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The Journal of Physical Chemistry, Vol. 82, No. 22, 1978
astable ion is even larger than that for glucose and this implies that the ions sampled are hydrogen bonded.
Conclusion The MIKE spectrometer can be used in a multiple reaction monitoring mode to determine kinetic isotope effects. Chlorine isotope effects for isolated phase ions can be large and their magnitudes depend on the internal energies of the ions sampled and on ion structures. The observation of large secondary isotope effects in adduct ions is noteworthy. Acknowledgment. This work was supported by the National Science Foundation (CHE 76-06142).
References and Notes (1) (a) R. M. Caprioli in G. Waiier, Ed., "Biochemical Applications of Mass Spectrometry", Wiley, New York, N.Y., 1972,Chapter 27. (b) V.
J. Shiner and W. E. Buddenbarum, MTP rnt. Rev. Sci.: Phys. Chem., Ser. Two, 5, (1975). (2) (a) H. Budzklewicz, C. Djerassi, and D. H. Williams, "Mass Spectrometry of Organic Compounds", Holden-Day, San Francisco, Calif., 1967. (b) J. L. Holmes, MTP Int. Rev. Sci.: fhys. Chem., Ser. Two, 5 (1975). (3) J. T. Watson, "An Introduction to Mass Spectrometry: Biomedical, Environmental and Forensic Applications", Raven Press, New York, N.Y., 1976. (4) M. M. Green, J. M. Moldowan, M. W. Armstrong, T. L. Thompson, K. J. Sprague, A. J. Hass, and J. J. Artus, J. Am. Chem. Soc., 98,
851 (1976).
F. Hatch and B. Munson
(5) N. Uccella, I. Howe, and D. H. Williams, Org. Mass Spectrom., 6, 229 (1972). (6) M. Bertrand, J. H. Beynon, and R. G. Cooks, Org. Mass Spectrom., 7, 193 (1973). (7) (a) C. Lifshitz and M. Shaplro, d . Chem. fhys., 45, 4242 (1966);
(b) R. G. Cooks, J. H. Beynon, R. M. Caprioii, and G. R. Lester, "Metastable Ions", Elsevier, Amsterdam, 1973,p 101-104. (8) (a) Ch. Ottinger, Z. Naturforsch. A , 22,20 (1967);(b) R. D. Smith and J. H. Futreii, Org. Mass Spectrom., 11, 445 (1976). (9) The method resembles multiple ion monitoringi0 in GC/MS except that the reactant as well as the product ion is selected. Related procedures have been developed by Anbar et ai." (10) C. G. Hammar and R. Hessiing, Anal. Chem., 43, 298 (1971). (11)J. H. McReynoids and M. Anbar, Anal. Chem., 49, 1832 (1977). (12)J. H. Beynon, R. G. Cooks, W. E. Baitinger, J. W. Amy, and T. Y. Ridley, Anal. Chem., 45, 1023A (1973). (13) R. W. Kondrat and R. G. Cooks, Anal. Chem., 50, A81 (1978). (14) For typical resuks see (a) R. L. Julian and J. W. Taylor, J. Am. Chem. Soc., 98, 5238 (1976);(b) T. H. Cronartic and C. G. Swan, ibid., 98, 545 (1976). (15) J. F. Litton, Ph.D. Thesis, Purdue university, 1976. (16) H. P. Tannenbaum, J. D. Roberts, and R. C. Dougherty, Anal. Chem., 47, 49 (1975). (17) Compare J. H. Bowie and S.G. Hart, rnt. J. Mass Spectrom. Ion Phys., 13, 319 (1974). (18) (a) 6. S.Freiser, R. L. Woodin, and J. L. Beauchamp, J. Am. Chem. SOC.,97, 6893 (1975);(b) D. P. Martinsen and S.E. Butrill, Jr., Org. Mass Spectrom., 11, 762 (1976);(c) T. L. Kruger and R. G. Cooks, Tetrahedron Lett., 50, 4555 (1976). (19)V. Franchettl, B. S.Freiser, and R. G. Cooks, Org. Mass Spectrom., 13, 106 (1978). (20) (a) R. G. Cooks and T. L. Kruger, J . Am. Chem. Soc., 99, 1279 (1977);(b) D. Cameron, T. L. Kruger, and R. 0. Cooks, unpublished results.
Relative Rate Constants for Reactions of CH5+ and C2H5+with Hydrocarbons by Gas Chromatography-Chemical Ionization Mass Spectrometryt Frank Hatch$ and Burnaby Munson" Deparfment of Chemistry, University of Delaware, Newark, Delaware 19711 (Received December 7, 1977; Revlsed Manuscript Received July 25, 1978)
Relative rate constants for the reactions of C2H6+and CH6+with a homologous series of normal alkanes (C6-Cl0, Clz) and several aromatic hydrocarbons have been measured by a gas chromatographic-chemical ionization mass spectrometric technique of reactant ion monitoring (RIM). The method is described which utilizes the advantages of precise chromatographic sample introductionin combination with high pressure mass spectrometry. The reactant ion current is monitored as the compounds of interest are separately eluted and passed through the spectrometer ion source. The relative rate constants for the total ion-molecule reaction are obtained without regard to the types of products that are formed. By selecting a few reference rate constant values, absolute rate constants were obtained. Comparisons with theoretical values of rate constants and rate constants obtained by other techniques are made.
Introduction .~ Much work has been done during the past 20 years on the determination of rate constants of gaseous ion-molmany of the early studies, agreement ecule reactions. within a factor of 2 between experiments done under not well-defined conditions was satisfactory. Within the past few years, however, the precision and presumed accuracy in the determination of rate has increased and differences of 25 % are often considered significant.i-5 M~~~ extensive sets of data are also available now for ~
w.
