Kinetics of Gas Phase Ion-Ion Recombination in NO+ +X- -+ NO+X for X being Chlorine, Bromine and Iodine BY NIGEL A. BURDETT AND ALLAN N. HAWURST* Department of Chemical Engineering and Fuel Technology, Sheffield University, Mappin Street, Sheffield, S1 3JD Received 25th March, 1977 The rate coefficient kl for the gas phase recombination of NO+ with halide ions X- in NO++X- -+ NO+X has been measured in flames of CzH2 + 02+N2 over the temperature range 2200 to 2650 K. Chlorine, bromine and iodine have been used as X. All kl values are in the range 0.8-2.1~ lo-* ion -l cm3 s-l, corresponding to cross-sections (d) of -lo-’’ mz. For each halogen, kl has a negative temperature cuefficient. Also at any one temperature, ki is largest for X being chlorine and smallest for iodine. In general, these measurements are in agreement with Olson’s “ absorbin8 sphere ” model for ion-ion recombination.Although the gas-phase recombination of NO+ with free electrons has been fairly extensively studied,lS the neutralization of NO+ with negative ions has not, apart from that with NOT at 300 K. In fact, ion-ion recombination has only been investigated experimentally on a handful of occasions, in spite of theoretical treat- ments of the topic having ab~unded.~ This work aims to measure the rate constant for NO+ recombining with halide ions in reaction (I) for X being chlorine, bromine and iodine. This has proved possible because in the burnt gases of a flame of C2H2+O2+N2 the dominant charged particles are H30+, NO+ and the free electron, with concentrations up to - loll ions ~ r n - ~ .In an acetylene flame, ions are first produced by CH+O + CHO++e- occurring in the reaction zone, although some possibly originate from CH + C2H2 + C3H; + e-. A primary ion rapidly reacts with neutrals present, such as NO and H20, giving NO+ and H30+, which are stable enough to persist into the burnt gases. Both these ions then recombine with free electrons in reactions (11) and (III) NO++X- + NO+X (1) NO++e- + N+O (11) H30++e- + H+H+OH (111) and in addition an equilibrium can be set up slowly’ between these two positive ions in reaction (IV) H30+ +NO + NO+ + H2O + H. (W When a halogen is added to such a flame, it exists as either free atoms X or as molecules of the hydrogen halide, with their concentrations being coupled by a rapid balance * of reaction (V) HX+H = X+H2.(V) 6364 ION-ION RECOMBINATION In addition, a minute fraction (< 1 in lo5) of the halogen atoms exist as X-. These are created in reaction (IV) which also becomes rapidly eq~ilibrated,~~ lo although this conclusion has been questioned.ll The effect of the presence of X- ions is to open up other routes for the disappearance of positive ions in reaction (I) and in its counterpart for H30+, i.e. which has already been studied.12 It has been shown that conditions can be created when reaction (11) is the dominant ionic reaction in the burnt gases of a flame. In this work the gradual addition of a halogen to the burner supplies brings process (I) into increasing prominence, thereby enabling its rate to be measured.HX+e- + X-+H, (VI) H30++X- -+ N,O+H+X, ( W EXPERIMENTAL The C2H2 flamcs, the burner and mass spectrometer have been described.l In this work small quantities (<1 vol. %) of a halogen were added to the unburnt gases of a flame by saturating a small part of the N2 supply with an organic halide. For chlorine either CHC13 or CC14 were used, for bromine n-C3H7Br and for iodine CH31 or C2H51. A knowledge of the vapour pressure of the volatile liquid, together with the gas flow being saturated, enables the rate of supply of halogen atoms to the flame to be deduced. These additives break up completely in the reaction zone giving mainly X atoms or HX molecules. The amounts of X- detected have been shown not to reflect accurately the concentrations of these ions at the point of sampling in the flame, because the equilibrium (VI) is fast enough to shift as the sampled gases cool whilst entering the spectr~rneter.