 9a. This is in close agreement with the deductions made from the temperature measure- ments above and demonstrates a possible explanation of the results of Leroy and Steacie. EFFECT OF MERCURY VAPOUR PRESSURE ON RATE.-Darwent's 3 observations of variation of rate of photosensitized decomposition with change in mercury vapour pressure is inconsistent with curve J at low pressure. An alternative explanation of his results would be that his radiation was not sufficiently collimated so that radiation which would be absorbed at high mercury vapour pressures would at lower pressures be able to pass through the sides of the vessel although his conditions were such that collimated radiation would all be absorbed before reaching the bottom of the vessel even at the lowest pressure of mercury used. Using an uncollimated beam from the mercury lamp, the rate of decomposition varies as reported by Darwent (table 3), when the mercury vapour is in equilibrium with liquid mercury at 30" C and at 0" C.By collimating the beam with two circular stops such that the most oblique radiation could not fall on the walls of the vessel, the rates obtainedA . B . CALLEAR A N D JAMES C. ROBB 29 were independent of mercury vapour pressure (table 3).These experiments were carried out using 5 mm pressure of ethylene in each case. f i h e (min) (7.5 I FIG. &-Initial pressure rise during the photolysis of ethylene at different total pressures carried out at 20" C. The curves have been vertically displaced for the sake of clarity. (1) 6.1 mm Hg pressure (3) 6 mm Hg pressure (2) 1.0 mm Hg pressure (4) 1.5 mm Hg pressure. TABLE 3 rate (collirnatcd) rate (uncollimated) prcssure riselmin pressure riselmin expressed in mm absolute expressed in mrn absolute temp. O C 0 3-85 x 10-3 74.4 x 1 0 - 3 10 3-93 x 10-3 - 30 3-85 x 10-3 114.0 x 10-3 DISCUSSION The overall rate as a function of pressure measured manometrically is in good agreement with that obtained by temperature measurements. The rate of reaction obtained from curve J, fig.6, is plotted on fig. 9~ for comparison with that obtained by direct pressure measurements. These curves are fitted at 0 and 150 mm pressure. They are both in excellent agreement with the expression where P is the pressure of ethylene and A and B are constants. The plot of R against P2 is shown in fig. 9 ~ . The information obtained here is consistent with the following reaction sequence, excluding decrease in quenching below 1 mm. rate of decomposition = A/(1 + B P ) , > I HglSo 4- h~ -+ Hg3P1 Hg3P1 4- C2H4 -+ HglSo + C2&* c2H4* -+ c2H2 + H2 k2 C2H4* + 2C2H4 -+ 3GHi k3 This leads to a kinetic expression30 THERMAL METHOD The deactivation process involving an apparently three-body collision is rather difficult to interpret.Two possible explanations may be put forward. It may be that C2H4* + C2H4 --f C4H8*, perhaps in the form of a cyclobutane or butene molecule which has a relatively long existence, considerably longer than the dura- tion of the average bimolecular collision. Subsequent collision with an ethylene molecule would then lead to the stabilization of the three ethylene molecules. Since there are no C4 hydrocarbons formed, this mechanism would seem unlikely. An alternative explanation might be that the excited ethylene has energy consider- ably in excess of that required for decomposition, and that two successive fruitful collisions may be necessary before the molecule is rendered incapable of decom- position. One estimate7 puts the energy of activation at about 85 kcal/mole, while the maximum energy available is 112 kcal and the reaction is only 42 kcal endothermic.That the degradation of the energy of excited ethylene may occur in steps, is supported by Laidler's 8 suggestion that since excited ethylene may be FIG. 9. (A) Variation of the initial rate of pressure increase as a function of pressure carried out (B) Variation of reciprocal quantum yield with (pressure)*. at 20" C. The dotted curve is obtained from curve J, fig. 6. in a triplet state, the degradation of the electronic energy will be slower than the degradation of the vibrational energy of the molecule. These two alternative deactivation processes lead to the expression rate = A/((1 + BP)(1 + CP)). introducing a term in P in the lower line as well as the P2 term.This expression interprets the results more satisfactorily than the simple bimolecular expression rate = A/(1 + BP). Assuming that each collision leads to energy transfer, the cunsecufive collision theory leads to an average lifetime of C2H4* of 5 x 10-9 sec, since about half the excited ethylene inolecules are deactivated by a pressure of 40 mm of normal ethylene. If the deactivation is a true three-body process, the average lifetime can be estimated from Bodenstein's formula,g o}h = ratio of ternary collisions to binary collisions. o is the molecular radius and A is the mean free path. Assuming that every ternary collision leads to deactivation, the half-life time of C2H4* is about 2 x 10-6 sec.A . B . CALLEAR AND JAMES C . ROBB 31 The experiments conducted in presence of argon and krypton also indicate a three-body mechanism, but the lower deactivating efficiency compared with ethylene makes it necessary to carry out the reaction over a higher pressure range than could be employed here owing to the dificulties introduced by convection currents in a reaction vessel at pressures much in excess of 150 mm.With helium, it might appear that the form of the curve relating rate of decomposition to pressure is in better agreement with rate = A/((1 + BP)(l -1- CP)}, but the high thermal conductivity of helium makes the tcmperature changes in the system very small so that accuracy is poor. From the data presented on the fall off in quenching of Hg3P1 by C02 and by ethylene, a comparison of the quenching cross-sections can be made directly, by finding the pressure at which 50 % quenching occurs. Taking the quenching cross-section 10 of CO2 at 3.54 A2, the quenching cross-section of ethylene would be 30 A2.A value obtained by Steacie 11 of 48 f 5 A2 is in qualitative agreement with this estimate. No evidence has been found in these experiments to suggest that Hg3P1 is significantly quenched by ethylene to the metastable Hg3Po state, as has been suggested elsewhere,3 and it has also been shown that there is no reason to suppose that C2H4* decomposes heterogeneously on the walls of the reaction vessel. The fresh information obtained in the low pressure region showing that the rate is maintained to about 1 mm pressure is in accord with the known quenching cross- section of ethylene for Hg3P1.The quantum yield of close to unity is considerably higher than previously proposed. The value of the method described above can be said to lie in the speed and accuracy with which measurements of reaction rate can be made. These two advantages arise from the fact that the rate of reaction is obtained from the total quantity measured and not by a difference of two large quantities such as in pressure measurements or in measurements of concentration of reactant by some physical method. It would not be possible, for this reaction, to estimate the amount of products formed since the whole character of reaction changes if significant amounts of hydrogen are produced. This thermal method requires a reaction time of only about 1 sec to enable a rate measurement to be made and in that time no effective change in reactant concentration has occurred and only an insignificant amount of products is formed. I t is of interest to note that it has proved possible to measure a primary quantum efficiency without measuring the absolute quantum input to the reaction system, such measurement being often subject to some uncertainty. The authors wish to thank The Anglo-Iranian Oil Company and Imperial Chemical Industries Ltd., for financial support in obtaining some of the apparatus, and one of them (A. B. C.) wishes to thank the Department of Scientific and Industrial Research for the award of a maintenance grant. They are both apprecia- tive of the interest in this work which has been shown by Prof. H. W. Melville, F.R.S., and for the many valuable suggestions made by him. 1 Leroy and Steacie, J. Chem. Physics, 1941 , 9, 829. 2 Darwent, J. Chem. Physics, 1951, 19, 258. 3 Darwent, J. Chem. Physics, 1952, 20, 1673. 4 Callear and Robb, to be published. 5 Pearson, 2. physik. Chem., A, 1931, 156, 56. 6 A.P.Z. research project 44 (Carnegie Inst. Tech.). 7 Steacie and Leroy, J. Chem. Physics, 1942, 10, 22. 8 Laidler, J. Chem. Physics, 1942, 10, 43. 9 Bodenstein, 2. physik. Chem., 1922, 100, 1 18. 10 Mitchell and Zemansky, Resonance Radiation and Excited Atom (Cambridge Uni- 11 Steacie, Can. J. Res. B, 1940, 18, 44. Selected values of properties ofhydrocarbons, heats of combustion (1945-46), table 0 n, 8 n, 25 n. versity Press, 1934).

ISSN:0366-9033    

DOI:10.1039/DF9541700021

出版商:RSC    

年代:1954

数据来源: RSC

摘要:

THE TEMPERATURE PATTERN METHOD IN THE STUDY OF FAST CHEMICAL REACTIONS BY DAVID GARVIN," VINCENT P. GUINN,** AND G . B. KISTIAKOWSKY Gibbs Memorial Laboratory, Department of Chemistry, Harvard University, Cambridge, Massachusetts, U.S.A. Received 18th January, 1954 Polanyi's technique of spherically symmetric " highly dilute flames " has been modified for the study of those fast gaseous bimolecular reactions which are not accompanied by useful optical phenomena. The new method involves the measurement of the temperature pattern within and without the reaction zone under conditions of very small thermal gradients and preponderantly diffusional mass and heat transport. An idealized theory of such measurements is developed and it is shown that the chosen experimental arrange- ment satisfies reasonably well the theoretical requirements.Some of the results obtained with reactions between boron trifluoride and a series of amines are discussed and the limitations of the method are emphasized. Nonetheless, it should be of a rather wide usefulness in the studies of very fast gaseous reactions. The development af the technique of " highly dilute flames " by Polanyi and his coworkers 1 was a major step forward in the field of chemical kinetics. It made possible a direct measurement of the rates of very fast gaseous reactions in terms of the frequency of molecular collisions. The method was applied success- fully to a variety of reactions of metal vapours with halogens and halogen com- pounds. Except for a few investigations in which the extent of the reaction zone was followed by the measurements of the spread of the solid deposits of the reaction products on the walls of the reaction vessel, the measuring techniques revolved around the resonance absorption and fluorescence of metallic vapours.Either gives, in effect, the total volume of the reaction zone of two inter-diffusing reactants. It seemed to us desirable to extend the principle of the method to chemical systems in which the reaction zone cannot be determined by optical density measure- ments and the condensation on the walls of the reaction products with an accom- modation coefficient unity is at least in question. Such extension is indeed possible with the aid of temperature pattern measurements within the reaction zone. In the following we shall present the idealized theory of the measurements, its prac- tical adaptation, a few of the results obtained and their critique.Consider a constant finite source of reactant Y in an infinite atmosphere of a uniformly distributed reactant Z . Let the two concentrations be denoted by y, z, respectively. If Y and Z undergo a bimolecular reaction with a rate given by kyz and the diffusion coefficient of Y in the atmosphere is given by D,, a steady state may be reached which is described by the Poisson equation, (1 1 .kz v 2 y - - - y = 0, D Y Making the assumption that the diffusion coefficient and the rate constant are invariant throughout the system, the equation yields for a spherically symmetric case with r being the distance from the source, 1 k c2 = - y = - (A1 exp(cr) + A2 exp(- cr} ; Dy '* * Department of Chemistry, Princeton University, Princeton, New Jersey.** Shell Development Company, Emeryville, California. 32DAVID GARVIN, VINCENT P . GUINN A N D G . B . KISTIAKOWSKY 33 Introducing the boundary conditions that y = 0 at r = co and that the flow from the source is b = 4nkz yr2dr, J: the solution is reduced to b exp(- cr) 4nDY r ’ y -= (3) (4) This is the form used by Polanyi, except that the steepness of the exponential permitted him to neglect the l / r term in estimating the value of c from the approxi- mate radius of the reaction zone. When the reaction is accompanied by a heat change Q, the thermal steady state is given by the equation, Qkz b exp(- cr) = 0, 02T-t ___ ___ __- K 4nDy r where K is the thermal conduction coefficient.Taking it also to be independent of r, and assuming that the source reactant is entering the system at the tempera- ture of the atmosphere, the solution is A3 Qb exp(- cr) T = - - - 4- A49 r 47r~ r One boundary condition is obtained from Laplace’s equation for heat conduc- tion at such large distances from the source that reaction is insignificant, Qb 4r2Kn V T + - - - z o o . (7) The other results when the temperature at a variable distance r is compared with the temperature at some fixed distance r l . Then The temperature difference AT is seen to be determined by a proportionality factor Qbl47rtc and a form factor c, which latter does not involve the thermal conduction coefficient. A particularly effective way to apply this equation to the experimental data, for which we are indebted to Mr.Paul C . Mangclsdorf, Jr., is to plot the quantity r n T in arbitrary units against r, as is shown in fig. 1 . The region outside the reaction zone is then represented by a rising straight line; the vertical distance between any point on the descending branch of the curve within the reaction zone and the extension of the straight line is Kexp(- cr). By taking such distances at two or more points, the proportionality factor K is eliminated and the ratio between the rate constant and the diffusion coefficient is obtained. The assumption that D,, k and K are independent of r, made in integrating eqn. (1) and (9, imposes an experimental requirement that the reactants be diluted with a large excess of an inert carrier gas, to maintain a nearly constant mean free path and to keep The much more dubious assumption that z is constant throughout the reaction zone, which we shall consider at the end of this article in more detail, certainly presupposes that the total quantity of 2 in the reaction system be much larger than that of Y .The bimolecular reactions to be studied must be fast, since otherwise the experiments would have to be carried out at such high pressures that convection could not be avoided. Tsmall. B34 TEMPERATURE PATTERN METHOD EXPERIMENTAL It is a Pyrex cylinder of 10 cm int. diani. and ca. 40 cm length, The " atmosphere ", a mixture of reactant 2 and a carrier gas at 0.05 to I mm pressure enters at B, flows through the reactor at linear velocities of the order of I to 10 cm/sec and, together with reaction pro- ducts, is eliminated a t D through a regulating gate valve, a cold trap, and a high-capacity mechanical oil pump.The " source " reactant Y, with added carrier gas, enters the reactor through the nozzle A at linear velocities of the order 103-104 cm/sec. The ratio of the flow rates of the two reactants in each experiment is such that a substantial excess of the atmospheric reactant is flowing through the reactor. The pressure in the reactor is measured by a McLeod gauge connected through C. The temperature pattern in the diffusion region surrounding the nozzle is measured by a movable thermocouple T, whose leads T' are brought out of the reactor through a thin-walled 3/32-in. stainless steel tubing joined to a stouter brass tubing F which can be slid and rotated in a double, packed, bushing G, the inner space E of which is evacuated by the pump.Above the cover plate which mounts the bushing are located suitable gears and scales to read the vertical and horizontal position of the tip of the thermocouple. The measurements are carried out in a reactor shown schematically in fig. 2. rnT I , cm FIG. 1 .-The theoretical radial temperature pattern and a plot of experimentally determined rAT (in cm microvolts) against distance (in cm) from the nozzle. A FIG. 2.-A schem- atic drawing of the apparatus. These scales are calibrated with the aid of a cathetometer in reference to the nozzle tip each time a new thermocouple is mounted. The " hot " junction of the thermocouple is a 0-5 x 0.5 x 0.1 mm silver foil to which are soldered in a V the 0.05 mm iron and constantan wires.The junctions to the copper lead-in wires are at the base of the stainless steel tubing. The thermocouple is held rigid relative to the tubing by a thin glass fibre cemented to the wire some distance from the tip. The reactor is immersed to near the cover plate in a liquid thermostat ; to insure a steady temperature at the " cold " thermocouple junction, its supporting tube is passed through an auxiliary bushing H cemented to the wall of the reactor. It is to be noted that in order to apply eqn. (8) the distance from the cold junction to the nozzle need not be known, provided the temperature of the former either follows the local gas temperature or (as in the present arrangement) stays constant.In the earlier experiments,% 3 the temperature differences were measured to 0.1 pV, i.e. 0402", by a Leeds and Northrup Wenner-type potentiometer and a mirror galvano- meter. In the more recent still unpublished work of Mr. Richard Williams, use was made of a Perkin-Elmer DC amplifier, gaining thereby nearly an order of magnitude in the sensitivity of the thermal measurements.DAVID GARVIN, VINCENT P . GUINN AND G . B . KISTIAKOWSKY 35 To date, all experiments with this system have been concerned with the reaction of boron trifluoride and an assortment of amines. These reactions were shown by othcrs 4 * 5 ~ 6 to result in the formation, through a co-ordinate bond, of bimolecular adducts, F3B-NR3 with very little, if any, side reactions.Their rates were found by us to be fast cnough for the application of the described technique. The reactants, mixed with suitable pro- portions of the carrier gas, are admitted to the reactor through fine capillaries from large supply flasks, the pressure in which does not vary significantly during each run. The flow through the capillaries is calibrated by the various gas mixtures used and is adjusted to the desired values by varying the pressure in the supply flasks. particular experiment the ratio v/Dy was 16 cm-1. Lower nozzle velocities (down to v/Dy == 5 cm-1) bring the centre of the radial gradient pattern closer to the nozzle tip but leave it spherically symmetric to the accuracy of these measurements. At still lower -' 336 TEMPERATURE PATTERN METHOD Assuming a spherically symmetric mass flow from the nozzle at an essentially constant pressure, the time required by a gas volume element to move a distance r from the centre of the nozzle tip is t == 4r3/3vr$, (9) where v is the linear gas velocity through the nozzle tip and ro is its radius.With the larger nozzle used (ro = 0.046 cm) and the data of a typical run (v = lo4 cm/sec), the time required for a displacement to a distance of 1 cm from the centre is then 0.05 sec. On the other hand, the Einstein diffusion equation gives 0.0005 sec as the time for an average displacement of 1 cm due to molecular diffusion in the atmosphere (P = 0.1 mm) surrounding the nozzle. The ratio of these calculated times decreases as one chooses smaller distances from the nozzle but it is evident that only within a few nozzle radii is the hydrodynamic flow fast enough to interfere materially with the molecular diffusion.Indeed, the replacement of the above nozzle by one with ro = 0.028 cm produced no measurable changes in the tem- perature pattern, although the hydrodynamic flow was reduced by a factor of three FIG. 4.-A plot of the observed rate constants in the system BF3 + NMe3 against the ratio of the linear nozzle gas velocity to the diffusion coefficient. because less carrier gas was used in the nozzle gas mixture. Perhaps a more sensi- tive test of the effects of hydrodynamic flow is an analysis of a large number of runs, to reduce the effects of accidental errors of rneasuremcnt. In fig. 4 are plotted rate constants for the chemical system BF3 + Me3N against v/D, char- acterizing each experiment. One does observe a slight downward trend in the k’s with increasing v/D,, as expected since the hydrodynamic flow tends to keep the atmospheric reactant Z from penetrating close to the nozzle tip.The effect, however, is slight, being just noticeable over the random scatter of experimental points and an extiapolation to vJDy = 0 would not change significantly any of the conclusions reached. Within the v/Dy range of 5 to 16 cm-1 the temperature patterns were found to fit eqn. (8) very well with several reactant pairs used interchangeably as the nozzle and the atmospheric reactants. Thus the circles in fig. 1 are taken from a run with BF3 as the nozzle reactant and Me2HN in the atmosphere, which was carried out by Mr.R. Williams. In some measure this exccllent fit, typical of a great majority of runs madc under properly chosen conditions, is surprising because a rough calculation of the heat transfer by the gas to the receiver plate of the hot junction of the thermo-D A V I D GARVIN, VINCENT P . G U I N N A N D G . B . KISTIAKOSWKY 37 couple and of heat conduction along its wires does indicate that the hot junction, notwithstanding its substantial area, cannot have the temperature of the adjoining gas layers to the accuracy of these measurements. A concern with this situation has led Mr. Williams in his current work to use thermocouple wires of only 0.017 mrn diameter and to arrange the thermocouple so that the wires are tangential to the isothermal surfaces, rather than nearly normal to them, as was the case for the V-shaped couples.The absolute temperature differences measured with the new couple may be slightly different from those previously obtained. The absolute values, however, are not involved in the calculation of the rate constants and the form of the temperature pattern has remained the same. One must conclude therefore that although significant heat losses may occur along the wires of the couple, their effect on the thermocouple junction is linear in AT and is therefore without influence on the interpretation of the data. The theory assumes no disturbance of the temperature pattern by the measuring instrument and this may not be true if the thermocouple acts as a catalyst for the reaction.In the course of runs with each thermocouple, it became lightly coated with non-volatile reaction products but this had no effect on the thermal measure- ments, In one series of runs the couple was coated with perfluorinated hydro- carbon, again without noticeable effect on the results. One is thus justified in concluding that surface reaction is insignificant which is anyway highly probable in view of the nature of the reactions studied. A condensation of the reaction products on the couple might drastically alter the predicted thermal gradients. With one reaction mixture tried, boron trifluoride and ammonia, the couple became rapidly coated with reaction products and the observed temperature patterns could not be interpreted by eqn.(8). With all the other reaction mixtures thc bimolecular adducts apparently did not condense on the couple because the slight deposits formed (in amounts smaller by orders of magnitude than in the ammonia reaction) were entirely non-volatile, in contrast to the known vapour pressures of the bimolecular adducts.4-6 An assumption is implicit in the theory of these experiments that the reaction energy, which is contained initially in thc adduct molecules, is converted so rapidly into the Boltzmann distribution of all the adjacent molecules that the only observ- able transport of energy is by ordinary thermal conduction. But it is well known 8 * 9 that the energy exchange between vibrational and translational degrees of freedom is quite slow, in some instances requiring as many as 105 collisions for the transfer of a vibrational energy quantum.In contrast to this number, if it is tentatively assumed that the thermocouple averages the temperature over a region of 1 mm3, the product molecules in a typical experiment suffer only a few hundred collisions before migrating out of such a volume. An attempt was made therefore to change the unknown rate of energy equilibration by substituting helium for nitrogen as the carrier gas. The rate constants were found to be unchanged 3 but this re- assuring finding might still not be due to a very rapid rate of energy equilibration. Let us make the extreme assumption that the product molecules do not equilibrate their energy with other gas molecules at all but do transfer it to the surface of the thermocouple.The product molecules are subject to diffusion which is described by an equation equivalent to that of heat conduction (6), except for the propor- tionality factor. The local rate of production of product molecules is proportional to the rate of local heat generation used in eqn. (6). Thus, on the basis of this extreme assumption, one should still obtain an equation for the apparent tempera- ture pattern which is equivalent to eqn. (8) except for the proportionality factor. Undoubtedly the reality lies somewhere between this extreme assumption and that which forms the basis of eqn. (6), because the experimental results do show that the product molecules lose some of their energy on collisions with other gas mole- cules or inevitably dissociate.A mathematical treatment of this intermediate proposition appears to be rather complex and one can only hope that its result is analogous to those following from the two extreme assumptions.38 TEMPERATURE PATTERN METHOD The experimental measurements lead to the quantity c = (kz/Dy)* and thus give in principle the ratio between the rate constant and the collision frequency. Unfortunately the numerical relation between the collision frequency and the diffusion coefficient 10 is not accurately known for multicomponent gaseous mixtures of different molecular weights and sizes. This uncertainty, however, is slight compared to other sources of error in the present method and therefore the simple kinetic theory equation 3 2 4 (RT)3/2 My + Ma 6 Dy = 4 (> NP(0y + MyMa ) ' was used for the computation of Dy.The symbols have their usual kinetic meaning, the subscript y referring to the nozzle reactant and subscript a to the atmosphere. The molecular cross-section and weight of the latter were calculated as mole fraction averages of the corresponding properties of the atmospheric reactant Z and the carrier gas. The results of the measurements of the reactions of boron trifluoride with mono- methyl, dimethyl and trimethyl amines have been already described.3 The scatter of the rate constants observed was rather large-nearly a factor of two in repeated experiments-which is not surprising considering the indirect relation between the thermal patterns and the rate constants. In essence the data show that the reactions proceed through a two-step mechanism, kr k- I Y + Z z Y Z * ; Y Z * 4- MTYZ + M, which leads to the observed pressure dependence of the rate constants, The following table gives the numerical data obtained.TABLE 1 .-REACTIONS OF BF3 WITH THREE AMINES amine NHzCH3 NH(CHd2 N(CH3h kl 8 x 1011 3 x 1013 4 x 1012 cm3/mole sec k2ik- 1 2 x 10s I x 107 1 x 109 cm3/mole Thus the rate constants kl for the formation of the energy-rich intermediates approach the collision number (ZO, ca. 1014) between the reactant molecules. This suggests that the activation energies involved are insignificant, an interesting con- clusion in view of the evidence 6 for strains which exist in the adduct molecules and the change of the BF3 configuration from a coplanar into a tetrahedral one. There appears to be no regular progression of the parameters of eqn.(11) in the series of the three amines, dimethyl amine having the highest extrapolated rate at high pressures but the shortest lifetime of the intermediate YZ*, as shown by the smallness of the ratio k21k-1. The large uncertainty of individual rate constants and the small number of runs made with dimethyl amine are apparently responsible for this conclusion. More recent experiments of Mr. Williams, shortly to be published, place dimethyl amine closer to the other two by modifying its parameters in eqn. (11). In line with this observation Mr. Williams finds that the rate con- stants of arnines more complex than trimethyl amine have no measurable pressure dependence. Evidently the lifetimes of these complex energy-rich intermediates are too long to be detected in the pressure range accessible by the present technique.These results are so consistent with the general theories of chemical kinetics that one is tempted to discontinue further critical discussion of the experimental method, but there does exist onc assumption in its idealized mathematical theory which may be responsible for a substantial inaccuracy of the absolute values of the rate constants reported. It is the assumption that the atmospheric reactantDAVID GARVIN, VINCENT P . GUINN AND G . B . KISTIAKOWSKY 39 Z is uniformly distributed right to the centre of the nozzle orifice. As noted above, the mass flow from the nozzle would by itself keep the atmospheric reactant only out of the immediate vicinity of the nozzle, a volume too small to affect substantially the calculated rate constants. But another source of concentration gradients of the atmospheric reactant-its depletion due to reaction near the nozzle-may be far more significant.The exact theory calls for the integration of partial differential equations (1) for both reactants, followed by the integration of the resultant heat flow equation. It has not been possible to accomplish this analytically. Recently Cvetanovic and LeRoy 11 have carried out an approximate integration of the diffusion equations, applicable to the boundary of the reaction zone and have shown that significant corrections must be applied in the calculation of rate constants from the radii of highly dilute flames because of the depletion of the atmospheric reactant.It may be anticipated that the corrections applicable to the present method are larger because it relies on the distribution of reactants within the reaction zone. The available experimental data tend also to demonstrate the existence of this effect. An inspection of the results obtained with boron trifluoride and trimethyl amine 3 shows that when the smaller-and hence faster diffusing-BF3 was chosen as the atmospheric reactant, the calculated rate constants were slightly higher than with the reversed arrangement. In Mr. Williams’ experi- ments, with still larger amine molecules, the ratio of rate constants observed when the reactants were interchanged rose to almost a factor of two. Some of this discrepancy may be due to the incorrect calculations of the diffusion coefficients,lo owing to uncertainties in molecular cross-sections, etc., but the reality of the dis- crepancy can hardly be doubted.While the difficulties of an analytical integration of the system of equations involved appear rather formidable, work on this problem is now in progress in this Laboratory and it is expected that the solution will be available in the near future. With the availability of this solution, the method of temperature patterns should become one of rather wide applicability and of quite acceptable accuracy, compared with other methods applicable to very fast reactions. One of its attractive features is that the concentration of the nozzle reagent need not be known, provided it is low enough not to exhaust the atmospheric reagent. Thus the method should be rather suitable for reactions of atoms and free radicals introduced through the nozzle, provided, of course, that the overall reaction mechanism does not involve several reaction steps with comparable rate constants. 1 Polanyi, Atomic Reactions (Williams and Norgate, London, 1932). 2 Vincent P. Guinn, Thesis (Harvard University, 1949). 3 Garvin and Kistiakowsky, J. Chem. Physics, 1952, 20, 105. 4 Laubengayer et al., J. Amer. Chem. SOC., 1948,70,2274; 1945,67, 164; 1943, 65, 5 Burg and Green, J. Amer. Chem. SOC., 1943, 65, 1838. 6 Brown et a!., J. Amer. Chem. SOC., 1948, 70, 2793, 2878 ; 1947, 69, 1137 ; 1945, 7 Heller, Trans. Faraday SOC., 1937,33, 1556. 8 Kneser, J. Acous. SOC. Amer., 1939, 5, 122. 9 Kantrovitz, J. Chern. Physics, 1946, 14, 150. 10 Kennard, Kinetic Theory of Gases (McGraw-Hill, New York, 1938). 11 Cvetanovic and LeRoy, Can. J. Chem., 1951,29, 597. 884. 67, 1765, etc.

ISSN:0366-9033    

DOI:10.1039/DF9541700032

出版商:RSC    

年代:1954

数据来源: RSC

摘要:

T€E APPLICATION OF FLASH TECHNIQUES TO THE STUDY OF FAST REACTIONS BY R. G. W. NORRISH AND G. PORTER Department of Physical Chemistry, The University, Free School Lane, Cambridge Received 2 1 st January, 1954 Three experimental difficulties arise in the study of rapid reactions. These are the necessity for rapid homogeneous initiation, the lack of isothermal conditions and the loss of sensitivity in methods of detection when the time available for measurement is reduced. Flash photolysis is particularly suitable for rapid initiation and flash spectro- scopy reduces the limitations caused by the other two effects. Potentialities and limitations of these techniques are discussed and reference is made to possible methods of detection other than the usual photographic and photoelectric recording of electronic absorption spectra.Any direct investigation of the kinetics of chemical change involves the measure- ment of some parameter as a function of time. When the times are shorter than a few seconds three fundamental experimental difficulties arise : (1) The time of reaction may be comparable with, or less than, the time required for the homogeneous non-equilibrium condition to be established throughout the reacting mixture. The two commonest methods of initiating a reaction are by mixing and by raising the temperature, and if the chemical reaction is fast com- pared with rates of diffusion or thermal conduction, the latter processes may become rate determining, and no information is then obtained about the rate of the chemical reaction. (2) No reacting system which has a finite heat of reaction is strictly isothermal since a temperature gradient is always established between the centre of the re- acting mixture and the walls of the containing vessel.When the rate of reaction is rapid compared with the rate of thermal diffusion, this temperature gradient can no longer be ignored and indeed is often responsible for the major part of the change in the variable observed. For very fast reactions the conditions may be nearly adiabatic. (3) The accuracy of measurement of a physical quantity by available techniques decreases with the time available for its observation. The study of the fastest reactions therefore requires the use of the most powerful methods of initiation and detection available.A corollary of this statement is worthy of mention. The time of measurement, in the above sense, is the total time available to the recording apparatus for a given numerical value to be obtained. It is therefore possible in principle to increase the accuracy of measurement, however fast the rsaction, by (i) duplication of detectors for a single experiment, (ii) duplication of experiments for a single detector. These statements are direct consequences of the theory of errors. The time factor may be introduced into an experimental investigation of a rapid reaction in a number of ways. One method, which overcomes the difficulty of the short time available for measurement, is the flow technique in which the system is made time invariant.1 A second method, which includes sector and allied techniques,z modulates the source of initiation at a frequency comparable with the rate of the reaction investigated and studies only the permanent products of the reaction.The third method, with which we are concerned here, involves direct measurement on the fast reaction as a function of time in a static system. 40R. G . W. NORRISH AND G . PORTER 41 It is always to be preferred to less direct methods, such as the sector technique, which depcnd on an inferred reaction mechanism which, with the notable exception of polymerization reactions, is usually uncertain. It has advantages over the flow technique in that faster reactions can be studied, theoretical difficulties in the treat- ment of flow systems are avoided, and smaller quantities of material are required. Owing to the difficulties enumerated above very few methods have so far been developed for the direct study of reactions in static systems in times of the order of milliseconds or less, by the measurement of concentrations of the intermediates themselves.One such method is the study of fluorescence, which is, of course, restricted to the study of excited electronic states. The flash photolysis technique 3 is one of the few at present available which are of general applicability, and we shall consider the three experimental difficulties already enumerated with particular reference to this method. THE HOMOGENEOUS INITIATION OF REACTION The difficulties of producing rapid homogeneous mixing or temperature rise in static systems have been mentioned.With liquid systems the most rapid mixing by the stopped-flow technique cnables reactions with half-times of a few milliseconds or more to be studied4 and rather longer times are required for gaseous reactions. An interesting method of rapid heating by means of shock waves has recently been described,s but this does not give a static homogeneous system of the typc being considcred here. Most methods of initiating reaction, such as the electrical discharge, are either inhomogeneous in effect or of very limited application. Practically the only other generally useful method of initiation is by means of radiation, in particular by visible or ultra-violet light. There is no practical limit to the rate at which change is propagated throughout the material by photochemical initiation since it is determined only by the time of transit of light through the reaction vessel. It is fortunate that photochemical initiation is also most specific and readily amenable to theoretical treatment.The main disadvantage of photochemical techniques for the very rapid initiation of reaction is that the chemical effects produced in times of the order of microseconds are very small when conventional light sources are used. When this difficulty is removed by the introduction of flash sources, in particular those of the electronic discharge type, the method becomes one of great potentialities. Whilst energies of over 10,000 J can be dissipated in a single flash, and overall efficiencies of light output of over 15 % in the region between 4000 and 2000 A may be obtained,6 the more important considerations for our purpose are the effective flash duration and its intensity.The intensity is best expressed by the statement that the flux of radiation between 2000 and 4000 8, which may be passed through a reaction vessel is of the order of 1 einsteinlsec, the radiation being fairly evenly distributed ovcr this wavelength region. The light output from an elec- tronic flash rises very rapidly to a maximum and decays exponentially, the duration of this decay dctcrmining the shortest time which can be studied. At present this is one or two microseconds. If the rcaction follows directly upon the flash, the fastest reaction which can be studied has, therefore, a half-time of about 5 psec. If, as nearly always occurs in explosive reactions, there is an induction period between the flash and the beginning of observable reaction, this limitation no longer exists and changes occurring in times of about one microsecond have been studied.7 Changes of still shorter duration are frequently mentioned in connection with studies of detonating explosives but these refer to the propagation of an intense self-luminous effect rather than the variation of an external parameter by a homogeneous system.The photochemical effect produced by a flash of one or two microseconds is only measurable under favourable conditions, in particular when the light absorp- tion of the material is high. Under less favourable circumstances the effect must42 APPLICATION OF FLASH TECHNIQUES be increased by using a flash of longer duration and the maximum rate which can be studied is consequently decreased.The only source which at present compares in intensity with the electronic flash is of the " argon candle " type in which the illumination is produced by a detonating explosive. Intensities ten or a hundred times higher can be obtained in this way but the experimental difficulties of obtaining the necessary reproducibility would be very great. The photochemical method of initiation of reaction is a rather general one and, although ideally suited to the purpose of producing free radicals and atoms for subsequent study, it is not limited to this type of fast reaction. By suitable arrangement of conditions the effects of photolysis may be used to produce a wide variety of changes of which the following are examples : (i) the production of free radicals and atoms at sufficiently high concentration for the study of their physical properties and their chemical reactions; (ii) elevation to an excited state for fluorescence and quenching studies; (iii) population of a metastable electronic state ; (iv) elevation to a non-equilibrium distribution of vibrational and rotational (v) preparation of supersaturated systems for the study of nucleation, growth (vi) homogeneous initiation of explosion for the study of its mechanism and (vii) homogeneous elevation of temperature. The last application is an important one which needs some elaboration. The difficulty of raising the temperature of a system very rapidly and homogeneously has already been mentioned, On the other hand, information is often required about the properties of molecules at very high temperatures, especially in connec- tion with the technically important aspects of combustion such as flames and explosions.If ordinary methods of heating, such as the admission of the material to a heated vessel, are used, the molecule may have decomposed by a relatively slow reaction before the temperature required is attained, and heterogeneous wall reactions are often troublesome. The heating effect associated with flash photo- lysis, which is discussed in more detail in the next section, and which for most applications is to be eliminated, may be itself used for this purpose. An example is the study of the mechanism of carbon formation in the homogeneous gas phase at very high temperatures8 It is easily possible to raise the temperature of a gas by over 1O00" C in a time less than one millisecond by this method, as may be seen from a consideration of the fact that, if each molecule absorbs one quantum, of average wavelength 3000A during this period, the heat available is 100 kcal/mole.The heating effect is usually accompanied by photochemical decomposition, but if the absorbing substance has a discrete spectrum in the region of absorption, showing no dissociation, a purely thermal effect can be obtained, which, if great enough, may result in pyrolysis. These conditions are approached when benzene or sulphur dioxide are used to effect the energy transfer. levels for the investigation of energy transfer ; and coagulation of sols; of the free radicals involved ; NON-ISOTHERMAL NATURE OF RAPID REACTIONS Considering, as an example, air at one atmosphere pressure contained in a long cylindrical vessel 2 cm in diameter, the gas being heated instantaneously to 100" C and the wall remaining at 20" C, the time taken for cooling, by the wall, to reach the centre of the vessel will be about 10-1 sec.This may be considerably longer than the duration of the reaction being investigated. Such a temperature rise is by no means unusual and would be obtained, for example, if 0-5 % of the molecules absorbed light of wavelength 2537& if the net enthalpy change of the overall reaction was zero and if the specific heat of the gases was 6 cal/mole. Although the total heating effect will not normally be obtained until reaction is complete, a considerable fraction of the effect occurs almost instantaneously onR .G . W . N O R R I S I I A N D G . PORTER 43 photolysis owing to the excess kinetic energy of the dissociation products and, in some cases, the collisional deactivation of electronically excited molecules. These theoretical expectations have been fully confirmed experimentally by studies of the change in spectral intensity distribution of absorbing substances after illumination.9 In gaseous systems the most troublesome consequence of the photochemical heating effect is the resultant concentration gradient which is developed between the centre of the reaction vessel and the cold walls, the pressure throughout the gas being, of course, constant.Since the thermal capacity of the wall is relatively high, it remains near its original temperature and immediately after the flash the gas near the wall is cooled, the increased concentration there being accompanied by a decreased conccntration at the centre of the vessel. When eventually all the gas has once more cooled to the wall temperature the concentration gradient disappears but at intermediate times the gradient rises to a maximum which, in the above example of 100" C rise, results in a decrcase in concentration along the axis of the vessel of over 10 %. It is important to realize that this effect is common to all photochemical systems and that the relative effect, expressed as the ratio of true photochemical decomposition to the concentration gradient effect will be of comparable magnitude at lower intensities.For example, Rabinowitch 10 measured the rate of recombination of iodine atoms in a continuously irradiated system by the decrease of absorption by iodine molecules. Both the true photo- chemical effect and the thermal effect were very small but in several experiments the latter effect was the greater. In liquid systems the temperature rise is much less owing to higher thermal capacities but, since it is usually necessary to use very refined experimental tech- niques to detect the small changes obtained, the effect may still be of extreme importance. For cxample, Melville and his collcagues 11 used very sensitive methods to measure changes in refractive index and dielectric constant for an analysis of photochemically induced polymerization reactions and found that the major part of the observed effects were to be attributed to the temperature change alone. There are a number of examples in the literature, particularly those in- volving reactions of atoms and radicals formed by electrical discharges, where these thermal effects are not discussed although they would appear to have had a most important bearing on the results obtained.There are two ways out of the dilemma. Firstly, in designing any experiment for the study of fast reactions, the method of detection must be chosen to be more sensitive to the parameter required than to temperature. Such methods are not numerous and a solution of the problem which has everything to commend it experimentally is to follow the reaction by the temperature change itself.For the measurement of concentration, which is the parameter usually required, absorption spectroscopy is probably the most suitable method which, as long as the concen- tration gradient effect is eliminated, is relatively insensitive to temperature. The second possibility is to increase the thermal capacity of the system. This is done automatically in solution where temperature rises are rarely greater than a small fraction of one degree. In the gas phase it can be achieved by working in the presence of a high rclative partial pressure of inert gas. For example, in some studies by the flash technique of the rate of recombination of iodine atoms 12 the calculated temperature rise was less than 1" C although the corresponding percentage decomposition into atoms was as high as 50 %.Hence the relative concentra- tion gradient effect is negligible. The same precaution eliminated any significant temperature effects in studies of the reactions of C10, CS, S2, etc.13 METHODS OF DETECTION AND MEASUREMENT It is required to measure some property of the system as a function of time over a period which may be of the order of microseconds. The parameter usually required is a concentration, either of the original material or of the intermediates or products, and the measurement must satisfy the following requirements :44 APPLICATION OF FLASH TECHNIQUES (i) It must not itself change the parameter measured. (ii) It must be possible to obtain the measurement with the required accuracy in a time short compared with the time of reaction.(iii) The variable which is measured must be sensitive to changes in the para- meter required and insensitive to other changes, in particular to the tem- perature effects discussed above. The number of physical measurements by which concentrations may be deter- mined in a static system and which fulfil these requirements is very limited. It is doubtful whether there is any method at present, apart from absorption spectro- scopy, which satisfies these requirements and which is also, in principle, applicable to the detection and measurement of all chemical species. In practice observations have so far been limited almost exclusively to the visiblc and ultra-violet regions of the spectrum and, although this greatly restricts the species which can be followed, it will continue to be a most important method owing to the fact that two powerful and convenient detectors are available-the photographic plate and the photo- electric cell.It may be useful to mention briefly the relative merits of these two detectors as applied to fast reactions. photoelectric dctectors are far preferable to photographic ones for the study of fast reactions since they can have response times as low as 10-8 sec and can be made sensitive enough to detect a few photons/sec. These advantages have little relevance to rapid absorption spectroscopy, however, where the essential factor is the magnitude of the change produccd by absorption relative to that of the statis- tical fluctuations in thc photocurrent, i.e.the signal/noise ratio. This ratio is proportional to the square roots of the light intensity and of the shortest time interval which can be resolved. With the highest intensities at present available from continuous light sources it is not possible to design an electronic instrument giving resolutions comparable with those obtained even with medium-sized spectro- graphs whilst at the same time scanning a wavelength interval of a few hundred angstroms in a time short compared with a reaction time14 of, say, 10-4 sec. This can, however, be readily achieved by means of flash photographic spectro- scopy. The superiority of the photographic method in this respect is to be traced mainly to the inefficient use of light sources in the photoelectric technique.The intensity of available sources is limited by the possibility of conducting away the heat and can of course be increased if the lamp is operated for only a short time. If a pulsed flash source with constant output of a few milliseconds duration were developed for use with photoelectric detectors, an improvement in resolving power of several factors of ten would result. The clectronic flash discharge through an inert gas gives a continuous spectrum, overlaid by broad atomic lines over the whole visible and quartz ultra-violet region and is sufficicntly intense to record on standard spectrographic plates, at a dispersion of 2A/mm, in a time of about 20psec. Our experience is that the photographic and photoelectric methods are complementary, their relative usefulness being summarized as follows.FLASH PHoTocRAPHIc.-Ideal for a preliminary survey of the wavelength region ; almost essential for recording complex line structure of transient spectra ; most sensitive means of detection and estimation of a weakly absorbing substance with a discrete spectrum ; preferable for measurements of relative intensities at different wavelengths and at one time. It has the disadvantage that kinetic studies require separate experiments at different times, but this is partially compensated by the good rcproducibility of the flash intensities and the climination of all system- atic errors by the arbitrary order of experiments which may be introduced. PHoToELEcTRIc.-Particularly useful for extended kinctic studies on a single absorption spectrum covering a wavelength region of several angstroms ; superior to the photographic, point by point, method when the relative change in absorbed PHOTOGRAPHIC AND PHOTOELECTRIC METHODS.-It might at first appear thatR .G . W. NORRISH AND G . PORTER 45 intensity is small, since if this change is less than 5 % it becomes comparable with the scatter of the results obtained by photometric methods. It is essential for kinetic measurements on changes occurring in times less than about 20psec. Very little trouble is experienced by either of these methods in connection with the requirement mentioned above that the method of measurement shall not significantly affect the result. Even when a photographic flash, which dissipates the same energy as the photolysis flash, is used, the geomctric arrangement'is such that the photochcmical effect produced by the former is rarcly detectable.Nor- mally the photolysis flash is between five and fifty times greater in energy than the photographic flash. In the photoelectric method the intensity of the continuous source is much lower and there is no danger of detectable stationary state concen- trations of intermediates being formed. With a strongly absorbing substance and a source of the highest available intensity it may be necessary to use a shutter to prevent photolysis by this source occurring for longer than about one second before the photolysis flash is fired. flash techniques which have so far been developed is the exclusion of intermediates such as CH3, CH2, H02 and many other free radicals, especially of the saturated hydrocarbon type, which appear to have no strong transition in the Wavelength region discussed.Although all these substances must have electronic transitions in the further ultra-violet region, it is probable that most of these would be con- tinuous and not easily detected above the continuous spectra of the parent mole- cules and permanent products. For this reason, and also because vibrational frequencies and moments of inertia are required for the calculation of thermo- dynamic and kinetic data, the vibration-rotation and rotation spectral regions are more promising. No suitable method for very rapid investigations in these regions has yet been developed, however. In the vibration-rotation region of the infra-red the difficulty is due to the absence of suitably sensitive rapid-recording detectors.Photocells of the lead selenide and telluride type have a response time of about 10-4 sec but if full use is made of this time the sensitivity, or signal/noise ratio, obtainable with the most intense sources of infra-red radiation is so low that even the detection of high radical concentrations, such as those obtained by flash photolysis, would hardly be possible. They have the additional limitation of being restricted to wave- lengths shorter than about 5p. This confincs the investigation to the least char- acteristic frequencies, such as C-H and 0-H stretching, which would be difficult to follow in the presence of very similar frequencies arising from parent and product molecules in much higher concentrations.The Golay cell also has a short response time and no such wavelength limitation, but its scnsitivity is even less than that of the photocells. Until some fundamentally new technique is developed it seems that the best that could be done in the near infra-red region would be a point by point wavelength investigation of a reaction with a half-time of one millisecond or longer. Once a characteristic new band was found, kinetic studies at a single frequency would be possible. For slower reactions scanning instruments are possible, one recently developed for the study of emission from explosions having a scanned interval of 1 . 5 ~ and a repetition rate of 100 per second.15 The most promising spectral rcgion for development in this field is the micro- wave band.Not only are spectra in this region a very specific means of analysis, once the identity of the molecule responsible for the absorption has been estab- lished, but the rapid recording techniques are already developed. The response time of many existing instruments would be sufficient to begin the study of a number of interesting reactions with half-times of the order of milliseconds and there is no fundamental reason why this response time should not be greatly shortened. There might, however, be considerable practical electronic diffculties connected with the necessary proximity of the flash discharge and the waveguide and detector. There is also a rather serious limitation of the method to reactions at low pressures, INFRA-RED AND MICROWAVE ABSORPTION.-The most important hiitation Of the46 APPLICATION OF FLASH TECHNIQUES since pressure broadening greatly decreases the sensitivity of detection at pressures above about 0.1 mm Hg.Not only would heterogeneous wall reactions become a complicating factor at such pressures but, since it would usually be impossible to use a large excess of inert gas, the tempcrature effect would be very great and, apart from its other disadvantages, this would result again in a loss in sensitivity due to Doppler broadening. OTHER METHODS Of the great number of physical properties which can be used to follow a reaction there are very few which satisfy the requirement of being insensitive to temperature changes relative to changes in concentration.The few which are suitable in this respect, such as diamagnetic susceptibility and electronic polarizability are not specific enough to be useful. The measurement of ternperaturc itself is a method which can be made very sensitive to small changes and furthcrmore, by using very fine resistance wires or thermojunctions, response times of less than one milli- second can be attained. Another serious difficulty now arises, especially in gaseous systems, that the detector itself, the platinum resistance wire, for example, must be directly exposed to the light of the flash, since the gas immediately adjacent to it must also be so exposed. The result of this is an absorption of energy by the wire, which may produce a much greater effect than the energy absorbed by the gas itself, and an entirely spurious record of the gas temperature. ]In liquid systems, where the relative thermal capacity of the wire is small, this effect would only be serious when it was rcquired to investigate thc reaction at times shorter than those required for temperature equitibrium between the wire and the bulk of the liquid to be established. In this brief account of the experimental potentialities of the flash techniqucs we have purposely stressed the limitations and difficulties since much effort can be expended in developing elaborate apparatus which is extremely sensitive to a quite uninteresting, and, after the event, an easily predictable effect. 1 Hartridge and Roughton, Proc. Roy. SOC. A, 1923, 104, 376. 2 Melville, Proc. Roy. SOC. A, 1934, 146, 751. 3 Porter, Proc. Roy. SOC. A, 1950, 200, 284. 4 Roughton, Investigation of Rafes and Mechanisms of Reactions (Intcrscience, 1953), 5 Carrington and Davidson, J. Physic. Chem., 1953, 57, 418. 6 Christie and Porter, Proc. Roy. SOC. A , 1952, 212, 398. 7Norrish, Porter and Thrush, Proc. Aoy. SOC. A , 1953, 216, 165 and Nature, 1953, 8 Knox, Norrish and Porter, J. Chem. SOC., 1952, 1477. 9 Norrish and Porter, Proc. Roy. SOC. A, 1952, 210, 439. 10 Rabinowitch and Lelimann, Trans. Faraday SOC., 1935, 31, 689. 11 Majury and Melville, Proc. Roy. SOC. A, 1951, 205, 496. Grassie and Melville, 12 Christie, Norrish and Porter, Proc. Roy. SOC. A, 1953, 216, 152, and unpublished 13 Porter and Wright, Faraday SOC. Discussions, 1953, 14, 23, and unpublished work. 14 Porter, Faraday SOC. Discussions, 1950, 9, 60. 1s Bullock and Silverman, J. Opt. SOC. Amer., 1950, 9, 608. p. 691. 172,71. Proc. Roy. SOC. A, 1951, 207, 285. work.

ISSN:0366-9033    

DOI:10.1039/DF9541700040

出版商:RSC    

年代:1954

数据来源: RSC

摘要:

REACTIONS OF ATOMIC OXYGEN WITH MOLECULAR OXYGEN BY RICHARD A. OGG, JR. AND WILLIAM T. SUTPHEN Chemistry Department, Stanford University, Stanford, California Received 5th February, 1954 Oxygen gas highly enriched in 018 isotope has been used for rate studies of the exchange reaction The relative proportions were followed by mass spectrometer analysis. Addel i: otopically normal ozone is found to catalyze attainment of this equilibrium, the reaction being very rapid in comparison with 018 exchange between 0 2 and 0 3 . This precludes the direct 0 atom transfer reaction between 0 2 and O3 as being appreciably involved. The only alternative appears to be the ultra-rapid exchange reactions exemplified by 0 + 0018 -+ 00 -t 0 1 8 Vagaries in the dissociation of ozone make a precise determination of the rate constant very difficult, but an activation energy of practically zero and a " normal " frequency factor somewhat less than 1012 mole-1 cm3 sec-1 appear indicated.Some uses of the system as a reagent for detecting production of 0 atoms are discussed. The present study suggests that at low pressures the concentration of 0 atoms exceeds that cor- responding to equilibrium with 0 3 and 0 2 , an effect attributed to energy chains. 016016 -k 0 1 8 0 1 8 J 2016018. The term " very fast " or " ultrarapid " reaction is employed in the sense of being characterized by a very large rafe constant. An ultrarapid second-order reaction of suitable type may be reduced to a pseudo first-order reaction of con- venient time scale by the device of drastic reduction of one reactant concentration, employing an accurately known chemical equilibrium to control and measure this concentration.The classic gas phase example is the ultrarapid reaction H 1- H-H (ortho) H-H (para) + H, whose rate is best studied 1 by utilizing the extraordinarily small but very accurately known equilibrium concentration of atomic hydrogen in hydrogen gas at moderate pressures and temperatures. It appeared to the authors that an even more rapid reaction should be the analogous identical exchange between atomic and molecular oxygen. The moderate activation energy of the hydrogen exchange corresponds to a short-range potential barrier-there is no chemically stable H3 species. However, the well-known stability of the 0 3 species indicates that the short-range interactions between 0 and 0 2 should be in the sense of a potential well.One would thus expect a truly negligible activation energy for the oxygen identical exchange reaction-the rate constant for this process should approach the limit for ultrarapid reactions. Since 016 and 0 1 8 isotopes have nuclear spin quantum number zero, the exist- ence of both orfho and para species for 016016 and 018018 is precluded. Prac- tical study of the exchange reaction in question can be achieved only by its effect on approach to isotopic equilibrium between molecular oxygen species. The rarity of 017 makes the only usable equilibrium the following That the rate of attainment of this equilibrium is completely negligible under ordinary conditions 2 precludes interference by formation of so-called " 0 4 ".If 47 016016 4- 0 1 8 0 1 8 2016018.48 REACTIONS OF ATOMIC OXYGEN this latter species is really formed at low temperatures in liquid oxygen, it cannot have a ring structure. While the 0 - 0 2 exchange reaction in principle could be studied by the thcrmal establishment of the above isotopic equilibrium, the very great dissociation energy of 0 2 would demand inconveniently high temperatures. An equilibrium which a t room temperature offers oxygen atom concentration of suitable magnitude is that involving ozone, It was appreciated that there was possibility of interference from the conceivable direct exchange reaction between 0 2 and 0 3 , exemplified by ooo:k + 00 2- 00 -t- o*oo, where the asterisk indicates the isotope labelling.As will appear from the expcri- mental studies, this direct reaction is fortunately so slow in comparison with the atomic processes as to offer negligible interference. A preliminary account of these studies has already appeared.2 0 3 0 2 -1- 0. EXPERIMENTAL The samples of enriched gaseous oxygen containing some 25-30 % 018 isotope were made available through the courtesy of Prof. A. 0. Nier of the University of Minnesota. The enrichment had been accomplished by thermal diffusion, starting with approximately 1.5 % 018 content. Since at this level the abundance of 018018 is very low, and only moderate temperatures are encountered in the diffusion columns, the enrichment should be predominantly in the 016018 species. This proves to be the case, typical samples displaying the following approximate values of the abundance ratios as found by the mass spectrometer, 34/32 = 1, 34/36 = 100.Hence initially, (34/32) (34/36) = 100. Isotopic equilibrium was established in some samples to check the reliability of the mass spectrometer analysis. The methods employed were the passage of an elcctric discharge from a Tesla coil, or irradiation with a mercury resonance lamp of a sample confined in a silica glass vessel containing liquid mercury at room temperature. By either method the final experimental value of (34/32) (34/36) was found to be in accurate agreement with the theoretically expected value of 4.00. The samples were storcd for use in Pyrex glass containers provided with a hollow-bore high-vacuum stopcock.Connection to the vacuum system was through suitable ground joints. Ozone was prepared from isotopically ordinary oxygen (which was dried by slow dis- tillation from the liquid), by passage through an ozonizer incorporated into the vacuum system. The effiuent, containing approximately 2 % 0 3 , was condensed with liquid nitrogen directly into the reaction vessel. Since the ozonizer proved quite consistent in yield, the desired quantity of ozone could be obtained by metering the volume of oxygen used. This was achievcd by use of a special burette to measure the volume of liquid oxygen evaporated. The mixture of oxygen and ozone in thc vessel was kept cooled with liquid nitrogen, and pumped until no further oxygen was evaporated. (The volatility of 0 3 is negligible at this temperature.) The final determination of the exact amount of ozone in the sample was made by determination of the amount of oxygen produced by pyrolysis.In most experiments the extent of ozone decomposition during contact with the enriched oxygen was small, but it could be very accurately assayed by consideration of the 018/016 ratio in the oxygen after contact. Any reduction of this ratio below the initial figure was due to dilution with 016 isotope produced by ozone decomposition. As described below, the remaining ozone was quantitatively yyrolyzed at the termination of the experiment. The only inert gas so far employed extensively is carbon dioxide. Samples were dried by careful evaporation from the solid, and stored in vessels attached through stopcocks to the vacuum line.From manometric measurement of the pressure, and the known volume of the storage bulbs, an accurately measurcd quantity of carbon dioxide could be condensed in the reaction vessel by cooling with liquid nitrogen. The typical reaction vessel was constructed from a 100cm3 I<jcldahl flask of Pyrex glass. It was provided with a relatively long slender ncck terminating in a hollow-bore stopcock and ground joint. The volume of the flask, relative to that of the various storage bulbs, was carefully determined by a series of gas expansions and manometricRICHARD A . OGG, J R . AND WILLIAM T . SUTPHEN 49 measurements of pressure. Hence, the introduction of a measured gas sample into the calibrated flask allowed computation of the corresponding concentration.Description of a typical experiment follows. The approximately known ozone sample was introduced as described above. With the deoxygenated ozone still condensed at liquid nitrogen temperature, the measured sample of carbon dioxide was introduced, of course condensing. The vessel was then opened to the enriched oxygen reservoir, and a sample was introduced, the quantity being determined by initial and final mano- metric pressure ineasurements on the storage bulb of known volume. The nitrogen coolant was then replaced by an acetone 4- solid carbon dioxide bath, and the vessel was allowed to remain at the corresponding temperature for a period depending upon the size of the carbon dioxide sample in the flask. (For the highest pressures used this approached as much as an hour.) The object of this procedure was to vaporize the ozone and as much as possible of the carbon dioxide, allowing them to mix thoroughly with the oxygen by diffusion.At this low temperature the reaction was negligibly slow. After the mixing procedure the flask was rapidly prewarmed and was then immersed in a water bath maintained at constant temperature. After a measured time interval the vessel was withdrawn from the water bath and rapidly cooled with liquid nitrogen, thus “stopping” the progress of the reaction. The oxygen gas was then transferred from the flask to the sample tube used for the mass Spectrometer analysis. In order to conserve the invaluable enriched oxygen supply a special pumping piocedure was em- ployed to facilitate as nearly complete transfer as possible.The portion of the vacuum line to which the reaction vessel was attached was of very small volume, and was provided with a side arm filled with silica gel. After opening the stopcock of the nitrogen cooled reaction flask this side arm was cooled with liquid nitrogen. This had the result of ad- sorbing the oxygen gas practically quantitatively on the silica gel. The reaction vessel stopcock was then closed, and that of the sample tube (attached to the same section of the line) was opcned. By warming the silica gel the oxygen was desorbed and allowed to expand into the relatively large sample tube. Repeated mass spectrometer analyses demonstrated conclusively that repeated sorption and desorption with the silica gel did not alter the 36, 34 and 32 proportions in the enriched oxygen sample.The trace of oxygen gas remaining in the reaction vessel was removed by direct exhaustion with the vacuum pump. Complete removal of oxygen was necessary to avoid errors in the estimation of the 018/016 ratio in the ozone. Repeated outgassing of the condensed ozone and carbon dioxide assured iiegligible retention of oxygen. The reaction flask was then warmed to a temperature of several hunhed degrees Centigrade and was maintained at this condition until pyrolysis of the ozone proved complete. The vessel was again cooled with liquid nitrogen and the quantity of oxygen gas produced by the pyrolysis was determined by manometric measurement of pressure. (The coolant nitrogen was maintained at a rixcd level on the slender neck to minimize uncertainty to the temperature of the gas sample.) This oxygen gas was then transferred to another sample tube for mass spectrometer analysis.As an additional precaution a sample of the remaining carbon dioxide was also taken for mass spectrometer analysis. However, in no case was the 018/016 ratio in the carbon dioxide found to be greater than the natural value. This is proof that the role played by the carbon dioxide is purely physical. Such possible reactions as 0 1 8 -I- c02 y2 0 -I- OCOlS are slow in comparison with the other steps. For the few photochemical experiments reported, the reaction vessel was fashioned from a 100 cm3 flask of fused pure silica, with a silica to Pyrex graded seal. This vessel was also used for some of the thermal runs.Such intercomparisons as have been made indicate that results from the Pyrex and silica vessels are indistinguishable. This constitutes the principal experimental indication of the essentially homogeneous character of the reaction. As indicated in the previous communication 2 the earlier analyses were carried out with mass spectrometers at the Uiiiversity of California. A few analyses were also ob- tained at the laboratories of the Consolidated Engineering Corporation, Pasadena, Cali- fornia. The Stanford Research Institute has recently acquired a mas sspectrometcr manufactured by the above corporation, and this instrument has been used for all recent work. In the analysis, emphasis is placed on the 34/32 and 34/36 ratios. The abundance of the 0 1 7 species is too low to necessitate any corrections.It was found desirable to determine the relative magnitude of mass number 28, as this gave a measure of possible nitrogen contamination, indicative of any air leaks.50 REACTIONS OF ATOMIC OXYGEN RESULTS To minimize the wordiness of presenting the data, the approach toward equilibrium in the reaction will be referred to by the admittcdly rather crude term “scrambling ”. The term “ isotope exchange ” will (unless specifically defined otherwise) refer to approach toward equilibrium in the set of reactions exemplified by 016016 3- 018018 zz 2016018 016018 -/- 016016016 .( 016016 + 018016016. The earlier studies on the ozone catalysis of “ scrambling ” were carried out without addition of foreign gas, and constituted the principal basis of the previous report.2 As will be noted in the discussion, these studies are not satisfactory for quantitative evaluation of the rate constants for the important reaction steps.They did, however, serve to demon- strate the feasibility of the extended study, in that they strikingly demonstrated the fact that the scrambling was rapid in comparison with the isotope exchange. ‘Table 1 gives in considerable detail the data relevant to a typical example of these earlier experi- ments. In presenting this and the remainder of the analytical results, the symbol 0i* under “ sample analyzed ” refers to the enriched oxygen gas sample introduced initially into the vessel, and finally separated by fractional distillation from the residual ozone, as described above.The symbol 02(03) refers to the oxygen gas sample produced by pyrolysis of the ozone, as described above. The “ initial analysis ” given for this refers to a sampIe of oxygen gas used for the preparation of the ozone. TABLE 1 No added foreign gas ; temp. 0” C ; initial partial pressure 0 3 , 50 mm Hg ; time interval, 15 min ; initial partial pressure 0 2 , 15 mm Hg initial final sample analyzed 34/32 36/34 yo 01s 34/32 36/34 % 0 1 8 0,9002 0.0115 31.0 0.4145 0.0685 17-2 0 2 ( 0 3 ) 000399 - 0.20 04065 040071 0.33 0 2 * The analytical results in table 1 were obtained with the Consolidated Engineering Nier Isotope Ratio instrument, and are regarded as especially trustworthy. Consideration of the above data exemplifies the conclusion indicated in the previous report -namely that the isotope exchange is slow as compared with the scrambling.It will be observed that the final 0 1 8 abundance in 0 3 has been but slightly increased above the initial value. Had isotopic equilibrium between 0 2 and 0 3 been reached, the abundance of 0 1 8 would have been approximately 5.2 atomic percent. On the other hand, in the 0 2 * the initial value of (34/32) (34/36) is 78, whereas the uncorrected final value is 6.0. It must be noted that some decomposition of the 0 3 has occurred, as indicated by the decrease of 0 1 8 from 31.0 to 17.2 %. Since the ozone is practically pure 016, this means dilution with the species 016016, i.e. 32. When decomposition of this is extensive the detailed correction is rather complicated.However, a first approximation is simply to subtract the corre- sponding jitzal excess 32, and to estimate the (34/32) (34/36) product is the hypothetical residual oxygen. This corrected product is 10.9. Comparison with the limiting value of 4.0 indicates the extensive scrambling. A further comment on the evaluation of the analytical results may be made. Simple dilution with isotopically normal oxygen, i.e. “ 32 ”, unaccompanied by true scrambling, can of couise reduce the product (34/32) (34/36) to any value, including the range less than 4.0. However, this would leave the ratio 34/36 unaffected. Since the enriched oxygen used is deficient in the species 36, a qualitatively reliable index of scrambling is the increase in the ratio 36/34. Such an increase is seen in table 1.A Considerable body of such experiments as that in table 1 indicated always the same sense of result, i.e. that ozone caused scrambling, accompanied by a relatively slow isotope exchange. In the attcmpt to permit more nearly quantitative evaluation of the rate phenomena, these experiments were modified by addition of carbon dioxide at moderate pressures and by change of temperature. A selection of results fiom such experiments appears in table 2. The analytical results in this case were obtained with a WestinghouseRICHARD A. OGG, J R . A N D WILLIAM T. SUTPHEN 51 mass spectrometcr, in which the isotope ratios are found from peak heights. There was a considerable background at mass 36, and in consequence the vitally important ratio 36/34 is solnewhat uncertain, especially for small values.The enriched oxygen used in these experiments had initial 34/32 and 36/34 of 0.925 and 0.0234 respectively. The initial product (34/32) (34/36) was thus 39.6. The final value of this product quoted in table 2 has been corrected for oxygen dilution as discussed before. In several cases the ozone decomposition was so slight that this correction is of no significance. TABLE 2 final 0 2 * final Oz(O3) cxpt. O" temp time C O ~ P Of,'' O/n' g$ ___- mi' mm HE! mm Hg mmHg mm Hg 34/32 36/34 ( ~ ~ & ~ 34/32 36/34 %Ols 30 0 15 0 19.6 523 51.2 28 0 15 200 18.5 38.2 35.0 29 0 15 500 20.2 51-7 51-7 31 0 16 207 18.4 41-1 39.7 34 0 10 203 5.4 26.5 24.8 35 0 10 211 5.3 26.4 25.3 36 0 10 213 5.4 14.4 14.6 39 $27 2 204 19.7 35.1 33.3 38** -22 4 217 5.3 34.6 33.5 40** -17 8 158 26.0 17.4 17.3 0382 0.521 0.68 1 0.567 0.408 0.459 0.665 0.450 0.634 0.805 0.1 15 0.0640 0.043 0.063 1 0.0523 0.060 1 0.0678 0.0565 0.0408 0.0360 6.7 1 13.7 23.1 15.3 16.9 15.7 13.0 17.3 21.2 23.6 0.00896 0.01 10 0.02 10 00226 0.008 19 0.009 10 0.00985 0.0096 000986 0.0176 - 0.44 - 0.54 - 1.02 - 1.10 - 0.40 - 0.44 - 0.48 - 047 - 0.48 - 087 ** bath, chilled acetone.While a more dctailed appraisal is given in the later discussion, it may be mentioned here that the data in table 2 present unexpected features. The increase of COz pressure, while causing the expected acceleration of isotope exchange, actually inhibits the scrambling reaction. Also, the temperature coefficient of the reactions is surprisingly low. As a working hypothesis it was proposed that the equilibrium between O3,02 and 0 is seriously disturbed at low pressures, possibly due to an energy chain in the ozone pyrolysis.It was expected that sufficiently large quantities of foreign gas would effectively suppress TABLE 3 44 4-21 15 2.0 46 -150 5 2.0 49 $35 5 2.0 52 $21 15 2.0 53 1-35 10 2.0 54 -1-50 3 2.0 47 0 375 2.8 51 -k97 5 2.0 451 -1-17 15 2.0 482 1-22 15 2.0 503 +21 15 1.0 19-7 25.6 23-7 20.3 33-3 26.5 20.3 27.7 24-6 10.5 29.6 23.3 10.0 24.0 19.7 9.6 25-3 19.8 19.2 29.6 22-1 20.8 30.7 11.1 19.8 30.0 28.1 20.2 24.0 7.3 20.0 34.8 5.4 0-600 0.399 0.7 13 0.386 0.432 0.309 0.387 0.174 0.55 0.15 0.1 3 0.0602 0-0427 0.0207 0,0275 0.0303 0.025 1 0.022 1 0.0461 0.0405 0.0377 0.0341 13.4 20.0 43.0 34.0 3 1.3 32.3 42.0 22.9 21.7 0.00940 - 0.47 0.00853 - 0.43 0.00962 - 0.48 0.00783 - 0.39 0,00798 - 0.40 0.0111 - - 0.0872 0.0222 - 0.0141 - - 0.115 0.0294 - 0.106 0.0280 - - - - 1 Pyrex flask, irradiated with intense red light ; 2 silica flask, irradiated with ultra-violet light ; 3 silica flask, irradiated with ultra-violet light.these vagaries-a continuation of the effect demonstrated in 30, 28 and 29. In conse- quence, a further series of experiments was undertaken, in which the partial pressure of carbon dioxide was made as large as feasible. The corresponding details are given in table 3. The analyses of this set were performed with the new mass spectrometer of the Stanford Research Institute. The enriched oxygen used in expt. 41 to 52 inclusive had initial 34/32 and 36/34 of 0.915 and 0.0185 respectively, and thus an initial product (34/32) (36/32) of 49.5.The oxygen used in expt. 53 and 54 had initial 34/32 and 36/34 of 0.964 and 000978 respectively, and hence an initial product (34/32) (34/36) of 98.6. Included in table 3 are also the52 REACTIONS OF ATOMIC OXYGEN results of three photochemical experiments. The light source in expt, 45 was a high- pressure mercury arc, from which spectroscopic tests showed a high flux in the red region absorbed by ozone. The Pyrex flask served to filter any ultra-violet light absorbable by ozone. The source in expt. 48 and 50 was a low-power mercury resonance lamp, delivering most of its radiant energy at 2537A. This is strongly absorbed by ozone, and it will be noted that considerable photolysis resulted. The product (34/32) (34/36) has been corrected for isotope dilution as before.It will be observed that this number has not been set down for some of the experiments -the inferences drawn from these are essentially qualitative. An explosion caused the loss of the pyrolyzed ozone in expt. 54, but the scrambling results are still significant. As in the previous tables, when no entry appears under 36/34 for the O2(O3), this means that the ratio was too small to measure accurately. Detailcd appraisal of the data in tablc 3 is deferred to the discussion, but it may be noted that the expected " quenching " effect on the scrambling of adding carbon dioxide at high pressure has been observed. This is most strikingly shown by expt. 47 at 0" C.In spite of its protracted duration, the scrambling is negligible as compared to the experiinents (at corresponding temperature) whose results appear in table 2. Expt. 51 at 97" C shows that sufficient temperature elevation makes both scrambling and isotope exchange quite rapid. However, the isotope exchange still lags behind. For the enriched 0 2 the final (34/32) (34/36) is 3.78, indicating practical scrambling equilibrium. However the ratio 34/32 in the O2(O3) is only 0.0872 as compared with 0.174 for the 0 2 * . Exchange equi- librium has not been attained. A point of interest is that the Oz(03) from expt. 51, 48 and 50 all show a value very close to 4.0 for the product (34/32) (34/36). DISCUSSION There is admittedly some question as to whether the reported results corre- spond to a truly homogeneous reaction.Exhaustive tests with packed flasks are planned for future work. However, the exchange of silica and Pyrex vessels caused no noticeable effect on the thermal reaction. In the high-pressure carbon dioxide experiments the gaseous diffusion should be sufficiently slow to ensure a minimum effect of surface reaction, and most emphasis is placed on these. Finally, the photoreaction is certainly essentially homogeneous, and apparently must involve the same significant step effecting scrambling as does the thermal reaction. In subsequent discussion it is provisionally assumed that no surface reactions need be considered. The general state of the experiniental data is still far from satisfactory in allow- ing accurate evaluation of rate constants, but a t least certain qualitative features of the mechanism seem reasonably established.The very considerable body of data shows invariably that scrambling is much more rapid than exchange, and hence that the possible reaction 000 + 0 0 1 8 -+ 00 + 00018, etc. (1) cannot be significantly involved in the scrambling. Rather crude estimates indicate that this calls for the activation energy of (1) to be a t least some 30 kcal/ mole. It appears that the scrambling can be reasonably attributed only to the expected atomic oxygen reaction 0 + 0 0 1 8 --+ 00 + 018, etc. k2 (2) However, the factors determining the stationary concentration of 0 are appar- ently not as simple as was inferred in the previous communication.2 For purposes of discussion, it is proposed that the high-pressure carbon dioxide experiments listed in table 3 correspond most nearly to the establishment of true equilibrium between 0 3 , 0 2 and 0.From the accurately known thermodynamic properties of these three species 3 the equilibrium constantR I C H A R D A . OGG, JR. AND WILLIAM T. SUTPHEN 53 has the value at 25" C of 2.29 x 10-12 atm, or 9.35 x 10-17 molelcm.3 If thermo- dynamic equilibrium is maintained, the reaction is a pseudo first-order process whose rate constant k, = Kk2[03]/[02]. At 25" C, ka = 9.35 x 10-17362[03]/[02] sec-1. The reverse reaction at corresponding equilibrium between O 3 , 0 2 and 0 is a pseudo first-order reaction whose rate constant kb = 4Kk2[03]/[02]. The time for half approach of initially pure 016018 to the equilibrium mixture with 016016 and 018018 is In [(2/ka + kb)].At 25" C this would have the value 1.5 x lOls[02]/k2[03] sec. If the ratio [03]/[02] were chosen as 1.5, which is representative for the data in table 3, the time would be 1015/k2. For this to be of the order of magnitude of 103 sec, the corresponding value of k2 would be 1012 mole-1 cm3 sec-1. Were the value of k 2 to be as large as indicated in the previous paragraph, the corresponding activation energy would be negligible. The change in the rate constant k, with temperature would thus be determined only by the change in K. This in turn would be conditioned by the dissociation energy of 0 3 into 0 2 and 0, namely 25 kcal/mole. With other conditions constant, an increase from 25" C to 50" C should increase k, by a factor of 101.4.From consideration of the rather erratic data in table 3, the increase does not seem to be as great as this. However, the data in table 3 shows a considerably greater temperature coefficient than that in table 2. The most plausible conclusion to be drawn from the above is that the partial pressure of carbon dioxide used in table 3 has improved the approach toward equilibrium between 0 3 , 0 2 and 0, but still not "quenched" completely the strange behaviour shown in the data of table 2. In light of this fact, it can scarcely be said that a very accurate estimate of k2 and its activation energy can be made. However, the most plausible figure indicated by the present data would be a prac- tically temperature independent value somewhat smaller than 1012 mole-1 cm3 sec-1.Such a figure seems reasonable for the exchange reaction anticipated in the discussion. If a figure of the above magnitude be accepted for k2, one is forced to the conclusion that at the low pressures corresponding to table 2 the stationary concen- tration of atomic oxygen is in very considerable excess over that corresponding to equilibrium with 0 2 and 0. A suggested cause of such an cffect is related to the irreversible pyrolysis of ozone. The mechanism in agreement with experimental studies 4 at high oxygen pressures calls for practical equilibrium between 03, 0 2 and 0, and the relatively slow step This reaction is exothermic by some 92 kcal/mole. Equipartition would produce " hot " molecules of 46 kcal/mole. In collision with 0 3 these could cause dissocia- tion of the latter into 0 2 and 0.One is thus faced with the likelihood of a branch- ing energy chain. The concentration of 0 atoms maintained by such a process could well exceed by a large factor the equilibrium value, even for relatively slow pyrolysis. Foreign gas molecules should have the effect of collisionally deactivat- ing the " hot " 0 2 molecules, and hence partly suppressing the abnormal production of 0 atoms. That this suppression is incomplete even at 2 atm of carbon dioxide is suggested by the data in table 3. Some remarks may be made on the photoreaction. The experiment with intense red light gave no significant increase in scrambling rate over the thermal value. The ultra-violet experiments on the other hand, gave a relatively enormous increase.There seems to be no reasonable doubt that the primary photoprocess at 2537A" involves dissociation of 0 3 into 0 2 and 0. On the other hand, it seems most probable that with red light an electronically activated molecule is 2 016018 --j 016018 + 018018 ka 016016 + 018018 -+ 2016018 kb 0 3 + O+ 2 0 2 .54 MECHANICAL METHOD FOR ACTIVATION formed, which may be collisionally deactivated, or may undergo metathetic re- action with 0 3 . Such mechanistic decisions are probably typical of the most useful application of the above studies in their present state, inasmuch as they are not sensitive to the rather considerable numerical uncertainty in the experi- mental value of the rate constant for the 0 atom exchange reaction. The above studies do not yet give very extensive information about the quasi- unimolecular dissociation of 0 3 into 0 2 and 0, except to indicate that the inert gas concentration so far used is still extremely far from producing approach to the asymptotic high pressure limit.It appears that a really precise determination of the rate constant k2 will demand production of 0 atoms by the thermal dissociation of 0 2 itself, i.e., by the experi- ment analogous to the ortho-para hydrogen interconversion.1 This study is con- templated for the future. Its completion should allow more nearly precise evalua- tion of the factors leading to abnormal 0 atom concentration in ozone pyrolysis. 1 Farkas, Orthohydrogen, Parahydrogen and Heuvy Hydrogen (Cambridge University 2 Ogg, Jr. and Sutphen, J. Chem. Physics, 1953, 21, 2078. 3 Latimer, Oxidation States of the Elements (Prentice-Hall, New York, 1952), p. 36. 4 Wulf, J. Amer. Chem. SOC., 1932, 54, 156. Press, London, 1935), p. 66. ADDENDUM Since the submission of our paper to the Discussion, the work in question has been pursued actively. The quantity of new data considerably exceeds that given in the present communication. It is intended to incorporate this, together with a more detailed dis- cussion, in a future separate communication. For thc present, the impact of the new work may be summarized in the statement that it supports the conclusions arrived at in the present paper. Some specific points may be emphasized. It has now been clearly demonstrated that experimental variation of the surface to volume ratio in the reaction vessels is without effect, and hence that the reactions in question are truly homogeneous. The effect of added carbon dioxide up to pressures as high as 16 atm has been followed systematically. The presently indicated inhibitory effect on the " scrambling " reaction has been found to approach an asymptotic limit. At this limit the experimental activation energy agrees satisfactorily with the dissociation energy of 0 3 into 0 2 and 0. The conclusions regarding energy chain quenching appear thoroughly substantiated. The effective rate constant for isotope exchange shows the monotonic dependence on carbon dioxide pressure expected from quasi-unimolecular reaction rate theory.