Taken in p a r t from the Ph.D. Thesis of Francis Hatch, University of Delaware, June, 1977, and presented in part at the 25th Conference on Mass Spectrometry and Allied Topics, D.C., May, 1977. t Philip M o r r i s Research Center, Richmond, Va. 23261.
0022-3654/78/2082-2362$01 .OO/O
comparisons with predictions from theories.6-'0 Data on rate constants for reactions of an ion with an homologous series of compounds have indicated an increase in rate constant with an increase in molecular weight which was attributed to an increase in exothermicity of rea~ti0n.ll-l~ Recently we have reported the combination of a gas spectrometer chromatograph with a a separator which allows either electron impact or chemical ionization operational5 Subsequently, we reported the technique of reactant ion monitoring as an alternative method for detection in GC/MS.16 In these latter experiments, significant differences were noted in the relative sensitivities of different compoundswith the same ion. These differences are attributed to differences in rate constants for reaction of the ion with different molecules. We wish to report the results of our experiments using the 0 1978 American Chemical Society
Reactions of CH5+ and C2HC with Hydrocarbons
GC/MS technique to obtain relative rate constants for the reactions of an ion with different molecules. Experimental Procedure The instrument for these experiments was a duPont 21-llOB mass spectrometer, which has been modified for high pressure operation and connected to a Hewlett Packard 7620A gas chromatograph with a direct interface (no separator). The performance of this combination has been reported previ0us1y.l~ In these experiments He, N2, and CH4 were used as carrier gases for the gas chromatograph; however, the majority of the experiments were done with He as the carrier gas. Flows of 1-6 mL (STP) were diverted into the mass spectrometer to give pressures of 0.1-0.6 torr in the source of the mass spectrometer. The fraction taken into the mass spectrometer was constant during any one experiment and varied from 0.05 to 0.2. Methane was introduced into the source of the mass spectrometer from a separate gas handling manifold and was mixed with the He or N2from the gas chromatograph before entering the source. The pressure of CH4was generally 0.5 torr but was varied from 0.2 to 1.2 torr in some experiments. The majority of the separations were obtained with a 12 f t X 1/8 in, 10% SE-30 on Chromosorb W(HP) column (Applied Science Laboratories) with approximately 5000 theoretical plates. The column temperatures were varied from 60 to 120 "C depending on the mixtures being separated. The conditions were arranged so that a chromatographic experiment took 10-20 min for completion. Baseline resolution of peaks was always obtained to simplify the determinations of peak areas. Peak widths in. a t half-height were 5-25 s. Other columns (6 f t X Chromosorb 102 and 12 ft X l/s in. Pentosil) were used and identical results (f5%) were obtained for relative rate constants. In order to minimize the possibility of peak broadening and adsorption losses in the transfer lines, they were maintained at -200 "C. The peak widths of the gas chromatographic traces (flame ionization detector) and of the mass spectrometric traces (reactant ion current) were essentially the same. Flame ionization detector (FID) traces were obtained simultaneously with mass spectrometric traces in all experiments. Reproducibility of FID peak areas for the same mixture under a given set of conditions was f5%. Reproducibility of relative FID peak areas for the same mixture was fl-2%. Occasional experiments in which anomalies were observed in the FID chromatographic traces were not analyzed for kinetic data. The samples used in these experiments were obtained from commercial sources and were used without further purification. Gas chromatographic and mass spectrometric analyses indicated that no impurities were present at concentrations greater than 2 YO. The samples were prepared volumetrically in a solvent which had a retention time much less or much greater than the compounds of interest. From the concentrations of the solutions, the sizes of the samples introduced to the gas chromatograph (0.1 to 1 pL), and the fraction of the effluent taken into the mass spectrometer (0.05-0.2), we estimate that samples of - 5 pg were generally introduced into the source of the mass spectrometer. We may estimate the ratio of sample to carrier gas in the following manner. The molar density of the carrier mol/mL at STP. A typical injection into gas is 4.5 x the gas chromatograph contained 50 pg of sample (heptane, 100 g/mol). A peak half-width of 10 s corresponds to a baseline peak width of about 20 s. For a carrier gas flow rate of 30 mL (STP)/min, this full peak width corresponds
-
The Journal of Physical Chemistry, Vol. 82,No. 22, 1978 2363
to a carrier gas volume of 10 mL for dispersal of the sample mol/mL for the conand an average value of 5 X centration of sample. The ratio of sample to carrier gas Methane was mixed with then was approximately the carrier gas in approximately equal amounts; therefore, the ratio of sample to methane was approximately These gas phase concentrations of samples were sufficient to produce decreases in reactant ion current in some experiments as large as 30% at the peak maxima. The ion currents for the reactant ions were recorded on a strip chart recorder after passing through the electron multiplier and the amplifiers of the peak matching circuit of the duPont 21-llOB mass spectrometer. Much of the ion current of the reactant ion was balanced by a small potential and the decrease in reactant ion current could be read on a more sensitive scale. It was readily possible to adjust conditions such that nearly full scale deflections (-20 cm) were observed for the peaks in an experiment. The peak areas were obtained as the product of peak height and width a t half-maximum. In order to obtain a high accuracy for the peak width measurements (the limiting factor), the recorder was run at a rate of 5 in./min. The temperature of the source block was maintained at 150-200 "C, although this temperature is not known accurately. The effluent from the gas chromatograph was heated in the transfer lines and mixed with methane heated to approximately this temperature; consequently, the temperature of the carrier gas and sample was 150-200 "C. No systematic variation of temperature was attempted. It is necessary that the