2845
High Pressure Mass Spectrometry (3) W. J. Russell, J. F. Zettler, G. C. Blanchard, and E. A. Boling, "New Approaches to the Rapid Identification of Microorganisms", C. Tiborilleni, Wiley, New York, N.Y., 1975, pp 393-406. (4) P. D. Zemany, Anal. Chem., 24, 1709 (1952). (5) E. Reiner. Nature (London),206, 1272 (1965). (6) E. Reiner and W. H. Ewing, Nature(London), 217, 191 (1966). (7) E. Reiner, J. J. Hicks, R. E. Beam, and H. L. David, Am. Rev. Respir. Dis., 101, 656 (1971). ( 8 ) P. G. Vincent and M. L. Kulik, Appl. Microbiol., 20, 957 (1970). (9) H. L. C. Meuzelaar and P. G. Kistermaker, Anal. Chem., 45, 587 (1973). (10) H. R. Schulten, H. D. Becky. H. L. C. Meuzelaar, and A. J. H. Boerboom, Anal. Chem., 45, 191 (1973). (11) J. P. Anhalt and C. Fenselau, Ana!. Chem., 47, 219 (1975). (12) B. D. Mitchell and A. C. Birnie, Differential Thermal Analysis", R. C.
McKenzie, Ed., Academic Press, London, 1970, Chapter 24. (13) C B. Murphy, ref 12, Chapter 23. (14) E. K. Gibson and S. M. Johnson, Thermochim.Acta, 4, 49 (1972). (15) A. L. Yergey, F. W. Lampe, M. L. Vestal, E. J. Gilbert, and G. J. Fergusson, "Gassification of Fossil Fuels under Oxidative, Reductive and Pyrolytic Conditions", Final Report to EPA, Project No. 68-02-0206 (US. Government Access: EPA-650/2-73-042). (16) S. R. Prescott, J. E. Campana, P. C. Jurs, T. H. Risby and A. L. Yergey, Anal. Chem.,'40, 827 (1976). (17) "Modern Plastics Encyclopedia", McGraw-Hili, New York, N.Y., 1946, pp 460-477. (18) H. L.Friedman, G. A. Griffith, and H. W. Goldstein in "Thermal Analysis", Vol. 1, R. F. Schwanker, Jr., and P. D. Gam, Ed., Academic Press, New York, N.Y., 1969, p 405.
Arrival Time Distributions in High Pressure Mass Spectrometry. 5. Effect of €/P on Measured Apparent Heats and Entropies of Reaction G. G. MeiseIs,* R. K. Mltchum,+ and J. P. Freeman* Department of Chemistry, University of Nebraska-Lincoln, Lincoln, Nebraska 68588 (Received May 25, 1976) Publication costs assisted by the University of Nebraska
The temperature dependence of the equilibrium involving the proton transfer between methane and carbon dioxide and their protonated analogues has been investigated at a series of values of the field strength EIP. The apparent values of A S and AH were found to depend on EIP; experimental uncertainty in the former was too large to establish systematic trends. The latter decreased approximately linearly with EIP; limiting values of AH = -1.58 f 0.06 kcal/mol and A S = 1.7 f 0.3 eu are in good agreement with those obtained by flowing afterglow and ICR techniques.
Introduction High pressure mass spectrometry has been employed extensively in recent years for the measurement of ionic equilibria in the gas phase.?-4 Values for A S and AH are derived from studies of the temperature dependence of the equilibrium constant K . Such measurements may be subject to systematic these fall into two categories. One results from uncertainties in the conditions prevailing in the ion source. These are of interest here. Another is associated with the problems of ion sampling, discrimination, collision induced dissociations, and similar processes which are primarily external tc; the reaction region. Two complications exist within the reaction region itself. The first is caused by the time dependence of the approach to eq~ilibrium.~,g Time resolved measurements are now accepted as essential. The second difficulty arises from the occasional use of extraction fields in high pressure mass spectrometers of the chemical ionization type, or in drift tube mass spectrometers. It is well known that average ion energies are shifted upward by applied fields and that the ion velocity distributions lose Maxwell-Boltzmann character at higher values of ElP.9JoIn this investigation we report our findings on the effect of EIP on measured values of the equilibrium Present address: NCTR-FDA, Jefferson, Ark. 72079. Present address: Department of Chemistry, University of Hawaii, Honolulu, Ha. +
constant under conditions where equilibrium is totally achieved. We have chosen to study the equilibrium
CO*H+ + CH4
COz
+ CHb+
(1)
for several reasons. It is one of the earliest studies by high pressure mass spectrometry in the laboratory of Professor Franklin." A careful study of this system has also been made by the flowing afterglow technique,12and has received support from another investigation employing ion cyclotron resonance.13 The previous findings should provide a reliable reference point against which to evaluate our observations. Lastly, the enthalpy change associated with the equilibrium of reaction 1is relatively small, so that the equilibrium reaction should proceed rapidly and ions should be thermalized quickly. The small exothermicity of the reaction also leads to the hope that processes external to the ion source such as collision induced dissociation, etc., will affect both ions approximately equally in spite of the substantial difference in mass.
