Hydrogen forming reactions of thermal electrons in hydrogen halides: kinetics and thermodynamics

Hydrogen for~~~gng reactions of thermal electrons in hydrogen halides: kinetics and thermodynamics

SURJIT S. N . ~ G R A AND DAVID ANTHONY ARMSTRONG Depori171ent of C!zel?iisti.j. Ut~icersitj of Calgirr.y, Cu(gn~;~,, Alra., Cc12ada T2.M 1iV4

Received May 14, 1976

SURJIT S. NAGRA and DAVID ANTHONY ARMSTRONG. Can. J. Chem. 54, 3580 (1976). New competition kinetic studies of electron reactions in HCl and HBr in the 10Is to 1020

molecule cm-3 concentration region are reported and shown to support the findings of earlier investigations. The capture of thermal electrons by (HX): dimers is examined from a kinetic and thernrodynamic point of view. The (HX)2-'"intermediate previously proposed by several groups is considered to be involved in both systems. Differences in the magnitudes and concentration dependences of the rates can be explained, if reaction 5b is fast (k56 = 1013 s+) in

[jb] (HX)2-4 H + XHX-

HBr but relatively slow in HCl < 2 X 109 s-1, where [6u] and [6b] are the major product- forming reactions. Thern~ochemical data show [5b] to be strongly favoured energetically in

HBr, and close to thermoneutral in HC1. Reaction 6h is energetically favourable in HC1. The present data require an autoionisation life-time of -10-l2 s for (HX)I-'". From other considerations that of HX-" is expected to be 2 10-1". This means that formation of (HX)2-* must take place by collisions of electrons with HX molecules which are in effect already interacting. Production of stabiiised HX- from (HX):-* does not appear to contribute in HC1, but

may occur in other HX systems. The general implications of the mechanism for electron capture in HF and HX mixtures with other polar vapours are mentioned.

SURJIT S. NAGRA et DAVID ANTHONY ARMSTRONG. Can. J. Chem. 54. 3580 (1976). On rapporte de nouvelles Ctudes cinitiques par des rkactions de compitition d'electrons dans

HC1 et HBr dans 1'Ccart de concentration de 10's a 10'0 niolCcules par cm-3; on montre que ces Ctudes sont en accord avec les resultats obtenus anterieurement. On examine la rCaction de capture d'klectrons therrniq~~es par des dimkres (FIX): partir de point de vue cinitique et thermodynarnique. On considkre que l'intermediare (HX)2-:\ qui avait ete propose antirieure- ment par plusieurs groupes, est iniplique dans chacun des systkmes. On peut expliquer les amplitudes et les dependances des vitesses sur la collcentration si la reaction [jb] est rapide

(k5b % 1013 s-1) dans FiBr rnais relativement lente dans HC1 < 2 X lo9 s-I, oh [6n] et [6b] sont les riactlons majeures conduisant a des produits.

Les donnCes thermodynamiques montrent que [5b] est particulitrement favoris6 du point de vue Cnergktique dans le cas de HBr et pratiquement therrnoneutre dans HC1. Au point de vue CnergCtique, la reaction [6b] est favorable dans le cas de HCl. Les donnCes actuelles in~posent un temps d'autoionisation de -1 0-I2s pour A partir d'autres considCrations, on croit que celui de HX-* est <_ 10-13 s. Ceci signifie que la formation de (HX):-:' doit se produire par des collisions d'electrons avec des n~olCcules HX qui sont en fait dejB en interaction. I1 ne semble pas que la production de HX- stabilisi B partir de (HX)2-* contribue dans HCI; toutefois il peut se produire dans d'autres systkmes. On mentionne les implications generales du

mecanisme pour la capture d'electrons dans les melanges de H F el de MX avec d'autres vapeurs polaires.

[Traduit par le journal]

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NAGRA AND ARMSTRONG 3581

Introduction

Electron capture reactions in gaseous hydrogen haiides have been studied by physical (1, 2 ) and chemical (3-7) methods. In HI dissociative capture

[I] e- + HX - H + X- (X = F, C1, Br, I)

has a large cross section (1) and zero energy threshold, which means that it is undoubtedly the main reaction of low energy electrons in this gas (8). As one proceeds to the halides of lower molecular weight the threshold energy of [ I ] becomes progressively larger (see comparative data on AE0298,[,1 in Fig. la) and the cross sections smaller (I), making it a less and less likely process for electrons of thermal energies. In fact from previous radiation chemistry studies

REACTION NUMBER

REACTION NUMBER

FIG. 1. Energy changes calculated for various electron capture reactions in hydrogen halides. C HF, 0 HCI, A HBr; filled points are AEo2,,, open ones AGoz9,; reaction numbers are given on the abscissa.

(3-8) with the con~petition kinetic technique this reaction appears to be relati\.eiy unimportant in HBr arid HCl. However, in the 0.1 to 4 atni pressure region there is evidence for a different thermal electron capture mechanism with a rate which is second order in hydrogen halide concentration. In general terms it can be described by one or a combination of the three overall processes [2u]. [2b], and [2c].

[2al e- + 2HX H2 + X2-

t2bl e- + 2HX = EI + XHX-

PC] e- + 2HX HX + HX-

The rate in HBr is much larger than in HC1, where it is also sensitive to total gas pressure (6, 8). However, careful consideration1 of the results and conclusions in refs. 1, 3, 4, 5 , 6 , and 7 has led us to propose a common mechanism for capture in the two gases. This is based on reactions 3 through 7.