current of the reactant ion remain constant for the duration of a gas chromatographic experiment, and, therefore, that the electron current remain constant. Satisfactory operation was achieved with a collinear arrangement in which the filament was moved to the "back" of the source block and the electrons enter the source along the z axis, the path of the ions. A fairly large control plate with a 0.9-mm hole, maintained at +600 V with respect to the filament and 0 to +50 V with respect to the block, was used to control the electron and ion currents. Our present limitation is the stability of this control circuit. Work is planned to improve the stability. There are no repellers in the collinear source. However, there is perhaps a potential gradient within the source because of penetration of voltages from the focus plates through the ion exit slit and from the electron control plate through the electron entrance slit. The magnitude of any plasma potential in the source is not known. The majority of the experiments reported in this paper were done without any potentials applied within the source. A few experiments were performed in which a potential of a few volts was applied to the ion exit plate of the source of the mass spectrometer which was insulated from the block with 1/32-in.Teflon. This collinear source has been successfully used for many chemical ionization studies in our laboratory. The distance from the electron entrance to the ion exit is about 7.4 mm in this arrangement and only about 2.5 mm in the normal or orthogonal configuration in which the electron entrance axis and ion exit axis are perpendicular to each other. The ionic distributions in a high pressure mass spectrum of methane are essentially the same in the two sources. The absence of significant amounts of primary ions (CH4+)indicates that the primary ions are formed predominantly in regions sufficiently far from the ion exit of this collinear source to allow reactions to occur. In both sources, primary ions are formed at different positions along the ion exit axis so that there is a distribution of ionic
-
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The Journal of Physical Chemistty, Vol. 82,No. 22, 1978
path lengths and reaction times for the secondary ions CH5+and CZH5'. The ion currents obtained at the detector in either the collinear or normal orthogonal source with 70-eV electrons are less than 1% of the ion currents obtained at the detector with 450- or 630-V electrons at pressures of CH4greater than 0.3 torr. Consequently, those ions formed very near the electron entrance with the longest path lengths and reaction times do not escape the ion source. Average residence times, f, for CH5+and CzH5+in the source are difficult to estimate because of uncertainties in path length and field strengths. The mobilities of CH5+ and C2H6+in CHI have been measured: Ko(CH6+,CH4) = 2.32 f 0.02 cm2/V s at STP and KO(C2H6+, CHI) = 2.28 f 0.02 cm2/V s.I7 If we assume a potential gradient of 5 V/cm across the source, then v(CH5+)= 1.4 X lo4 cm/s at 1torr or 2.7 X lo4cm/s at 0.5 torr. If the average path length for the reactant ions is about half the depth of the source or approximately 0.3 cm, then f is 11p s at 0.5 torr and 21 v s at 1 torr. An approximate experimental value for f can be obtained by using the kinetic treatment given subsequently, the maximum decrease in reactant ion current, an estimate of the maximum concentration of the sample in the source of the mass spectrometer, and an approximate value for the rate constant of reaction. With a value of 1 X lo-' cm3/molecules for h(CzH5", n-C6H14),13 we obtain an estimate of 9 p s for the reaction time of C2H5+ at 1.2 torr. These drift velocities contribute about 0.01 eV to the energy of the ions under these conditions compared with an average molecular kinetic energy of 0.06 eV at 423
F. Hatch and B. Munson
pg samples of hydrocarbons were eluted from the gas chromatograph. These results confirm our belief that no new loss processes are introduced by the low concentrations of the hydrocarbons of this study. The relative peak areas or relative rate constants for heptane and cyclohexane with respect to hexane were independent of sample size from 1.5 to 9 pg. The absolute areas for each compound, or the extent of conversion, increased with increasing sample size at a constant pressure, temperature, and split ratio. In other experiments it was shown that peak areas of the decreases in reactant ion currents were directly proportional to the size of samples introduced into the gas chromatograph, all other conditions being held constant, under conditions similar to those used in this study.lg Relative rate constants were measured for n-pentane, n-hexane, cyclohexane, and n-heptane under several different conditions. Methane and He/CH4 or N2/CH4 mixtures were used at total pressures from 0.6 to 1.8 torr and He/CH4 or Nz/CH4 ratios from 1 / 2 to 2/1. The extents of conversion of reactant ion (the peak areas) with a given compound were different under these different conditions because the average reaction times were different. However, the relative areas or relative rate constants were essentially independent of all of these variations within an experimental precision of f 5 % . Consequently, we may say that either the reactant ions have little internal energy or that the rate constants for CH5+ and C2H5+ with the different alkanes have very similar dependences on internal energy so that their ratios are K. independent of internal energy. Although it is likely that the majority of CH4+and CH3+ions are produced by direct Possible complications in high pressure mass specelectron ionization in He/CH4 mixtures, these results trometry with respect to low pressure studies include indicate that the method of formation of the primary ions, differential ion losses from diffusion to the walls and CH4+ and CH3+ (Penning ionization, charge transfer, recombination, and differences in abundances of primary electron ionization),has no significant effect on subsequent ions formed by the initial high energy electrons (630 or 450 reactions of the product ions, CH5+and CzH5'. V) and secondary electrons. Neither process appears to Since there was probably a small potential gradient in be significant in the methane system since the ratio of ion the source in these experiments, the ion energies would currents, 117/&g, at high pressures is the same as the ratio of ion currents, Iie/I15, at low pressures and the