Experimental Section The experimental procedures have been described previ0usly.1~Briefly, an Atlas CH-4 mass spectrometer was modified by the installation of a high pressure ion source and differential pumping system. Gases were maintained in sepThe Journal of Physical Chemistry, Vol. 80, No. 26, 1976
2846
G. G. Meisels, R. K. Mitchum, and J. P. Freeman IO0
0 0-
0
0
.
0
.
0
0
m/e 17
0 45
0
0 0
0 0
8
0
8
0
8 0
I
I
6
12 p sac
Figure 2. Variation of apparent equilibrium constant K, with f/P;top to bottom: X193 O C ; -t 209 O C ; A , 226 O C ; 0 , 2 3 8 O C ; 0 , 2 5 0 O C . 18
23
Figure 1. Arrival time distributions of C02H+ ( d e 45) and CH5+ ( m / e 17) at a field strength of 15.6 V cm-I Torr-', 441 K, and 0.35 Torr total source pressure containing 10% CH4 in Con; normalized at maxi-
mum.
arate 5-1. stainless steel reservoirs; composition and total pressure were established using a Baratron capacitance gauge whose sensing arm was attached directly to the ion source. All experiments were performed at a concentration of ca. 10%COz in methane. Temperatures of the source block were adjusted by resistance heating and monitored with a calibrated thermistor. Time resolved measurements were made by pulsing the electron gun through the application of a 0.5-ps pulse to 9090transparent tungsten mesh between the filament and the ion source block to reverse the 3-V negative bias on the screen. The pulse also triggered a time-to-pulse height converter which was terminated upon arrival of an ion a t the electron multiplier detector. The arrival time of each single ion appearing at the detector was sorted on a 400-channel TMC pulse height analyzer. A complete arrival time spectrum could usually be accumulated in a period of approximately 10 min. The output of the memory of the analyzer was transferred onto paper tape and eventually processed on an IBM 360 computer. Ion residence times in the source were calculated by subtracting from the arrival times the flight time between the ion source exit and the detector, as described previ0us1y.l~
- - - / j ?7.00
Results Residence time distributions of COzH+ and C W b + were obtained over a range of values of temperature and EIP (V cm-l T o r r 1 ) . Representative distributors are given in Figure 1 and demonstrate clearly that the normalized arrival time distributions can be overlaid completely. This was the case at all temperatures and values of EIP employed in this investigation. Equilibrium measurements were made thereafter in a time averaged (dc) mode and are shown in Figure 2 as a function of E / P at several temperatures, and in Figure 3 in the form of Van't Hoff plots. It was noted that results were reproducible only when source and supply gases were scrupulously clean and free of moisture. The Journal of Physical Chemistry, Voi. 80,No. 26, 1976
Y.80 r1.20
11.w
5.W
5.20
U.60
1000/T [OEG.K)
Flgure 3. Van't Hoff plots of Ke at various field strength. EIP increases
from top to bottom.
Discussion
Identity of arrival time distributions for two ions so disparate in mass as CHj+ and COzH+ is possible only when the proton spends part of its time on methane and part of it on COz with a substantial number of interchanges, at least 5.15 It was, therefore, not necessary to rely upon arrival time distributions for the establishment of equilibrium constants. The advantages of dc measurements for evaluating the temperature dependence of the equilibrium position are primarily the
High Pressure Mass Spectrometry
much increased sensitivity and higher signal-to-noise ratio of such measurements, since the continuous measurements provide ion signals several orders of magnitude more intense than those observed in the pulsed mode. It is evident from Figure 3 that Van’t Hoff plots depend on EIP. Ion behavior in applied fields has been described by the well-established Wannier expression for average ion energies an equation derived on the basis of the retention of a Maxwell-Boltzmann distribution of ion energies:
+
= 3/2kTot 3/2(M, Mg)Ud2
(1)
where k is the Boltzmann constant, Mi the mass of the ion (g), MG the mass of the neutral drift gas, u d the drift velocity of the ions in question (cm SI), and To is the gas temperature (K). This permits a qualitative understanding of the change of AH, with E/P. As E / P and therefore U d increase, the second term on the right-hand side becomes more important, the ion energy becomes greater than that defined by To, and the energy barrier for reaction less important; hence, AH,appears to decrease. Equation I may be developed in an attempt to derive more quantitative insight. Young and Edelson16 and Parkes17 have shown that eq I may be used to derive the effective joint temperature T J , a of . ~ion a colliding with neutral B of mass MB.
