BONDING IN HETEROMOLECULAR IONCLUSTERS
823
1 Bonding in Heteromolecular Ion Clusters. N202+
by G. S. Janik and D. C. Conway Department of Chemistry, Terns A&M University, College Station, Terns
+
(Received July 16, 1966)
Equilibrium constants for the reaction Nz Oz+ = NzOz+ have been determined mass 0.08 kcal/mole, spectrometrically from 177 to 249°K. It was found that A H O Z O=~ -5.69 ASozoo = -18.9 i 0.4 eu, and the bond energy Do(Nz-O2+) = 5.51 i 0.11 kcal/mole. The Do(Nz-02+)is about three times larger and the A S O z o o is at least 2 eu more negative than predicted by the loose cluster model in which it is assumed that the Nz and Oz+ are freely rotating in the complex and isotropic interaction potentials are used. When anisotropic interaction potentials are used in which the ion-quadrupole interaction is considered, the bond energy and entropy change computed from the potential curves are in reasonable agreement with the experimental data.
Introduction When ions are generated in the gas phase, they may form ion-molecule complexes, the so-called ion clusters.2* Equilibrium constants for reactions of the type A B+ = AB+ (1)
+
and bond energies Do(A-B+) have been calculated by Eyring, et C Z Z . , ~ ~ by approximating the interaction potential between A and B+ as the sum of a LennardJones potential between the neutral molecules and the ion-induced dipole interaction energy. In the FER2b model, as in the earlier EHT3 model, the complex is taken to be loose; i.e., it is assumed that the A and B+ are freely rotating in the cluster and isotropic interaction potentials are used. However, it has been shown that homomolecular ion clusters are much more stable than predicted. Thus, Do(Nz-N2+) is seven times larger4 and Do(Oz-O2+)is five times larger5 than those obtained by the FER model. In addition, the model predicts that [04+]/[02+] = 1 at 10 atm pressure at 288’K, whereas this ratio was actually observed a t a few torr. This has been interpreted as evidence for the importance of electron-exchange interactions in homoniolecular ion clusters.6 This still leaves the question of the applicability of the F E R model when the ligand is nonpolar and exchange interactions are a minimum; Le., when the ionization potential difference IP(A) - I P ( B ) >> DO (A-B+). To elucidate the nature of the bonding in such heteromolecular clusters, the equilibrium
*
Nz
+ Oz+ = N2Oz+
(2)
has been studied.
Experimental Section To determine the equilibrium constant for reaction 2, the ion ratio (NzOz+)/(O~+)was determined mass spectrometrically as in the 04+investigation.6 The apparatus and experimental procedure are the same as in the previous investigation except as follows. (1) The gas was purified by passing it over 5-A Molecular Sieve and through two glass bead-packed liquid Nz traps. Nitrogen was condensed in the first trap, so the Nz gas could be purged by bubbling it through the liquid. (2) The gas was cooled by a 0.25411. 0.d. by 8ft Cu coil heat exchanger and passed through a new ionization chamber (Figure 1). The heat exchanger and all but about 2 cm of the apparatus shown in Figure 1 were immersed in a 4.2-1. dewar which was filled with various organic slush baths or a Dry Icetrichloroethylene mixture. The temperature of the bath was determined with a calibrated thermocouple. (3) The sensitivity was increased threefold by using a (1) Taken in part from the doctoral dissertation of G . S. Janik. (2) (a) 9. C. Lind, “Radiation Chemistry of Gases,” Reinhold Publishing Corp., New York, N. Y., 1961; (b) T. Fueno, H. Eyring, and T. Ree, Can. J . Chem., 3 8 , 1693 (1960). (3) H.Eyring, J. 0. Hirschfelder, and H. S. Taylor, J . C h m . Phys., 4,479 (1936). (4) R. N. Varney, ibid., 31, 1314 (1959); 33, 1709 (1960). (5) J. H.Yang and D. C. Conway, ibid., 40, 1729 (1964). (6) D. C. Conway and J. H. Yang, ibid., 43, 2900 (1965).
Volume 71, Number 4
March 1967
824
G. S. JANIK AND D. C. CONWAY
2.1 Ci titanium tritide ionization source. (4) The ions effused into the mass spectrometer through six 18-p holes in the 0.1-mil Pt foil window. ( 5 ) A time-offlight mass spectrometer was used. Since the spectrometer is not a commercial instrument, it will be described in more detail. After entering the spectrometer, the ions were pulsed out of the "trapping grids" (Figure 2) a t a frequency of 29 kHz with the focusing pulse.' The ions were gated by applying a delayed pulse to the gate grids at the end of the drift tube.s The delayed trigger was obtained
,z,
DEFLECTOR GRIDS
FOCUSING LENS
...-
. -.,
8 7
..