ratio 117/129 be slightly different at different pressures because the drift velocities decrease with increasing pressure. The absence is essentially constant from 0.4 to 1.5 torr in the collinear of any significant variation in ratios of peak areas (or ratios source. In this respect, the collinear source is equivalent of rate constants) with a factor of 2 change in pressure to the normal or orthogonal source.18 indicates that the rate constants are either relatively inAlthough it appeared to us to be intuitively obvious that dependent of ion velocity in this range or that the rate the decreases in reactant ion current across a chromatoconstants of CH5+ and CZH5+ with these hydrocarbons graphic peak resulted from reactions of the reactant ions have the same functional dependence on ion velocity so with the sample, it was necessary to show that the results that their ratios are independent of velocity in this range. were not attributable to instrumental effects. A set of Experiments were done on a mixture of pentane, hexane, experiments was performed in which a small negative cyclohexane, and heptane in an orthogonal source for potential (2.7 V) was applied to the ion exit plate of the comparison with the data obtained with the collinear mass spectrometer source and the total positive ion current source. The results of the two sets of experiments for the collected on the ion exit plate was recorded during a relative rate constants were identical within the experichromatographic experiment. For the sample size normental error of f 5 %?O Experiments were also done in this mally used to obtain kinetic data (2-5 pg), variations of orthogonal source in which a small potential (5 V) was 1-2% of the total ion current were observed across a applied to the ion exit plate and relative rate constants (or chromatographic peak, For samples of 10 pg, 5% variarelative areas) were determined. This increase in ion tions were noted. For large (>lo pg) samples of halovelocity and ion energy caused a small decrease in the genated compounds at high electron currents (for which extent of reaction, but the relative rate constants were no data are reported in this study) significant ion losses unaffected by this applied potential within the experiwere observed in the source of the mass spectrometer mental precision of There may be a small effect which we attributed to recombinationreactions. However, of ion velocity on relative rate constants, and experiments for the hydrocarbons of these experiments, there were no are planned to study this effect and the effect of temindications of changes in recombination or diffusion loss perature on relative rate constants carefully. rates of the reactant ions caused by the presence of the Experiments were also performed in which small low concentrations of samples. In similar experiments the amounts of an impurity, acetone, were added to the gas ion current was collected on the focus plates (2.5 mm from mixture and no effects were noted on the relative rate the ion exit plate in the vacuum chamber). Variations of constants. Several different mixtures of hydrocarbonshave approximately 1% were detected in this ion current as 2-5
Reactions of CH5+ and C,H,+ with Hydrocarbons
The Journal of Physical Chemistry, Vol. 82, No. 22, 1978 2365
been used and the same relative rate constants have been obtained. It is faster and more convenient to use temperature programming of the gas chromatographicoven for mixtures which cover a wide boiling range. The relative rate constants (relative to hexane) from the programmed temperature experiments were slightly lower than the relative rate constants from the isothermal experiments and the differences are slightly larger than the combined error limits of the two measurements. In these programmed temperature experiments, there was a gradual decrease in flow through the gas chromatograph with increasing oven temperature and, consequently, a gradual decrease in pressure within the source of the mass spectrometer: a decrease of about 0.1 torr (out of 1torr) from the elution time of hexane to the elution time of dodecane. This decrease in total pressure during a single experiment causes a decrease in the extent of reaction of the reactant ions with the later eluting samples and, therefore, a decrease in the relative rate constant of decane with respect to hexane, for example, when compared with the isothermal value. Precise flow control to maintain a constant pressure in the source of the mass spectrometer will eliminate this problem. The change in pressure was smaller toward the end of the chromatogram between the heavier alkanes; consequently, the results are in relatively good agreement: k(decane)/k(octane) = 1.35 f 0.08 from the isothermal experiments and 1.33 f 0.08 from the programmed temperature experiments. Different mixtures and different GC conditions were used since it was not possible to obtain a good isothermal chromatogram for a mixture of all of these compounds. Each new compound was run in a mixture which contained two compounds whose relative rate constant had been determined previously and whose relative rate constant was used to check the behavior of the system. The rate constant for reaction of decane relative to hexane, for example, was obtained by multiplying k(decane)/k(octane) and k(octane)/k(hexane) and the estimated error was obtained by the standard propagation of errors technique. The data for the relative rate constants of CzH5' with the n-alkanes were obtained over a period of about 3 months with many minor changes in experimental conditions with no significant changes in the relative rate constants. The average relative standard deviation for the ratios of rate constants from all of these experiments is f5%. Since it is the changes in reactant ion currents that are measured in these experiments, it is the total reaction rate constant that is determined. The reactions of CH5+ are proton transfer reactions. The reactions of CzH5' are proton transfer, hydride transfer, and addition. Because of the small changes that occur in the source of the mass spectrometer that may be attributable to instrumental effects, we feel that accurate values of relative rate constants cannot be obtained by this technique if the rate constants are very small cm3/molecule s) or if one of the rate constants is less than 5% of the reference rate constant. Results and Discussion The decreases in reactant ion current across a gas chromatographic peak can intuitively be attributed to reactions of the reactant ions with the sample, but the quantitative relationship is not obvious. Under the conditions of the chemical ionization experiments, we can consider the following simplified model, using CH4 as the reagent gas: CH4 + e