The present publication begins by exploring the feasibility of the above mechanism. Subse- quently we reexamine the conclusions of the earlier competition kinetic studies in the light of new results from similar experiments and of recent work (9) on electron thermalisation rates. The mechanism is then shown to be capable of explaining the results of the earlier studies and those reported here, provided kr is much larger for HBr than for HC1. Finally the general implications of these findings are discussed.

'This research was supported by NRCC Grant No. A3571. A preliminary report was given at Colloque Weyl IV. See J. Phys. Chem. 79, 2875 (1975).

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3582 CAN. J. CHEM.

Experimental

114ateriuls Hydrogen chloride (electronic grade), hydrogen bro-

mide (99.8";), carbon dioxide (99.6';), and sulphur hexafluoride (99.99:;) were all obtained from the Matheson Company. Propane (research grade) was obtained from the Phillips Petroleum Company. Hydro- gen chloride was purified by -,-irradiation as a liquid at Dry Ice temperature and several distillations through copper turnings and a trap (ethanol-nitrogen slush) at 170 K. Hydrogen bromide was purified by irradiating the gas at room temperature with X-ray followed by distillation through copper turnings and a trap at 170 K. Purified HBr and HCl were stored at liquid nitrogen temperature. All other gases were purified in the vacuum line by trap-to-trap distillation from 170 to 70 K. Middle fractions were stored in bulbs attached to the mercury- free preparation line.

Apparatus and Procedure The radiation source, cell, and preparation procedures

were essentially as described in ref. 7. The low temperature experiments with HBr were carried out by placing the cell in an insulated vessel containing Dry Ice (for 200 K), and ethanol-water (56:44 by volume for 243 K) freezing mixtures. For high temperature radiolysis the reaction cell containing HBr was heated in an aluminium container wrapped with an electrothermal heating tape and placed in a well insulated fibre glass container. The temperature as measured with an iroll-constantan ther- mocouple was maintained constant within x 1 deg during irradiation (30 min) by regulating the variac power supply. Mixtures of HCl and buffer gases were irradiated at room temperature only.

Product analysis was as previously reported (7).

Dose Rate Determinatiorzs Ionization measurements have been previously dis-

cussed in detail (7). The dose rate Dm in eV2 per hour for each mixture was calculated from the sum of the dose rates of all the components each taken as (3600IS W/e) where IS is the saturation ionization current for the required partial pressure of that component, e is the electron charge, and W, the energy In eV required to create an ion pair in the pure component. For two gases 1 and 2, the W values, ionization currents per unit pressure (or J values) and F12, the weighed mean stopping power ratio for the spectrum of energies of the electrons traversing the Pyrex chamber, are related by the expression

Using our measured J values and stopp~ng power ratios given In the tables of Huyton and Woodward (10) we calculated W values of HC1 and SF6 as 25.5 and 34.97 eV, re~pectively.~ These are in good agreement with the literature values of 25.0 (1 1) and 34.9 (12) for HC1 and SF6 respectively. The magn~tude of W for propane (23.45 eV) was taken from ref. 11. All others were as used in ref. 7.

20ne eV = 1.60 X 10-19 J and one eV per molecule =

96.49 kJ mol-1.

Results and Dissussion

( I ) Proclltction of ( H X h - * Although the existence of HX- ions does not

appear to have been confirmed by experiment, calculations by a variety of methods (13-15) suggest that some H X molecules may have a positive electron affinity. For this reason we included reaction 5c in the mechanism. Further, some theoretical studies (cf. ref. 15, curve D in Fig. 2 of ref. 16, and the potential energy (PE) curves in Fig. 1 of ref. 14 imply that in these instances a large part of the potential energy curve of HX- may lie below the zero point vibrational level of FIX in the Frank Condon region, making transitions of the type:

highly probable. As originally recognized by Chen and Armstrong (3) one must therefore consider the possibility of the (HX)2-* intermediate being formed in reactions 8 and 9 as an alterna- tive to [3] and [4].

We now examine evidence relating to the magnitude of k-s , which appears in the expression for the rate of formation of the intermediate via [8] and [9], oiz: d[(HX)2-*]/dt =

k9k8k-8-1[HX]2[e-]. This rate constant can be identified as the reciprocal of T,, the autoionisation lifetime for HX- 2 z ~ i o n s in vibrational levels correlating with HX '8' (u = 0) and electrons of thermal energy (-0.04 eV). The magnitude of ra. will be equal to firHX-', where rHX is the entry width for the capture reaction in Breit- Wigner formalis~n (17, 18). Since the H X orbital into which the extra electron goes is a u orbital, its coupling with s-wave electrons is not for- bidden by symmetry (16). Thus, as previously pointed out (14, 16), rRX is expected to be large and 7, relatively small, smaller for example than 2 X 10-l2 s observed (19) for 02-*(211s) +

02(3z) + e- where d-wave electrons are involved and the angular momentum barrier has an appreciable effect (16, 17).