I"
.n
10 cm
1
.
Figure 2. Schematic of the time-of-flight mass spectrometer and polarity of the grid potentials. The dashed lines indicate the potentials when either the focus pulse or the gate pulse is applied. Typical static grid potentials ( V )are as follows: 1 and 2, -0.5 and +2.1, respectively (trapping grids); 3 and 4, -490; 5 and 6, -490 (gate grids); 7 and 8, +60 (repeller grids). To pass the repeller grids an ion must have the proper mass and be in the shaded region between G 1 and G2 when G1 is pulsed.
DEFLECTOR GRIDS
ACCELERATING GRO TRAPPING GRIDS
-TRITILM
SOURCE
THERYOCOLUE
TO PRES GAUGE
Figure 1. Ionization chamber and bottom part of the mass spectrometer.
from a Type 546 Tektronix oscilloscope and the gate pulse from a Type 214A Hewlett-Packard pulse generator. Ordinarily, a rather wide gate pulse of 58-v amplitude was used, such that any ion which received a gate pulse would pass the repeller grids and be detected by the Bendix M-306 ion multiplier, which was fitted with a Cu-Be cathode. Under these conditions the effective resolutions M / A M = 27. The ion intensity was determined by conventional pulse-counting techniques. The resolving time of the amplifierion is 10 scaler is 1 psec, and the drift time of the 02+ psec. Thus it can be seen that only one pulse is recorded if two ions of the same mass are pulsed down the drift tube :it the same time. Therefore, the observed counting rate, R, was corrected by up to 3% to the true counting rate, R*, by the relation
R*
= R/(1
Ths Journal of Physical Chemistry
- Rrt)
(El)
where rf is the reciprocal of the (focus) pulsing f r e quency. Since 0 4 + and N4+are much more stable than N202+ and IP(N2) > IP(O2),reaction 2 can only be studied where the 02+is formed by charge with (NJ >> (02) exchange.'" Although (N4f) >> (N2+), a rough estimate of the required 0 2 pressure can be calculated from the rate constant of 2 X 10-lo cc/sec obtained" for charge exchange with N2+ at room temperature. At the maximum flow rate (1000 cc/sec) it takes the ions sec to reach the Pt window, so the O2 pressure must be of the order of torr. Initially (196 and 249°K) sufficient 0 2 was bled into the Nz stream to produce the 02+at this flow rate, but the rest of the data were taken at a flow rate of 250 cc/sec since there was sufficient 0 2 in the "pure" N212to form 0 2 + under these conditions. There were no major and/or N4+. impurity peaks other than 04+ (7) W. C. Wiley and I. H. Mclaren, Rev. Sci. Instr., 26,1150 (1955). (8) W.E.Glenn, Jr., AECD-3337, Jan 1952. (9) This can not be defined quantitatively because of the low intenslty a t the extremes of the peak. If the peaks were gaussian, this would correspond to a 1% contribution of the M AM peak to the M peak intensity. The resolution could be adjusted to 100 (full width at half-height) to prove spectral purity. (10) Simple charge exchange between N z + and 02 is more than 2000 times as probable as the reaction to produce N O + NO [P. Warneck and W. P. Poschenrieder, Bull. Am. Phvs. Soc., 11, 505 (1966)l. (11) W. L. Fite, J. A. Rutherford, W. R. Snow, and V. A. J. van Lint, Discussions Faraday SOC., 33, 264 (1962). (12). Matheson, prepurified grade, with the 0 2 content listed as typically 8 ppm.