-
+
CH4+ 2e
(1)
CH4++ CH4 CH4++ S CH5++ S
5 CH5++ CH3
kb
kc
(2)
products
(3)
products
(4)
In actuality, reaction 1should be considered as a series of reactions with electrons of different energy. However, it has been shown that the rate constants for reaction of CH4+and CH3+with methane are insensitive to energy of the electrons forming these primary ions.lI2l The experiments are performed under conditions such that the concentrations of the ions are substantially less than the concentrations of the neutral molecules. Therefore, the reactions obey first-order kinetics. If [SI / [CHJ = 0.001-0.005, then reaction 3 may be neglected in comparison with (2) because kbjk, rv 2. Then d[CH,+]/dt = ka[CH4+][CH4]- kc[CH,+][S] (5) [CH4+]= [CH4+loexp(-{k,[CH41 + kb[S]]t) [CH4+loex~{-k,[CHdt) (6) The symbols have their usual meaning, [SI = concentration of S in molecules/cm3,k = rate constant in cm3/molecule s, and t = ionic reaction time. The following expression can be obtained for CH5+ in the presence of sample, S:
Since k,[CH4] ditions [CH,+l
>> kb[S] under these experimental con-
[CH4+10(1- ex~~-k,[CHdtI) exp(-k,[SItl
(8)
In the absence of sample [CH,']
= [CH4+]0(1- exp{-ka[CH4lt))= [CH,+lo
(9)
Making this substitution, one obtains the following expression: [CH,+I = [CH5+IoexPkkcWIt)
(10)
If one replaces [CH5+]by 117, the ion current of CH5+,then the difference in ion current of the reactant ion CH5+in the presence and absence of sample, S, is given by (11) AIl7 = 1170 - 11,0 exp(-k,[S]t) This equation may be rearranged to give an expression for kC
k, = {In [1- ~ l , / ~ l , o l ~ / [ s l ~(12) In the mixtures, He/CH4 or Nz/CH4, two additional reactions may be involved in the formation of the primary ions, CH4+and CH3+. We would then add the following to the previous set of equations: M+ + CH4
-kCH4++ M klb
M*+CH,-CH,++M
(la) Ob)
The equation for [CH4+]becomes a more complicated one [CH4+]= alexp(-kla[CH4]t) + az exp(-klb[CH4]t) + ([Ch+]o- a1 - az) exP(-ka[CH41t) ( 5 4 in which a1 = kl,[M+Io/(kb- kla) and a2= klb[M*]/(kb klb). The equation for [CH5+]is similarly complicated by
2366
The Journal of Physical Chemistry, Vol. 82, No. 22, 1978
additional terms. However these terms for [CH5+]are eliminated in the difference in ion current of CH5+in the presence and absence of sample. Consequently, eq 12 will hold for these mixtures as well as for pure CH4, as long as substantially all CH4+ is converted to CH5+ and the sample to methane ratio is very small. In a GC/MS experiment, f is the average ionic residence time which is unknown but constant during an experiment as long as the pressure and any potentials in the source are kept constant. 117' is the value for the ion current of CH6+in the absence of sample, or the baseline of the trace. A17 is the decrease in ion current when the sample passes through the source of the mass spectrometer, or the peak height of the mass spectrometric signal at any concentration of the sample. The total amount of the sample that passes through the source is known from the fraction of gas flow taken into the source of the mass spectrometer and the amount of material injected into the GC column. The total amount of material is related to the area under a chromatographic peak, either integrated or taken as width times height. In these experiments we used the areas from the peak maxima and peak widths at half-height. Then, one obtains the following: [ S l m a x = uyStotal/ v 6 w i / 2 (13) In this equation Y is the fraction of carrier gas and sample taken into the mass spectrometer (obtained from the ratio of flow rates), SbM is the total number of moles of material injected onto the GC column, V, is the volume of the source, W1/2is the peak width a t half-height, and a is an instrumental proportionality constant which depends on the chart speed and range of the recorder. From (12) and (13) one obtains the equation k, = -{ln
[
1-
%]I{=)
(14)
In this equation (A117)maxis the peak height at the maximum, and the other quantities have been defined. The terms I17O, and W l j zare obtained experimentally for each compound. The other terms are constant for a given set of experimental conditions. The time, t , in this equation is the average reaction time for the reactant ion, CH5+in this case. If one takes the ratio of rate constants for the same ion with two different compounds, the following equation results:
In this equation, the mole ratios are obtained from the composition of the mixture as prepared and the other terms are obtained from reactant ion traces. A summary of all of the data for relative rate constants of C2H6+with a series of alkanes is given in Table I. The average values, standard deviations, and number of replicate determinations are reported. The average relative standard deviation for these measurements is h570 Although hydrocarbon systems have been studied more thoroughly than most other systems,1 there are few data for reactions with the higher hydrocarbons. Table I1 summarizes the data that are available on rate constants for reaction of CzH5+with alkanes. In order to compare the relative rate data, Table I, with the Langevin collision rates and other experimental data, it is necessary to choose I
F. Hatch and 6.Munson
TABLE I: Relative Rate Constants for Reaction of C,H,+ with Hydrocarbonsa
kC compd n-pentane n-hexane cyclohexane n-heptane n-octane n-nonane n-decane n-dodecane
k/k(n-hexane)
lo+
k L d ke(ICR)
cm3/molecule s
0.68 * 1 1.12 * 1.33 + 1.59 f 1.89 f 2.11 f 2.45 *
0.03(22) 0.72 1.66 1.09 1.06 1.76 1.31 0.04(38) 1.19 1.71 0.08(48) 1.42 1.86 0.08(21) 1.69 1.96 1.72 O.lO(15) 1.99 2.05 0.12(19) 2.25 2.14 0.20b 2.60 2.30 aP 1 torr; CH,, CH,/He, CHJN, mixtures; source temperature = 150-200 "C;samples = 2-10 pL. The values in parentheses indicate the number of replicate determinations. We have estimated k(dodecane)/ k(hexane) to be 2.46 from k(dodecane)/k(hexane) = [k (dodecane )/k (octane)] [ k (octane )/k (hexane)] and 2.43 from [k(dodecane)/k(decane)][k(decane)/k(hexane)], using data from dodecane from a programmed temperature experiment, Calculated, assuming that e see k(C,H,+, n-octane) = 1.69 X lom9c m 3 / ~ o l e c u ls, text. d Langevin rate = 2 n e ( ( ~ / p ) "see ~ , ref 25 and 26. e Reference 13.