ISSN:0366-9033    

DOI:10.1039/DF9541700047

出版商:RSC    

年代:1954

数据来源: RSC

摘要:

54 MECHANICAL METHOD FOR ACTIVATION A MECHANICAL METHOD FOR THE ACTIVATION OF FAST REACTIONS BY T. H. BULL* AND P. B. MOON Department of Physics, University of Birmingham Received 2nd February, 1954 By relatively simple mechanical means, pulsed beams of molecules moving with speeds up to about a kilometre per second can be obtained. Heavy atoms and molecules moving at such speeds carry energies of the order of I0 kcal/mole and may react with other molecules with which they collide. Preliminary experiments have been made on the formation of CsCl by the impact of CC14 on Cs. During the past few years, a technique has been developed by which gas mole- cules at low pressure are swept up by the tip of a rotating blade and are flung off with the speed of the tip added to their thermal velocities.Since the speed of the * Present address: 1. C. I., Ltd., Butterworth Res. Lab., Welwyn, Herts.T. H . BULL AND P . B. MOON 55 tip may reach 105 cmlsec, the kinetic energy given to heavy molecules can be very substantial; for a molecular weight of 200, 10s cmlsec corresponds to 105 J/mole or about 24 kcal/mole. If such a fast molecule collides with some other molecule, it is possible that chemical reaction may ensue and, at first sight, it seems attractive to surround the rotor with a mixture of two gases and look for reaction products. It turns out, however, to be extremely difficult to distinguish any such effect in the presence of reactions occurring by the ordinary thermal mechanism in the gas or at the walls of the vessel ; it seems better to select a more-or-less collimated beam of one type of molecule and to direct this beam into another vessel where it meets a stream of the other molecules. Products of reactions genuinely due to high-speed impact must then be formed in the localized region of space where the beams cross ; more- over, they must be formed at identifiable instants of time, since the high-speed beam arrives in pulses, one for each revolution if the rotor carries a single blade.If both the projectile and the target molecules are heavy, but not so complex as to possess many degrees of freedom, a useful picture of the situation is obtained by ignoring thermal energies in comparison with the kinetic energy &qv,.2 corre- sponding to the mass ml of the projectile and the velocity vT of the rotor tip.Con- servation of momentum reduces the available energy by the factor m2/(ml + where m2 is the mass of the target molecule, the remainder going to the kinetic energy of the complex. Since this factor is typically of the order of Q, the avail- able energy is rather low for the activation of chemical reactions; in addition to choosing heavy molecules for study, it is clearly desirable to investigate examples where the activation energy is likely to be low. We owe to Prof. H. W. Melville the suggestion that reactions between alkali metal atoms and halogen compounds should be studied, and such reactions are attractive for another reason : the alkali metals and their compounds are sensi- tively and rapidly detectable by surface ionization on a hot filament.Though the technique requires further development before results of chemical significance can be obtained, it is felt that an account of the methods and preliminary results may be of interest. EXPERIMENTAL The apparatus, constructed of Pyrex glass, is shown in outline in fig. 1. Descriptions of the rotor and of the method of driving it have been given elsewhere,ls 2 and for present purposes it will be sufficient to say that the rotor blade was of aluminium alloy and that the effective area of the tip was about 0.25 cm2. At the highest speed used in these particular experiments (1500 revlsec or 6 x 104 cmlsec), the tip sweeps a volume of 15 l./sec. By a continuous-flow method, the pressure of CC14 in the rotor vessel was adjusted to be about 2 7 x 10-4 mm corresponding to a kinetic theory free path of about lOcm and to a vapour density of 2.5 x lO-gg/cm3. The mass of CC14 swept up by the tip each second was thus of the order of 4 x 10-5 g.A small fraction of these fast mole- cules passed through the slit s, through the region R (into which a stream of caesium atoms could be injected at a later stage of the work) and into an open-ended cylinder K which received electrons emitted by the hot tungsten filament F. As each pulse of mole- cules passed through the electron stream, some became ionized and caused an increase in the current to the anode. These pulses of current could be amplified and displayed on an oscilloscope with a time-base synchronized to the frequency of the rotor. Typical records are shown in fig.2a; the sinusoidal lower trace is a time-marker at twice the frequency of the rotor. Such records not only demonstrate the pulsed nature of the high-speed molecular beam ; they also give the actual time of flight of the pulse from the rotor to the detector. Table 1 shows the measured speed of the middle of the pulse compared with the speed of the rotor tip. The molecules in the pulse have a higher speed than the rotor tip, the roughly constant difference being about what would be expected from the thermal velocities with which they leave the tip. The next stage in the experiments was to introduce caesium vapour into the region R. This was done by breaking, with a magnetically-operated device, a tube containing caesium56 MECHANICAL METHOD FOR ACTIVATION metal which was surrounded by an oven 0.The caesium pressure was adjusted so that a CC14 molecule crossing the caesium stream would have an appreciable chance of making a collision but would be unlikely to make more than one collision with a caesium atom. - 0-- k CgE!.g-’ @pjRr Hor irontol Section FIG. 1. The caesium vapour was localized as far as possible by a liquid-air trap having as its lower end a hollow ring C through which the CC14 beam passed on its way to the detcctor. The cylinder K was now made negative with respect to the tungsten filament, which acted as a surface ionization detector both of caesium and of any CsCl that might be formed. TABLE 1 rotor CC4 “ positive ion ” tip speed pulse speed pulse speed ratio cmlsec cm/sec cm/sec 1.52 x 104 3-5 x 104 4.7 x 104 1.3 2.92 x 104 4.5 x 104 4.9 x 104 1.1 4-33 x 104 6.1 x 104 5.2 x 104 0.87 6-52 x 104 8.2 x 104 6.7 x 104 0.81 RESULTS Fig.26 shows the pulses that were observed. They are undoubtedly due to caesium ions leaving the tungsten filament, but whether they represent the arrival of Cs atoms or of CsCl molecules cannot be determined dircctly. From the times at which these positive ion pulses are observed, relative to those at which the CCI4 pulses reach the detector, it is possible to deduce the mean velocity with which the pulse of Cs or CsCl travels from R to F. Table 1 shows the results obtained, the last column giving the ratio of the pulse velocity to that of the carbon tetrachloride. If the caesium were in the form of atoms resulting from elastic collisions, this ratio should, from simple dynamics, be 1.07; for complerely irtelastic collisions it would be 0.54.Caesium chloride molecules would have velocities dependent on what fraction of the encrgy released in the reaction appears as kinetic encrgy. Detailed analysis of these results shows them to be consistent with the supposition that the observcd pulses are due to CsCl molecules formed in a reaction in which thc release of kinetic energy is about 3 kcal/molc ; but it is entirely possible that the pulses contain some Cs atoms, either projected without chemical change by the CC4 moleculesFIG. 2b. [To face page 56T. H . BULL AND P . B . MOON 57 or due to a small amount of caesium vapour entering the rotor chamber and being returned as a high-speed beam along with the main beam of CCl4 molecules.The survival of atomic caesium in the rotor chamber in the presence of CC14 vapour seems unlikely ; without any carbon tetrachloride in the rotor chamber the pulses due to caesium reacting to the detector directly from the rotor were only a fifth as large as ion pulses observed in the main experiment. Some experiments were performed in which mercury vapour replaced the carbon tetrachloride ; in this case, elastic collisions only are possible, and the speed of the forward- projected caesium atoms should be 1.2 times that of the incident mercury atoms. In three experiments, the ratio was found to lie between 1.16 and 1.27. DISCUSSION The results summarized above show that it is possible to obtain intense beams of heavy atoms or molecules, moving at known and roughly equal speeds consider- ably greater than those of thermal agitation at ordinary temperatures. It appears possible to study the collisions they make in crossing another stream of atoms or molecules, by observing the times of arrival of the products of such collisions at a suitable detector.Other methods of producing molecular beams for collision studies include the neutralization of positive ions of known specd,3,4 and the selection by rotating shutters of a portion of the velocity-spectrum of a molecular beam emerging from an oven.% 6 The neutralized-ion method is at its best for kinetic energies substanti- ally higher than those obtainable by the present method, while the oven-and-shutter technique is restricted to energies within the thermal range.The rotor method has the disadvantage of being suitable for comparatively heavy molecules only, but the advantage of providing a relatively high intensity ; the flux of neutral molecules through the collision region in the present experiments was the equivalent of several microamperes of singly-charged ions. All three methods seem to deserve further development ; for in spite of their chemical interest, single collisions between neutral atoms and molecules have hitherto been less studied than collisions involving ions or electrons. We should like to acknowledge many stimulating discussions with Dr. D. G. Marshall, who made some of the preliminary experiments leading to those here reported. The rotors were skilfully made by Mr. J. B. Saul. Part of the apparatus was obtained through a Royal Society Government Grant, and one of us (T. H. B.) is indebted to the Department of Scientific and Industrial Research for a mainten- ance award. 1 Marshall, Moon, Robinson and Stringer, J. Sci. Instr., 1948, 167, 478, 2 Moon, J . Appl. Physics, 1953, 4, 97. 3 Horton and Millest, Proc. Roy. SOC. A , 1946, 85, 381. 4 Amdur, Kells and Davcnport, J. Chem. Physics, 1950, 18, 1676. 5 Kofsky and Levinstein, Physic. Rev., 1948, 74, 500. 6 Marple and Levinstein, Physic. Rev., 1950, 79, 223.

ISSN:0366-9033    

DOI:10.1039/DF9541700054

出版商:RSC    

年代:1954

数据来源: RSC

摘要:

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. Rev., 1933, 44, 193.

