Explosive Oxidation of Hydrogen Sulphide : Self-heating, Chain-branching and Chain-thermal Contributions to Spontaneous Ignition BY PETER GRAY AND MALCOLM E. SHERRINGTON*T School of Chemistry, The University, Leeds LS2 9JT Received 7th March, 1974 The spontaneously explosive oxidation of hydrogen sulphide in a 290 cm3 vessel has been in- vestigated over a temperature range 280-360°C and between pressures of 10 and 120 mmHg. Con- ditions for ignition have been mapped on ap,Tdiagram. Very fine thermocouples (25 pm Pt-Pt/Rh) have been used to detect and measure self-heating, and special emphasis has been laid on the direct measurement of the size and form of the temperature against time histories for different initial con- ditions or locations on the ignition diagram. The effects of reactant proportions and of added diluents (with different thermal conductivities) on the second and third ignition limits have also been studied. Although the reaction exhibits many features traditionally associated with purely branched chain explosions, the direct temperature measurements have revealed extensive self-heating under very varied conditions of pressure and temperature. Boundaries may be drawn on the ignition diagram that separate the regions where a combined chain-thermal mechanism is responsible for explosions (I) from those which may be considered as purely thermal (11) or isothermal branched chain (111) in nature.The measured temperature against time histories provide novel experimental support for the unified theoretical treatment of chain and thermal explosions of Gray and Yang.Critical tempera- ture rises are smaller than would be expected on a purely thermal basis, and induction times are longer. In the chain-thermal region, the rate of self-heating immediately prior to ignition is not always rapid ; indeed, temperature excesses may be relatively steady or even decreasing when spon- taneous explosion takes place. We should expect similar behaviour in the hydrogen-oxygen reaction. Explosions in gaseous systems commonly arise either from branched radical-chain reactions that accelerate most isothermally, or from self-heating accompanying highly exothermic reaction. Recent studies of the explosive decomposition of chlorine dioxide have demonstrated that it is of the former type, ignitions occurring with little or no change in the temperature of the reacting gas.In contrast, the decompositions of diethyl peroxide and methyl nitrate,3 and the oxidations of hydrazine and mono- methylhydrazine all involve substantial self-heating both under non-explosive conditions and prior to explosion. The onset of ignition in these reaction^^-^ is thermally controlled, and their course is in excellent agreement with the predictions '-' of thermal explosion theory. Of course, not all gas-phase ignitions can be attributed to purely branched chain or purely thermal processes; attempts to separate the two may be misguided if in such cases the progress of the reaction is not dominated by either mechanism alone, but instead is the result of both chain and thermal effects.An important unification of thermal and branched-chain explosion theory was made by Gray and Yang.' They applied their ideas to the hydrogen + oxygen reaction and especially to the oscillatory reactions and other complexities found in the oxidation of hydrocarbons. Recent experimental investigation^'^-^^ have established the occurrence of significant t present address : Esso Research Centre, Abingdon, Berks. OX13 6AE. 2338P. GRAY AND M. E . SHERRINCTON 2339 temperature changes in hydrocarbon oxidations, and have shown that the complex behaviour observed cannot be interpreted in purely branched chain or purely thermal terms. It is the purpose of the present study to discover the extent to which self-heating contributes to the onset of explosive behaviour in the gas-phase oxidation of hydrogen sulphide, and to examine quantitatively the chain-thermal regime of the reaction.In many ways, the oxidation of hydrogen sulphide closely resembles that of hydrogen, and the more convenient conditions of temperature and pressure required for ignition make it particularly suitable for experimental investigation. Many of the features of the oxidation of hydrogen sulphide are also to be seen in the oxidations of am- monia ’ and carbon disulphide,16 so that information obtained in its investigation may assist in interpreting other reactions. Early work on hydrogen sulphide was primarily concerned with the location of explosion limits on a pressure against temperature diagram. The existence of what was taken to be a simple lower bound was established by several worker^,'^-^^ until Yakovlev and Shantarovich20 found another explosion region at yet lower pressurss.‘Their work 2o demonstrated the existence of three explosion limits over a range of temperature, and they mapped the “explosion peninsula” situated between the first and second limits. More recently, Marsden investigated the reaction mass- spectrometrically in the neighbourhood of the third limit. He concluded that S 2 0 was the most likely important branching intermediate, and except during explosion he found no evidence for diatomic SO. He also detected the formation of hydrogen prior to ignition. Gray and Yang’s unified theory * predicts qualitative differences in the develop- rnent of temperature rises between cases where both thermal and radical effects are important, and cases where reaction is thermally controlled.Principally, the maxi- mum temperature excesses compatible with stability are less when chain branching occurs than those expected from purely thermal theory, and the temperature evolution prior to ignition can show more varied forms. In a purely thermal explosion, the reactant temperature rises moderately at first, inflects, and then proceeds at an increasingly rapid rate, culminating in explosion. By contrast, a chain-thermal ignition may be preceded by a relatively steady, or even by a decreasing reactant temperature which persists until the discontinuous increase in temperature accom- panying explosion itself. Accordingly, in this work, temperatures and pressures are measured for the stoichionietric mixture 2 H2S + 3 O2 both near to the ignition limits and under other conditions.Interest is directed in particular to the nature, magnitude, and duration of explosive and non-explosive temperature against time histories. Attention is also paid to the effects of inert diluents on the explosion limits and to the variation of these limits with the reactant proportions, these results providing useful additional evidence in assessing the degree to which self-heating and radical processes combine to con- tribute to ignitions in this reaction. EXPERIMENTAL MATE R I A 1, S All gases were taken from cylinders. Hydrogen sulphide (Matheson Co.) was frozen under liquid nitrogen and degassed before use by trap-to-trap vacuum distillation.Oxygen, nitrogen and carbon dioxide (B.O.C. Ltd.) were dried by trapping water at -79°C. Helium, neon, argon, krypton (B.O.C. Ltd.) and hexafluoroethane (Matheson Co.) were used without further purification.2340 CHAIN-THERMAL IGNITION I N HzS COMBUSTION APPARATUS The reaction vessel was a Pyrex sphere (radius 41 mm, volume 0.29 dm3) heated in an electric furnace and thermostatted to better than 0.5"C. Measurements of reactant temperatures at the vessel centre during reaction were made by a very fine thermocouple constructed by butt welding 25 pm diameter platinum and platinum/l3 % rhodium wires (Johnson Matthey) to produce a junction less than 50 pm in size. The junction and supports were coated with silica to minimize catalytic effects. The thermocouple entered the vessel from above, along the vessel's vertical diameter, with its " hot "junction at the vessel centre ; the cold junction was kept at 0°C.Pressure measurements were made by a sensitive pressure transducer (Langham-Thompson UP 2), readings being accurate to & 1 Torr. Signals from the thermocouple and transducer were amplified and displayed on a storage oscilloscope (Tetronix 564 B). Temperature changes could be reproduced to better than _+ 1°C. The reaction vessel was connected to a conventional glass vacuum line by means of an electro- magnetic valve. Gas-pressure measurements in the vacuum line could be made either with a glass spiral gauge, or by means of a wide-bore mercury manometer. The spiral gauge was used where the gas pressure was less than 20 Torr ; otherwise, the mercury manometer was used and read with a cathetometer.PROCEDURE Gas mixtures of the required compositions were made up manometrically and allowed sufficient time (greater than 30 min) to mix completely. These mixtures were subsequently admitted to the evacuated vessel through the electromagnetic valve normally opened for 0.1 s ; opening the valve