-
TABLE 11: Rate Constants for Reaction of C,H,+ with Alkanes
k,
cm3/molecule s
n -pentane
0.92 i 0.21'" 1.40b 1.09 f O . O l C ~ d n-hexane 1.58 f 0.32= 2.30b 1.31 f 0.03C1d 1.05 i 0.07e 1.9Sf n-heptane 2.20 f 0.77a 2.20b 1.43 i 0.12e cyclohexane 1.6b9C n-octane 2.54 f 1.11'" 1.72 f 0.02d 1.66 f O . l O e a J. W. Long, Ph.D. Thesis, University of Delaware, 1972. Reference 11. Reference 22. Reference 13. e C. W. Polley, unpublished data, University of Delaware. T. Y. Yu and F. H. Field, Org. Mass Spectrom., 8, 267 (1974).
an absolute value for a reference compound. From the data of Table 11, there is no obvious choice. We may consider that the values of Long for n-octane are perhaps high and have a very wide range. The other two values are in reasonable agreement with each other. We have chosen the value of k(C2H5+,n-octane) as 1.69(-0.13,+0.05) X cm3/molecule s. These absolute rate constants are given in Table I1 along with the values calculated for the Langevin collision rates using the average polarizabilities of the hydrocarbons.21 With this choice of the reference value, one may see that the experimental rate constant is essentially equal to the Langevin rate constant for nonane and decane. It appears that the rate constant for dodecane is slightly larger (13%) then the Langevin rate constant. However, given the uncertainties of the absolute measurements, we feel that the two values may realistically be considered as equal. Additional data with even larger hydrocarbons, both alkanes and cycloalkanes, are needed to establish the trend. The most precise data with which to compare our results are the recent ICR datal3 which are also listed in Table I. Qualitative agreement with the other data is all that may be expected. The relative and absolute values of rate
The Journal of Physical Chemistry, Vol. 82,
Reactions of CH,+ and C2HSf with Hydrocarbons
TABLE 111: Relative Rate Constants for Reaction of CH.+ with Hvdrocarbonsa
kb com.od n-pentane n - hexane cyclohexane n-heptane n-octane n-nonane n-decane
P
-1
k/k(hexane) 1 1.05 i. 1.22 i 1.48 f 1.76 i 1.81 i
0.02(6) 0.03(12) 0.06(8)
0.11(3) 0.08(5)
kLC
1.49 1.56 1.81 2.20 2.62 2.69
2.00 2.18 2.12 2.32 2.45 2.57 2.69
2.42 2.68
torr; CHJHe; source temperature = 150-200 "C; 5-wg samples; 5 standard deviation (number of replicates). Calculated assuming k(CH,+, n-decane) = k L . See ref 34. Langevin rate constant, see Table I. a
1978 2367
TABLE IV: Relative Rate Constants for Reaction of C,H,+ with Aromatic Hydrocarbonsa
kd
cm3/molecule s
No. 22,
h,b
compd n-octane n-decane benzene toluene o-xylene cumene
k/k(C,H,,) 1 1.30 + 1.07 + 1.20 i 1.33 + 1.41 +
0.06 0.03 0.03 0.05 0.06
kL,c
cm3/mol- cm3/molecule s ecule s (1.69) 2.20 1.81 2.03 2.25 2.38
1.96 2.14 1.64 1.79 1.93 1.98
P 1torr; He/CH,; source temperature = 150-200 "C; 5-wg samples; i standard deviation; nine'replicates. Calculated assuming k(C,H,+, n-octa&) = 1.69 X Langevin rate constant, see Table I. cm3/molecule s.
C2H6+with these compounds. The precision is *5%. constants from these experiments differ by amounts which One may readily note that these rate constants also are larger than the presumed experimental error: h(ocincrease more rapidly with increasing polarizability than tane)/k(hexane) = 1.31 f 0.03 from the ICR data and 1.59 predicted by the Langevin theory: h(CH6+,octane)/kf 0.08 from these results. There is no obvious explanation (CH6+,hexane) = 1.12 from the Langevin theory vs. 1.48 for this discrepancy. One possible explanation lies in the from Table 111. One may also observe that the change differences in temperatures of the experiments. Some slow appears to level off with increasing molecular weight: ion-molecule reactions have negative temperature k(decane)/k(nonane) = 1.03 f 0.07 is less than h(hepc o e f f i ~ i e n t and s ~ ~the ~ ~relative ~ ~ ~ rate constants of these tane)/h(hexane) = 1.33 f 0.08. The rate constants for experiments were done a t 150-200 "C and the ICR exCH5+are perhaps approaching the Langevin rate as did periments were done a t room temperature, -25 "C. the rate constants for CzH5'. There is a smaller change However, no temperature variations have been observed with increasing molecular weight for CH6+than for C2H6': for these reactions and although the rate constants are k(decane)/k(hexane) = 2.1 for CzH6+and 1.8 for CH5+. lower than the Langevin limits or collision rate constants, There are even fewer data for comparison with these these rate constants are not really small. Many fast results for CH5+ than for comparison with the results ion-molecule reactions have rate constants that are esobtained for CzH5+. The only directly comparable data sentially independent of t e m p e r a t ~ r e Other . ~ ~ ~ exper~~~ are those of Meisels, Mitchum, and S r ~ k and a ~ these ~ iments are planned to investigate this discrepancy and values, for pentane and hexane, are also given in Table 111. possible temperature effect. It is also possible that our One should note, however, that these rate constants appear results may be in error because the ionic reaction times to be significantly larger than rate constants reported by are actually average values. The invariance of relative rate others for reaction of CH5+ with other slightly smaller constants to changes in experimental parameters suggests nonpolar compound^.