T j , a .=~ To t Mgud2/3k
4.m
u.m
I. 00
8.00
E/P [VClLT/CM*TPJRR)
Figure 4. Apparent heat of reaction AH, and its dependence on €1 P. 9
(11)
The drift velocity Ud is given byla ud
= 2.79KaoEToIP
(111)
where Kaois the reduced mobility which, for ion a drifting in a mixture of neutrals A and B of mole fraction composition X A and X B , is given by Blanc’s law19
Kao = [XA/Ka.Ao-k XB/K,.B~]-~
(IV)
where K,-AO is the reduced mobility of ion a in the pure gas A. Insertion of eq I11 and IV into eq I1 yields TJ,a= - ~Toll
+2.59M~/k[x~/K~.~~
‘I
80.00
Ibo.00
[E/P)*
X B I K ~ - B O ] - ~ T O ( E I P(V) )~I where M B is in grams. The term in parentheses is a correction factor to To. I t can be estimated by inserting the relationship18
KO = 3 5 , 9 1 6
t
(VI)
where CY is the polarizability in Bohr radii cubed and the reduced mass; eq VI is based on the Langevin drift theory. T J differs from To by more than 10% for CHj+ drifting in CH4IC02 mixtures when EIP exceeds ca. 5 V cm-1 Torr-’ (at 500 K). T J , a is . ~not the same as TJ,b-A.When two ions considerably different in mass drift in a mixture and when the mean ion energy exceeds the thermal energy greatly, the effective temperature of the two ions will not be the same; in our system, it will be approximately 50% greater for the reverse reaction of the equilibrium described by reaction 1at high fields. That is, the effectivejoint temperatures are not the same for the forward and reverse reactions. This is a complication only when both reactions have finite activation energies. An attempt to interpret the field dependence of results quantitatively can be based on the operational definitions of enthaply AH, and entropy ASe which are derived from Van’t Hoff plots, assuming the applicability of the standard thermodynamic relationship
PhO.00
(VOLT/CMwTORRI
3k.00
[
10.
w
Figure 5. Apparent heat of reaction ASe and its dependence on El P.
In K , = AS,/R - AH,/RT,
(VI11
The subscript e indicates that the quantities derived do not necessarily correspond to the true thermodynamic ones. Clearly, eq V can represent translational energy only. Insertion of T~,*-B from eq V for T , in eq VI1 is simplified since the forward reaction should not have an activation energy. One may then identify a with CHb+, A with CH4, and B with C02. There is, of course, a serious difficulty inherent in such an approach. The derivation of the drift temperature leading to eq V is based not only on the assumption that translational Maxwell-Boltzmann distributions are preserved for ions, but disregards entirely energy transfer into internal modes. Yet the use of eq V as a “temperature” assumes that T~,,.Bdescribes the population of all energy states of the ion. At best one may therefore expect any quantitative relationships to reflect only qualitative trends, and dependencies on “effective” temperatures much weaker than those expected for thermodynamic temperature changes of the same magnitude. These complications are well k n 0 ~ n . ~ 6 J ~ , ~ ~ , ~ ~ At field strengths less than about 5 V cm-l Torr-l, binomial expansion of the full equation and neglect of higher terms leads to The Journal of Physical Chemistry, Vol. 80, No. 26, 1976
Alan Goren and Burnaby Munson
2848
In K , = AS/R
+ [2.59lHM(COz)/R] X [X(CH4)/Ko(CH5+in CH4)
+ X(C02)/K0(CH5+in COz)]-2[E/P]2- AH/RTo
(VIII)
One would expect from eq VI11 that the slope of a Van't Hoff plot should yield the thermodynamic value of AH even in the presence of low fields while A S should be weakly dependent on E/P. This is not supported by our results (Figures 4 and 5 ) ; while A S may indeed vary somewhat with E/P, the magnitude of the expected change is too small to be detected reliably. AHe, however, appears to be quite sensitive to the presence of applied fields in sharp contrast to eq VIII. Two explanations are possible. The first relies on experimental uncertainty and a systematic error in obtaining the slope of Van't Hoff plots. Linear dependence is forced upon these curves, and it may well be that the change in slope is an artifact. It is more probable that the nonadherence to eq VI11 reflects the inadequacy of the assumptions underlying the derivations. Meand ASe extrapolate smoothly to E / P = 0, where their values of AH' = -1.54 f 0.06 kcal/mol and AS' = 1.7 f 0.3 eu are in excellent agreement with AZP = -1.5 kcal/mol and ASo = 1.5 eu obtained by flowing afterglow12 and ICR13 techniques; at higher field strength, our equilibrium constant is also in good agreement with that reported by Kasper and Franklin.ll We must conclude, however, that the evaluation of energy dependent phenomena such as equilibrium constants and rate constants and resulting derivation of heats of reaction and activation energies in high pressure sources which employ external fields in the reaction region are subject to systematic error unless the field strength approaches zero.