Estimates of r , for electrons of kinetic energy near AEoO for reaction 1 are accessible from experimental data. For example the fact that the reverse reaction for HCl(20) has a cross section

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close to the Langevin value means that autoionisation must occur in a period much shorter than the time a rebounding H and X- pair would spend in the potential well of HX, 5 4 X 10-l4 s. This observation agrees with the fact that Christophorou, Compton, and Dickson (1) reported T, - 4 X 10-Is s from their study of dissociative attachment in HCl and HBr. An even shorter T, (< 10-Is s) is obtained from r,, = 1.8 eV, which was used by Fiquet- Fayard to obtain a theoretical fit to structure in the energy dependence of the dissociative capture cross section for HCI (16). For electrons of thermal energy T, should be larger than the above estimates, because r usually decreases with decreasing energy.3 If we assume a half power dependence on KE, which seems reasonable for an s-wave electron (18), and take AEo298 = 0.82 eV for HCI and 0.39 eV for HBr then, it follows that T, for thermal energy electrons (-0.04 eV) should be < 10-l3 s.

The average velocity of HC1 molecules at 298 K is -4 X lo4 c n ~ s-I and that of HBr is less. Thus the distance between an HX-* ion and an HX molecule could only change by about 4 X 10-gcm or about one-tenth of the MX collision diameter (21) during the average lifetime of HX-*. Since HX molecules with that separation would already be interacting with each other (re in the intermolecular potential is 3.7 X lop8 cm (22)) and because the de Broglie wavelength X of a 0.04 eV electron is 68 X cm, the concept of [8] and [9] occurring as separate processes is somewhat unreasonable. The production of the (HX)2-* intermediate via [3] and [4] is therefore to be preferred over [8] and [9]. This is of course equally true if the potential energy curve of HX- lies above the zero point level of HX and reaction 8 is unfavourable.

(2) Thernzoclj~namic Considerations The (HX):! dimer molecules formed in reaction

3 are assumed to be bound by relatively weak hydrogen bonding or dispersion forces. As such they belong to the general class of weakly bound dimers known as van der Waals molecules (22). The equilibrium constants estimated for HC1 and HBr from PVT data (23) using methods given in ref. 24 are both in the range 2.5 to 3.0 X cm3 molecule-' at 298 K. (An identi-

3See ref. 67 for evidence of this in more complex molecular systems.

cal value was derived for HC1 on substituting the magnitudes of re and E k from ref. 22 in the statistical mechanics equation and plot in Fig. 8.2 of ref. 24).) For the nonpolar molecular gases in which dimer molecules have been studied in some detail the equilibrium constants from such calculations are in reasonable agreement with experimental dimer populations found in mass spectrometric studies (22,25). For HX molecules one must recognize that the intermolecular potential will not be isotropic and hydrogen bonding interactions will lead to preferred orien- tations. In the case of H F spectroscopic studies (26) and several different theoretical calculations (27, 28 and references therein) agree on a linear F-H . . F arrangement with the second F-H bond at an angle of about 160" to this axis as being the most stable configuration. AE,31 for the H F dimer lies in the range -21 to -29 kJ mol-I (27, 28). Discrete lines in the infrared spectrum of HC1 have also been attributed to a hydrogen bonded dimer (29, 30) and from the temperature dependence of the integrated ab- sorption intensities AEr3] was estimated to be 9.0 kJ mol-I.4 A slightly higher value of 11.3 kJ mol-I uas obtained in a CNDO calculation for a linear dimer (3 1). We found no published values of AE,,, for HBr, but one would expect it to become progressively smaller in the series HF, HCI, HBr due to the decrease in polarity.

The average of the two AEf3] values for HC1 is - 10 + 1.3 mol-I giving AH0298,[31 = - 12.6 kJ mol-I. If one con~bines the values of AG0298 calculated from K for HC1 at 298 K with this, then AS0298,131 = -83 J K-l mol-I. Noting that earlier estimates of standard entropies of di- merisation are near - 109 J K-I mol-I for H 2 0 (32) and H F (33). where AErsI - -20 kJ mol-I (34), and change t o ~ a r d - 80 for more weakly bonded dimers with AE near - 12 kJ mol-I, the above result for HC1 is entirely reasonable. For HBr the decrease in entropy may be smaller, since (HBr)2 is likely to be less tightly bound. However, subsequently we use the same parameters for reaction 3 in HBr as in HCI. We also use a published (33)value of AS0298 ,~31 = - 108 J K-I mol-I in HF, and do not consider the

4Actually this was interpreted as the value of AHI3,. However since the experiments were run at constant density we interpret it as a AE,3.. Also because of the - 5 105, uncertainty we make no distinction between AEOo,,,, and AE298,i31 here or for HF.

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3584 CAN. J . CHEM. VOL. 54, 1976

TABLE 1. Spectroscopic parameters for X 2 and XHX- ions

Value

Parameter BrZ- BrHBr- C12- ClHC1- F2- FHF-

I / 10-3 cm2 g-1 (calcd.) 4.70 7.35 vl/cm-l 1 70a 170d vz/crn-1 -580d v3 /c~n-l 670d EA of Xy/kJ mol-1 242" D298,XHx-/kJ m0l-I 75t

g, = 2 for X2- and 1 for XHX-

~ - ~~-~ - ~

aReference 36. bReference 37. CReference 38. dReferences 29-41, ?Mean of 220 (36) and 260 (38). fReference 42. QReference 43. hReference 44. (Reference 45. lReference 46.

higher polymers, which are knoun to exist (27). When reaction 4 is taken in sequence with

each of [5a], [5b], and [5c]. the reactions 5'c1, 5'b, and 5'c

[5'nl e- + (HX)2 i=' H2 i- X2- t5'bl e- + ( H X ) ~ c H + XHX-

[s'cl e- + (HX)2 = HX + HX-

are derived. Likewise combination with [3] ulzd [4] leads to the overall capture reactions 2a, 2b, and 2c given in the Introduction. We begin our analysis of the thermodynamic feasibility of the mechanism by calculating AGOz9*, and A f f o 2 9 * for these overall processes.

