Homogeneous Isotope Exchange ReactionsPart 3.-H2S+D,BY GRAHAM PUTT* AND DAVID ROGERSSchool of Molecular Sciences, University of Sussex, Brighton BN1 9QJReceived 24th May, 1976The kinetics of the early stages of the exchange reaction in H2S + D2 mixtures [H2S, 0.55-9.34 Torr(1 Torr = 133 N m-2) ; D2, 0.55-6.39 Torr] have been studied in a static system at 808-937 K. Theeffects of excess argon and surface to volume (slu) ratio were studied. The initial rate is independentof s/v and in the absence of Ar is described bywhered[HDS]/dt = +k[H2S][D2]*loglo(Sk/dm3 mol-.& s-l) = 12.10+ 0.25-(11 860+ 220)t/(T/K).The results are in agreement with a homogeneous radical chain mechanism, initiated and terminatedheterogeneously. The rate constants for3HSHZS -> HS*+HZ6HS.+ D2 -+ HDS + Ddeduced arelog10(k3/dm3 mol-' s-l) = 10.44+0.25-(330& 220)/(T/K)logl,(kb/dm3 mol-' s-l) = 10.13 +-0.25-(3530_+220)/(T/K).To our knowledge there has been no previous study of H2S/Dz exchange in astatic system at high temperatures. A single pulse shock tube (S.P.S.T.) study ofthe first 20 % reaction in excess Ax at 1260-1590 K was interpreted in terms of a fourcentre molecular mechanism involving vibrationally excited reagents. Several studieshave been made of the reaction of H with H2S at low temperatures by flow dis-charge 2 s and f i s h photoly~is.~-~ No high temperature kinetic data is availablefor this reaction.EXPERIMENTALAPPARATUSThe conventional static system and reaction vessels a and b have been described?.OREAGENTSResearch grade D2 (Air Products >99.99 %) was purified by diffusion through nickel.'High purity Ar (Air Products 99.998 %) was purified by several freeze-pump-thaw cycles andby passage over spluttered sodium. O2 was < 10 p.p.m. H2S was prepared from sodiumsulphide and conc. sulphuric acid, dried over P205, and purified by five freeze-pump-thawcycles and fractional distillation. Mass spectrometric analysis showed no traces of 02,H20 or higher sulphides (< 10 p.p.m.).t = Ea/2.303 R. All errors are standard deviations.5G . PRATT AND D. ROGERS 55ANALYSISMass spectrometric analysis of H2S+ HDS+ D2S mixtures is complicated by the foursulphur isotopes. At ionisation energies < 14.4 eV, fragmentation was negligible and therelative isotopic abundances were thus found.The 70eV cracking patterns of HDS andD,S were calculated assuming that molecular ions have the same intensities and the prob-ability of D loss is 0.44 times that of H 1 0 ~ s . ~ Calibration accuracy was verified by analysisof reacted mixtures containing large percentages of HDS and D2S at both 70 eV and 11 eV.The analyses for H2S, HDS and D2S agreed within 4%. For all subsequent quantitativeanalyses m/e = 34 to 36 were used at 70 eV.RESULTSQualitative analysis showed that Sz products were not formed (<0.01 %>. Thedeuterated hydrogen sulphides were formed consecutively (fig. 1) and the initial ratefor HDS was equal to that for HD (fig. 1). This is good evidence that there is no100 600 1200timeisFIG.1.-Formation of reaction products for conditions T = 855 K, [H2S]i = 0.56 Torr, [DJi =0.56Torr. 0 HDS, HD, point common to both, 0 D2S. Inset: Formation of D2S forconditions T = 937 K, [H,S]i = 0.57 Torr, [Dz]i = 0.57 Torr, showing the acceleration of rate ofproduction in the initial stages.c 30 1.0 2.0In(P/Torr)FIG. 2.