~* lo This gives a loss of X- ions, in spite of the sampling time being -0.5ps.This of course reflects the rapidity of both steps in reaction WI). RESULTS In these C2H2 flames it was found that the degree of hydration of ions such as NO+ and H,O+ was much less than in H2 flames of a similar temperature. Typically, at 2200 K the ratios [H30+]/[M30~H20] and [NO+]/[NOfH,Q] are roughly 500 and 2000 in a C2H2 flame (depending on factors such as sampling hole size), but 3 and 40, respectively, in a H2 one. This is largely attributed to [H20] being smaller in C2Hz flames, but in addition C2H2 flames usually have thinner boundary layers around the sampling orifice, as well as shorter expansion times for the sample entering the first vacuum chamber of the mass spectrometer.The overall result is convenient, for it means that the difficulties of measuring [H,O+] when hydration is considerable are much diminished. In fact, in this work we have assumed that H30+ and NO+ are detected with identical sensitivities. One unexpected feature was the detection of positive halogen ions with iodine and bromine added, but not with chlorine. For bromine, Br+ and to a much less extent Brz were observed, but with iodine I+, I+H20, 12+ and 1; were found. In the latter case I+ is the most abundant, with a concentration exceeding that of 1: by at least a factor of 10. Both 12+ and I,’ usually had negligibly small concentrations.All these positive halogen ions appear to be formed in the reaction zone, in that their observed abundances decreased along the burnt gases. The positive ions of bromine always represented an insignificant portion of all the positive ions present, and in this sense could be ignored. However, with iodine, I+ was often the principal positively charged species in and close to the reaction zone. This is shown in fig. 1 for iodine in flame 5, (2380 K) where [H,O+] is always fairly small and the principal positive ion is I+ close to the reaction zone and NO+ after -7 mm downstream,N. A . BURDETT AND A . N. HAYHURST 65 It is convenient to deal first with the results for chlorine and bromine, which are not complicated by the presence of significant amounts of new positive ions.Fig. 2 shows profiles for [NO+] and [H,O+] along the axis of flame 6 (2200 K) with no NO or halogen added and with chlorine present. In the absence of additives, [NO+] peaks at - 12 mm from the reaction zone and subsequently decays downstream, being then larger than [H,O+]. The effect of C1 is to increase [NO+] and [H,Q+] and shift the maximum [NO+] downstream. Qualitatively, this must arise from recom- bination of NO+ and H,O+ with free electrons in reactions (11) and (111) being 5 10 15 20 axialldistance from reaction zonelmrn FIG. 1.-Concentration profiles for NO+, I+, H30+ and I- along the axis of flame 5 for 0.2 vol. % of iodine added. 0 10 20 30 LO distance from reaction zone/mm FIG. 2.-Experimental plots of [NO+] (triangles) and [H30+] (circles) along the axis of flame 6 ; A and 0 give ion concentrations in the absence of halogen and A and 0 are for chlorine added (0.34~01 %).1-366 ION-ION RECOMBINATION replaced by the slower processes (I) and (VII). Well downstream [NO+] % [H30+], so that H30+ can be ignored. Otherwise this condition can be achieved by the addition of small amounts of NO, with care being taken to avoid complications from the reverse of reaction (11) producing NO+. We first discuss observations made under conditions where NO+ is the major positive ion and the analysis is similar to that employed in a study l2 of reaction (VII). The decay equation is : -~ d"o+l = k,[NO+][X-] + k,[NO+][e-], dt where kl and k, are the recombination coefficients of reactions (I) and (11), respectively.Using the charge balance [NO+] = [e-]+[X-] and the equilibrium constant K6 of reaction (VI) to relate [e-] and [X-1, we obtain This suggests that the recombination plot of I/[NO+] against time has a gradient S, equal to the right hand side of eqn (I), i.e. Here 2 = K6[HX] J(K,[HX] + [HI) and represents the fraction of the negative charge carried by the halide ion. In general 2 is a function of axial distance along a flame S, = k,+(k,-k,)Z. 10 20 30 40 distance from reaction zone/mm FIG. 3.