initiated measurements of temperature against time and pressure against time histories, which could be displayed simultaneously on the storage oscilloscope. Critical pressure limits for ignition at a particular vessel temperature were determined as the mean of the closest subcritical and supercritical reactant pressures that could be observed. The dependence of the critical ignition limit on vessel temperature, on the variation of the composition of the reactant mixture, and on the extent of dilution with inert gases was investigated.In general, the different ignition limits were sufficiently separate from each other for there to be no confusion over which particular limit was being determined. Difficulties were encountered only in the immediate vicinity of the " lobes " i.e. where dpldt-, GO. Subcritical temperature against time histories were followed for over 100 pairs of values of initial temperature and pressure in the non-explosive region of the ignition diagram, the maximum temperatures achieved always being recorded. Under supercritical conditions, interest centres both on the maximum temperatures achieved before ignition and on the qualitative form of the temperature against time histories for different initial conditions (p, T ) around the ignition boundary.RESULTS IGNITION I N STOICHIOMETRIC MIXTURES The most striking feature of the gas phase reaction in a stoichiometric mixture of hydrogen sulphide and oxygen is the existence, under certain conditions of vessel temperature, of multiple critical pressure limits separating explosive from non- explosive behaviour. As in the hydrogen + oxygen reaction there is first a low pressure limit p 1 above which the reaction is accelerated to explosion by degenerate branched radical chain processes alone. At higher pressures, a second limit p 2 is reached beyond which ignitions cease. This limit increases with increase in ambient tempera- ture. I t eventually merges with a third limit p 3 at the root of the explosion peninsula.The dependence of critical total pressures on ambient temperature for the stoichio- metric mixture, 2 H,S + 3 02, are shown in fig. 1. The points a, b, c, d indicated in this figure correspond to four characteristically different modes of behaviour.100 80 60 4 8 b 4 --.. 40 2 0 0 F+G. 1 .-Dependence of critical ignition pressure on vessel temperature for stoichiometric mixture 2H2S + 3 O2 ; induction periods (seconds) indicated by broken arrows. O L 0 I EXPLOSIONS 10 NON -EXPLOSIVE R EACTl ON EXPOSIONS I I I 20 30 40 50 60 %HzS FIG. 2.-Composition-dependence of second ( p z ) and third ( p 3 ) ignition limits for mixtures of hydro- gen sulphide and oxygen at 340°C.2342 CHAIN-THERMAL IGNITION IN H2S COMBUSTION All explosions are characterized by rapid (almost discontinuous) changes in both temperature and pressure, and at all but the very low pressures, explosions are accompanied by a visible flash.The light is generally easily observable, being pink in colour above the third limit but becoming both feebler and bluer as the ignition boundary is traversed, until near the first limit (less than 5 Torr) it is too feeble to be detected. The lengths of the periods vary with the initial conditions of pressure and temperature or position on the ignition diagram. Where self heating accompanies ignition, induction periods are generally short (1-3 s), while under isothermal conditions they are often very long (frequently in excess of 1-2 min), the length of the induction period increasing continuously along the ignition boundary from a to d.Typical values corresponding to marginally explosive conditions are indicated on fig. 1 . For pressures and tem- peratures near to the merging of the second and third limits (between b and c), induction periods are intermediate between the two extremes, ranging from 8-10 to around 20-30 s. All ignitions are preceded by induction periods. IGNITION LIMITS FOR NON-STOICHIOMETRIC MIXTURES The behaviour of the reactant mixture is dependent on its composition as well as on pressure and temperature, and to display it adequately, a three-dimensional ignition diagram is necessary. An extensive study was not attempted but fig. 2 shows the variation of the critical explosion pressure with mole percentage H2S along the second and third limits for an ambient temperature of 340°C.At the second limit, the critical pressure p 2 rises linearly with decreasing H2S content, explosion becoming progressively easier for increasingly lean mixtures. Similarly, explosion also becomes easier with decreasing H,S content along the third limit, p 3 falling rapidly at first but varying more slowly where the two limits p 2 and p 3 merge (ca. 23% H2S). Thus, at 340°C for mixtures containing marginally less than 23 % H2S, ignitions are observed over the entire pressure range. One aspect of the merging of the second and third limits is that, at a vessel temperature of 340°C and a reactant pressure 36 Torr, this composition represents the tip at which p 2 and p 3 coalesce.The behaviour of the third limit with respect to reactant composition in the oxidation of hydrogen sulphide contrasts markedly with the simpler behaviour found in the oxidation of methylhydrazine, where the critical ignition pressure passes through a minimum value situated between the stoichiometric and equimolar com- positions, and rises rapidly for mixtures much leaner than stoichiometric. In the oxidation of hydrogen sulphide however, the limitp, does not pass through a minimum value but continues to decrease past the stoichiometric composition (40 % H2S), right up to the point at which it merges with the second limit and explosion becomes inevitable. IGNITIONS IN DILUTED MIXTURES The effects of dilution by inert gas on the critical ignition pressures have been investigated at the third and second limits.(i) In the first type of experiment carried out, mixtures of hydrogen sulphide, oxygen and diluent in the ratio 2 :3 :3 were used, the third explosion limit being determined at different ambient temperatures. Three diluents were used, helium, neon and krypton, and the results are expressed in fig. 3 as a plot of the critical partial pressure of the reactants required for ignition, p(H,S) + p ( 0 2 ) against ambient temperature. Helium and neon increase the critical explosion pressure at the lowerP . GRAY A N D M . E. SHERRINGTON 2343 ambient temperatures (i.e. make explosion more difficult) but their effect diminishes with increase in temperature, and dilution with neon has very little effect near the merging of the second and third limits (around point b).Krypton lowers the critical explosion pressure, making explosion easier, and the lowering is marked all along the limit. Ta/"C FIG. 3.--Effect of dilution on critical partial pressure, p(H2S)+p(02), at the third limit for mixtures 2 H2S + 3 O2 + 3 diluent at various vessel temperatures. (0, helium, A, neon ; 9, krypton). I I I I I 1 I 0 10 20 30 40 50 60 70 % diluent FIG. 4.-Effect of dilution on critical partial pressure, p(H2S)+p(Oz), of second limit p z in mixtures 2 H2S+3 O2 +diluent. Ambient temperature 340°C. 0, helium ; A, argon ; 0, nitrogen ; 0, carbon dioxide ; x , hexafluoroethane.2344 CHAIN-THERMAL IGNITION I N H2S COMBUSTION (ii) In the second type of experiment, the dependence on dilution of the critical partial pressure for ignition p(H,S) +p(O,) was examined at the second limit for a constant ambient temperature of 340°C.Fig. 4 shows the effect of five diluents, helium, argon, nitrogen, carbon dioxide and hexafluoroethane. In all cases the explosive region contracts and explosion is made harder ; the second limit is lowered by dilution, the extent of the depression being approximately linear with degree of dilution. Helium and argon depress the limit least; carbon dioxide and hexa- fluoroethane depress it the most. EXTENT OF SELF-HEATING UNDER SUBCRITICAL CONDITIONS Over a hundred temperature against time histories have been recorded in the non- explosive region. Although both the magnitude and duration of the temperature histories vary widely under different initial conditions of temperature and pressure, certain basic features are common to them all.The thermocouple always registers a brief (ca. 0.1 s) initial cooling as the cold reactant mixture enters the hot vessel. The temperature then rises above that of the vessel and passes through a maximum value before returning to ambient as the reactants are consumed and the reaction is completed. 100 80 40 20 0 1 1 - 300 ,/ 320 34 0 360 TaI0C FIG. 5 .