ISSN:0366-9033    

DOI:10.1039/DF9541700058

出版商:RSC    

年代:1954

数据来源: RSC

摘要:

RELAXATION TECHNIQUES FOR FAST REACTIONS A STUDY OF THE DISSOCIATION OF NITROGEN TETROXLDE BY S. H. BAUER AND M. R. GUSTAVSON Department of Chemistry, Cornell University, Ithaca, New York, U.S.A. Received 28th January, 1954 Attention is called to the thermodynamic and kinetic features of those reactions which are " fast " and for which relaxation techniques must be used. The various methods which have been applied to the study of the nitrogen tetroxide dissociation are briefly discussed as examples of the variety of available devices. In the method we used, the gas was expanded relatively slowly and isentropically by making it flow through a properly shaped nozzle ; then it was rapidly compressed (in an interval of several microseconds) in front of an obstacle set in the stream parallel to the flow lines.The observed difference between the original pressure and the stagnation pressure is shown to be directly proportional to the entropy gained in the latter non-equilibrium compression. Experimental details and data on C02 and N2O4 are given. A general relaxation theory is set up for systems which must be represented by several groups of degrees of freedom, wherein equilibrium exists within the groups but not among the groups. The rate of establishment of complete equilibrium is evaluated in terms of a spectrum of relaxation times, both for the case when the perturbation is im- pressed as a step function and when it is introduced as a specified function of the time. At the present stage of development, the data obtained with the above apparatus allow the direct evaluation of an average relaxation time ; individual values can be estimated by a trial-and-error process.An effort is being made to develop an inversion scheme for deducing the spectrum. The average values found for C02 and N2O4 are compared with those reported by other investigators. An anaIysis of the errors inherent in this method is presented. Fast chemical reactions are characterized by a limited value for (APIRT), where AF+ denotes, as usual, the increment in free energy upon transformation of the reactants from their standard states to the transition state on their path to form products. For unimolecular processes the available laboratory devices set the lower limit for this ratio to be about 16; for bimolecular reactions it is 3-4. These estimates are based on an assumed time resolution of the order of a micro- second and is subject to change since a large variety of experimental procedures continue to be developed.The procedures reported thus far range from rapid spectrophotometric devices, to " diffusion flames ", to the use of repeated spectro- graphic recording with controlled " time gates ". Attention is called to one group of fast reactions for which the applicable techniques are distinctly limited to relaxation processes. This group is characterized by the additional condition 1 AF"/RTI is about 12 or less Such reactions which have been treated are in- herently simple, uncomplicated by side reactions. The thermodynamic functions for these changes have been well established.Indeed, it is the latter which makes it possible to apply relaxation techniques successfully. The description of changes in linear systems in terms of the response of coupled relaxation processes is being actively extended at present.1 The concept is an old one which can be traced to Maxwell,2 who introduced it in his model for explaining shear viscosity of gases. Strictly speaking, its application to chemical kinetics 3 is not legitimate because in chemical systems, even for slight departures from equilibrium, the response to perturbations may not be strictly linear.4 However, 6970 RELAXATION TECHNIQUES the notion is convenient to use ; when a quantitativc formulation is undertaken one must investigate whether the rate of rcvcrsion to equilibrium in that particular case may be sufficiently well approximated by an exponential decay or a linear combination of exponential functions.Given a system which satisfies the above conditions for AF” and AF*, it will be found to be at equilibrium. To prepare the system for a kinetic study, a per- turbation must be introduced over an interval comDarable to or shorter than [‘O”’ ‘““‘“‘1, where n is the order of the reaction. ?he number of (concentrati onP dLevi& available is‘ decGedly limited. Of proven utility are rapid compressions,s, 667 which in effect inject enthalpy into the system, and intense light flashes 8 which produce electronic excitation followed by selected chemical reactions. Other methods such as pulsed beams of electrons or ions have yet to be developed.To observe the rate of return to equilibrium, similarly short-response time devices must be used for the measurement of concentration, either of selected chemical species or of overall density. As an alternate, a steady-state flow process may be set up so that instruments with relatively long response times may be used for measuring concentrations as a function of position along the flow lines? Finally, phase-shift detection is a useful and sensitive procedure when the perturbations imposed are periodic. The following brief account of the techniques which have been used in the study of the rate of dissociation of nitrogen tetroxide will call attention to the usefulness of each as well as to its specific limitations. EXAMPLES OF RELAXATION TECHNIQUES The absorption of ultrasonics due to lag either of the instantaneous heat capacity or the specific volume behind the pressure wave has been carefully analyzed in the recent literature.l*.12 It is perhaps essential to emphasize that absorption measurements of high reliability over a considerable frequency range are needed to permit deduction of reliable rate constants. It took almost 40 years for these restrictions to be fully appreciated. The notion that rate constants can be esti- mated from the dispersion of sound is the oldest suggested procedure for studying fast chemical reactions. Attempts to determine the rate of dissociation of nitrogen tetroxide 13 and of the aliphatic acid dimers 14 from the speed of sound measure- ments were doomed to failure. In addition to the relatively large and to some extent indeterminate corrections which must be made for gas imperfection,ls the measurements of speed of sound as a function of frequency appear to be particu- larly sensitive to the presence of impurities and to errors arising from the adsorp- tion of gases on the walls of the vessel.The chief difficulty, however, is that the dissociation of a gas even as simple as N2O4 is not a single process. Hence any detected dispersion or absorption region somehow must be identified with a par- ticular rate process or with a combination of processes. Unless the concentrations of individual chemical species are determined as a function of time, such an identi- fication must be considered in all relaxation procedures for the measurement of rapid changes in chemical state.Nevertheless, as a result of serious cfforts to measure sound dispersion in nitrogen tetroxide, limits were set for the uni- molecular rate constant, 3 x 104 < k < 4 x 105 sec-1 at about 0” C. Brass and Tolman 16 set up a steady-state flow which in effect subjected the equilibrium mixture of N2O4 + NO2 to a sharp pressure drop. With an array of thermocouples, they followed the return to equilibrium by observing the additional heat increment due to association as the gas flowed down the tube. Although many objections to this expcriment were noted by the authors, they provided another “ lower ” estimate of 8.2 x 104 sec-1 at 1 atm and 25” C for the unimolec- ular rate constant. In the most recent efforts to settle this matter a steady-state flow system 9 and a very rapid compression 6 have been utilized.Carrington and Davidson passedS . H . RAUER A N D M . R . GUSTAVSON 71 a weak shock through an equilibrium mixture of N2O4 -t N02. Thus they sub- jected the gas to an adiabatic non-isentropic compression, and followed the subse- qucnt dissociation of the tetroxide with light of wavelengths which were absorbed preferentially by either the NO2 or N2O4. Because they used photometers with low dispersion, they averaged thcir concentration determinations over most of the vibrational levels, so that to a large extent they eliminated the relaxation processes connected with vibration-translation energy transfer. These studies were made in the presence of a large excess of nitrogen, over the temperature range - 20" C to 28" C , and over a nitrogen pressure range 0.5 to 4 atm.The sample tempera- ture could be taken to be the same as that of the ambient nitrogen, which was computcd from the Mach number of the shock wave. Thus they eliminated the necessity for correcting for the AHoAa contribution to the energy term. They reportcd that around 1 atm the rate law is - d[N204]/dt = k[N204][N2] ; k = 2.0 x 1014 exp (- 1 lOOO/RT) 1. mole-1 sec-1. At higher nitrogen pressures, the rates are less than the values predicted by the above equation, and they estimated that the limiting first-order rate constant for the dissociation of Nz04 is kuni = 1016 exp (- 12900/RT)sec-1. This is equivalent to a rate constant of 3.4 x 106 sec-1 at room temperature. The method with which the rest of this paper is concerned approaches as a limiting case the almost instantaneous compression (10-3 psec) attained in a shock tube. Ours is a steady-state flow experiment, in which the rate of enthalpy iniput is smooth and controllable with an injcction time ranging from 1 msec to 1 psec. The instrumentation is rather simple and the method is not limited to systems in which a.t least one component has a strong absorption in the visible or ultra- violet.Finally, we can and have worked with the pure mixture as well as with diluted systems. But the procedure suffers from other limitations. Firstly, large quantities of the gas must be handled (as yet we have not successfully set up a circulating system); and, the quantity which is measured is characteristic of the system as a whole-it is not a specific rate or a concentration change.Indeed, a net entropy gain is determined. Thus all relaxation processes enter these measure- ments. THE IMPACT TUBE EXPERIMENT The method was devised by Kantrowitz 17 for the study of vibration relaxation in gases. It depcnds on the flow characteristics of gases (in the incompressible flow regime) through nozzles and past obstructions. Let us start with the gaseous mixture at equilibrium in a reservoir, essentially at rest. Its state is described by po, To, ao, uo = 0. It is allowed to flow into another reservoir maintained at a lower pressure p1, through a properly shaped, smoothly converging nozzle. Since the time over which pressure changes occur in flow through the nozzle is large compared to the equilibration time of the gas, the adiabatic expansion may be con- sidered to occur by a series of infinitcsimal equilibrium steps and the entropy change is zero.The enthalpy of the gas is lessened by an amount equal to the kinetic energy of mass motion of the gas : 401 = 0 7 AS01 = 0, AH01 - &Mu12. These quantities are defined per mole of N2O4, were all the gas reduced to that state; M is the molecular weight of the tetroxide, and 111 is the terminal mass velocity at the nozzle exit. The enthalpy of the gaseous mixture has thus been decreased by converting thermal and chemical energy into mass motion. This step may be considered as prepnration of the sample. At the exit of the nozzle, the gas is at p1, Ti, q, u1, but since the association step is exothermic, not oiily is TI < To, but also eel< ao.In other words, although the pressure is decreased, the consequent lowering of thc temperature and hence of the equilibrium constant72 RELAXATION TECHNIQUES for N2O4 f 2N02 more than compensate for the pressure decrement in deter- mining the magnitude of a. The new state of the gas may be computed for any specified PO, To, p1 from entropy balance, and the equilibrium constant. (1 -t- a1)R In (Po/&) == ((1 -- adCp(2) +- 2&7(1)) In ( T o m Kp(T) = 4~.2p/(l - ~ 2 ) . W U 1 2 = CP(2)((1 - d T 0 - (1 - adT1) (2) The kinetic energy of the gas follows from enthalpy balance : + 2C.1) (uoTo - alTi) + AHo(ao - MI). (3) Cp(2), Cp(l) are the total heat capacities (per mole) of N2O4 and NO2 respectively, and the standard state for each constituent is taken to be 1 atm at TO.- >-- ___z FIG. 1 .-Stream lines (incompressible flow) for flow past an open ended cylindcr (Griffith). The gaseous mixture issucs from the nozzle in a stream and maintains this character until brought to rest. The kinetic energy of mass flow is then retrans- formed into random molecular motion and chemical energy. The essential feature of this experiment is that the stopping time can be made very short and hence the rate of injection of enthalpy very high. If in the central part of the stream an impact tube is placed parallel to the flow lines, the gas at the front face of the tube is brought to rest during an interval 3d/2ul sec (cf is the outside diameter of tube). The hydrodynamic solution for the flow profile had to be obtained.18 Fig.1 and 2 show the stream lines and velocity against time plot, for the central stream line respectively, which Griffith computed for a square-end tube, with an opening 0.620 d. Thus, compression times of the order of a microsecond can be readily attained with impact tubes of 0.03 cm diam. and flow velocities of 0.8 Mach. This is comparable to relaxation times (T) of the processes we are in- terested in-the redistribution of energy between translational and vibrational modes,% 19 the dissociation of molecules with relatively weak bonds, etc.S . H . BAUER AND M. R. GUSTAVSON 73 For each system, appropriate variables must be introduced which allow full description of the non-equilibrium state of the gas.We have trcated the N204+NO2 systems as a mixture of ideal gascs in which the chemical degree of freedom cc and the communal vibrational temperature 8 may lag behind the translation-rotation temperature T. As one limiting case consider dlul < ~ ~ i ~ . This corresponds to an instantaneous energy imput, since all the degrees of freedom except translation and rotation remain " frozen-in " during the compression time. The pressure and temperature rise, and the immediate state of the gas may be computed from The entropy condition depends on the assumption that the only degrees of freedom which are involved follow the compression, and these remain at local equilibrium. p2 > p1; T2 > TI ; 02 == TI ; a2 = a1 ; uz = 0 q12 = 0, (As12)i.c. = 0, (AH12)i.c.= +Mu12* u'=( t' = P ("/dl FIG, 2.-Time dependence of velocity and of kinetic encrgy for inass flow (dashed curve), at the central stream line. Zero time was taken at one diameter upstream, where the disturbance of the tube is negligible (based on Grifith's curves). The numbers along the abscissa scale should be divided by 4. The numbers along the right ordinate, du'2/dt', should be multiplied by 4.74 RELAXATION TECHNIQUES Note that p2 and T3 will be slightly less than po and TO, respectively, while a3 > ao. The pressure defect (PO -- p2)i.c. is a measure of the maximum possible entropy gain for the gas. To compute it one need only make an assumption as to which degrees of freedom do not lag, and have available the pertinent thermodynamic quantities.The simultaneous solution of these equations is somewhat cumber- some, and is best performed by successive approximations. Typical values for the nitrogen tetroxide case are given in table 1. The thermodynamic quantities needed for this computation are the heat capacities and the equilibrium constant as functions of the temperature. (i) For NO2 the fundamental frequencies used to calculate the heat capacity are20 v = 648, 1320 and 1621 cm-1. The resulting values : C'(N02) in cal mole-1 deg.-1 To K 9.07 298.2 9.03 293-2 8-99 288.2 (ii) For N2O4 the fundamental frequencies used to calculate the heat capacity are : 21 380, v10 = v12 = 500 cm-1. v7 represents the torsional mode and is assumed to be TABLE SUMMARY OF COMPUTED PRESSURE DEFECTS FOR N2O4 - NO2 (To = 25" C) V l = 1265, V2 = 1360, V3 = 752, V4 = 813, V5 Vg = 1744, V 7 = ?, Vg = 283, Vg = V 1 1 = vibrationa1 modes and only chemical chemical reaction lag reaction lags 0 --+ 1 transition (eq.) - Mu1212 " T2 (pO-m)i.c. T2 (P0-m)i.c.2 m 01 (cal/mole) (c./::!) (OC) (atm) CC) (atm) 0.3000 25 03000 0.3259 0.0 0.00 22 0-2449 0.3189 158.6 1.20 19 0.1993 0.3119 317-1 1.70 16 0.1614 0.3048 475.7 2.08 0.5000 25 0.5000 0.2580 0.0 0.00 22 04097 0.2518 147.1 1.16 19 0-3348 0.2455 293.6 1.63 16 0.2725 0.2391 442.5 2.01 0*7000 25 0.7000 0.2201 0.0 0.00 22 05756 0.2144 140.5 1.13 19 04720 0.2086 280.4 1.60 16 0.3856 0.2027 421.9 1.96 (T2)iSc. easily computed from AH12 = Mu12/2 = (1 - 25-00 04000 25-00 04000 35.41 0*0009 30-49 0*0005 45.90 0,0035 35-95 04015 56-49 0*0080 41.36 0.0038 25.00 0*0000 25.00 O*oooO 3487 0.0014 29.86 0.0006 44.78 0.0055 34.66 0.0024 54-95 0.0124 39-56 0.0052 25.00 0-0000 25.00 0~0000 34.53 0.0020 29.49 0.0009 44.08 0.0074 33.94 0.0029 53.87 0.0166 38.45 0-0065 .1> (CT(2) + 2alcT(1)} (T2 - TI).sufficiently low so that the equipartition value, R, of the heat capacity is reached at room temperature. The resulting values : C'(N204) in cal mole-1 deg.-1 To K 18-88 298.2 18.73 293.2 18.58 288.2 The heat capacities at other temperatures were obtained by linear interpolation. pressure) were taken from the work of Verhoek and Daniels.22 (iii) The values of the measured ideal equilibrium constants (extrapolated to zero Kes. (atm) To C 0-1426 25 0.3183 35 0-6706 45 The logarithm of Keq. was plotted against the reciprocal of the absolute temperature, and a straight line was drawn through the points.The deduced magnitudes are AH& = 14,649 cal mole-1, AS;,, = 45.26 cal deg.-1 mole-1. These check well with the values given by the authors ; they were recomputed to insure that a consistent set of constants were being used. This must be done, since differences between large numbers appear in the computations.S. H. BAUER AND M. R. GUSTAVSON 75 For the 7th and 8th columns, CT(NO~) = 4R, C~(N204) = 5R and Co was obtained by subtracting the corresponding CT'S from the Cp's. The lortional mode v7 was included in C~(N20.4) as a non-lagging degrec of frccdom. For the 9th and 10th columns, CT was sct equal to the entirc C,,. This siiiiplified the calculations somewhat; however, Cp had to bc taken as tempcrature dependent.KINETIC FORMULATION In order to obtain information on the rate of approach to equilibrium the compression time and equilibration time must be adjusted to be of the same order of magnitude; then a fraction of the maximal entropy will be observed. The regimes designated as (2, 3) merge, so that by a continuous sequence equilibrium (1) goes to equilibrium (3) through a non-equilibrium region. To describe this transition, the thermodynamic quantities must be written as time derivatives, and kinetic quantities must be introduced. For the general case of a mixture of two reacting individually ideal gases related by A2 = 2A with both lagging and non- lagging degrees of freedom, the time rate of entropy change may be written as In the following, a is not an equilibrium value [eqn.