+
+
BONDING IN HETEROMOLECULAR IONCLUSTERS
825
Results To prove that reaction 2 is a t equilibrium, the flow rate was decreased by a factor of four from the maximum a t 12 torr and 249°K and a factor of two from 250 cc/sec a t 12 torr and 227°K. In each case the increase in reaction time caused less than a 1% change in the equilibrium constant, KP. This also shows that the m/e = 60 peak is not the complex between NO and NO+ produced by a reaction such as
N2
+ Oz+
+(NO)2+
(3)
+
which is exothermic by 22 Do(NO-NO+) kcal. [On the basis of the small value obtained for AH", -5.69 kcal, it is apparent that the observed (equilibrium) ratio of the 60/32 peaks cannot be [(NO)2+]/ (02+).] Since the ion density is a function of flow rate, these experiments also show that the electric field strength in the ionization chamber was not large enough t o cause an appreciable increase in the kinetic energy of the ions.5 The twofold reduction in flow rate a t 227°K resulted in a fourfold reduction in ion intensity. The average of the equilibrium constants determined at four N2pressures, p (3,6,9,and 12 torr), are reported in Table I. Two corrections have been applied to
and the ion in the denominator of the Kp expression (see Appendix). No correction was made for mass discrimination by the ion multiplier, although this was minimized since the ions were accelerated to 5000 v between the repeller grids and the cathode of the ion multiplier and the pulse-counting technique was used. The usual method of evaluating the enthalpy change, AH", is from a plot of log K vs. 1/T. However, this is not a good method when AH" is small and there is a large contribution to the heat capacity from the internal degrees of freedom. In the present case there are not very many internal degrees of freedom, so the heat capacity change, ACpO, could be estimated or even assumed to be zero to obtain AH". I n the latter case AH"20~= -5.64 kcal/mole for reaction 2. However, to obtain AHoo the vibrational frequencies of the weak modes must be estimated. In addition, it is best to treat all ion-cluster data by a general method which can be used for the large clusters which have been studied6 where heat capacity effects are relatively large. In this met,hod standard free energies are evaluated a t each temperature from the relation AGO = -RT In 760Kp. The left side of eq E3 is computed as a function of the temperature difference, AT, and AG2'
- (ACP")TR[AT - TZIn (Tz/Tl)] (AH2O)v
Table I: Corrected Equilibrium Constants, KP, for Reaction 2
+ (AHio)v + T2[(AS2O)v (ASio)v] = AGIO
Temp,
K,
x
- ATASi'
(E3)
108
OK
torr-1
177.3 195.5 227.4 249.1
937 f 31= 212 f 8 32.0 f 0 . 7 8 . 7 2 f 0.25
A G O l
and the entropy change, ASol, a t temperature
T1 are determined by least-squares analysis. In this
equation (ACP")TR is the contribution to the heat capacity change in reaction 2 from the translational and rotational degrees of freedom and (AHOJv and a Standard deviation. (AS",)v are the change in enthalpy and entropy, respectively, a t temperature Ti due to the weak vibrational modes. Contributions from the strong modes these constants. (1) The uncorrected constants ( K P ) ~ are assumed to cancel. On the basis of entropy conwere found to decrease by up to 18% over this pressure siderations and theoretical calculations to be presented, the NzOz+ is taken to be nonlinear with no internal range. Since the drift tube pressure p d a p and N202+ rotations, so there are four weak modes. The frehas the larger geometrical cross section, it is possible quencies of these modes were estimated by an iterative that this is caused by the N202+ being preferentially scattered out of the ion beam in the drift tube. The technique since the frequencies must be derived from slope of each In ( K P )vs. ~ pd curve was used to correct ASl" by statistical mechanics in order to calculate the constants to ( K p ) O a t zero pressure. (2) Mass dis(AHoi)v and (ASor)v. Since the frequency distribution of the weak modes crimination occurs in mass transport to the window of is unknown, two vibrational models were used. In the spectrometer and in the trapping grids. The result of an approximate analysis is model I all frequencies were assumed to be the same; in model I1 the frequencies were distributed over a KP = (KP)O[(md -k M I / ( % M)]"' (E21 factor of five in a geometrical series. It can be seen from the results given in Table I1 that ASOZOO is relawhere M , m,, and md are, respectively, the masses tively insensitive to the uncertainties in the frequency of the neutral gas molecule, the ion in the numerator,
+
Volume 71, Number 4
March 1967
826
G. S. JANIK AND D. C. CONWAY
Table 11: Entropy Data for Reaction 2 a t 200’K (in cal/mole deg) Max A
Geometry
P Tb
3.25 3.25 2.90 2.90
Rectang Rectang
ASom
( A s ” )tran
- 18.95c - 18,94c - 18.95‘ - 18.93’
-32.08 -32.08 -32.08 -32.08
‘Distance between molecular centers a t potential minimum.
(Aso)rot
(Aso)vib
3.12 3.12 3.25 3.25
10.01 10.02 9.88 9.90
* 02+is a t the top of the T.
distribution and the geometry of the cluster. This is 0.08 kcal/ also true of A H o z m which equals -5.69 mole for the four cases considered. By correcting AHozooto OOK, Do(Nz-Oz+) is found to be 5.53-4 and 5.47-8 kcal for models I and 11,respectively.