-Self heating accompanying oxidation of hydrogen sulphide. Stoichiometric mixture 2 H2S + 3 O2 Contour lines for temperature rises of 0, 10, 20, 30,40°C. L corresponds to predicted ignition limit from purely thermal theory. At the lower vessel temperatures (around 300°C) and near the third limit, the maximum temperature excess is high (over 40"C), but the reactants maintain this value only momentarily.Further along the limit, at higher vessel temperatures and lower pressures, the maximum self-heating observed just below the third limit de- creases, falling to values between 20 and 30°C near point b. Under these conditions the maximum excess is maintained by the system for several seconds. The degree of self-heating for different initial conditions is displayed in fig. 5 by contour lines corresponding to quasi-stationary temperature rises of AT = 10, 20, 30 and 40°C.P . GRAY AND M . E. SHERRINGTON 2345 The dotted contour line AT = 0 separates the isothermal and non-isothermal regimes. Clearly, both the isothermal and non-isothermal regimes are quite extensive. Self- heating is still observed around point c (see fig.1) under conditions normally described as near the second limit and where, classically, ignitions might have been ascribed to branched chain processes alone. At lower ambient temperatures (300-32OoC), departures from isothermal behaviour are readily observed under conditions well below the third limit ; marked temperature rises are still found for initial pressures of only one half the appropriate critical values. Farkas reported l9 the existence of temperature rises preceding ignition, i.e. above the third limit, but not in sub-critical systems. The inability of Thompson l7 to detect any self-heating in the non-explosive regime and his report of not more than 1 degree rise even after partial ignitions are probably to be attributed to his use of unsuitable temperature measuring equipment. Non-explosive Explosive 0 Ta = 296°C Pc = 83 torr 4 (a) (b) ? Ta = 343°C 5 Pc = 51 torr (4 u iz Ta = 352°C Pc = 34 torr (4 u Ta = 325°C 5 Pc = 12torr t L I I l L 155 ""t 501 t FIG.6.-Non-explosive and explosive temperature against time histories at the four points a, by c, d indicated on ignition diagram in fig. 1 (a and b are located on the third limit ; c and d on the second). SUPERCRITICAL AND SUBCRITICAL TEMPERATURE AGAINST TIME HISTORIES Supercritical mixtures show temperature against time histories prior to ignition initially similar in appearance and magnitude to those observed in corresponding subcritical cases. When ignitions occurred, whether above the third limit or between the first and second limits, they were all marked by a sudden discontinuous jump in temperature.Fig. 6 shows four pairs of temperature against time histories cor- responding respectively to pairs of points marginally above and below a, b, c and d Curves 6(a) are for low ambient temperatures and for high reactant pressure up around the third limit. The evolution of both the non-explosive and explosive of fig. 1.2346 CHAIN-THERMAL IGNITION I N H2S COMBUSTION temperature histories closely resembles purely thermally controlled behaviour. 2 , 5 The maximum stable temperature excess (ca. 45°C) is high, and the development of temperature just before explosion, accelerating the reaction to ignition is rapid. Curves 6(d) are for conditions situated at the lower part of the second limit.No temperature excess at all is observed in the non-explosive reaction, nor is there any rise in temperature prior to ignition in the explosive case. The temperature against time traces closely resemble the behaviour reported for the chlorine dioxide decomposi- tion and are typical of purely isothermal chain branching processes. Initial conditions correspond to points on fig. 1, situated close to the region where the second and third limits merge : b is on the upper portion, corresponding to the lowest part of the third limit and c on the lower portion, corresponding to the highest part of the second limit. At b, the reaction attains a steady temperature excess which in the explosive case is increasing only slowly right up to the moment of ignition.The magnitude of the maximum temperature excess attainable (ca. 2SOC) is smaller by some 3040% than would be predicted on a purely thermal basis. On the temperature record 6(c), the temperature excess is smaller still, the maximum value being only about 12°C; in the explosive case, the temperature has actually passed its maximum and is falling when explosion occurs. The temperature traces represented by curves 6(b) and 6(c) correspond to behaviour which cannot be satisfactorily explained on either a purely thermal or a purely chain basis; both mechanisms are contributing in varying degree to these ignitions. Curves 6(b) and 6(c) are quite different. DISCUSSION Previous work on the oxidation of hydrogen sulphide has concentrated on the explosion and the identification of intermediates responsible for chain-branching.The present experiments are in reasonable quantitative accord with earlier work 7-21 so far as the location of explosion limits, the variation of induction periods, and the effects of composition and diluents are concerned ; some specific comparisons are referred to below. The principal aim of the present study, however, is the evaluation of the relative contributions of physical and chemical processes to ignition. By the direct detection and measurement of temperature changes accompanying reaction we are able to define the conditions in which thermal factors or chain-branching factors can alone account for the observed behaviour, and to map the conditions in which neither mechanism is completely dominant but where both compete for control of stability of the reaction.The findings are important not only for this oxidation but for the kinetically related hydrogen + oxygen system. THE ISOTHERMAL REGION Beneath the zero self-heating contour line (AT = 0) of fig. 5, reaction is truly isothermal. This contour bounds a region that contains the entire first ignition limit, the ignition peninsula and most of the second limit. Throughout this region, iso- thermal branched chain reactions make the important contribution, and thermal effects play an insignificant role. This is also confirmed by the qualitative form of the temperature histories preceding ignitions [fig. 6(d) where ignition occurs without any previous self heating.] It is only near the uppermost part of the second limit, where the second and third limits merge, that any significant degree of self-heating is observed, and even there the limiting temperature excesses are small, typically only a few degrees centigrade.The effects of dilution at the second limit further support the conclusion that thermal factors have little to do with ignitions in this region.P . GRAY AND M. E. SHERRINGTON 2347 Ignition is made harder in all cases, the explosive domain contracting and the critical pressure being lowered in proportion to the amount of diluent added. The simple monatomic gases helium and argon have least effect on the limit, and the polyatomic gases carbon dioxide and hexafluoroethane have the greatest. These differences are to be interpreted 23 in terms of the different “third body’’ efficiency of the diluents.Any change in this efficiency in turn induces corresponding changes in the rate of homogeneous chain termination of the radical reactions. The addition of any inert gas increases termination, and polyatomic molecules, being more efficient as third bodies than monatomic molecules, have the greater relative effect on the lowering of the ignition limit, as is found here. Work by Davies and Walsh 24 confirms these results ; they report that the efficien- cies of diluents in lowering the second limit diminish in the order CO, > N, > He > Ar, and that the efficiencies decrease slightly as the temperature rises, but are relatively insensitive to reactant proportions. An estimate for the activation energy of chain-branching can be got from the temperature- dependence of the second limit RT2(d lnp,/dT) if this originates in varying com- petition between a chain branching reaction with activation energy Eb and a termina- tion process without activation energy (as may be assumed for the hydrogen + oxygen ignition diagram).Here, E2 is 122 kJ mol-’, significantly greater than the value of Yakovlev and Shantarovich.20 Under no circumstances is the limit raised. Detailed knowledge of the elementary reactions involved is still lacking. THE THIRD LIMIT AND THE EXTENT OF THERMAL CONTRIBUTIONS In contrast to the behaviour observed near the first and second explosion limits, reaction along the third limit is far from isothermal, and strong self-heating persists for conditions well removed from the limit itself.In view of the marked degree of self-heating, it is illuminating to contrast the measured critical ignition pressures with predictions derived from the theory 6*7 appropriate to purely thermal explosions. Simple conductive theory predicts that, along a thermal ignition limit, the dimension- less heat release rate 6 is a constant and that a graph of ln(p,,/T ;) against 1 /Ta should be a straight line of gradient E/2R, where pcr is the critical total ignition pressure at ambient temperature T,, and E is the effective activation energy of an isothermal reaction with second order pressure-dependence overall. Fig. 7 shows how the conditions at the third limit for the ignition of 2 H,S + 3 0, obey this relation for the higher pressures and lower temperatures, and how the limit deviates from linearity as the temperature increases and the critical pressure falls.The deviation of the limit from thermal prediction is discernible at temperatures above 310°C. This deviation may be thought to reflect the extent to which chain processes become progressively more important as the temperature rises and the third limit approaches the explosion peninsula. From the linear portion of the graph in fig. 7 we derive a value for the activa- tion energy E3 of 98+5 kJ mol-l. Earlier workers 1 7 v 1 * reported values of 80 to 84 kJ mol-l for E3, but the discrepancy is not significant because they forced their lines through points corresponding to the root of the peninsula where chain-branching contributions are present.The broken line L on figure 5 corresponds to the straight line portion of fig. 7. At and above L, ignitions can be interpreted on a purely thermal basis; beneath it, ignition is increasingly influenced by branched chain reactions. These influences are reflected in (i) the response to variations in reactant proportions (ii) the influence of dilution by inert gases.2348 CHAIN-THERMAL IGNITION I N H2S COMBUSTION The effects of reactant composition on the ignition pressure have been described for an ambient temperature of 340°C. based on purely thermal factors 6*7 would suggest that on passing from hydrogen sulphide-rich to hydrogen sulphide-lean mixtures the critical ignition pressure should fall to a minimum value and then begin to rise again.Observed behaviour is significantly different from this. The ignition pressure ( p 3 ) is seen to decrease past stoichiometric (40% H2S) to the point where it merges with the second limit ( p 2 ) and explosion becomes inevitable. This behaviour in lean mixtures reflects the changing nature of the limit ; as the hydrogen sulphide content decreases so the chain influence becomes pro- gressively more marked until, at the composition (ca. 23 %) conditions that correspond to the root of the peninsula, the second and third limits meet. Simple considerations 0.6 n 2 4 --.- W CI 0.4 0.2 1 .o 0.8 - - - - - - - NON-LINEARITY DUE TO THE SECOND LIMIT I .66 1.70 I .74 I .7a lo3 KITa In (pc/T,2) on 1 ITa is linear on purely thermal theory.) FIG. 7.-Predicted and observed temperature dependence of third ignition limit.(Dependence of The effects of dilution on the critical ignition pressures also reflect the changing nature. The three diluents were chosen because of their widely different thermal conductivities. According to a stationary state treatment,7 the effect of diluents on purely thermal explosion is to make the explosion easier or more difficult according to whether the overall conductivity A of the gaseous mixture is lowered or raised : pCrccA. As expected, helium and neon, with high thermal conductivity, make ex- plosion harder at the lower temperatures and higher pressures, but further along the ignition limit where thermal influences are less their effect is quite small. Krypton lowers the limit over a wider range, possibly because it makes thermal explosion easier {lowers p 3 ) and terminates branched chains effectively (lowers p z ) .P .GRAY AND M. E . SHERRINGTON 2349 THE CHAIN-THERMAL REGIME The boundaries of the isothermal region and of the pure thermal ignition have been discussed above. Between them lies the region where both chain-branching and thermal contributions are important, and whose description and interpretation require the framework of unified treatment. Certain interactions, indirectly observed, between chain and thermal processes have been touched on already; two further features of ignition deserve emphasis here; both are derived from direct temperature measurements. The first is the reduction in the stably attainable temperature rise ATcr accompanying exothermic oxidation along the ther- mal limit ; the second is the qualitative difference in temperature against time histories preceding ignition nearer to the isothermal limit.(i) According to simple stationary conductive t h e ~ r y , ~ maximum stable tempera- ture excesses in a spherical vessel of about 1.61 RT;/E are allowed ; the excess expected rises to about 1.85 RT,2/E when consumption of reactants 25 is considered. Accepting the value of the activation energy derived from the linear portion of the plot in fig. 7, this corresponds to predicted critical temperature rises of about 45 to 50°C at T, = 3OO0C, in good agreement with the maximum stable rises experimentally observed near to point a. On simple theory, the critical excesses should increase monotonically (as T,2) with increase in ambient temperature around the ignition boundary.Fig. 5 indicates that the converse occurs : temperature excesses never reach such values ; at T, = 340°C, near point b, the highest sub-critical excess so far observed is only 28”C, around half that suggested on thermal grounds. The dis- crepancy increases around the boundary; near point c only a 12°C excess can be realized. Both are readily located. (ii) Temperatures also vary differently with time from the lively accelerations that are a prelude to purely thermal explosions : instead they may rise only sluggishly, be relatively steady or even decrease, as is the case near point c. on the unification of thermal and chain-branching theories of explosions, Gray and Yang outline qualitatively the results which have here been observed quantitatively in the oxidation of hydrogen sulphide.In the chain-thermal region of the reaction we are, by definition, concerned with the regime in which the two different mechanisms compete for control, and in many ways the combined effects reflect the compromise. Maximum stable temperature rises are predicted 26 and found to be markedly below their purely thermal counterparts, and the entire temperature development is slower paced. In particular, induction times are much longer than in purely thermal explosion, being typically of the order of 10-30 s, though these values are significantly shorter than the induction periods observed in the purely isothermal regime. The temperature excesses immediately preceding ignition are often surprisingly steady and the temperature “jumps” occur suddenly with little or no additional self-heating. Indeed, in the region where the second and third limits merge the reactant temperature is falling when ignition occurs.The contribution to the explosion under such conditions by branched chain radical processes is clearly very great. Similar behaviour might be expected near the second limit in the hydrogen + oxygen reaction but although falling temperatures before ignition have been reported 2 2 they appear to be the artificial consequence of the conventional “withdrawal” technique used to locate the limit : reactant temperatures fall by adiabatic expansion. In their original paper A re-investigation of this system would be timely.We are grateful to S.R.C. for the award of a studentship to M.E.S.2350 CHAIN-THERMAL IGNITION I N H2S COMBUSTION P. Gray and J. K. K. Ip, Combustion and Flame, 1972, 18, 361. D. H. Fine, P. Gray and R. MacKinven, Proc. Roy. SOC. A , 1970, 316, 223, 241 and 255; P. Gray, D. T. Jones and R. MacKinven, Proc. Roy. SOC. A , 1971,325, 175. H. Goodman, P. Gray and D. T. Jones, Combustion and Flame, 1972, 19, 157. P. Gray and E. B. O'Neill, Trans. Faraday ,Yoc., 1972, 68, 564. P. Gray and M. E. Sherrington, J.C.S. Faraday Z, 1974, 70, 740. N. N. Semenov, Chemical Kinetics and Chain Reactions (Oxford U. P., Oxford, 1st edn., 1935). D. A. Frank-Kamenetskii, Diflusion and Heat Exchange in Chemical Kinetics (Plenum, New York, 2nd edn., 1969). B. F. Gray and C. H.Yang, J. Phys. Chem., 1965, 69, 2747. B. F. Gray and C. H. Yang, 11th Symp. (Znt.) Combustion (Combustion lnst., Pittsburgh, 1967), p. 1099. l o C . H. Yang and B. F. Gray, J. Phys. Clrern., 1969, 73, 3395. B. F. Gray and C. H. Yang, Trans. Farnday SOC., 1969, 65, 1553, 1614. j 2 J. H. Knox and R. G. W. Norrish, Trans. Fauaday SOC., 1954, 50, 928. l 3 R. Hughes and R. F. Simmons, Combustion atid Flame, 1970, 14, 103. l4 J. F. Griffiths, P. Gray and P. G . Felton, 14fh Synzp. ( h t . ) Combustion (Combustion lnst., l5 J. N. Bradley, Trans. Fauaday Snc., 1967, 63, 2945, l6 A. L. Myerson and F. R. Taylor, J. Anzer. Clzem. Soc., 1953, 75, 4345. l 7 H. A. Taylor and E. M. Livingston, J. Chem. Plzys., 1931, 35, 2676. l 9 L. Farkas, 2. Elektrochem., 1931, 37, 670. 2o B.Yakovlev and P. Shantarovich, Acta Physicochim. U.S.S.K., 1937, 6, 71. 