(2) may not bc used]. The coefficients (per initial mole of N2O4) are : (1 + a)R P. 6. e P + {C0(2> - 2Co(i)) In (Tole) + As". The hydrodynamical momentum coiiservation equation yields dt dt (1 + a ) R T [ 2 (x)] which may be written for this case as - p A4 dU2 d p ___ - __ ~- T i s used here rather than 8 because only the translational energy is involved in the pressure. Substitution yields The time rate of enthalpy change may be treated in a similar manner.76 RELAXATION TE CHNIQUES For a mixture of ideal gases and with a constant, =--( M dU2 ) 2 dt" The last equation provides a relation for eliminating u2 and T from (9) : However, to a very good approximation,* this reduces to : A detailed reaction mechanism must now be introduced so that the time derivatives of 8 and a as well as the time dependence of their coefficients may be expressed as specific functions of the time.Subject to the boundary condition : as t -+ coy T -+ 8 -+ T3, and a -+ a3, eqn. (1 lb) is integrated along the flow path : - * Ce EE (1 - ?i)Ce(2) $- 2cCCe(1) is the average total vibrational heat capacity per original mole of N204. Let 4 be that equilibrium temperature which would be attained were the total perturbation injccted up to that instant allowed to produce an equilibrium condition. .- T2 N TO N T$. The local equilibrium degree of dissociation a - a Note that (ye) 1 ; (1 - a2) 2: (1 -S . H . BAUER AND M . R . GUSTAVSON 77 The total increase in entropy is computable from measured quantities.Thus, for any pair of states at equilibrium po, TO, and p2, 7'3, given the observed values (PO, To, p2), ao, a3 and T3 can be computed from eqn. (2) and (5). Then As03leq. = AS"(a3 - RO) + ((1 -- @-3)cp(2) + 2N3cp(l)} In (T3/7'0) Again, since (PO - pz)/po < 1 ; (a3 - ao)/ao < 1 A&3]eq. == ASYa3 - a d -I- CJTo - T3)/To -i- (1 + oro)R(po - p2)/po. A x = (- 2a3/Kp)Ap, and CpAT= - AH'Aa = (2a3AHo/Kp)Ap, ( 1 2 ~ ) A check on the validity of the approximations introduced may be made from the following typical values : (12b) A further simplification may be introduced. Since (TO - T3) is very small, AS03lcq. = ((1 + ao)a/m + 2x3AS"/I<p -I- 2xAH0/ToKP}(Po - P2)obse po = 0.700 atm, To = 298.2" K, po/p1 == 1.483, (PO - ~ 2 ) i . c . = 0.0074 atm, Ti = 292.3" K, (T2)i,c.= 317.3" K , a0 f: 0.2201, a1 -- 0.2086, ul = 1-60 x 104 cmlsec. for a and 8 lagging. (PO - P2)obs. = 0.0013 atm, (To - T3)O K = 0.78, (a3 - ao) = 04Xl093. KINETICS IN TERMS OF RELAXATION PROCESSES We have demonstrated 4 that although it is incorrect for a case such as the above to assume that the return to equilibrium is expressible in terms of one relaxation time constant, the kinetics may be properly described in terms of a spectrum of relaxation constants. Tn the following we have formulated a general theory which is applicable to the impact tube experiment, as well as to other cases. Unfor- tunately, we have not yet devised a procedure by means of which this spectrum can be deduced from our data. All we have successfully done is evaluate an average relaxation time. The general theory is developed in two stages.First, let us assume that the system is perturbed by a step function, of magnitude h", and define the following measures of departure from equilibrium : pTs = excess energy in non-lagging modes over final equilibrium value, pss = excess energy in lagging (vibrational) modes over final equilibrium value, pas = excess energy in reaction mode over final equilibrium value. At final equilibrium, T = T3, 0 = T3, and a = a3 : pTs = CT(T - ~ 3 ) ; CT = ( 1 - a)cT(2) + 2acT(1) ; - pes = Cde - T3); pas = AH"(a - a3). Since the system was displaced from equilibrium in an arbitrary manner, there will be a flow of energy between the various degrees of freedom-from translation78 RELAXATION TECHNIQUES and rotation into the vibrational modes (equilibrium between all of these is postu- lated), and into the chemical degree of freedom.Diagrammatically, k l . vibrational '2 chemical. -F ( energy ) --r ( encrgy ) * I k i i The fundamental kinetic assumption is that the rate of return to equilibrium is directly proportional to the instantaneous departure from that equilibrium state which would be attained were the system permitted to relax. The differential equations which express this are : Attention is called to the difference between these kinetic assumptions and the one which Kantrowitz 17 and Griffith 18 introduced. We focus attention on each species, and discuss its rate of return to equilibrium. On the other hand, these authors focus attention on the equilibration process itself, and assume that under all conditions the rate of energy flow is proportional to the magnitude of the instantaneous departure from equipartition.Griffith, in his thesis (p. 14) justified the latter assumption for the case of energy flow between translational and vibra- tional degrees of freedom. We have been able to generalize his argument only by a device, introducing " equivalent temperatures " and " equivalent heat capaci- ties " for all degrees of freedom (chemical, etc.). This can be done approximately for small deviations from equilibrium. The published formulation of these authors is applicable to cases wherein only a single adjustment is involved. Because of this difference, although our formulation appears to be similar to theirs, an extra integral appears in our final general equations, which vanishes for the case of a single relaxation time.As is well known, the system of linear simultaneous eqn. (13) has solutions of the form : 23 3 Pis(t) = 2 AU exp (- yjt) ; i == T, 8, tc, (14) j - 1 The yj's are roots of the determinantal equation, Thus, for a system of the type under discussion, thcre are thrcc rclaxation tiincs, l / y j . Further, in the specific instance whcrc thc perturbation is introduced as a step conversion of kinctic energy of mass motion into translatioiial and rotational energy, for the gas in front of the impact tubc the flow of energy is unidirectional, and all the primed rate constants vanish. Then y1 = (kl + k3); y2 = k2: 3'3 =; 0. (15)S . H . BAUER A N D M .R . GUSTAVSON 79 Substitution of the yl's into the simultaneous equations from which the deter- minant was derived, permits computation of the ratios of the Au's. Their magni- tudes are given by the initial conditions : - p+= ??T(Tz - T3); pi = CO(T1 - T3); p i -- hH"(a1 - 4. ( 1 6 4 Relations (16a) give the initial conditions in front of the impact tube. The second step is based on the postulate that the pp's are finearly dependent on the magnitude of the perturbation, h". Hence the corresponding Aij's are also linearly determined by h". Therefore, when a perturbation is imposed over an interval, so that h = h(t); 1, ($dt = h", the total effect may be divided into a sequence of infinitesimal steps, each con- tributing [$) dt] . Let some step occur at t f ; its contribution to the extent of disequilibration at a subsequent time t, is The complete solution is the sum over all these infinitesimal steps, In the present case, - = - - yd$t2), - so that at " M du2 M h" = - Jo (=)dt = -zu12.Introduce the dimensionless variables : 3 pi(tf) = - Aoe/(t' ; yjf), where j - 1 E j ' ( t f ; 7:) f exp(- yj'tf) 1; exp(y/t'+) dt'f, Both elf and 4' are negative quantities. Their magnitudes depend oiily on a dimensionless time variable, a dimensionless kinetic parameter u', and on the shape (not the size) of the impact tube. For a square-face impact tube, €1' and 4' have been evaluated graphically by Griffith 18 for five values of y f . An analytic expression is available for 4' for a " source-shape " impact tube, but the corresponding d had to be graphically evaluated by Kantrowitz.17 To complete the solution for a smooth input of enthalpy, the difference between pis and pi must be clearly stated.For a step input, the equilibrium temperature &term1 = 0.620 dcxternal,80 R E L A XA T I 0 N TE C H N IQ U ES T3 toward which the system is striving is related to the magnitude of the perturba- tion, h" == C~(7'3 - T I ) -1- c#(T3 - T I ) 4- AHO(a3 - a1). - Since a3 = [1cp(T3)/(4p f Kp(T3))1'3 (333/3T)p = ~ P ~ X ~ ~ A H " / R T ~ ~ K ~ ( T , ) r z Qs/AH0. Hence, for small increments, AHC(a3 - al)? Qs(T3 - T I ) is thus an " equivalent heat capacity ". cs = CT -1- Ce + QS, pTs = ?T(T - TI - ho/Cs) ; peS = Ce(O - T1 - h"/Cs), T3 = Ti + h"/Cs, - By extension, for a smooth input, replace in (16b) h" by additional revision is needed, since the local prcssure does not remain fixed, But, in the incompressible flow regime, p(l -1- a,) varies little, and may be replaced by an average value.Hence When this is inserted in an expression corresponding to (20), and differentiated, (3h/3t)dt. A slight sb p = p(l -1- a)RT = p(l -1- a,)R#. 4p N 4 < p(1 -t- a,)R $ = .n+. + = T~ t- Ji ($dt. Hence, to obtain expressions for the pi's, replace in the expressions for pis (eqn. (1 6a)) : T3 --t $. The latter is the equilibrium temperature which would be attained were the per- turbation to stop at that instant and the system allowed to rclax. Typical expres- sions are : Substitution into (1 lb) givesS . H . BAUER AND M. R. GUSTAVSON 81 Introduction of the general solutions leads to It is interesting to note that the (pio$') term of (190) cancels the 4' term in (27) since h" = C*(T3 - Tl)andpeo -- Ce(T1 - T3) = - hoco/C*, etc. Integration of (28) produces integrals of the form yj' (cj')2dt' and 3/j' q'cm'dt'.The first of these has been evaluated by Griffith 18 for a square-face impact tube and by Kantrowitz 17 for a source-shape tube, using graphical procedures. Plots of these as functions of y' are given in fig. 3. The second integral can be evaluated from the curves given by Griffith (ref. (18), fig. 5 ) for any desired combination. It is at this point that a simplification must be introduced. Eqn. (28) gives 9 terms involving the three unknown yj's, and except for a method of trial and error, we have been unable to devise a defined procedure for deducing these from the observed AS13.Indeed, for the general case, it appears at the moment that a second order dependence of (AS13)i,c. on the ratio of y's occurs. Hence for sim- plicity, assume that all the 7)'s may be approximated by an average value. Then, - 1: SO" (29) whereas for a smooth perturbation rg) = (29) [/(@I, whence follows from (12c). Thus, a single observed value of (PO - p2) for a selected (po/pl) permits the evaluation of an average relaxation time. EXPERIMENTAL THE EQUIPMENT AND PRELIMINARY DATA The following materials were used in this study : Nitrogen. Seaford, " dry ", from Airco ; specified purity, 99.99 %, with H2 as the impurity ; used without further treatment. Carbon dioxide. Matheson, " bone dry " grade ; specified purity, 99,956 % ; re- mainder, water ; before use, 12 lb of the gas were held over 3 Ib of reagent grade phos- phoric anhydride for 1 month, at 60 atm.Nitrogen ietroxide. Matheson ; specified minimum purity, 99 ; 0.01 % water ; remainder, lower oxides of nitrogen ; used without further treatment ; consistent differ- enccs observed between runs made with gas from differcnt cylinders. The nitrogen was used to sweep the apparatus free of moisture, for alignment, and the taking of " background " readings. Relaxation data were obtained for carbon dioxidc to tcst the equipment and to develop a definite procedure for its use. All previous apparatus had been designed for operation in the above atmospheric range. Due to thc fact that N204 boils at 21.3" C and has an apprcciable heat of vaporization (99.0 cal/g), the cylinders had to be heated in order to assure a sufficiently rapid flow of the gas.With a heating jacket kept at 250" C, the highest pressure which could be main- tained in this apparatus during the high flow runs (p&q - 1.8) was somewhat above82 RELAXATION TECHNIQUES 0.7 atm. After leaving their respective tanks both gases were passed through an " after- heater ". With carbon dioxide this served to compensate for the Joule-Thomson cooling ; for the nitrogen tetroxide it was needed to insure complete vaporization. Then the gas passed through Tygon tubing to the system, past a thermocouple and through a bubbler, the latter serving both to keep the input pressure from greatly exceeding atmospheric, and as a simple indicator for adjusting the gas flow (see fig.4). The gas then entered the first of two 12-1. reservoirs, which were connected through a pressure regulator. The latter was a Reynolds gas regulator equipped with a 0.010-in. Visqueen diaphragm. An arbitrarily variable pressure in a reference bulb was substituted for the " atniospheric " side, and hence it was possible to set the regulator so that the pressure in the second 12-1. bulb was hcld constant (to &- 0.1 mm Hg) at any value less than our supply pressure. loo I 50 - 20 10 - - 5 - (3 2 - 1.0 - 0.5 - 0.2 - I - 0 .2 .4 .6 .8 1.0 FIG. 3.-Dependence of relaxation integrals on the dimensionless relaxation time constant. To mercury difluobn pomp, Pyronl ond Mclsod gouges input wfety presswe release Boorht pump (via trap) Thernw B To electricol unit , ) and n-butyc FIG.4.-The flow system for sub-atmospheric runs. From the second reservoir bulb the gas flowed into the impact tube apparatus. A diagram of this unit had been published previously 4 without explanation ; for ease of refer- ence it is reproduced in fig. 5. The gas flows up the glass tube and over a thermocouple which measures the temperature TO before expansion. In all runs this temperature was nearly 25" C and differed by, at most, 2 deg. from room temperature. The gas next passed through a 200-mesh Monel metal screen sandwiched between two pieces of coarser Monel screening. This acted as a field of point sources and led to a smooth laminar flow up the polished stainless steel tube to the nozzle.Part way up this tube small holes con- nected it to a jacket so that the input pressure could be applied to a manometer which measured the initial.pressure po ; this pressure could also be applied to the outside of a mctal bcllows as indicated in the drawing. In designing the nozzle through which the gas flows into the expansion chamber it is important to make the time rate of energy change as small as possible so that complete equilibrium is maintained at all times. That is the case when dT/dt is minimized ; that is, when the mass acceleration occurs with a small rate of temperature drop. For the work with nitrogen tetroxide, a new nozzle was designed according to the equations : ur2 = const., r6x = const.,S . H . BAUER AND M. R . GUSTAVSON 83 where Y is the radius of the hole and u the flow velocity of the gas at a distance x from the base of the nozzle.The design was based on a length of 1.6 in. and an orifice diameter of 0.0700 in. before introducing the boundary layer correction. The outlet velocity was taken to be 17.2 m/sec and the von Doenhoff boundary-layer displacement thickness was computed using a value of 120 x 10-6 poises for the viscosity and an average density of 1.279 x 10-3 g cm-3. Corrosion of the brass nozzle used with carbon dioxide was found to be quite rapid when nitrogen tetroxide was passed through. It was observed, however, that duraluminum (24ST) withstood the action of the gas for a considerable period. Hence the nozzle was made out of a stainless steel jacket surrounding a duralu- niinum plug, in which the throat had been machined.Millivolt meter or/ Brown recorder I gas Inflow FIG. 5.-The impact tube apparatus, and schematic for electrical circuit of recording manometer. The expansion chamber was pumped on at the point marked " gas outflow " by a two-stage Hyvac pump of large capacity. For the nozzle described a pumping rate of approximately 20 1. (s.t.p.) per minute was necessary. A mercury manometer was also attached to the expansion chamber at this point to permit measurement of p1. It was found that for a fixed po any expansion ratio could easily be selected by adjusting a stop- cock interposed between the chamber and the pump. The difference between the initial pressure po and the final pressure p2 which exists at the face of the impact tube was measured by a bellows-type recording gauge.These two pressures were applied respectively to the outside and inside of a stainless steel bellows. The bellows used had a wall thickness of 0.0085 in., was 1-A. in. long by 3 in. in diameter, and had 23 convolutions. Its flexibility was such that a pressure differential of 1 atm produced a change in length of about 0.05 in. The top of the bellows was closed with a stainless steel plug which carried a stainless steel rod 14 in. long with the core of a differential transformer mounted at its tip. Thus the existence of a pressure defect, po - p2 > 0, resulted in a vertical displacement of the core which changed the coupling in the differential transformer. The resulting difference voltage was amplified, rectified and recorded.Provision was made for lateral adjustment of the core of the transformer within its encasing tube so that it would move freely in all positions.84 RELAXATION TECHNIQUES After adjustment of the tip of the impact tube so that it was centred over the nozzle exit, and its face set perpendicular to the flow (minimum pressure defect with N2) the pressure sensing device was caIibrated by applying a known pressure differential across the bellows. This was read with an n-butyl phthalate open-end manometer, attached as shown in fig. 4. The recorded voltage against pressure curve had an upward convexity. However, over a considerable period it was stable, reproducible, and showed no hysteresis. Pressure differentials could be read to a precision of - 1.2 x 10-5 atm.In some later runs the sensitivity was increased by about 35 % by finer adjustment. Flow conditions were checked with nitrogen, for which rotational and vibrational relaxation times are very much smaller than the compression time of the equipmcnt.18 The results of a typical run are shown in fig. 6. The sharp break at an expansion ratio of about 2.2 is due to the setting in of turbulence (and a shock wave). The smooth curve and low value of the defect compared to that for carbon dioxide indicates a regular " background " which can be corrected for. The fact that the nitrogen defect curve is small and linear below 10 c E/Pl FIG. 6.