The magnitudes of were calculated from A H o 2 9 * and A S 0 2 9 8 . The electron affinities of the X atoms used in calculating A H o 2 9 * and thence A E 0 2 9 8 were the ones recommended by Christophorou (1 I) . The bond dissociation energies of H z , HX, and X2 molecules were from ref. 35. The H X electron affinities were from ref. 13 (see comment on HF in section 7). The magnitudes and sources of corresponding parameters for the X 2 - and XHX- ions are given in Table 1. Expressions for AS0 were obtained from d(RT In Q)/aT, where R T ln Q is defined via the standard expressions A G O =

- RT In K = AEoO - R T In Q (24, 47). The statistical weights, vibrational frequencies, and

moments of inertia used for the atomic species and HX and H2 molecules in the partition functions for deriving & were taken from refs. 48 and 49. Those for the XHX- and X2- ions are listed in Table 1 along with their sources. The X2- ions were considered to be in their 2B,+ ground states (38). The contributions of vibrational modes with frequency > 500 cm-I to vibrational partition functions a t 298 K were taken as unity. The partition function for the free electron was based on Boltzman statistics, which are appropriate for our very low electron density (5104). A S o 2 9 * was found from a(RT In Q ) a T on substituting T = 298 K. Due to its low mas9 the entropy loss on removal of the electron is relatively small (12 J K-I electron-'; see Sackur Tetrode equation (24)). Thus the net entropy losses which arise from the efTect of this and of changes in the rotational partition functions are not large, for example, -26, -44, and - 12 5 K-I mol-I in HBr for [2a] , [2b], and [2c] respectively. For HC1 and H F they are smaller and we have not reported AS per se. However, the calculated values of and which are subject to an uncertainty of +25 kJ mol-I, are presented in Fig. la.

When allowance is made for the loss in entropy due to removal of e- reaction 2c has a negative

for any HX with an electron affinity

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greater than 1.3 k J m ~ l - ' . ~ Reaction 2a is seen to be strongiy endothermic in HF. Reaction 2b would be close to therrnoneutral (see the lower points of joined pairs) if the large (-213 kJ mol-l) theoretical and experimental (46) values of D298,X--EIX were correct. I-iowever, from their systematic studies of gas phase ion binding Yamdagni and Kebarle (45) state that the bond energy should be close to 125 k J mol-I, in which case [2h] is strongly endothermic. Thus present data in Fig. l a show no favourable channels for HF. The thermodynamic feasibility of thermal electron reactions other than [2c] in HBr is confirmed by the fact that [2a] and [2b] are exothermic and exhibit negative AG0298va1~~es. In HC1 [2a] is energetically favourable and [2b] close to thermoneutral.

The above findings for HBr and HC1 are highly significant to the present investigation, but we are also particularly interested in the thermo- chemistry of reactions 5a, 5b, and 5c. Since the total internal energy of the (H)O2-* con~plex is unaltered between its formation in reaction 4 and the instant at which one of [5n], [5b], or [5c] occurs, the AE0298 values for the latter reactions will be the same as for [5'ci], [5'b], and [5'c] respectively. The magnitudes of A Eo29 for these three reactions were obtained from those of [2a], [2b], and [2c] by subtracting the AE0298,[31 values given above. They are presented in Fig. 16, where a more expanded scale is used than in Fig. In. These results are considered further in section 7.

(3) Hydrogen Forrnatio~z ancl Competition Kinetics

The irradiation of gases with 60Co y-rays or other ionising radiation leads to the formation of electrons, positive ions, and neutral excited species. The reactions of ions and neutral excited species in hydrogen halide systems have been discussed elsewhere (8, 50), and here we shall concentrate entirely on hydrogen forming reactions of electrons.

Previous radiation chemical studies (4-6, 51)

5This was calculated from the loss in translational entropy of e-, and So2$,, was assumed to be the same for HX- and HX. The result is a maximum loss in entropy, since the entropy of HX- is likely to be greater than that of HX due to: (a) a gain in rotational entropy arising from the probably larger value of re, and (b) a larger vibrational contribution due to lower vibrational frequencies.