-Recombination plot of 1 /[NO+] against distance along flame 5 for chlorine concentrations in the unburnt gases as shown in vol. %. (or time), because it is affected by [HI being above its equilibrium value, which also can alter [HX] by a readjustment of reaction (V).In such a case the local ratio of the slopes of the recombination plots with and without halogen present is given by Some recombination plots for NO+ in flame 5 are shown in fig. 3, where the SJS, = 1 -(1 -kl Jk2) 2. (2)N . A. BURDETT AND A. N. HAYHURST 67 decrease in slope on the addition of chlorine is clear. In fact, in this case good straight lines are obtained for the region downstream of the maximum [NO+]. This linearity is fortuitous and is due to the insensitivity to distance of the function 2 in this particular case. In general curved recombination plots were obtained and their slopes S, obtained numerically after an initial smoothing.12* l4 These were then 0 I I I 1 I 0 0.2 0.4 0 . 6 0 . 8 1.0 z FIG. 4.-Experimental &/So for various 2 with chlorine added to flame 5 (0), and also bromine in flame 2 (A).In both cases data points are for sampling hole diameters in the range 0.10 to 0.17 mm. compared with the slope So for no halogen present and plotted against 2, according to eqn (2). Such a plot is shown in fig. 4 for bromine in flame 2 and chlorine in flame 5. In both cases it is evident that a straight line can be drawn through the data with an intercept of unity for 2 = 0. The slope of the best fit line gives k,/k2. It should be noted that fig. 4 has been drawn for a range of halogen concentrations and a variety of sampling hole sizes. The lack of any systematic variation with the latter confirms that there is no complication arising in this work by the observed [NO*] being falsified during sampling.The values of k , from the derived kl/kz and the k , measured previously are given in table 1. Whenever NO+ was not the sole dominant positive ion, as with iodine as additive, a different procedure for analysing the observations had to be adopted. In this case ions are disappearing by recombination in reactions (I)-(111) and (VII), as well as possibly in reactions (VIII) and (IX) I++e-+M + I+M (VIII) I++I- + I+I, (1x1 where M is any molecule acting as a chaperon. The overall decay equation is then In this equation [I-] is given by [e-][HX]K,/[H] and [HX] is obtained from the total amount of halogen added and K5, which along with K6 can be computed from normal68 ION-ION RECOMBINATION statistical mechanical procedures. [HI is known along each flame from measurements using the Sr+/SrOH+ technique.15 Charge balance gives [P+] = [NO+] + [H,O+] + [I+] = [e-]+[I-].In addition, it is known l3 that k , = 4.1 x that k7 can be taken l2 to be 1.2 x that k8 written in second-order form l 6 is 0.108 T-2 and k9 has been measured l6 as 9.0 x with all units being ions-l cm3 s-l. In this case, because k2 was measured in a previous paper,' k l is the only unknown quantity in eqn (3). TABLE MEASURED VALUES OF k l IN ion-' cm3 s-' flame temp/K lo7 kz lo8 kl(C1) lo8 kl(Br) lo8 kl(I) 1 2630 1.4 1.1 0.9 0.8 2 2650 1.4 1.3 1 .o 0.9 3 2590 1.5 1.4 1 . 1 1 .o 4 2490 1.6 1.5 1 .o 1 .o 5 2380 1.7 1.7 1.4 1.2 6 2200 1.9 2.1 1.6 1.4 Values of kl were thus arrived by substitution into eqn (3), the left hand side of which was obtained by numerically differentiating the concentration profiles of the three positive ions. In fact, as is clear from fig.1, NO+ did become the dominant positive ion at distances > 10 mm from the reaction zone, when recombination via processes (VIIT) and (IX) made little contribution to the right hand side of eqn (3). This approach of course depends on a calibration of the mass spectrometer, in contrast to the work with C1 and Br, where kl was obtained without a calibration by comparison with the well-established k Z . All the measured values of k l have been collected in table 1 together with those used for k2. The kl for C1 and Br are considered accurate to 70 %, whereas those for I are correct to within a factor of 2. This is because the dominant term on the right hand side of eqn (3) is that containing k l , so that errors in k3, k7, k8 and k9 are not of much consequence.DISCUSSION It is clear from fig. 5 that k l is greatest with Cl and smallest for I, as is the case l 2 for recombina- tion of the halide ions with H30+ in reaction (VII). In addition, kl depends on temperature in contrast with k7 and the indications of fig. 5 are that for all three halogens kl varies as T-2.5*2*2 . The magnitudes of k l are comparable with (marginally smaller than) those for k , indicating that their cross-sections are similar at nu2 - m2. The usual theoretical approach to bimolecular neutralization in A++B- -+ A+B involves a consideration of