-Pressure defects for nitrogen and carbon dioxide ; po = 0534 atm, To = 300.2" K. po/pI - 2.0 and passes through the origin is expected from ordinary hydrodynamic factors such as misalignment of the impact tube, temperature or pressure inhomogeneities, turbulence, etc.RESULTS The apparatus and method were tested with dry carbon dioxide. A plot of a typical run is shown in fig. 6. The observed pressure defects were reduced according to the procedure of Kantrowitz 17 and Griffith.18 A correction was applied for entropy gain TABLE 2.-AVERAGE RELAXATION TIMES (T == 1/yj) FOR COz IN THE SUB-ATMOSPHERIC RANGE - po(atm) p,,(atm) .r,,(psec) av. dev. in T 0.967 0.866 3.6 6 % 0752 0.673 5.4 4 % 0.534 0.478 6.0 10 % 0.341 0-305 4.8 17 % in the nozzle as derived by Kantrowitz. The mean pressure p during relaxation was taken as &(po +PI). Reduced values for the individual points are plotted in fig.7. These were averaged for each of the PO'S and summarized in table 2. The precision decreases with po due to the fixed precision in the differential pressure measurement by the recording manometer, and to the proportionately larger nitrogen background correction. These values are consistent with the data reported in the 1iterature.W 17, 24 Assuming that the transfer of energy is bimolecular, one cxpects the product, PT,S . € I . BAUER AND M . R. GUSTAVSON 85 which is proportional to the " collision number " to remain constant as long as the tem- perature and composition are not varied. This is demonstrated in fig. 7. Such a check on the bimolecular nature of the energy exchange process has previously been made by means of sonic measurcments.2s In this figure one also notes a general decrease in Pr with decreasing ji.This trend suggests that slight but constant amounts of impurity 8 3 - t: K IQ Kontrowitz (uncorrected 6- for AS nozzle1 - 4- e o O B c - Q 2- 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 2.2 2.0 @ 1.8' f 3 1.2 9 1.0 s 0.8 5 0.6 0.4 0.2 c 1.68 g 1.4 I FIG. 7.-(pT) for carbon dioxide. Individual runs shown ; the ordinate is proportional to the collision number. were picked up by the gas from the flow system.- The average of the results for the runs at the three highest PO'S, for carbon dioxide at T = 291.5 f 9" K, is (T&" == 3.2 x 10-6 sec atm (average deviation ~z 10 %). This corresponds to a collision numbcr of 2.8 x 104. DATA AND CONCLUSIONS ON NITROGEN TETROXIDE For nitrogen tetroxide the pressure defects found (uncorrected for background) were approximately a third of those for carbon dioxide. Corrected for background the ratio becomes nearly 1/4.This decrease in magnitude of effect was only partially compensated 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 o.d I I 1 I I I I 1 I 1 I I I I I I I I 1 FIG. 8.-A typical run for N204 ; PO = 0.485 atm, TO = 298" K. PdPl by an increase of 35 % in sensitivity of the pressure recorder. The net result was an in- crease in the average deviation of the nitrogen tetroxide results when compared to those for carbon dioxide. In contrast with the carbon dioxide data no decline in the slope of the pressure defect curve above intermediate expansion ratios was noticed, nor were sharp breaks found in the curve when the orifice exit velocity of the gas approached a Mach number of unity.The elimination of the former phenomenon is very probably due to the use of the longer and more carefully machined nozzle. The absence of a sharp break in the nitrogen tetroxide defect curves for expansion ratios around two is probably a86 RELAXATION TECHNIQUES result of very small temperature inhomogeneities due to operation close to the con- densation temperature of the gas. The measured defect did increase markedly in this region indicating an increase in turbulence. Since the exact point at which this turbulence began to contribute significantly to the magnitude of the observed defect was difficult to ascertain, no data above po/p1 = 1.7 were used to determine the relaxation time.In general, for po/p1 < 1.3 the nitrogen background became such a large fraction of the defect observed for nitrogen tetroxide that variations in this background were large com- pared to the difference between the nitrogen tetroxide defect and nitrogen defect. Hence, values below po/pl = 1.3 were also omitted from consideration. From a graph of the type shown in fig. 8 values of the nitrogen tetroxide defect minus that for nitrogen, at selected expansion ratios were obtained. Data were taken for two different cylinders and two impact tubes. When a run was repeated under the same TABLE 3.-EVALUATION OF AVERAGE RELAXATION TIMES ASSUMING BOTH VIBRATIONAL MODES AND CHEMICAL REACTION ARE LAGGING impact tube A tank M tank N u1 P O h (cm s= = 0.30 atm 1-30 1.37 1.40 1-55 1-50 1.69 1.60 1.83 1-70 1.94 x Id-4) po = 0.50 atrn 1.30 1.32 1.40 1.49 1-50 1.64 1-60 1-77 1.70 1.88 po = 0.70 atrn 1.30 1.30 1.40 1.48 1.50 1.62 1.60 1-75 1-70 1.85 run I11 1.5 2-13 0.212 2.3 1.88 0.197 3.4 1-73 0.176 4.5 1.60 0.167 .5*8 1-51 0.160 run I 2.4 2-21 0.231 3.9 1.96 0.177 5-6 1.78 0.147 7-5 1.65 0.132 9.5 1-55 0-122 run I1 3.4 2.25 0.242 5-5 1-97 0.161 7-9 1.80 0.125 10.5 1.67 0.109 13.3 1.58 0-103 70 E 44 d 0.307 0.277 0.240 0.223 0.2 13 0.338 0240 0191 0.168 0.154 0-360 0.216 0.158 0.1 35 0.127 7 (sec A S x 10+6) run VI 0.65 0-199 0.52 0.165 0.42 0,142 0.36 0.132 0.32 0126 run V 0.75 0.270 0.47 0.198 0.34 0.163 0.28 0-145 0.24 0.137 run IV 0.81 0-344 0.43 0.230 0.28 0.173 0.23 0.141 0.20 0.120 7' = l/y' = 7/70.7/ 0.280 0.222 0.184 0.168 0.160 0.413 0.280 0.218 0.188 0.176 0.575 0.337 0.237 0.182 0-151 7 (sec x 10+6) 0.60 0.42 0.32 0.27 0-24 0.9 1 0.55 0.39 0-3 1 0.27 1 -29 0.66 0.43 030 024 conditions with the same tank of gas, the pressure defects were customarily reproducible to within f 10 %.The impact tubes used had the following characteristics : 0.d. = 0.0292 cm, i.d./o.d. == 0.55, eccentricity < 1 % ; 0.d. = 0.0440 cm, i.d./o.d. = 0.51, eccentricity < 1 %. tube A : tube B : The observed corrected pressure defects were plotted against po/p1 and the smoothed values divided by the corresponding (PO-P2)iac. which had been previously computcd. This permitted the reading of y' values from fig. 3. A typical set is assembled in table 3. Having allowed for this factor, the relaxation times computed for the two impact tubes should be equal.Comparison of the results of runs at identical values of po and po/pI, and with the same tank of gas, leads to the ratios listed in table 4. Clearly the ratio of 7's for the two impact tubes depends on F. This indicates that two or more relaxation times are necessary to properly reduce the data. If the transfer of energy is bimolecular and the use of an average relaxation time is a good approximation, the product $7 @ is taken to be &(PO + P I ) ] , should remain constant as long as the temperature and composition are not varied. In table 5, values of jj and PT are displayed for runs I, I1 and 111, where 7 has been computed for both vibrational modes and chemical reaction lagging and for only the chemical reaction lagging.Fig. 9 is a plot of j% against jj for these two cases. If the above assumptions were strictly valid The only effect of changing the diameter of the impact tube is to vary TO.S . H . BAUER AND M. R . GUSTAVSON 87 all of the points in fig. 9 should fall on the same horizontal line to withintheir experi- mental error. Clearly this is not the case. One notes, however, that when reduced on the assumption that both the vibrational modes and chemical reaction lag, the points cover a considerably narrower range than when reduced on the basis that only the chemical 1.8- 0 x 1.6- E 1.4- !4 1.2- .5 1.0- %c 0.8- ' 0.6- 0.4- 0.2- 0,o I U TABLE 4 4 8 4 0 rg 0 89 0 0 0 ," 4 ooo 00 O 2 ' ' ' I ' ' T determined with impact tube A T determined with impact tube B POiPl 0.50 0.30 1-30 1 -40 1.50 1 -60 1.70 1.30 1-40 1 -50 1.60 1 a 7 0 0.90 0.86 0-86 0.82 0.77 2-16 1.88 1-56 1.35 1.23 reaction lags.One further notes from table 5 (or fig. 9) that there is a trend in the values of T computed for any run. This dependence cannot be due to the pressure, since jj varies by at most 15 % within a run, nor can it be due to temperature variations, since T = 4 TI 3. T2) varies by at most 2 % (note that lower T I ' S are balanced by accompanying higher 3"~'s) within a run. This variation also is reduced when one considers both the vibrati nal modes and chemical reaction lagging. In this connection it is interesting to 2.4 2.2 I - a 2.01 FIG. 9.-Reduced data for N2O4 ; T = 298" K ; rp against jj for tank M (runs I, 11,111). 0 calculated on basis of both vibrational modes and chemical reaction lagging.g calculated on basis of only chemical reaction lagging. note that a similar trend appeared in our measurements on carbon dioxide. It is probable that the use of several relaxation times associated with the different degrees of freedom would effect a more complete reduction of the data in both cases. From fig. 9 an estimate of the auerage relaxation time may be made by drawing the best horizontal line through those points calculated on the assumption that both the88 RELAXATION TECHNIQUES vibrational rnodcs and chemical reaction lag. At 25" C and 1 atm total pressure, this gives T = 0.14 psec. The effect of impurities is indicated by the runs made with two different tanks. The average difference between T values for the tanks M, N is approximately 30 % ; however, the ratio of the value of T obtained with tank N compared to tank M varies from less to greater than unity, depending on po.This may involve the matter of dilution of a rela- tively constant amount of impurities dcsorbed from the flow system at higher PO'S. It should be noted that before use the system was always swept clean with " dry " nitrogen and before data were taken the nitrogen tetroxide was run through the system until at a fixed po and po/pI a constant pressure defect was observed. It seems improbable that impurities would be present in the flow system in such amount and desorb in such a manner as t o produce such a constant measured defect for any appreciable time. It was also found possible at the end of a run to return to any stipulated set of conditions and obtain very nearly the same value for the pressure defect.These factors argue against the probability of gross impurities being introduced by the flow system, and indicate that the impurities in the gas as supplied by the manufacturer vary from tank to tank. It is not possible to ascertain the absolute magnitude of the error in T caused by these impurities, but it is probably less than a factor of two. TABLE 5.-EVALUATION OF AND 5. FOR RUNS I, 11 AND 111 run POlPl 111, po = 0.30 atm 1.30 1 -40 1.50 1 660 1 *70 I, po = 0.50 atm 1.30 1 *40 1 50 1 *60 1 -70 11, po = 0.70 atm 1.30 1 -40 1 -50 1 -60 1 -70 - (37) for bo!h ( r i ) for only P 0 and a laggmg u lagging 0.266 0.257 0.250 0.244 0.23 8 0.442 0.429 0-417 0.406 0.397 0-619 0.600 0.583 0.569 0.556 0.17 0.1 3 0.10 0.09 0.08 0.33 0.22 0.14 0.1 1 0.10 0.50 0.26 0.16 0.13 0.1 1 0.52 0.43 0.3 1 0.26 0.22 1-35 0.60 0.42 0.33 0.27 2-20 0.92 0.57 0.44 0.36 The magnitude of the error introduced into the computations due to the lack of pre- cise values for the necessary thermodynamic parameters may be investigated by com- puting the value of (po/p2)iSc. for various assumed values of the thermodynamic constants.One finds for the range of values used that a 0.1 % change in Cp(2) changes the value of (p0Ip2)i.~. by approximately 10 %. A change of 0.1 % in ASo also causes a change in (p0/p2)i.~. of this same order of magnitude. These parameters are known to approxim- ately 0.1 % and their method of computation assures the maximum of self-consistency.Hence, one may conclude that lack of sufficiently accurate knowIedge of the thermo- dynamic parameters introduces an error into the computed v$Iue of Cpo/p2>i,c. of roughly & 10 %. The error subsequently introduced in the magnitude of T is of this order of magnitude. That the interpretation of the experiment depends so strongly on thc values of these therniodynamic parameters is not surprising in view of the fact that [;(Po - p2)] - 2 x 10-3. i.c. In the experiment po - p2 is determined directly. On the other hand, the calculated values are obtained by subtracting two large numbers, and an error of 0.01 % in the computed value of p2 will change the computed value of po - p2 by roughly 10 %. The errors inherent in the present equipment are those due to lack of precision in reading the pressure, turbulence background, and zero-point wandering.All of these have been considered in detail. The maximum value of this uncertainty as actually ob- served over many experiments is -+ 0-2 mV at the recorder or j, 5 x 10-5 atm. HenceS. 13. BAUER A N D M . R. GUSTAVSON 89 the maximum crror in determining the corrected pressure defect of N2O4 is 11: 8 x 10-5 atm. Since a typical corrected pressure defect amounted to 0.5 x 10-3 atm this is equivalent to an error of + 15 %. The entropy gain in the nozzle due to the relatively slow expansion is negligible compared to the entropy gain on compression at the face of the impact tube. For the unimolecular formulation : N204 9- 2N02, r 117 = kf 4- kr 4CNO2, (ref.3). Substituting Carrington and Davidson's unimolecular rate constant for kf and the known Keg. gives T = 0.022 psec. kf M + N2O4 r-> 2N02 + My k, For the bimolecular case Use of Carringtonand Davidson's bimolecularrate constant for kfgives T== O.99psec. One atmosphere corresponds to a total concentration of - 0.04 mole 1.-1, and hence all of the data reported here were taken in the range where the bimolecular rate law applied. The average T deduced from the impact tube experiment is approximately one-seventh that calculated from the bimolecular rate constant based on the shock tube experiments. The difference may be interpreted as being due to the greater efficiency of collisions with nitrogen dioxide and tetroxide in exciting the nitrogen tetroxide molecule over collisions with nitrogen which was used as the carrier gas in the shock tube experiments.The conclusion is that the two experiments are in substantial agreement. In general, the theoretical treatments of both experiments are hampered by a lack of adequate hydrodynamic data. In the impact tube experiment this mani- fests itself in the inaccuracies involved in converting the measured pressure defects into relaxation times. In the shock tube experiment this difficulty manifests itself in the lack of ability to compute precisely the conditions behind the shock wave. Carrington and Davidson have estimated that an error of 0.6 % in the shock velocity means an error of 1.5" in the calculated temperature and an error of 15 % in the rate constant.Even if the shock velocity were known more accurately other workers have pointed out that simple theories do not predict the density fluctua tions with much accuracy.26 In the shock tube experiment the limit of resolution is set primarily by the time constant of the detector-amplifier and by the time required for the shock to cross the observing beam (E 4 psec in C . and D.'s apparatus). The limit of resolution of the impact tube type of experiment is set by the minimum diameter of the impact tubes which can be made and the maximum non-turbulent flow velocity. Impact tubes can be constructed as small as 0.01 cm while the maximum useful velocity is approximately 2 x 10-4 cm sec-1. This gives a time constant of cn. 0.5 psec. The relaxation time must be within a factor of 30 of this for an appreci- able defect to be observed, and hence the limit of time resolution of this type of experiment is ca. 0.02 psec. Relaxation times as long as 10-2 sec may be deter- mined by studying the entropy gain in the nozzle. This work has been supported by the Office of Naval Research. 1Hiedmann and Spence, 2. Physik, 1952, 133, 109. Marburg University Sym- posium, 2. Kolloidchem. (special issue Steinkopff, Darmstatt, 1954). 2 Maxwell, Phil. Trans., 1867, 157, 49. 3 Damkoler, 2. Elektrochem., 1942, 48, 62, 116. 4 Bauer, J. Chem. Physics, 1953, 21, 1818. Manes, J . Chem. Physics, 1953 21, 1791.90 G ENER A L D I S CIJ SSIO N 5 CofEn and Bauer, Rev. Sci. Itwtr., 1952, 23, 115. 6 Carrington and Davidson, J. Physic. Chem., 1953, 57, 418. 7 Rcslcr, I,in and Kantrowitz, J. Apjd. Phy.sics, 1952, 23, 1390. 8 Marshall and Ilavidson, J. Chem. Physics, 1953, 21, 659. Herzberg and Ramsay, 9 Hauer, in L. Farkas’ Memorial Volume (Research Council of Tsrael, Jerusalem, 100 Richards, Rev. Mod. Physics, 1939, 11, 36; (b) Slobodskaya, Izvest. Akod. Narrk, 11 Markham, Beyer and Lindsay, Rev. Mod. Physics, 1951, 23, 353. 1 2 Freedman, J. Chem. Physics, 1953, 21, 1784. 13 Tetcr, J. Chem. Physics, 1953, 1, 251. 14 Strother and Richards, J. Chetn. Physics, 1936, 4, 566. 15 Luck, Physic. Rev., 1932, 40, 440. Rourgin, Physic. Rev., 1935, 50, 355. I5a Kncser and Gauler, Physik. Z., 1936, 37, 677. 16 Brass and Tolman, J . Amer. Chem. SOC., 1932, 54, 1003. 17 Kantrowitz, J. Chem. Physics, 1946, 14, 150. 18 Grifiith, J. Appl. Physics, 1950, 21, 1319, thesis submitted to the Graduate School 19 Fogg, Hanks and Lambert, Proc. Roy. SOC. A, 1953, 219,490. 20 I-Ierzberg, Infrared and Raman Spectra of Polyatomic Molecules (Van Nostrand, 21 Giauque and Kemp, J. Chem. Physics, 1938, 6, 40 ; also ref. (20), p. 284. 22 Vcrhoek and Daniels, J. Arner. Chem. Soc., 1931, 53, 1186, 1250. 2 3 Matscn and Franklin, J. Amer. Chem. Soc., 1950, 72, 3337. Kirkwood and Craw- 24 Eucken and Numann, 2. physik. Chem. 1937, B 36, 163. Eucken and Jaacks, Euckcn and Bccker, Z. physik. Chem., 1934, B 27, 25 Bergmann, Der Ultraschall (Hcrzel, Zurich, 1949), p. 376. Walker, J. Chem. 26 Emrich, Mack and Skunk, abstracts of papers prcscnted at Cambridge (Mass.) Faraday Soc. Di.scus.sioizs, 1950, 9, 80. 1952), p . 95 f f ; also, J. Physic. Chem., 1953, 57, 424. S.S.S.R. Ser. Fiz., 1948, 12, 656. Porter, Proc. Roy. SOC. A, 1950, 200, 284. of Harvard University, 1949. New York, 1945), p. 284. ford, J. Physic. Chem., 1952, 56, 1048. 2. physik. Cllem., 1935, B 30,85. 219. Physics, 1951, 19, 494. mceting of thc Amer. Physic. SOC. (Jan. 1953, no. U, 1). Widoin and Bauer, J. Ctzem. Physics, 1953, 21, 1870.

ISSN:0366-9033    

DOI:10.1039/DF9541700069

出版商:RSC    

年代:1954

数据来源: RSC