^^,^^ Keeping in mind the data of to us that this is not a major source of error. Additional Table I that rate constants for reaction of C2H5+ with experiments are planned to obtain relative rate constants nonane and decane were essentially the same as the under very different experimental conditions. Langevin rate constants, we have calculated rate constants A general increase in rate constant with increasing for CH5+with the alkanes assuming that h(CH5+, n-decarbon number or polarizability or perhaps reaction excane) = hL. The value for the absolute rate constant of othermicity has been noted previou~ly,~l-'~ with which the CH5+with the hexane is substantially lower than the value present results agree. The present results comprise, reported by Meisels and co-workers and a reasonable however, the series with the greatest variation in molecular extrapolation indicates that our data are consistently lower weight for an homologous series. The model that is than their data. Similarly, we would estimate from the generally used for estimating reaction rates for iondata of Tables I and I11 that h(CH6+,C3H8) would be molecule reactions with nonpolar molecules predicts a significantly lower than the value of 1.54 f 0.15 X lo4 variation in collision rate constant with ( a / p ) l I 2 ,where a cm3/molecule s reported by Harrison and c o - ~ o r k e r s . ~ ~ is the polarizability of the neutral molecule and p is the reduced mass of the ion-molecule couple.26,26Data have It is not clear, however, that the Langevin rate constant been reported, however, for reactions with nonpolar represents a realistic upper limit for rate constants for molecules for which the observed reaction or collision rate reactions with nonpolar molecules. Line width studies by constants exceed the rate constants calculated from the ICR of nonreactive ions in CH4 gave collision frequencies Langevin polarizability theory.3i5,7$27-32 These differences that were about 20% larger than the Langevin collision have been interpreted by using the maximum value of frequencies for hydrocarbonsg and similar observations polarizability rather than the average value for anisotropic have recently been reported for other system^.^ It may be molecule^^^^^^^^ or by including quadrupole i n t e r a c t i o n ~ ~ s ~ ~that ~ ~ the ~ present agreement of experimental rate constants or by using a general potential for the ion-molecule infor hydride transfer with the Langevin rate constants is teraction containing terms in r4,r6,r2,et^.^^^ accidental and the reaction rate constants are substantially The variation with molecular weight, and therefore with less than the collision rate constants. However, none of polarizability, of these data is greater than the variation the present data with alkanes give indications of rate constants that are significantly larger than predicted by predicted from simple polarizability theory: k(C2H6+, n-octane)/k(C2H6+,n-hexane) = 1.11from polarizability the simple polarizability theory. theory and 1.59 f 0.08 from Table I. Table IV shows data for relative rate constants for Data for rate constants of CH5+with hydrocarbons are reaction of CzH5' with a few aromatic hydrocarbons. These data were obtained from mixtures which contained shown in Table 111. Fewer replicates were done in these n-octane and n-decane, for which the ratio of rate constants experiments, and the same procedure was followed that was 1.30 f 0.06, a value which is in excellent agreement was used for the determination of the rate constants for
The Journal of Physical Chemistry, Vol. 82, No. 22, 1978
2368
TABLE V: Relative Rate Constants for Reaction of CHs+with Aromatic Hydrocarbonsu compd
k/k(octane)
F. Hatch and B. Munson I
I
I
kb kLC cm3/molecule s
n-octane 1 2.20 2.45 n-decane 1.22 i: 0.03 2.69 2.69 benzene 0.95 i 0.03 2.09 2.02 toluene 1.06 f 0.03 2.33 2.22 o-xylene 1.18 i: 0.03 2.60 2.41 cumene 1.25 ?r 0.03 2.75 2.48 P 1 torr; CH,He; source temperature = 150-200 "C; 5-wg samples; i: stanpard deviation; five replicate analyses. Calculated assumjlg k(CH,+, n-decane) = k L . Langevin rate codstant, see Table I.
-
with the values of Table I, 1.33 f 0.10. Absolute values for rate constants are calculated from the value of k(C2H5+, cm3/molecules. The relative rate n-octane) = 1.69 X constants for reaction of C2H6+with the aromatic hydrocarbons are significantly larger than the rate constants for reaction of CzH5+ with paraffins of approximately the same polarizability or carbon number. Toluene and hexane have comparable polarizabilities (12.9 vs. 12.3 A3) and k(C2H5+, toluene)/k(C2H5+,hexane) = 1.91. A similar comparison for two C6 compounds shows a large difference: k(benzene)/h(hexane) = 1.70. The rate constants for reaction of C2H5+with the alkanes were less than or equal to the rate constants calculated from the Langevin polarizability theory. However, the rate constants for reaction of CzH5+ with the aromatic hydrocarbons exceed the collision rate constants calculated from the Langevin polarizability theory which are also given in Table IV. For benzene, the experimental rate constant is about 10% larger than the Langevin collision rate. Given the uncertainty in the absolute values of these rate constants, this discrepancy may not be real. However, if it is real, one can explain a rate constant this large by unit efficiency for the reaction and a collision rate constant that depends on the maximum polarizability rather than the average polarizability: [ a ( r n a x ) / a ( a ~ ) ] l=/ ~1-09for benzene. An interaction potential of only a few kcal/mol (reasonable since (M + C2H5)+ions are observed) would also be sufficient to provide a collision rate constant this much larger than the Langevin limit.g The average quadrupole orientation theory predicts rate constants for reaction with benzene that are essentially the same as, but slightly lower than rate constants predicted by the Langevin theory33and cannot explain this difference, if it exists. The experimental rate constants for reaction of C2H5' with toluene, o-xylene, and cumene are all larger than the values calculated from simple polarizability theory. The ratios of experimental rate constants to polarizability rate constants, kexpt/kL,increase with increasing dipole moment of the aromatic hydrocarbon. The effect of dipole moment on the rate constants is small, however: kexpt/kL(benzene, p = 0) = 1.10; kexp,/kL(toluene,p = 0.37 D) = 1.13; p = 0.62 D) = 1.17 and kexpt/kL(cumene, kexpt/kL(o-xylene, p = 0.65 D) = 1.20. If we compare the rate constants for reaction of CzH5+ with these slightly polar hydrocarbons with values from current theories we obtain the following values of k/kL from the ADO toluene, 1.02; o-xylene, 1.06; and cumene, 1.06; and from the Barker and Ridge model:1° toluene, 1.12; o-xylene, 1.22; and cumene, 1.22. Table V lists rate constants for reaction of CH5+with the same set of aromatic hydrocarbons whose reactions with CzH5+ were discussed. The procedure for obtaining the relative rate constants was the same as before and these
I
I
10
15
I
20
Q, 10-24 CM3
Figure 1. Plot of rate constant vs. polarizabllity for reactions of CH,' with hydrocarbons.