have sho~vn that electron scavengers reduce hydrogen forn~ation in irradiated HC1 by an amount, which correlates uith the >ield of electrons from ionisation measurements. A similar correlation exists for HBr when allowance is made for the small but significant proportion of electrons captured in [ l ] during thern~aiisation (3,7). Frorn the si~nilarity of results with different electron scavengers (HBr with CC14 ( 5 2 ) h n d SF6 (3,7), and HCI with SF6, CCL, and C7F14 (6)) and the known fact that SF6 cannot compete for kI atoms undergoing reaction 10 in I-ICl and HBr (8, 501, it appears that they do not interfere

with hydrogen forming reactions other than electron capture by HX. When the hydrogen halides are added to gases whose molecules are unreactive to thermal electrons the yield of hydrogen is usually enhanced and, more im- portantly, G,, w-hich is the maximurn reductio~l in G(H2) on the addition of other electron scavengers, generally corresponds closely to the electron yield calculated froin Gionisation (= 100,'W) for the sjrstem. The values of the total hydrogen yield and G, from present experiments with HC1-propane mixtures, which are plotted as a function of stopping power fraction of HCl (Z,,,)' in Fig. 2> serve to illustrate this point. G, rises with ZHCl and is w i t h i ~ ~ 10% of Gionisatiorl for ZIIcl = 0.2, which corresponds to 30 moi7, of HC1. Similar results were obtained in the present study for mixtures of HC1 with C 0 2 and C2F6 and have been reported previously for HBr with C 0 2 , G2F6, and Xe (7) , and with H2S (53). With HBr the scavenging of thermal electrons is usually complete at much lower [HX] (e.g.: < 10 molr< in C 0 2 (7)).

The foregoing observations lead to the conclusion that one molecule of hydrogen is pro- duced for every electron reacting with HCI or HBr. This requires that each 11 atom from [5b] and [6b] undergoes [lo]. Also each (FIX);?- pro- duced in [6a] and [7] must form a molecule of hydrogen. This would probably occur, after further clustering by HC1 (4), through [11]

61n this system the CKC13 yield from e- + CC14 +

C1- + CCI3. and CCl,. + HBr -, CHCI3 + Bra was also observed and found to be equal to the r e i o n in G(H2).

7As defined in ref. 7 Z = (1 + P*HX Pt/PH,,)-l, where P ~ H X is the weighted mean stopping power ratio.

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3586 CAN. J . CHEM.

FIG. 2. Ionization yields and hydrogen yields plotted as a function of stopping power fraction Z for mixtures of HCI and propane at 298 K. I=, total hydrogen yields; A, hydrogen yields due to electron reactions. The dashed line shows GioniZation Dose rates varied from 2.23 X 101" to 3.0 X 1018 eV g-1 h-1 for mixtures with total pressure 8.00 X lo4 to 26.67 X 104 N nl-'.

followed by [lo]. Similar reactions must occur for HX- if it is formed in [5c].

When HX is made to compete with known concentrations of an added electron scavenger, S, the results may be plotted in accord with expression 12 (7). The rate of electron capture per unit concentration of electrons (=(rate of electron capture by HX)[e-]-I)

(rate of e capture by HX)

k13[e-I

can then be obtained from the product of the rate constant k13 and the slope over intercept for this plot. The remainder of the present discussion is

confined to results for S = SF6, which by virtue of its high vapour pressure can be used over a wide range of temperatures. Also information concerning secondary reactions of the SF6- and SF5- ions formed by electron capture is available from ion cyclotron resonance experiments, which

FIG. 3. Typical plots of reciprocal of the reductions of hydrogen yield c.5. the reciprocal of the pressure of SF6 for mixtures of HC1 and propane at 298 K. Q, pressure of HCl; 5.33 X 10" N - ~ , total dose rate = 2.23 X 1018 eV g-1 h-1; A, pressure of HC1 and propane each equal to 5.33 X 10" m-2, total dose rate = 2.71 X 1018 eV g--1 h-1; S , pressure of tlCl and propane equal to 5.33 X 104 N m-2 and 21.33 X 104 N m-2respectlvely, total dose rate = 2.99 X loL8 eV g-1 h-1.

have shown that these ions are rapidly converted to XHX- in reactions with HC1 and HBr (54). Since XHX- ions are probably the main long- lived negative ion species in the absence of SF6 (see below), the use of this scavenger should have the advantage of not affecting ion recombination reactions. This conclusion is supported by the fact that the recombination coefficient in HC1 is unafl'ected by SF6 (55). It may be noted that rates of HX capture calculated from previous results with CC14 and C7FI4 (4, 6) are within a factor of two of those for SF6. In the present study k13 was taken as 2 X cm3 molecule-I s-I independent of the gas mixture (56). Figure 3 shows examples of results from the present study plotted in accord with expression 12.

It can be shown that rates of capture from experiments where HX fails to completely sup- press electron-ion recombination and electron- product reactions will be high by a fraction approximately equal to (Gionisation - G,),;G,. Since this correction is somewhat uncertain we have avoided experiments where it exceeds 10%. The usual uncertainty in the measured rates as judged by the standard deviations of points from plots like those in Fig. 3 was f 107 , .

(4) Rates of Electron Capture and Therr71alisation

Figure 4 shows a comparison on a log-log scale of the hydrogen halide concentration dependences of the capture rates for HBr and HC1 (see the upper and lower solid lines respectively).

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Warman and Sauer (9) have recently given rate coeflicients for the thermalisation of electrons ( K U ) in a number of gases. Where com- parisons can be made (e.g. for C02, C2H4, and certaln hydrocarbons) t h e ~ r results give experimental thermalisatlon t ~ m e s ~{h ich tend to be shorter, but generally agree within a factor of tivo with those calculated by Christophorou, Gant, and Baird (57) from the data of drift experiments. The lower dashed line in Fig. 4 is the rate of thermalisation due to hydrogen halide calculated by the method of Warman and Sauer and assuming a rate coefficient for HX equal to that of C 0 2 ( K , = 6 X cm3 molecule-' SF').