2 1 D. G. H. Marsden, Canad. J. Chem., 1963, 41, 2607. 22 J. A. Barnard and A. G. Platts, Combustion Sci. Tech., 1972, 6, 133. 23 W. Jost, Low Temperature Oxidation (Gordon and Breach, New York, 1965). *' D. A. Davies and A. D. Walsh, 14th Symp. ( h t . ) Combustion (Combustion Inst., Pittsburgh, 25 B. J. Tyler and T. A. B. Wesley, 11th Symp. (Int.) Cornbustion (Combustion Inst., Pittsburgh, 26B. F. Gray, Trans. Fmadzy SDC., 1969, 65, 2133. Pittsburgh, 1972), p. 453. H. W. Thompson and N. Kelland, J. Chenz. Soc., 1931, 1809. 1973), p. 475. 1967), p. 1115. Explosive Oxidation of Hydrogen Sulphide : Self-heating, Chain-branching and Chain-thermal Contributions to Spontaneous Ignition BY PETER GRAY AND MALCOLM E.SHERRINGTON*T School of Chemistry, The University, Leeds LS2 9JT Received 7th March, 1974 The spontaneously explosive oxidation of hydrogen sulphide in a 290 cm3 vessel has been in- vestigated over a temperature range 280-360°C and between pressures of 10 and 120 mmHg. Con- ditions for ignition have been mapped on ap,Tdiagram. Very fine thermocouples (25 pm Pt-Pt/Rh) have been used to detect and measure self-heating, and special emphasis has been laid on the direct measurement of the size and form of the temperature against time histories for different initial con- ditions or locations on the ignition diagram. The effects of reactant proportions and of added diluents (with different thermal conductivities) on the second and third ignition limits have also been studied.Although the reaction exhibits many features traditionally associated with purely branched chain explosions, the direct temperature measurements have revealed extensive self-heating under very varied conditions of pressure and temperature. Boundaries may be drawn on the ignition diagram that separate the regions where a combined chain-thermal mechanism is responsible for explosions (I) from those which may be considered as purely thermal (11) or isothermal branched chain (111) in nature. The measured temperature against time histories provide novel experimental support for the unified theoretical treatment of chain and thermal explosions of Gray and Yang. Critical tempera- ture rises are smaller than would be expected on a purely thermal basis, and induction times are longer.In the chain-thermal region, the rate of self-heating immediately prior to ignition is not always rapid ; indeed, temperature excesses may be relatively steady or even decreasing when spon- taneous explosion takes place. We should expect similar behaviour in the hydrogen-oxygen reaction. Explosions in gaseous systems commonly arise either from branched radical-chain reactions that accelerate most isothermally, or from self-heating accompanying highly exothermic reaction. Recent studies of the explosive decomposition of chlorine dioxide have demonstrated that it is of the former type, ignitions occurring with little or no change in the temperature of the reacting gas. In contrast, the decompositions of diethyl peroxide and methyl nitrate,3 and the oxidations of hydrazine and mono- methylhydrazine all involve substantial self-heating both under non-explosive conditions and prior to explosion.The onset of ignition in these reaction^^-^ is thermally controlled, and their course is in excellent agreement with the predictions '-' of thermal explosion theory. Of course, not all gas-phase ignitions can be attributed to purely branched chain or purely thermal processes; attempts to separate the two may be misguided if in such cases the progress of the reaction is not dominated by either mechanism alone, but instead is the result of both chain and thermal effects. An important unification of thermal and branched-chain explosion theory was made by Gray and Yang.' They applied their ideas to the hydrogen + oxygen reaction and especially to the oscillatory reactions and other complexities found in the oxidation of hydrocarbons.Recent experimental investigation^'^-^^ have established the occurrence of significant t present address : Esso Research Centre, Abingdon, Berks. OX13 6AE. 2338P. GRAY AND M. E . SHERRINCTON 2339 temperature changes in hydrocarbon oxidations, and have shown that the complex behaviour observed cannot be interpreted in purely branched chain or purely thermal terms. It is the purpose of the present study to discover the extent to which self-heating contributes to the onset of explosive behaviour in the gas-phase oxidation of hydrogen sulphide, and to examine quantitatively the chain-thermal regime of the reaction. In many ways, the oxidation of hydrogen sulphide closely resembles that of hydrogen, and the more convenient conditions of temperature and pressure required for ignition make it particularly suitable for experimental investigation.Many of the features of the oxidation of hydrogen sulphide are also to be seen in the oxidations of am- monia ’ and carbon disulphide,16 so that information obtained in its investigation may assist in interpreting other reactions. Early work on hydrogen sulphide was primarily concerned with the location of explosion limits on a pressure against temperature diagram. The existence of what was taken to be a simple lower bound was established by several worker^,'^-^^ until Yakovlev and Shantarovich20 found another explosion region at yet lower pressurss.‘Their work 2o demonstrated the existence of three explosion limits over a range of temperature, and they mapped the “explosion peninsula” situated between the first and second limits. More recently, Marsden investigated the reaction mass- spectrometrically in the neighbourhood of the third limit. He concluded that S 2 0 was the most likely important branching intermediate, and except during explosion he found no evidence for diatomic SO. He also detected the formation of hydrogen prior to ignition. Gray and Yang’s unified theory * predicts qualitative differences in the develop- rnent of temperature rises between cases where both thermal and radical effects are important, and cases where reaction is thermally controlled. Principally, the maxi- mum temperature excesses compatible with stability are less when chain branching occurs than those expected from purely thermal theory, and the temperature evolution prior to ignition can show more varied forms. In a purely thermal explosion, the reactant temperature rises moderately at first, inflects, and then proceeds at an increasingly rapid rate, culminating in explosion.By contrast, a chain-thermal ignition may be preceded by a relatively steady, or even by a decreasing reactant temperature which persists until the discontinuous increase in temperature accom- panying explosion itself. Accordingly, in this work, temperatures and pressures are measured for the stoichionietric mixture 2 H2S + 3 O2 both near to the ignition limits and under other conditions. Interest is directed in particular to the nature, magnitude, and duration of explosive and non-explosive temperature against time histories.Attention is also paid to the effects of inert diluents on the explosion limits and to the variation of these limits with the reactant proportions, these results providing useful additional evidence in assessing the degree to which self-heating and radical processes combine to con- tribute to ignitions in this reaction. EXPERIMENTAL MATE R I A 1, S All gases were taken from cylinders. Hydrogen sulphide (Matheson Co.) was frozen under liquid nitrogen and degassed before use by trap-to-trap vacuum distillation. Oxygen, nitrogen and carbon dioxide (B.O.C. Ltd.) were dried by trapping water at -79°C. Helium, neon, argon, krypton (B.O.C.Ltd.) and hexafluoroethane (Matheson Co.) were used without further purification.2340 CHAIN-THERMAL IGNITION I N HzS COMBUSTION APPARATUS The reaction vessel was a Pyrex sphere (radius 41 mm, volume 0.29 dm3) heated in an electric furnace and thermostatted to better than 0.5"C. Measurements of reactant temperatures at the vessel centre during reaction were made by a very fine thermocouple constructed by butt welding 25 pm diameter platinum and platinum/l3 % rhodium wires (Johnson Matthey) to produce a junction less than 50 pm in size. The junction and supports were coated with silica to minimize catalytic effects. The thermocouple entered the vessel from above, along the vessel's vertical diameter, with its " hot "junction at the vessel centre ; the cold junction was kept at 0°C.Pressure measurements were made by a sensitive pressure transducer (Langham-Thompson UP 2), readings being accurate to & 1 Torr. Signals from the thermocouple and transducer were amplified and displayed on a storage oscilloscope (Tetronix 564 B). Temperature changes could be reproduced to better than _+ 1°C. The reaction vessel was connected to a conventional glass vacuum line by means of an