*
stretching mode, the computed ASozM,is 2.3 eu more positive than the experimental value, which shows that the Oz+ and NZ are not freely rotating in the cluster. In addition, the experimental bond energy is about three times larger than predicted by this model. The entropy disparity suggests that the FER model be modified by introducing the anisotropy in the interaction potentials. We would also like to account for the nonuniformity in the electric field near an ion by considering the interaction between the charge on the 0 2 + and all the permanent and induced point electric multipoles on the N2.l3 However, because of the dearth of experimental data, the only interactions we can consider are the ion-induced dipole (VID)and the ion-quadrupole (VQ). The total potential is then
VT
=
VR
+ VD + VID + V Q
034)
where V R and VD represent, respectively, the repulsive and attractive parts of the van der Waals interaction between the neutral molecules. VD. Three models are used to account for the molecular attraction (dispersion) interaction. The first two are normalized to the experimental average potential (VD) = -(c)/S6 at the potential minimum (S,) = 3.861 A by assuming all collision angles to be equally probable. From viscosity data the value of (c) is found to be 1180 kcal A8.14 To use the London formulation15 of the interaction energy (model D l ) , one must assume that TI = s2 and PI’ = TZ’, where PI and rz represent the “characferistic mean (electron) oscillation frequencies” along and perpendicular to The J O U To j~Physical C h m k t r y
om -1
I
110 251 112 256
I1 I
I1
Standard deviation = 0.39 eu.
the Nz bond axis, respectively, etc., for Oz+, The equation for VD is then
alaz‘)X (sin 6 sin 8’ cos cp
Discussion If we use the FER loose cluster model with S, = 3 A and neglect the entropy associated with the weak
fw,
Vib model
-
~ ( ( Y I ~ z ’
a z a 2 ~cosz ) e
cosz e’
+
+
a2ai’
- 2 cos e cos
+
- a z a z / )x
~((YzCY~‘
+ aiaz’ +
~CYZCYZ’]
(E5)
+
where a = a1/3 2az/3 and a’ are angle average polarizabilities see (Figure 3). The bond polarizabilities are a1 = 2.43, a2 = 1.43, al’= 2.43, and az’ = 1.19 X lowz4cc.16 Model D1 is the only “dispersion” model in which the anisotropy in polarizability is considered. In the next two models, VD is taken to be the sum of isotropic atom-atom interactions. A
In model D2 c is obtained by equating - (c)/(S,$ to the angle average of E6 at (S,). The integration is straightforward. In model D3, c is calculated from the Slater-Kirkwood equation by the method outlined by Scott and Scheraga” except that the atomic polarizabilities are taken to be one-half the (molecular) angle average polarizabilities. VR. In all three repulsion models V R is taken to be the sum of atom-atom interactions. In model R1 4
j=1
(13) (a) A. D. Buckingham, Discussions Faraday SOC., 24, 151 (1957); (b) J. Stecki, Advan. Chem. Phys., 6 , 413 (1964). (14) J. T. Vanderslice, E. A. Mason, and W. G. Maisch, J. Chem. Phys., 31, 738 (1959). These authors use semiempirical combination rules to obtain the N r O z potential from the Nz-Nz and O r O z potentials. (15) F. London, J . Phys. Chem., 46, 305 (1942). (16) K. G. Denbigh, Trans. Faraday SOC.,36, 936 (1940). (17) R. A. Scott and H. A. Scheraga, J . Chem. Phys., 42, 2209 (1965).
BONDING IN HETEROMOLECULAR IONCLUSTERS
827
Table 111: Potential Minima Calculated for Nz-02+ by E q E4-E9 for
x
Q
= 0’
Sm,b
e’ = 900
modela
kcal
A -1
kcal AS
A
6 = 900
900 00
D1-Rl D2-R1 D3-R2 Dl-R3
2.103 2.103 2.55 0.0371
4.471 4.471 4.59 2.654
*.. 238 355
3.25 3.25
-1.76 -1.43 -2.31 -0.17
-4.84 -5.08 -6.07 -2.52
VD-VR
a
b,
10-5,
These models are discussed in the text.
C,
...