Acknowledgments. This investigation was supported in part by the United States Energy Research and Development Administration and by the D. J. Brown Fund of the University of Nebraska. We are sincerely grateful for this assistance.
References and Notes (1) This paper was presented in part at the 22nd Annual Meeting on Mass Spectrometry and Allied Topics, Philadelphia, Pa., May 1974. (2)(a) P. Kebarle and E. W. Godbole, J. Chem. Phys., 39, 1131 (1963);(b) P. Kebarle in "Ion-Molecule Reactions", J. L. Franklin, Ed., Plenum Press, New York, N.Y., 1972,Chapter 7. (3)D. P. Beggs and F. H. Field, J. Am. Chem. SOC.,93, 1567,1576 (1971). (4)S.L. Bennet and F. H. Field, J. Am. Chem. Soc., 94,5186 (1972). (5) C. Chang, G. J. Sroka, and G. G. Meisels, lnt. J. Mass Spectrorn. /on Phys.,
11. 367 (1973). C. Chang, G. G; Meisels, and J. A. Taylor, lnt. J. Mass Spectrom. /on Phys.,
12,411 (1973). A. J. Cunningham, J. D. Payzant. and P. Kebarle, J. Am. Chem. Soc., 94,
7627 (1972). G. G. Meisels, G. J. Sroka, and R. K. Mitchum, J. Am. Chem. SOC., 96,5045
(1974). G. H. Wannier, Bell Syst. Tech. J., 32, 170 (1953). S.B. Woo and S.F. Wong, J. Chem. Phys., 55,3531 (1971). S.F. Kasper and J. L. Franklin, J. Chem. Phys., 56, 1156 (1972). R. S. Hemsworth. H. W. Rundle, D. K. Bohme, H. I.Schiff, D. B. Dunkin, and F . C. Fehsenfeld, J. Chem. Phys., 59,61 (1973). R. H.Staiey and J. L. Beauchamp, J. Chem. Phys., 62, 1998 (1975). G. Sroka, C. Chang, and G. G. Meisels, J. Am. Chem. Soc., 94, 1052
(1972). G. Sroka, C. Chang, and G. G. Meisels, J. Chem. Phys., 55, 5154
(1971) C:E. ioungand W. E. Falconer, J. Chem. Phys., 57,918(1972). D. A. Parkes, Trans. Faraday Soc., 67, 7 1 1 (1971). (18) E. W. McDaniei, "Collision Phenomena in Ionized Gases", Wiley, New York, N.Y., 1964,Chapter 9. (19)A. Blanc, J. Phys. Radium, 7, 825 (1908). (20)S.P. Hong and S.B. Woo, J. Chem. Phys., 57, 2593 (1972). (21)W. Lindinger, D. L. Albritton, C. J. Howard, F. C. Fehsenfeld, and E. E. Ferguson, J. Chem. Phys., 63,5220 (1975). ,
Thermochemistry of Alkyl Ions Alan Goren and Burnaby Munson* Department of Chemistry, University of Delaware, Newark, Delaware 19711 (Received November 12, 1975)
Equilibrium experiments on hydride transfer reactions of tertiary alkyl ions and tertiary hydrocarbons have been made by high pressure mass spectrometry which give differences in hydride affinities of tert- butyl, tert-pentyl, and tert-hexyl ions. Good agreement is noted with previous work. The hydride affinities and heats of formation of the tertiary ions decrease with increasing molecular weight of the ions. The hydride affinities appear to approach a lower limit of 229 kcal/mol. From these data and ionization potentials of tertiary alkyl radicals, it is suggested that there is a small decrease in the dissociation energies of tertiary C-H bonds with increasing chain length. The literature data for secondary alkyl ions suggest a similar decrease toward a limit in hydride affinities of 246 kcal/mol with increasing chain length of the ions. The thermochemistry of alkyl and other hydrocarbon ions has been studied since the early days of mass spectrometry. A group contributions method for estimating heats of formation of gaseous ions was proposed many years ago1 which has been very helpful in estimating heats of formation of higher molecular weight ions for which data are not available. Accurate data for key compounds are essential for this procedure. Extensive calculations are now being made for heats The Journal of Physical Chemistry, Vol. 60, No. 26, 1976
of formation of alkyl ions2 and the accuracy of experimental data is not always sufficient to test these calculation^.^ Recent measurements have been reported on reversible gaseous ionic reactions of tertiary alkyl ions with tertiary alkanes and thermochemical data have been obtained from the temperature coefficients of the equilibrium constant^.^ Few data from equilibrium measurements are available for comparison, however, and significant discrepancies have been