electro- magnetic valve. Gas-pressure measurements in the vacuum line could be made either with a glass spiral gauge, or by means of a wide-bore mercury manometer. The spiral gauge was used where the gas pressure was less than 20 Torr ; otherwise, the mercury manometer was used and read with a cathetometer. PROCEDURE Gas mixtures of the required compositions were made up manometrically and allowed sufficient time (greater than 30 min) to mix completely.These mixtures were subsequently admitted to the evacuated vessel through the electromagnetic valve normally opened for 0.1 s ; opening the valve initiated measurements of temperature against time and pressure against time histories, which could be displayed simultaneously on the storage oscilloscope. Critical pressure limits for ignition at a particular vessel temperature were determined as the mean of the closest subcritical and supercritical reactant pressures that could be observed. The dependence of the critical ignition limit on vessel temperature, on the variation of the composition of the reactant mixture, and on the extent of dilution with inert gases was investigated.In general, the different ignition limits were sufficiently separate from each other for there to be no confusion over which particular limit was being determined. Difficulties were encountered only in the immediate vicinity of the " lobes " i.e. where dpldt-, GO. Subcritical temperature against time histories were followed for over 100 pairs of values of initial temperature and pressure in the non-explosive region of the ignition diagram, the maximum temperatures achieved always being recorded. Under supercritical conditions, interest centres both on the maximum temperatures achieved before ignition and on the qualitative form of the temperature against time histories for different initial conditions (p, T ) around the ignition boundary. RESULTS IGNITION I N STOICHIOMETRIC MIXTURES The most striking feature of the gas phase reaction in a stoichiometric mixture of hydrogen sulphide and oxygen is the existence, under certain conditions of vessel temperature, of multiple critical pressure limits separating explosive from non- explosive behaviour.As in the hydrogen + oxygen reaction there is first a low pressure limit p 1 above which the reaction is accelerated to explosion by degenerate branched radical chain processes alone. At higher pressures, a second limit p 2 is reached beyond which ignitions cease. This limit increases with increase in ambient tempera- ture. I t eventually merges with a third limit p 3 at the root of the explosion peninsula. The dependence of critical total pressures on ambient temperature for the stoichio- metric mixture, 2 H,S + 3 02, are shown in fig.1. The points a, b, c, d indicated in this figure correspond to four characteristically different modes of behaviour.100 80 60 4 8 b 4 --.. 40 2 0 0 F+G. 1 .-Dependence of critical ignition pressure on vessel temperature for stoichiometric mixture 2H2S + 3 O2 ; induction periods (seconds) indicated by broken arrows. O L 0 I EXPLOSIONS 10 NON -EXPLOSIVE R EACTl ON EXPOSIONS I I I 20 30 40 50 60 %HzS FIG. 2.-Composition-dependence of second ( p z ) and third ( p 3 ) ignition limits for mixtures of hydro- gen sulphide and oxygen at 340°C.2342 CHAIN-THERMAL IGNITION IN H2S COMBUSTION All explosions are characterized by rapid (almost discontinuous) changes in both temperature and pressure, and at all but the very low pressures, explosions are accompanied by a visible flash.The light is generally easily observable, being pink in colour above the third limit but becoming both feebler and bluer as the ignition boundary is traversed, until near the first limit (less than 5 Torr) it is too feeble to be detected. The lengths of the periods vary with the initial conditions of pressure and temperature or position on the ignition diagram. Where self heating accompanies ignition, induction periods are generally short (1-3 s), while under isothermal conditions they are often very long (frequently in excess of 1-2 min), the length of the induction period increasing continuously along the ignition boundary from a to d. Typical values corresponding to marginally explosive conditions are indicated on fig.1 . For pressures and tem- peratures near to the merging of the second and third limits (between b and c), induction periods are intermediate between the two extremes, ranging from 8-10 to around 20-30 s. All ignitions are preceded by induction periods. IGNITION LIMITS FOR NON-STOICHIOMETRIC MIXTURES The behaviour of the reactant mixture is dependent on its composition as well as on pressure and temperature, and to display it adequately, a three-dimensional ignition diagram is necessary. An extensive study was not attempted but fig. 2 shows the variation of the critical explosion pressure with mole percentage H2S along the second and third limits for an ambient temperature of 340°C. At the second limit, the critical pressure p 2 rises linearly with decreasing H2S content, explosion becoming progressively easier for increasingly lean mixtures.Similarly, explosion also becomes easier with decreasing H,S content along the third limit, p 3 falling rapidly at first but varying more slowly where the two limits p 2 and p 3 merge (ca. 23% H2S). Thus, at 340°C for mixtures containing marginally less than 23 % H2S, ignitions are observed over the entire pressure range. One aspect of the merging of the second and third limits is that, at a vessel temperature of 340°C and a reactant pressure 36 Torr, this composition represents the tip at which p 2 and p 3 coalesce. The behaviour of the third limit with respect to reactant composition in the oxidation of hydrogen sulphide contrasts markedly with the simpler behaviour found in the oxidation of methylhydrazine, where the critical ignition pressure passes through a minimum value situated between the stoichiometric and equimolar com- positions, and rises rapidly for mixtures much leaner than stoichiometric. In the oxidation of hydrogen sulphide however, the limitp, does not pass through a minimum value but continues to decrease past the stoichiometric composition (40 % H2S), right up to the point at which it merges with the second limit and explosion becomes inevitable.IGNITIONS IN DILUTED MIXTURES The effects of dilution by inert gas on the critical ignition pressures have been investigated at the third and second limits. (i) In the first type of experiment carried out, mixtures of hydrogen sulphide, oxygen and diluent in the ratio 2 :3 :3 were used, the third explosion limit being determined at different ambient temperatures.Three diluents were used, helium, neon and krypton, and the results are expressed in fig. 3 as a plot of the critical partial pressure of the reactants required for ignition, p(H,S) + p ( 0 2 ) against ambient temperature. Helium and neon increase the critical explosion pressure at the lowerP . GRAY A N D M . E. SHERRINGTON 2343 ambient temperatures (i.e. make explosion more difficult) but their effect diminishes with increase in temperature, and dilution with neon has very little effect near the merging of the second and third limits (around point b). Krypton lowers the critical explosion pressure, making explosion easier, and the lowering is marked all along the limit.Ta/"C FIG. 3.--Effect of dilution on critical partial pressure, p(H2S)+p(02), at the third limit for mixtures 2 H2S + 3 O2 + 3 diluent at various vessel temperatures. (0, helium, A, neon ; 9, krypton). I I I I I 1 I 0 10 20 30 40 50 60 70 % diluent FIG. 4.-Effect of dilution on critical partial pressure, p(H2S)+p(Oz), of second limit p z in mixtures 2 H2S+3 O2 +diluent. Ambient temperature 340°C. 0, helium ; A, argon ; 0, nitrogen ; 0, carbon dioxide ; x , hexafluoroethane.2344 CHAIN-THERMAL IGNITION I N H2S COMBUSTION (ii) In the second type of experiment, the dependence on dilution of the critical partial pressure for ignition p(H,S) +p(O,) was examined at the second limit for a constant ambient temperature of 340°C.Fig. 4 shows the effect of five diluents, helium, argon, nitrogen, carbon dioxide and hexafluoroethane. In all cases the explosive region contracts and explosion is made harder ; the second limit is lowered by dilution, the extent of the depression being approximately linear with degree of dilution. Helium and argon depress the limit least; carbon dioxide and hexa- fluoroethane depress it the most. EXTENT OF SELF-HEATING UNDER SUBCRITICAL CONDITIONS Over a hundred temperature against time histories have been recorded in the non- explosive region. Although both the magnitude and duration of the temperature histories vary widely under different initial conditions of temperature and pressure, certain basic features are common to them all. The thermocouple always registers a brief (ca.0.1 s) initial cooling as the cold reactant mixture enters the hot vessel. The temperature then rises above that of the vessel and passes through a maximum value before returning to ambient as the reactants are consumed and the reaction is completed. 