-Ln/ln order plot of initial rate against total pressure at T = 937 K, [H2S], = [Dzlj, vessel b.The solid line has a slope of 1.556I I0 1-0 2 0 3.0ln([H2S]t = o/Torr)FIG. 3.-Ln/ln order plot of initial rate against hydrogen sulphide pressure at T = 896 K, [DzJi =0.60 Torr, vessel 6 . 0 without added inert gas, argon added to a total pressure of 31 Torr. Thesolid line has unit slope.-6.50.5 1.0 1.5In(CDzlt = o /Torr)FIG.4.-Ln/ln order plot of initial rate against deuterium pressure at T = 913.5 K, [HZSJi =0.60 Torr, vessel b. The solid line has a slope of 0.5G. PRATT AND D . ROGERS 57exchange of HDS in the mass spectrometer or inlet system during analy~is.~ Noinduction period is detectable in HDS or HD production in fig. 1. In all subsequentkinetic studies the extent of reaction was limited (< 10 %) so that [D2S] was negligible.ORDERS OF REACTIONExperiments with stoichiometric mixtures gave good +-order plots (fig. 2). Thepartial orders w.r.t. H2S and D2 are 1.0 and 0.5 respectively (fig. 3 and 4). In con-trast to CH4/D2 exchange lo there is no curvature in these plots at high [H2S]/[D2]ratios. The initial rate is described byd[HDS]/dt = +k[H2S][D2]+ (1)over the whole range of reactant pressures studied.105 1-10 1.15 1.20103 KITFIG.5.-Arrhenius of plot sk. 0 s/v = 1.4 cm,-' s/v = 6.0 crn-l.INERT GAS ADDITIONFig. 3 shows the effect of addition of excess argon to a constant total pressure.The rate is unaffected at low [H,S]/[D2] ratios, but is reduced at high [H2S]/[D21ratios.S/V CHANGEChanging s]v from 6.0 to 1.4 cm-l had no effect on & (fig. 5).EFFECT OF TEMPERATURE+k was measured at 12 temperatures in the range 808-937 K (table 1). The leastlog,,(&/dm3 mol-1 s-l) = 12.10+0.25-(1 I 860+220)/(T/K).mean squares Arrhenius fit is58 H2S + DzTABLE 1 .-MEASURED $-ORDER RATE CONSTANTS FOR STOICHIOMETRIC MIXTURES AND DERIVEDVALUES OF k3 AND k6templK i808.0821.5821.5821.5836.5836.5836.5841.5841.5848.5848.5848.5860.0860.0860.0870.5870.5870.5874.0874.0883.5883.5883.5896.0913.5913.5913.5913.5937.0937.0937.0937.0937.0ressel*bbbbbbbabbbbb0bbbahbbbabbbbbbbaaa3kldmQ mol-f s-12.530(- 3)t5.197(- 3)4.779( - 3)4,859(- 3)7.816(- 3)8.618(- 3)9.765(- 3)9.824( - 3)1.001 (- 2)1.414(- 2)1.1 1 8( - 2)1.333(- 2)1.705(- 2)1.827(- 2)2.052( - 2)3.012(- 2)3.101(-2)2.701(- 2)2,976(- 2)3.583(- 2)4.53 8 (- 2)4.236(- 2)4.690(-2)7.71 5( - 2)1.333(- 1)1.361(- 1)1.731(- 1)1.750(- 1)2.131(- 1)2.559( - 1)2.448(- 1)2.261(- 1)2.476(- 1)k6/dm3 mol-1 s-*5.645(5)7.848(5)7.217(5)7.3 3 8(5)7.763(5)8.559(5)9.699(5)8.5 1 3(5)8.675(5)1-01 5(6)8.026(5)9.570(5)9.693 (5)1.089(6)1.221 (6)1.257(6)1.095(6)l.lM(6)1.330(6)1.330(6)1.242(6)1.374(6)1.669(6)1.910(6)1.952(6)2.485(6)2.512(6)1.806(6)2.169(6)2.075(6)1.916(6)2.098 (6)9.045(5)k3/dm3 mol-1 s-11.032(10)1.236(10)1.137(10)1.1 55( 1 0)1.042(10)1.148 (1 0)1.302(10)1.084(10)1.105(10)1.203(10)9.51 1(9)1.134( 10)9.545(9)1.022( 10)1.148(10)1.11 6(10)1.196( 10)1.042 (1 0)1.016(10)1.224(10)1.1 17( 10)1.044(10)1.155(10)1.249(10)1.221(10)1.248(10)1.589( 10)1.607( 10)9.439(9)1.134(10)1.084(10)1.002( 10)1.097(10)* a, slv 1.4 cm-' ; b, slv 6.0 cm-'.f- x(y) = x