3.15 3.70
00
00 900
00
-3.44 -3.60 -4.22 -2.01
-0.69 -0.74 -1.26 -0.06
S a t the potential minimum for most stable geometry.
the angle average of VR is fitted a t (S,) and 3.2 A to the experimental average potential (VR) = 3.04 X lo6 e-4.403s obtained from viscosity data.14 The equation relating (VR) to a and b has been given previ0us1y.l~ Model R2 is the model used by Scott and Scheraga” where D3 is used for the dispersion interaction, b is estimated by interpolating rare gas data, and a is estimated by minimizing the atom-atom Figure 3. Geometrical relationships for the N ~ O Zcomplex. potential curve a t the sum of the van der Waals radii Here d‘ and d are the internuclear separations in OZ+and Nz, taken from Bondi.l* In model R3 the values of a respectively, and ‘p is the angle between the Sd and Sd’ and b are those obtained by Vanderslice, et ~Z.,~*from planes. The electric field vector a t the center of the N, molecule lies in the plane defined by the z the potential curves for various states of NO by use of (dashed line) and z (bond) axes of the molecule. certain quantum-mechanical relations derived by a modified “perfect pairing appro~imation.”’~ VID. It is assumed that there is a charge q j = VID = -3.31, and VQ = -2.39 kcal/mole. The + e l 2 a t each 0 nucleus, so quadrupole moment has a strong influence on orientation; if it were zero, the rectangular geometry would VID =: -C ? ? q j COS yjn/Lj2 (E@ have the largest computed bond energy. n-1 2 j=1 As an independent check on the accuracy of the comVQ. The equation for VQ is13a puted potential curves, they will be used to estimate 2 (ASo),ib. It is assumed that the four weak modes that VQ = C @(3 COS’ yji - 1)/2Lj9 (E91 contribute to ( A L S ” ) are ~ ~ ~completely decoupled from j=1 the strong N2 and 02+stretching modes. I n addition, where the quadrupole moment Q = f(3z2 - r2)pdv/2 to simplify the computation, it is assumed that only for the linear molecule. Here p is the charge density one molecule moves in each of the Bz modes. The a t r and z is the projection of r on the symmetry axis. weak modes are then as follows: (1) N2-OZ+stretch Q is taken to be - (1.3 f 0.2) X where (AI), (2) Nz out-of-plane torsion (Bl), (3) Nz in-plane the sign of the moment comes from theoretical calcutorsion (B2), and (4) Oz+ in-plane torsion (B2). The lations.21 computed curves for in-plane motion are shown in Equations for r,, L,, and cos yjn were derived from Figures 4 and 5. The frequencies are estimated from the law of cosines (Figure 3) and used in evaluating the shapes of the curves a t S, in the usual way,22exVT on a digital computer. The computed potential torsion where the potential function cept for the 02+ minima are given in Table 111. It can be seen that the cos 20’)/2 is fitted to the potential A(VT) = Vo(l most stable structure is predicted to be T shaped and, curves with 0’ 2 54”. (At 200°K it is expected that with the exception of the last model, the agreement with the experimental bond energy is now good. How(18) A. Bondi, J . Phys. Chem., 68, 441 (1964). ever, model Dl-R3 is the poorest one for the present (19) C. A. Coulson, “Valence,” Oxford University Press, London, calculation as the R3 potential is not valid when r, > 1952, pp 166184. (20) G. Birnbaum and A. A. Maryott, J . Chem. Phys., 36, 2032 -2.8 A, whereas the potential curve derived from (1962). the viscosity data is reliable when S > -3.2 A.14 (21) C. W.Scherr, ibid., 23, 569 (1956). Let us consider model D1-R1 with 6’ = 90” and 6 = (22) G. Herzberg, “Molecular Spectra and Molecular Structure, 0” in more detail. At S,, VR = 1.85, V D = -0.99, D. Van Nostrand Co., Inc., Princeton, N. J., 1945, pp 62, 226. +
[’
1’
+
”
Volume 71, Number 4 March 1967
828
G. S. JANIK AND D. C. CONWAY
2145
2:70
2:95
3:20
3:45
3:fo
3:95
4:20
4a5
4%
4 95
S E PA RATION ( A NG.$ Figure 4. V T us. S when 8' = 90" and 'p = 0". The angle B between the axis of the N1 molecule and S is indicated for each curve. The potential energy curves for 8' = 90" and 'p = 90" are very similar to these.
e' < 54" in only a small fraction of the oscillations.) The results are w1 = 136, w2 = 102, w3 = 99, and w4 = 116 cm-1 from which (ASo)vi~ = 9.85 eu, in good agreement with the experimental result of 10.0 eu. From w1 the computed value of Do(N2-02+)for model D1-R1 is 4.65 kcal, somewhat lower than the experimental result. The computed bond energy would be larger if the V R V D potential were corrected for the plus charge on the 02+and if hyperpolari~ability'~* were considered. The first correction is probably not large, as the correction for model D3-R2 is estimated to be only 0.3 k ~ a 1 . The ~ ~ next terms in the chargemultipole interaction equation for N2 are the ionhexadecapole term (0: Lj-6) and the term ( a IJ,-~) for the interaction between the gradient of the field and the quadrupole moment induced by the gradient of the field.13E It is possible that these two interactions are not very important a t the molecular separations of interest, since the uncertainty in V R V D V Qis as large as the difference between the experimental and computed bond energies.