18 2 186 19 o 194 198 2 0 2 We regard this as a l o ~ + e r limit t o the thermalisa- log [HX] tion rate. slnce ~e have evidence (7) that HBr is

FIG. 4. Electroll reaction and thermalisation rates as a function of HX concentration in molecules ~ m - ~ . Lower solid line: Electron capture rate sml in HC1. Pure HC1: C ref. 6 , O ref. 8 ; @ ref. 4: present data; mixtures of 5.3j X 104 N ~ n - ~ of HC1 with 10.6, X 104 N nlm2 of:

C3H8, @ c2F6, 3s COz. Upper solid line: electron capture rate s-1 in HBr. Pure HBr: 0 ref. 7, 8 ref. 3; mixtures: with C2FSr COZ, and Xe, 0 and A from ref. 7, 1.33 X 104 N nl-' HBr with 25 .3 , X 104 N m-2 CO2 this study +. Electron thermalization rate for HX with K, = 3.6 X 10-8, -----. Electron thermalization rate for HX with K, = 6 X lom9, The points A and * are total thern~alization rates for 7.20 X 10" mm2 COz + 1.60 X lo4 N m-2 HBr and 10.67 X lo4 N m-2 C 0 2 + 5.33 X lo4 N m-2 HCI respectively.

\ ,

about six times better than C 0 2 as a n electron moderator in the 0.15 to 0.7 eV range. The uppermost dashed line was obtained on that basis i.e. K, for HX = 3.6 X cm3 molecule-' s-'. Some thermalisation rates for specific buffer gas - HX mixtures were calculated with the contribution of the buffer gas included and these are also shown. Except at the very highest HX concentrations with no buffer the thermalisation rates exceed the observed rates of capture by a large factor and it is evident that the electrons are reacting at energies in the thermal range near 0.04 eV.

( 5 ) Analj.sis of the HCI Data Application of the steady-state approximation to reactions 3 through 7 and I3 leads to 1141,

{ k , + k,[HX] + ~ , " [ M ] ) K ~ , [ H X ] ~ 1

{ k , + k , + kk,[HX] + k , " ' [ ~ l ] k l i m] which is equivalent to expression 12 with g,, the yield of scavengable electrons in the system, replacing G, and with:

- ( k , + k,[HXl + k,"[Mj 1 K ~ , [ H X ] ~ (Rate of e capture by WX)[e]- - jk, + k, + k,[HXl + k,"I[Mll

On imposing the conditions k , >> k,"[M] I ks[HX] > k, [15] becomes:

[I61 (Rate of e capture by HX)[e]-' = ( k , + k,'\'[M] I[HX]] Kk,k,-'[HXI3

The experimental rates from the various studies of HC1 which fall on the lower solid l ~ n e in Fig. 4 were all obtained in the absence of buffer gas i .e. for [MI = 0. In agreement w ~ t h [16] and the conclusions of refs. 5 and 6 the slope of the line through them is 3. When divided bq [HClI3 these rates, except for the highest [HCI] which may involve some non-thermal electrons and

was not included, lead to k,Kk,.k,-I = 10.4 + 0.7 X cm9 nmolecule-I s-I. The excellent agreement of the data from the two laboratories involved is demonstrated by the fact that this average is the same as the value given by the original data of Johnson and Redpath alone (6) and reported as their k7.

As shown by the points for added C s H s ,

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3588 CAN. I. CHEM. VGL. 54, 1976

FIG. 5. Rate:[HC1]3 cs. [iM]/[HCI] at 298 K for rnix- tures of varying coniposition: Cm. HCI and propane; @, MC1 and CO:. Pressure of HC1 was varied between 2.67 X 104 to 16.0 X 104 N m-2 and that of the buffer gas between 2.67 X lo4 to 21.33 X 104 N m-'.

C2F6. and CO, in Fig. 4 the addition of buffer gases enhances the rate of capture in HCl, a feature which is in accord with the ksA1[M] [HX] term on the right side of [16]. In their study Johnson and Redpath investigated the dependence of the electron capture rate on [HCI] in the presence of excess propane. They used N 2 0 as an electron scavenger and showed that the order in HC1 was reduced to t h o , which agrees with [ i 6 j for [MI >> [HX]. However, because the N 2 0 capture is a three body process and the rate coeflicient for N 2 0 as a third body was unknown, the rate coefficient for HCI under these conditions could not be obtained. We have determined rates of electron capture in HCl-propane mixtures of several compositions with SF6 as scavenger. From the linearity of the plot in Fig. 5 these are seen to conform to expression 17, which is a simple rearrangenzent of [16].

[I71 (Rate of e capture b j HX)[e]-1[HX]-3 =

I," [ h 3 + kSL1 kXj -< .I.