100 80 40 20 0 1 1 - 300 ,/ 320 34 0 360 TaI0C FIG. 5 .-Self heating accompanying oxidation of hydrogen sulphide. Stoichiometric mixture 2 H2S + 3 O2 Contour lines for temperature rises of 0, 10, 20, 30,40°C. L corresponds to predicted ignition limit from purely thermal theory. At the lower vessel temperatures (around 300°C) and near the third limit, the maximum temperature excess is high (over 40"C), but the reactants maintain this value only momentarily. Further along the limit, at higher vessel temperatures and lower pressures, the maximum self-heating observed just below the third limit de- creases, falling to values between 20 and 30°C near point b.Under these conditions the maximum excess is maintained by the system for several seconds. The degree of self-heating for different initial conditions is displayed in fig. 5 by contour lines corresponding to quasi-stationary temperature rises of AT = 10, 20, 30 and 40°C.P . GRAY AND M . E. SHERRINGTON 2345 The dotted contour line AT = 0 separates the isothermal and non-isothermal regimes. Clearly, both the isothermal and non-isothermal regimes are quite extensive. Self- heating is still observed around point c (see fig. 1) under conditions normally described as near the second limit and where, classically, ignitions might have been ascribed to branched chain processes alone.At lower ambient temperatures (300-32OoC), departures from isothermal behaviour are readily observed under conditions well below the third limit ; marked temperature rises are still found for initial pressures of only one half the appropriate critical values. Farkas reported l9 the existence of temperature rises preceding ignition, i.e. above the third limit, but not in sub-critical systems. The inability of Thompson l7 to detect any self-heating in the non-explosive regime and his report of not more than 1 degree rise even after partial ignitions are probably to be attributed to his use of unsuitable temperature measuring equipment. Non-explosive Explosive 0 Ta = 296°C Pc = 83 torr 4 (a) (b) ? Ta = 343°C 5 Pc = 51 torr (4 u iz Ta = 352°C Pc = 34 torr (4 u Ta = 325°C 5 Pc = 12torr t L I I l L 155 ""t 501 t FIG.6.-Non-explosive and explosive temperature against time histories at the four points a, by c, d indicated on ignition diagram in fig. 1 (a and b are located on the third limit ; c and d on the second). SUPERCRITICAL AND SUBCRITICAL TEMPERATURE AGAINST TIME HISTORIES Supercritical mixtures show temperature against time histories prior to ignition initially similar in appearance and magnitude to those observed in corresponding subcritical cases. When ignitions occurred, whether above the third limit or between the first and second limits, they were all marked by a sudden discontinuous jump in temperature. Fig. 6 shows four pairs of temperature against time histories cor- responding respectively to pairs of points marginally above and below a, b, c and d Curves 6(a) are for low ambient temperatures and for high reactant pressure up around the third limit.The evolution of both the non-explosive and explosive of fig. 1.2346 CHAIN-THERMAL IGNITION I N H2S COMBUSTION temperature histories closely resembles purely thermally controlled behaviour. 2 , 5 The maximum stable temperature excess (ca. 45°C) is high, and the development of temperature just before explosion, accelerating the reaction to ignition is rapid. Curves 6(d) are for conditions situated at the lower part of the second limit. No temperature excess at all is observed in the non-explosive reaction, nor is there any rise in temperature prior to ignition in the explosive case.The temperature against time traces closely resemble the behaviour reported for the chlorine dioxide decomposi- tion and are typical of purely isothermal chain branching processes. Initial conditions correspond to points on fig. 1, situated close to the region where the second and third limits merge : b is on the upper portion, corresponding to the lowest part of the third limit and c on the lower portion, corresponding to the highest part of the second limit. At b, the reaction attains a steady temperature excess which in the explosive case is increasing only slowly right up to the moment of ignition. The magnitude of the maximum temperature excess attainable (ca. 2SOC) is smaller by some 3040% than would be predicted on a purely thermal basis.On the temperature record 6(c), the temperature excess is smaller still, the maximum value being only about 12°C; in the explosive case, the temperature has actually passed its maximum and is falling when explosion occurs. The temperature traces represented by curves 6(b) and 6(c) correspond to behaviour which cannot be satisfactorily explained on either a purely thermal or a purely chain basis; both mechanisms are contributing in varying degree to these ignitions. Curves 6(b) and 6(c) are quite different. DISCUSSION Previous work on the oxidation of hydrogen sulphide has concentrated on the explosion and the identification of intermediates responsible for chain-branching. The present experiments are in reasonable quantitative accord with earlier work 7-21 so far as the location of explosion limits, the variation of induction periods, and the effects of composition and diluents are concerned ; some specific comparisons are referred to below.The principal aim of the present study, however, is the evaluation of the relative contributions of physical and chemical processes to ignition. By the direct detection and measurement of temperature changes accompanying reaction we are able to define the conditions in which thermal factors or chain-branching factors can alone account for the observed behaviour, and to map the conditions in which neither mechanism is completely dominant but where both compete for control of stability of the reaction. The findings are important not only for this oxidation but for the kinetically related hydrogen + oxygen system.THE ISOTHERMAL REGION Beneath the zero self-heating contour line (AT = 0) of fig. 5, reaction is truly isothermal. This contour bounds a region that contains the entire first ignition limit, the ignition peninsula and most of the second limit. Throughout this region, iso- thermal branched chain reactions make the important contribution, and thermal effects play an insignificant role. This is also confirmed by the qualitative form of the temperature histories preceding ignitions [fig. 6(d) where ignition occurs without any previous self heating.] It is only near the uppermost part of the second limit, where the second and third limits merge, that any significant degree of self-heating is observed, and even there the limiting temperature excesses are small, typically only a few degrees centigrade.The effects of dilution at the second limit further support the conclusion that thermal factors have little to do with ignitions in this region.P . GRAY AND M. E. SHERRINGTON 2347 Ignition is made harder in all cases, the explosive domain contracting and the critical pressure being lowered in proportion to the amount of diluent added. The simple monatomic gases helium and argon have least effect on the limit, and the polyatomic gases carbon dioxide and hexafluoroethane have the greatest. These differences are to be interpreted 23 in terms of the different “third body’’ efficiency of the diluents. Any change in this efficiency in turn induces corresponding changes in the rate of homogeneous chain termination of the radical reactions.The addition of any inert gas increases termination, and polyatomic molecules, being more efficient as third bodies than monatomic molecules, have the greater relative effect on the lowering of the ignition limit, as is found here. Work by Davies and Walsh 24 confirms these results ; they report that the efficien- cies of diluents in lowering the second limit diminish in the order CO, > N, > He > Ar, and that the efficiencies decrease slightly as the temperature rises, but are relatively insensitive to reactant proportions. An estimate for the activation energy of chain-branching can be got from the temperature- dependence of the second limit RT2(d lnp,/dT) if this originates in varying com- petition between a chain branching reaction with activation energy Eb and a termina- tion process without activation energy (as may be assumed for the hydrogen + oxygen ignition diagram).Here, E2 is 122 kJ mol-’, significantly greater than the value of Yakovlev and Shantarovich.20 Under no circumstances is the limit raised. Detailed knowledge of the elementary reactions involved is still lacking. THE THIRD LIMIT AND THE EXTENT OF THERMAL