x 1Oy.DISCUSSIONProduct analysis establishes the stoichiometry of the reaction studied kineticallyasH2S +D2 = HDS +HD.It is not possible to say whether the four centre mechanism contributes to our mea-sured rate to a small extent. The rate predicted for the four centre process by therate expressions obtained in S.P.S.T. work for our typical conditions (H2S = 1.0Torr, D2 = 0.6 Torr, Ar = 26.4 Torr, T = 896 K) is two orders of magnitude lessthan the observed rate of exchange. Some other mechanism must account for thebulk of the observed reaction.The kinetic results have great similarity to those observed for CH4/D2 exchange loand strongly suggest a similar chain mechanism. In the methane exchange, initiationbyD2 -+ 2D (1G .PRATT AND D. ROGERS 59was shown to be negligible compared with dissociation of methane, even though bothprocesses are subject to surface catalysis. Initiation of the H2S exchange byis 57 kJ mol-l less endothermic than methane dissociation and should therefore bethe dominant radical generating step. The rapid processes,H2S + HS*+H (2)H+H,S --+ HS*+H, (3)H+D, + HD+D (4)will convert H to the main propagating species D and HS-.the propagating stepsFor long reaction chainsD+H2S + HD+HS- ( 5 )HS*+D2 -+ HDS+D (6)control the ratio [D]/[HS*] = k6[D2]/k5[H2S]. k6/k5 is close to K , [the equilibriumconstant for the reverse of step (3)] since the isotope effects will not be large. At900 K k6 Jk5 N K; = 3 x [using the thermodynamic data of ref.(I 1) and (12)].Hence [HS-] % ID] and of the terminations,2D -+ D2 (-1)D+HS*-+HDS ( 7 4or --+ HD+S (76)(34or -+ H,S+S (86)HS* + HS- 4 H,S,reaction (8) should be dominant if all processes are homogeneous. Previous work atlow temperatures 2-6 has favoured route (86) for the HS. combination step and route(7b) is included by analogy with this. However the reactionis known l 3 to have an activation energy of 21-29 kJ mol-I, and this analogy suggeststhat reaction (7b) is probably negligible compared with (7a). No S2 compoundswere detected in the products in this work. This observation is consistent with thelong chain hypothesis and provides no evidence for the relative rates of steps (80) andH+OH*-+ H,+O(3b)-The long chain steady state approximation yieldswhere R = [H2S]/[D2].Since k , < k,, comparison with the experimental rate law(I) shows that k-,/k, Q k5/k6 2: 3 x lo3 at 900 K, which is very reasonable, andk8/k7 << k6/k5 which is more difficult to understand. However, the effect of addingexcess Ar indicates that increasing ks [step (8) will be third order] causes the secondterm in the denominator of eqn (11) to become significant at large values of R, result-ing in the observed rate reduction (fig. 3). This in turn suggests that step (7) mustbe surface catalysed, otherwise no pressure dependence would be observed in (k,ks/k6k7). This conclusion is further supported by the observation that induction periodswere negligible. At the temperature (855 K) to which fig.1 refers this shows that boththe initiation and termination steps are at least 4 x lo4 times faster than the homo-geneous values predicted by the estimate of Burcat et al. for step (2) together with thecalculated equilibrium constant for the reverse