The ratio of the slope over intercept gives I(,C3Ha kS = O.Sg. The similar but less extensive data for C 0 2 %ere also in accord nith [I?] and showed that kSCoz A. = O.gO

The use of ion-nolecule reaction rate theory (58) leads to values of 1.2 X 1.1 X and 0.8 x cm3 molecule-I s-"or k k kk,C3Hs, and h b C " ~ respectively From these Ne find kSC3"8 k S = 0.9, and ASC0z k , = 0 67, In reasonable agreement uleh the experimental ratlos. Accepting h , 2 cm3 molecule-l s-I and K =

3 >( an3 molecule-', the11 from h,Kk,-

/c,-l = 10.4 x cm9 molecule-3 ss-I one obtains k,k,-I = 3.5 X lO-I9 cin3 molecule-'. As stated in Section 1 a large entry width is expected for reaction 8. The entry width for capture of electrons by the (HX), dimes should therefore also be large (17) and the cross section for reaction 4 close to the theoretical n~aximum value of X2(4r)-"I, 59). Taking k, = i5 X X2(4n)-I, where 6 is the relative velocity of' the electrons and (HX)2 dimers, its magnitude is found to be ry3 X 10-7 cm3 ~nolecule-I S-I a t 298 K. Hence, k, --hj kC1'3.5 x 10-l9 2 iOIZ s-l, and T, for the (HX)2-* ion is about 10-l2 s. The enhancement over T, for the monomer HX-" (5!O-13 S, see above) is in keeping with the fact that auto- ionisatio~l lifetimes increase with the number of internal degrees of freedom in structurally related molecules (59).

The fact that the HCl results conform to expression 17 indicates that reactions 50: 5b, and 5c are negligibly slow. The sum of their rate constants k , must be less than - 2 0 5 of the lowest k,[HX] value used here, which is 2 X lo9 s-I. Once this condition is accepted then, as the above discussion shows, the observed rates can be accounted for by individual rate coefficients w ~ t h reasonable magnitudes.

(6) Analysis of the HBr Data The [HBr] dependence of the rate of electron

capture (see upper solid line in Fig. 49 differs from that for HC1 in that the rate in the concentration range studied is: ( a ) inuch larger, (b ) de- pends on the square rather than the cube of [HX], and ( c ) the points obtained with and without buffer gases lie on the same line, indi- cating no significant effect of buffer gas on capture rates. As previously shown the kinetics can be represented by expression 18. With K = 3 X c1n3 molecule-], the value of Kk, = 1.0 X lo-" ccm6 molec~~le-2 s-I calculated

1181 (Rate of e capture by HX)[e]-I = Kk,[HXI2

f r o n the results in Fig. 4 for a temperature of 298 K requires kc -?r. 3 X em3 molecule-3 s-l. This is the same as used in the above discussion for the HC1 system. Also, if k, c~ 1012 s-I as estimated for iiC1, then the condition for the overall rate expression 15 to become simpli- fied to [18] is k, >> k, > k , [ H X ] + k,"'[Ml. In other words either one of reactions 5u through 5c or a combination of them is now faster than the autoionisation of (HX)2-*.

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2 3 4 5 --?/q0-3

FIG. 6. Arrhenius plot for (Kkck13-1) for the thermal e!ectror, capture in MBr sybtem in the temperature range 200-393 K.

When applied to [14] the same condition leads to:

By studying the magnitudes of (slope)(intercept)-l from plots of ey. 19 for data at different temperatures we obtained the temperature dependence of Kkck13-l. The results are presented as an Arrheni~ls plot in Fig. 6 . The slope of the solid line (least mean squares fit) corresponds to Ec - EII3, + AEL3] = - 3.74 kJ mol-l.

From work elsewhere (60) the temperature dependence of k l 3 in the range used here appears to be small, though one might expect a small negative dependence on T due to the inverse dependence.of the capture cross section on mean electron energy, which has been observed in drift experiments (1 1). Actually this type of energy dependence (i.e. energy exponent near - 1) of cross sections is frequently observed for molecules with capture cross sections approaching the maximum of X2(4n)-I (11). Since the magnitude of Kk, can oniy be explained for a, near X2(4a)-I (see above) one must assume that the temperature dependence of k, would be similar to that of k l i and therefore 8E13] must be near to

-3.7 kJ mol-I. This is somewhat less than the average of the literature values for HCi(- 10 kJ mol-I), as would have been expected.

A further point of interest derived from the experiments at different temperatures was that G(H2) from HBr in the absence of scavenger was within experimental error ( i 0 . 2 molecules per 100 eV) the same over the range 200 to 394 K. This agrees with the fact that C(F12) from HC1 has previo~isly been shown to be the same at 200 and 298 K (4). Unfortunately the greater complexity of the capture mechanism and the fact that minute traces of chlorine scavenge (HX),- (4) make determinations of Ec - E1131 + El,, irn- practical in that system.

(7) Cnirr/1l2arisotzs of' Dlf i ren t HX Systems The discussion in the preceding sections has

shown that the mechanism based on reactions 3 through 7 is able to account for the capture rates observed at 298 K over the concentration ranges 1018 to 2 X IQl9 molecilles cm-3 in HBr and l0l9 to loz0 molecules cm-I in MCi. It also holds over the temperature range 200 to 394 K in HBr. The change in the magnitude of k , from 5 2 X lo9 s-I in HC1 to > 1012 s-I (i.e. > k,) in HBr is the only alteration in the kinetic parameters required to explain the difference in behaviour for the two gases. The sma!l value of k, in HC1 indicates that even the clearly exothernlic reaction 5a does not proceed readily. Since it requires the two H atoms aizd the two X atoms to approach each other, its slowness may be explained by their electrostatic repulsions, which ~ o u l d mitigate against this geometry in the dimer and iead to the preferred linear hydrogen bonding interaction. The absence of reaction 5c in HC1 may be due to the fact that dissociation of (HCi)2-* does not give stabilised HCl-. Therefore it cannot be taken as direct evidence against the existence of this species. The uncertainties in our calculations are such that aE0298,rsbl may be slightly positive in HC1. Alternatively the slowness of [5b] in this system may be due to a small activation energy barrier. The present results and those of ref. 6 support reactions 6rs and 6h as the rate con- trolling processes in HCI, while other work (4, 61) implies that k6ak6h 22 1.7 in HCl and E 3.4 in DCl. If reaction 20 is taken in sequence with [5'b] one obtains [6'b].