data represent the averages of five replicate analyses done on the same day. As with the alkanes, one notes that there is a smaller range of rate constants for reaction of CH5+ with these aromatic hydrocarbons than the range of rate constants observed for reactions of C2H5+ with the same hydrocarbons. The absolute rate constants are calculated from the assumption that k(CH5+,n-decane) = kL = 2.69 X lo-' cm3/molecule s. Also, one notes that the rate constants for reaction of CH5+ with the aromatic and paraffinic hydrocarbons are consistently larger than the rate constants for reaction of CzH5+ with the same compounds. The ratio k(CH5+)/k(CzH5+)for all of the compounds is 1.24 f 0.09, essentially the same as the square root of the inverse ratio of reduced masses. This ratio of rate constants is in agreement with expectations from the polarizability theory. It also indicates internal consistency in the data since the absolute values for the rate constants for reactions of C2H5+were based on an experimental value which has no specific functional dependence on mass. The values of rate constants for CH6+ were based on a Langevin rate constant which does have a dependence on the square root of the reduced mass. The rate constant for reaction of CH5+with benzene is within experimental error the same as the rate constant from the Langevin theory. The difference that is noted in Table V is too small to warrant discussion. For the other aromatic hydrocarbons, kexpt/kLincreases with increasing p = 0) = 1.03; kexpt/ dipole moment keXpt/kL(benzene, kL(toluene, p = 0.37 D) = 1.05; keXpt/kL(o-xylene, p = 0.62 D) = 1.08; and kexpt/kL(cumene,p = 0.65 D) = 1.11. These ratios may be compared with calculated values from ADO t h e ~ r y : ~toluene, J 1.02; o-xylene, 1.06; cumene, 1.06; and the Barker and Ridge model:1° toluene, 1.12; o-xylene, 1.22; and cumene, 1.22, The calculated values for k/kL are independent of the masses of the ions. This increase in k(expt)/k(collision) with increasing carbon number has been observed previ~usly'~-'~ and has been attributed to an increase in reaction efficiency with increasing exothermicity. Figures 1 and 2 illustrate the trends in the data for reactions of CH5+ and CzH5' as plots of k vs. polarizability. For reactions with the lower alkanes, C3-Cs, it is likely that thers is an increase in reaction exothermicity with increasing molecular weight of the hydrocarbon. The large difference between k(benzene)and k(hexane) for both CH5+ and C2H5+could also be explained in terms of an increase in reaction efficiency with increasing exothermicity because proton transfer to benzene (and the other aromatic hydrocarbons) is con-
Reactions of CH5+ and C2H5+ with Hydrocarbons
The Journal of Physical Chemistry, Vol. 82, No. 22, 1978 2369
(Langevin) theory for large (Ca-CiO) hydrocarbons. A small effect of dipole moment is observed for alkylbenzenes. The rate constants for reaction of C2H6+with the higher alkanes and with benzene may slightly exceed the Langevin rate constants, but the effect is not large. Rate constants for reaction of CH5+with the hydrocarbons are consistently larger than rate constants for reaction of C2H5+ with the same hydrocarbons, by a factor of 1.24, approximately the same as [~(C2H,+)/y(CH5+)]1/2. Rate constants for reaction of CH6+ and C2H5+with aromatic hydrocarbons are consistently larger than rate constants for reaction with n-alkanes of the same carbon number or polarizability. Only one cycloalkane was used, but rate constants for reaction of CH5+ and C2H6+with cyclohexane were significantly larger than the rate constants for reaction with an alkane of the same polarizability.
;2 , o yl
U 3
. _I
8
M
mU 0 3
2 1.0
References and Notes
N-cg I
10
I
15
a,10-24
20 C M ~
Figure 2. Plot of rate constant vs. polarizability for reactions of C2H5+ with hydrocarbons.
siderably more exothermic than proton transfer or hydride abstraction with hexane (and the other The presently available data, however, indicate that the hydride affinities of alkyl ions reach an essentially constant value at C7and therefore the heats of hydride transfer reactions would be essentially constant for alkanes larger than heptane.3G38Some additional explanation is needed for the increase in reaction efficiency with increasing molecular weight. It is not merely a difference between hydride and proton transfer reactions. CH5+reacts by simple proton transfer or dissociative proton transfer with both alkanes and alkylbenzenes. CzH6+reacts by hydride transfer with the alkanes and by both hydride and proton transfer with the alkylbenzenes. Perhaps it is worthwhile to consider that the exothermic reactions of CH5+and CzH5+with aromatic hydrocarbons occur with unit efficiency because there is no hindrance toward the initial attack and addition of the ions to the T orbitals. Hydride transfer between C2H6+ and the alkanes perhaps involves more restricted attack by the ion along the C-H bond. Proton transfer from CH5+ to alkanes perhaps requires a specific orientation for insertion into the C-H or C-C bond. One may note from Figures 1 and 2 that the rate constants for reaction of both CH5+and CzH5+ with the more rigid cyclohexane are about 25% larger than the rate constants for the more flexible alkanes of the same polarizability. Conclusions This work has demonstrated that relative rate constants for reactions of an ion with a series of compounds can be obtained with a GC/CIMS technique of reactant ion monitoring. Relative total reaction rate constants are obtained, but information about rates of formation of specific product ions is not directly obtainable from these data. With a few accurately known reference values, one can obtain absolute rate constants for reaction. Rate constants for reactions of CH5+and C2H5+with hydrocarbons were obtained which are in reasonable agreement with rate constants obtained by other techniques. The rate constants increase with increasing molecular weight (polarizability) of the hydrocarbons and approach the value calculated from simple polarizability
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