CONTRIBUTIONS In contrast to the behaviour observed near the first and second explosion limits, reaction along the third limit is far from isothermal, and strong self-heating persists for conditions well removed from the limit itself. In view of the marked degree of self-heating, it is illuminating to contrast the measured critical ignition pressures with predictions derived from the theory 6*7 appropriate to purely thermal explosions.Simple conductive theory predicts that, along a thermal ignition limit, the dimension- less heat release rate 6 is a constant and that a graph of ln(p,,/T ;) against 1 /Ta should be a straight line of gradient E/2R, where pcr is the critical total ignition pressure at ambient temperature T,, and E is the effective activation energy of an isothermal reaction with second order pressure-dependence overall. Fig. 7 shows how the conditions at the third limit for the ignition of 2 H,S + 3 0, obey this relation for the higher pressures and lower temperatures, and how the limit deviates from linearity as the temperature increases and the critical pressure falls.The deviation of the limit from thermal prediction is discernible at temperatures above 310°C. This deviation may be thought to reflect the extent to which chain processes become progressively more important as the temperature rises and the third limit approaches the explosion peninsula. From the linear portion of the graph in fig. 7 we derive a value for the activa- tion energy E3 of 98+5 kJ mol-l. Earlier workers 1 7 v 1 * reported values of 80 to 84 kJ mol-l for E3, but the discrepancy is not significant because they forced their lines through points corresponding to the root of the peninsula where chain-branching contributions are present. The broken line L on figure 5 corresponds to the straight line portion of fig. 7. At and above L, ignitions can be interpreted on a purely thermal basis; beneath it, ignition is increasingly influenced by branched chain reactions.These influences are reflected in (i) the response to variations in reactant proportions (ii) the influence of dilution by inert gases.2348 CHAIN-THERMAL IGNITION I N H2S COMBUSTION The effects of reactant composition on the ignition pressure have been described for an ambient temperature of 340°C. based on purely thermal factors 6*7 would suggest that on passing from hydrogen sulphide-rich to hydrogen sulphide-lean mixtures the critical ignition pressure should fall to a minimum value and then begin to rise again. Observed behaviour is significantly different from this. The ignition pressure ( p 3 ) is seen to decrease past stoichiometric (40% H2S) to the point where it merges with the second limit ( p 2 ) and explosion becomes inevitable.This behaviour in lean mixtures reflects the changing nature of the limit ; as the hydrogen sulphide content decreases so the chain influence becomes pro- gressively more marked until, at the composition (ca. 23 %) conditions that correspond to the root of the peninsula, the second and third limits meet. Simple considerations 0.6 n 2 4 --.- W CI 0.4 0.2 1 .o 0.8 - - - - - - - NON-LINEARITY DUE TO THE SECOND LIMIT I .66 1.70 I .74 I .7a lo3 KITa In (pc/T,2) on 1 ITa is linear on purely thermal theory.) FIG. 7.-Predicted and observed temperature dependence of third ignition limit. (Dependence of The effects of dilution on the critical ignition pressures also reflect the changing nature. The three diluents were chosen because of their widely different thermal conductivities.According to a stationary state treatment,7 the effect of diluents on purely thermal explosion is to make the explosion easier or more difficult according to whether the overall conductivity A of the gaseous mixture is lowered or raised : pCrccA. As expected, helium and neon, with high thermal conductivity, make ex- plosion harder at the lower temperatures and higher pressures, but further along the ignition limit where thermal influences are less their effect is quite small. Krypton lowers the limit over a wider range, possibly because it makes thermal explosion easier {lowers p 3 ) and terminates branched chains effectively (lowers p z ) .P .GRAY AND M. E . SHERRINGTON 2349 THE CHAIN-THERMAL REGIME The boundaries of the isothermal region and of the pure thermal ignition have been discussed above. Between them lies the region where both chain-branching and thermal contributions are important, and whose description and interpretation require the framework of unified treatment. Certain interactions, indirectly observed, between chain and thermal processes have been touched on already; two further features of ignition deserve emphasis here; both are derived from direct temperature measurements. The first is the reduction in the stably attainable temperature rise ATcr accompanying exothermic oxidation along the ther- mal limit ; the second is the qualitative difference in temperature against time histories preceding ignition nearer to the isothermal limit.(i) According to simple stationary conductive t h e ~ r y , ~ maximum stable tempera- ture excesses in a spherical vessel of about 1.61 RT;/E are allowed ; the excess expected rises to about 1.85 RT,2/E when consumption of reactants 25 is considered. Accepting the value of the activation energy derived from the linear portion of the plot in fig. 7, this corresponds to predicted critical temperature rises of about 45 to 50°C at T, = 3OO0C, in good agreement with the maximum stable rises experimentally observed near to point a. On simple theory, the critical excesses should increase monotonically (as T,2) with increase in ambient temperature around the ignition boundary. Fig. 5 indicates that the converse occurs : temperature excesses never reach such values ; at T, = 340°C, near point b, the highest sub-critical excess so far observed is only 28”C, around half that suggested on thermal grounds.The dis- crepancy increases around the boundary; near point c only a 12°C excess can be realized. Both are readily located. (ii) Temperatures also vary differently with time from the lively accelerations that are a prelude to purely thermal explosions : instead they may rise only sluggishly, be relatively steady or even decrease, as is the case near point c. on the unification of thermal and chain-branching theories of explosions, Gray and Yang outline qualitatively the results which have here been observed quantitatively in the oxidation of hydrogen sulphide. In the chain-thermal region of the reaction we are, by definition, concerned with the regime in which the two different mechanisms compete for control, and in many ways the combined effects reflect the compromise.Maximum stable temperature rises are predicted 26 and found to be markedly below their purely thermal counterparts, and the entire temperature development is slower paced. In particular, induction times are much longer than in purely thermal explosion, being typically of the order of 10-30 s, though these values are significantly shorter than the induction periods observed in the purely isothermal regime. The temperature excesses immediately preceding ignition are often surprisingly steady and the temperature “jumps” occur suddenly with little or no additional self-heating. Indeed, in the region where the second and third limits merge the reactant temperature is falling when ignition occurs. The contribution to the explosion under such conditions by branched chain radical processes is clearly very great. Similar behaviour might be expected near the second limit in the hydrogen + oxygen reaction but although falling temperatures before ignition have been reported 2 2 they appear to be the artificial consequence of the conventional “withdrawal” technique used to locate the limit : reactant temperatures fall by adiabatic expansion. In their original paper A re-investigation of this system would be timely. We are grateful to S.R.C. for the award of a studentship to M.E.S.2350 CHAIN-THERMAL IGNITION I N H2S COMBUSTION P. Gray and J. K. K. Ip, Combustion and Flame, 1972, 18, 361. D. H. Fine, P. Gray and R. MacKinven, Proc. Roy. SOC. A , 1970, 316, 223, 241 and 255; P. Gray, D. T. Jones and R. MacKinven, Proc. Roy. SOC. A , 1971,325, 175. H. Goodman, P. Gray and D. T. Jones, Combustion and Flame, 1972, 19, 157. P. Gray and E. B. O'Neill, Trans. Faraday ,Yoc., 1972, 68, 564. P. Gray and M. E. Sherrington, J.C.S. Faraday Z, 1974, 70, 740. N. N. Semenov, Chemical Kinetics and Chain Reactions (Oxford U. P., Oxford, 1st edn., 1935). D. A. Frank-Kamenetskii, Diflusion and Heat Exchange in Chemical Kinetics (Plenum, New York, 2nd edn., 1969). B. F. Gray and C. H. Yang, J. Phys. Chem., 1965, 69, 2747. B. F. Gray and C. H. Yang, 11th Symp. (Znt.) Combustion (Combustion lnst., Pittsburgh, 1967), p. 1099. l o C . H. 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