1201 XHX- $- HX X-.2HX

[6'b] e- + (HX)2 + HX H + X-.2MX

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3590 CAN. 1. CHEM.

This would have the same AEo2g8 as [6bj. Using Yamdagni and Kebarle's thermochemical data for X-.2HX ( 4 9 , we find BEo2g8 [6b1 = - 52 kJ mol-1 for HC1. Given that exothermic ion- molecule reactions normally have low activation energy and are rapid, there is therefore a reasonable probability of [6b] competing with the stabilisation process [6a] and proceeding with khb near cm3 molecule-l s-I.

The evidence for prod~lction of clustered (HX),- via [6u] was based on the effects of chlorine (4). The assumption that chlorine did not compete with HC1 for thermal electrons was based on mass spectrometric observations (4). It is borne out by a recently reported rate coefficient for thermal electron capture by chlorine (62). The small value of 3 X lop1' cm3 molecule-I s-I means that for the conditions where scavenging of (HX),- was observed in refs. 4 and 61 ([HCl] =

2 X 1019 and [C12j 5 1017 molecules ~ m - ~ ) the rate of electron capture by chlorine would have been "<3 X lo7 s-I, which is an order of magnitude less than that by HCi (see Fig. 4). The experiments of ref. 62 also showed that the effective two body rate coeficient for capture of electrons by HC1 is < 2 X 10-l3 cn13 s-I in a flow system a t a total concentration of --1016 molecule cmW3 and with [HCl] - 2 x 10lS molecule ~ m - ~ . If we neglect (k,[HX] + kSMl[M]) and assume k, -- 2 X 10g ss-I and k,Kk,-I =

cm6 molecule-2 from section 5, the present mechanism predicts an effective two body coefficient of < cm3 molecule-I s-I. Values above this would imply the occurrence of processes not detected in our pressure regime, and may indicate that stable ions can be formed through capture of electrons by interacting H C l - buffer gas n~olecules in the flow system.

On grounds similar to those stated above for HCl, the geometry of the dimer species is also likely to favour [5b] over [5uj in HBr. Given that [5b] is exothermic (see Fig. Ib), the dissociation of (HBs)~-* to H and BrHBrp resembles the dissociation of HI-* to M and I-. The fact that the latter process competes favourably with autoionisation /cT[,, in HI h. X2(4n)-I (1)) pro- vides a rationalisation for the large value of kSb ^V 1013 s-l, which is required to accornmo- date the HBr results. The data in Fig. Ib suggest that reaction 5c may also occur, but as stated above stable HBr- ions have not been observed and this reaction is less certain than [5b].

As shown in Fig. lb the product channels for (MFI2-* are much less favourable than are those for HCI.$ Thus if electron capture occurs via the dimer mechanism one must expect it t o proceed through reactions 611 and 7 as in HC1, and lead to clustered (HF),-. The situation is complicated by the fact that in this system hexamers and other polymeric species may take part in electron capture. However, pulse radiolysis investigations \vould be useful for determining whether clustered negative ions with significant lifetimes were formed. and uhether their structure was similar to that of the solvated electron in dense ammonia and hater vapour (63).

In closing we wish to point out that a modified form of the present mechanism should apply to mixtures of the hydrogen halides with ea te r (64) or hydrogen sulfide (53, 65). Thus Huyton and Woodward (65) attributed elec:ron capture in HC1-M2S mixtures to reaction 21 and a more rapid capture was observed in HBr-M2S mixtures

[211 e + HCI + HzS 4 Products

(53). We suggest that HX---H2U complexes are involved in these systems. Furthermore we would point out that formation of linear dimers and higher polymers of polar molecules, which d o not individually possess a positive electron affinity, will lead to dipole moments greater than those of the monomers. This should strongly increase the interactions with electrons (see dis- cussions of the effect of dipole moment in ref. 66 and earlier references cited in ref. 11), and may provide a nucleus for initial electron localisation, which could be followed by clustering and permanent solvation.

I . L. G. CHRISTOPHOROU, R. N. COI\IPTON, and H. W. DICKSON. .T. Chem. Phys. 48, I949 (1968) and references cited therein.

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80ne should note that the points in Fig. 1 (a) and (b) for reactions [2C] and 15161 in HF are based on E.A. .v -42 kJ mol-1 from ref. 13. This value is supported by theoretical calculatiolls carried out subsequent to those of ref. 15 and considered to be more reliable (K. D. Jor- dan, private communication).

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Documents

Hydrogen forming reactions of thermal electrons in hydrogen halides: kinetics and thermodynamics