step. The absence of s/u effect o60 HZS + D2,k is consistent with both steps (2) and (7) being surface catalysed, and this largecatalytic factor is sufficient to account for the above low ratio of k,/k,.The $-order rate constant may be written in terms of equilibrium constants ( K )and kinetic isotope effects f i = k 2 / k 7 , f2 = k-5/ks and f3 = k-3/166 as& = k,W2K,f,f,), (111),k = k3(K2KSflf2)+/K3f3. (IV)or,Thermodynamic data was taken from ref. (1 1) and (1 2), fl was calculated as before.OThe value is insensitive to the properties of the activated complex.lo f 2 andf3 werecalculated using an activated complex obtained by the 3 atom model BEBO method.14The properties of the complex are given in table 2 and the temperature variation off2 andf, is given in table 3. In Arrhenius form these calculated equilibrium constantsand kinetic isotope effects areK,/mol d n r 3 = 5.71 8 x lo3 exp[ - 45 509/(T/K)]K3 = 1.640 exp[ + 68 668/(T/K)]Ks = 2.662 exp[ + 73OO/(T/K)]fl = I. 1121 exp[ -290.2/(T/K)]2f2 = 1.0226 exp[ + 109.4/(T/K)]f3 = 1.2482 exp[ + 483.1 /(T/K)].1 2TABLE 2.-T)ROPERTIES OF ACTIVATED COMPLEX (H-H-sH)$ CALCULATED BY B.E.B.0.(3 ATOM MODEL) ; DATA FROM REF. (14) AND (15), UNITS CONSISTENT WITH EQUATIONS OFproperty an1V*/kJ rno1-IRl/AFl /dyn cm-1F22/dyn cm-lF12/dyn cm-lF4/ergD,/kJ mol-lPYP31A-lH-H-Sv*/cm-lVstr/cm-lvblcrn-1H-D-Sv* Icm-IVStJcm-lvbfcm-lv*/cm-lVstr/cm-lvb/cm-'D-D-SREF.(14)complex0.1275.531.2911.379- 0.1286(5)3.7747(5)0.0422(- 11)0.51 52(5)684.9i2208.7453.1497.0i21 82.9423.7488.0i1593.6321.3H2 HzS1 .oo0.745.73( 5)1.3464.28(5)457.71.0411.94(8)427737223054396.60.9321.723(8)Q These standard symbols are defined in ref. (14G . PRATT AND D. ROGERS 61TABLE 3 .-CALCULATED KINETIC ISOTOPE EFFECTST/K 650 700 750 800 850 900 9502f2 1.303 1.192 1.182 1.172 1.163 1.155 1.147f 3 2.610 2.483 2.375 2.283 2.204 2.135 2.074Hence from eqn (111)loglo(k6/dm3 mol-1 s-') = 10.13 5 0.25 - (35305 220)/(T/K).Using eqn (IV) givesloglo(k,/dm3 mol-l s-l) = 10.44+0.25-(330522O)/(T/K).No low temperature measurements of k6 are available for comparison.However,Arrhenius expressions for k , obtained previously arefor T = 243-368 K [ref. (3)] andlog1,(k,/dm3 mol-I s-l) = 9.89kO.05-(373+ 13)/(T/K)for T = 190-464 K [ref. (4)]. The agreement for the very low activation energy ofthis abstraction is certainly well within our relatively large experimental error, butour pre-exponential factor is higher though by less than two standard deviations.The rate constant for 808-937 K found here is some three times greater than predictedby the low temperature Arrhenius lines. This factor lies outside experimental errorand is consistent with the expected upwards curvature of the Arrhenius plot for anH atom transfer.A temperature dependence of the pre-exponential factor A =BT1s0 is sufficient to account for the curvature.10g10(k3/dm3 11101-l S-') = 10.01 f0.02-(367& 1 l)/(T/'K)We thank the S.R.C. for a maintenance grant (to D. R.).A. Burcat, A. Lifshitz, D. Lewis and S. H. Bauer, J. Chem. Phys., 1968, 49, 1449.J. N. Bradley, S. P. Trueman, D. A. Whytock and T. A. Zaleski, J.C.S. Faraday I, 1973,69,416.D. von Mihelcic and R. N. 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