+
+
+
Appendix An analysis of mass transport throughout the ionization chamber is difficult because of the lack of symThe Journal OF Physical Chemistry
metry and certain uncertainties, such as the rate of ionization and the electron temperature. In addition, it appears that only part of the data was taken a t the ambipolar diffusion limit.24 However, to determine the mass discrimination factor, the mass transport equation
rc0=
- Dt(dnt/dz)
+ k1n& + nrvz
(E10)
need only be solved in the region close to the window. Here rts,E,, and Y, are, respectively, the ith ion current per unit area, the electric field strength, and the linear velocity of the gas stream in the z direction (normal to the Pt window). The diffusion coefficient, Dl, and mobility, ICt, for each ion of density nl are related by the equationlZ4D J k , = kT/e, where k is the Boltzmann constant. It is estimated that the Zn, varied from 1 X 106 cc-1 (3 torr, maximum flow) to 2 X lo7 cc-l (12 torr, one-fourth maximum flow). These ion densities correspond to Debye lengths,24 A+ for the positive ions of 0.08-0.02 cm. Let us confine our discussion to the region within 0.5A+ of the window (23) The method used is similar t o that outlined in ref 5 and is not considered to be very accurate. (24) W. P. Allis and D. J. Rose, Phys. Rev., 93,84 (1954).
BONDING IN HETEROMOLECULAR ION CLUSTERS
829
25 Figure 5. VT us. S when e = 0” and cp = 0”. The angle 6’ between the axis of the Oz+ ion and S is indicated for each curve.
where it is certain that -D,(dn,/dx) >> ntv,. Therefore, the last term in eq E10 can be neglected and the resulting equation solved to yield
+
since25D, 0: [(na, M)/rn,M]”2 where mi and M are the masses of an ion and neutral gas molecule, respectively. The next question is whether or not reaction 2 is at equilibrium 0.5X+ from the window. The ni decreases fairly rapidly between 0.5X+ and the wall,24so the diffusion term in eq E10 can be taken to be dominant. The mean time, T,, for an ion to reach the wall is then -X+2/8Di = secZ6 The mean time, T ~ for ~ re, action 2 to approach equilibrium can be estimatedn from the rate constant for ion-molecule collisionsa*2* and the estimated rate constant for dissociation of the resulting N202+*.29 It is found that T, >> req, which means that reaction 2 is a t equilibrium within 0.5X+ of the window and the equilibrium ratio (nl/n2)eq is given by eq Ell.30
The time that an ion spends between the trapping grids is A d & , where A is a constant. Therefore, the probability that an ion which enters the spectrometer will be between the trapping grids when the focus pulse is applied is A l / m 2 / r P Combining this result with that given above, we find that (nl/ndep = (IdIdI(m2
+ M ) / ( r n +~ M)1”’
(E12)
where I1/Iz is the observed ion current ratio. Acknowledgments. The authors wish to thank The Robert A. Welch Foundation for its generous support of this research and the Phillips Petroleum Co. for awarding G. S. J. a fellowship. (25) L. B. Loeb, “Basic Processes in Gaseous Electronics,” University of California Press, Berkeley, Calif., 1961, p 53. (26) See ref 25, pp 53, 191, 200. (27) D. C. Conway, J . Geophys. Res., 69, 3304 (1964). (28) K. Yang and T. Ree, J . Chem.Phys., 35, 558 (1961). (29) (a) M. Burton and J. L. Magee, J. Phys. Chem., 56, 842 (1952); (b) R. A. Marcus and 0. K. Rice, ibid., 55, 894 (1951). (30) Given that the reaction is at equilibrium far from the window, the other limit is when there is a point close to the window where niv,>> - Di(dni/dz) kiniE, and sea>> sW. Then ( n ~ / n a=) ~ ~
n./n,.
+
Volume 71,Number 4
March 1967