the pseudocrossings of the initial and final potential energy surfaces according to Landau-Zener theory l7 or some version of it.One such modification is due to Olson l8 and considers the recombination of ions, such as molecular ones, for which there are many pseudocrossings, because of the large number of electronic, vibrational and rotational states. This approach defines a critical distance R, between A+ and B-, such that there is unit probability of reaction for all separations < R,. The resulting recombination coefficient given by this " absorbing sphere model " is The measurements have been plotted in fig. 5 as log kl against log T. 1.1 .:(-J(1+&) 8nkTN . A . BURDETT AND A. N . HAYHURST 69 where p is the reduced mass of A+ and B-, k is Boltzmann’s constant and e is the electronic charge. R, is obtained from empirical correlations 9 of the dependence of the matrix elements on interparticle separation and is characterised by the reduced mass of the ions FIG.5.-Logarithmic plots of kl against T for the three halogens. Table 2 gives values of R,, as well as a comparison of the rate coefficients kl and k7 as computed from the absorbing sphere model (at 2000K) with those measured experimentally here and earlier. The agreement between theory and experiment is satisfactory, being within the error limits of both values, except possibly for iodine ions. The measured coefficients show a much greater variation from one halogen TABLE 2.-vALUES OF R, AND SOME EXPERIMENTAL AND THEORETICAL RECOMBINATION COEFFICIENTS FOR ION-ION NEUTRALISATION AT 2000 K IN UNITS OF lo-* ions-l cm3 s-I species experimental theoretical Rc/nm H30++ C1- 4 .1 3.4 1.67 H30++ Br- 2.7 3.2 1 . 7 6 HSO++I- 1 . 2 3.3 1.86 NO++ Cl- 2.7 3.0 1 . 6 9 NO++ Br- 2.0 2.7 1 . 7 6 NO++ I- 1 . 7 2.8 1.89 to another than do the computed ones. Also, recombination appears to be faster with H30+ than NO+ to a slightly greater extent than predicted. Finally, the theoretical approach outlined above gives a T-* dependence on temperature, since here e2 % R,kT. This compares with the To*o*2-o found l 2 for H30+ recombining with halide ions in reaction (VIII) and T-2*5*2.2 for NO+ here. Clearly, the accuracy of these measurements would have to be very significantly improved to check the predicted T-* dependence. Finally, we have measured 16* 2o the recombination coefficients for A++B- -+ A+B, for A being an alkali metal, Ga, In or TI, and B a halogen.The pair Na/I gives the largest coefficient of 3 x ions-l cm3 s-l in a flame at 2080 K, and the smallest measureable one was 1.5 x 10-l2 ion+ cm3 s-l for Rb/Br and Cs/I, both at 1820 K. Some pairs, particularly with Cs and Rb, have values too small to be measured. In general, it is clear that ion-ion recombination is characterised by the70 ION-ION RECOMBINATION nature of the " crossing " of the initial and final potential energy curves of the system, but broadly speaking the process is faster for molecular ions than atomic ones, because of the extremely large number of these pseudocrossings. This work was made possible by financial support from the S.R.C., which is gratefully acknowledged. N. A. Burdett and A.N. Hayhurst, J.C.S. Faraday I, 1978, 74, 53. C. F. Hansen, Phys. Fluid, 1968, 11, 904. B. H. Mahan and J. C . Person, J. Chem. Phys., 1964, 40, 392. M. S. W. Massey and K. B. Gilbody, Electronic and Ionic Impact Phenomena, Vol. 4, Recombi- nation and Fast Collisions of Heavy Particles (O.U.P., Oxford, 2nd edn, 1974). P. F. Knewstubb and T. M. Sugden, 7th Int. Symp. Combustion (Butterworths, London, 1959), p. 247; H. F. Calcote and D. E. Jensen, Adu. in Chemistry ser., No. 58 (Amer. Chem. SOC., 1966), p. 291 ; A. N. Hayhurst and D. B. Kittelson, Combustion and Flame, to be published. J. A. Green and T. M. Sugden, 9th Int. Symp. Combustion (Academic Press, New York, 1963), p. 607. N. A. Burdett and A. N. Hayhurst, 16th Int. Symp. Combustion (The Combustion Institute, Pittsburgh, 1977), p. 903. L. F. Phillips and T. M. Sugden, Canad. J. Chem., 1960,38, 1804. N. A. Burdett and A. N. Hayhurst, 15th Int. Symp. Combustion (The Combustion Institute, Pittsburgh, 1975), p. 979. H. F. Calcote, 15th Int. Symp. Combustion (The Combustion Institute, Pittsburgh, 1975), p. 990. lo N. A. Burdett and A. N. Hayhurst, Proc. Roy. 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