Relative bond strengths in ion-molecule clustering reactions

:

Internatidnal Joour?&of Mass Spectrome~ry and ion Physics Elseiier

Publishing

cOm$&xy,

Amsterdam.

: Print&l in tbk Netl&lands

-

RELAT~E REACTIONS.

ROOD.

STRENGTHS

IN

ION-MOLECULE

CLUSTERING

A. GOOD

Department of Chemistry, University of Ceyion, Peradeniya, Sri Lanka (C’eyIon) (First

received20 January 1972; in final form I4 July 1972)

ABSTRACT

A semi-empirical sociation

rate expression has been used to calculate the bond dis-

energies of iorkmolecule

clusters from

their experimentally

observed

third order rate constants_ The ageement between theory and experiment is sufficiently good to enable the estimation of unknown bond dissociation energies by this method, with some reservations in the case of negative ions.

IhmODUCTION

A recent investigation of third-order ion-molecule reactions of the association type’ showed that the available experimental data could be correlated quite well with an energy-transfer mechanism, using the standard GioumouiisStevenson equation2 for the rate of a second order ion-molecule reaction. In the present work, this result will be applied to a comparison of the relative strengths of bonding in a number of ion-molecule clusters. The results obtained will be correlated with the available experimental data wherever possible.

THEORY

The theoretical expression is that derived previously’, with one modification. Correction has now been made for the possibility of an ion-permanent dipole attraction existing between the reactants.- The Gioumousis-Stevenson equation can be modified by assuming that such-an attraction will have a simple additive effect on the total attraction, and hence on the reaction rate. Thus, for a reaction ofthetype: Ii +B + products Int. 3. M&s Spectrok. Ion Phys., 10 (i972/73)

(1) -.

379

the modified equation may easily be derived, as shown by Waltan3,

to be:

(2) In this expression, e represents the charge on one electron, ag and- J+ are, respectively, the polarisability and the dipole moment of the molecule B, and m is the reduced mass. The other symbols have their usual meanings. If the parameters are expressed in terms of the cgs system, then the rate constant has the units molec-l cm3 see-‘. Jf eqn. (2) is then substituted for the Gioumousis-Stevenson result in the previously reported expression’ for the process:

then we obtain the general result, for the forward rate constant,

kf, that:

Here A is the frequency factor associated with the unimolecular decomposition of the cluster (I’ - B)“, AYXis the mass of species X, and s is the Rice-RamsbergerKassel parameter related to the number of vibrational degrees of freedom in the I’ - B cluster. The rRT term represents the internal enerw of the I’ * B cluster in the ground state. Th+.e rate constant k, is expressed, here and subsequently, in the units molec-’ cm6 see- ‘. In the cases where either B or M have permanent dipole moments of zero, or where B and M are chemically identical species, eqn. (4) will be simplified. If the dipole moment of both B and M is zero, then eqn. (4) reduces to the expression which has been previously reported’. It should be noted that, as previously, our model assumes that the efficiency of stabilization of (I’ - B)* can be related simply to the excess energy which is to be removed, as in eqn. (2.4) in ref. 1, and thus that any particular (I’ - B)* species loses a characteristic average amount of energy on each collision. The assumption of a dire; t linear reiationship between the amount of energy to be lost and the number of collisions necessary to lose it, appears to be reasonable for an average molecule. The properties of M, i.e. mass, polarisability and dipole moment, are taken to affect only the collision number. With the choice of reasonable values for the parameters A, r and s it is possible to calculate predicted values for the bond dissociation energies D(I+-B) from the experimentally determined values of kf . Equation (4) may also be used without modification in the treatment of negative ion clustering. 380

ht.

J. Mass Spectrorn. Ion Phys., 10 (1972/73)

RESULTS

Equation (4) was applied to a number of reactions for which experimental rate constant values were available. Clusters of less than four atdms, i.e. where either or both of I’ and B were atomic species, were excluded from study in view of the probable significant contribution of an intermediate-complex mechanism, as in neutral reactions of this type. The choice of parameters was made- follows:

(i) Four-aforn clusters For an 1’ - B cluster containing four atoms, the value of A was taken as 5 x IO’” set-l. The value of r was taken as 3, that is the internal ener_q was regarded as consisting of three translational and three rotational terms, with no vibrational contribution. The value s = 6 was used on the assumption that the cluster was non-linear and that all the vibrational modes could be involved in decomposition_ There is some theoretical evidence’ that the NGi- cIuster may be linear, but this has not finally been established, and n.3 allowance was made for this possibility in the present treatment.

(ii) Larger clusters For I’ - B clusters containing more than four atoms, the A and r vah~s chosen remained the same, but in this case a value of s-2 = &(3N-8) was used, on the assumption that for larger clusters, only about half the vibrational degrees of freedom would be involved. N represents the number of atoms in the cluster. The only exception occurred in the case of the hydrated proton clusters: where the vibrational contribution to the internal energy of the molecule was assumed to be half that expected classically. This assumption was made on the basis of recent infrared investigations of the H50zi fiefs. 5, 6) and H,O,+ (ref. 7) ions which indicated a number of vibrations of a sufficiently low frequency to contribute to the specific heat of the cluster. Thus a value of r = $N was taken in these cases. Possible vibrational contributions to the specific heats of other clusters have not been allowed for.

(iii) Eflect of parameter

values upon D

In view of the way in which the parameter values have b;en assigned, we should consider the effects of an incorrect choice of parameter-. upon the D values. The value taken for the number of active vibrations represents the chief source of possible error. Assuming that this lies between haIf of and all of the total number of vibrations, then the maximum possible error is a factor of two in the (s-2) value, and this would cause the calculated value of D to be squared. However, we might expect errors of similar magnitude for clusters of similar size and ht. J. Mass SpectrLm.

Ion

Phys.,

10 (1972/73)

381

structure, and so rhe relative values obtained should be in better agreement than this. We can then choose a value of A so as to give the best agreement between the theory and experiment. The value of A should also be physically acceptable and our chosen value would be reasonable for first-order neutral decompositions’* ‘. Similar data are not availa.ble for ion-molecule reactions, but values of 3.3 x 1Ol4 and 3.6 x 1014 (set-‘) were calculated for A(O,+) and A(N,+) using known values1 of D and k. A change of a factor of 10 in A would cause the calculated D value to change by a fact or of 101’(s-2). However, as A has been selected by a “normalization” procedure, we cannot strictly separate errors in (s-2) and A_ The data will be internally consistent whatever values are chosen, so long as we assume that we have formulated general laws of behaviour which apply to all the clusters. Thus our interpretation of (s-2) and A in a “physical” sense is not strictly necessary and in the absence of full physical data we might better regard them merely as mathematical constants which are derived from simultaneously solving all those equations for which both II and k are known. In this way we diminish their generality but not their present usefulness. TAijLE

1

CALCULATED

Ah’D EXPERIMENTAL B

N*+

NL

_%I

NZ

Nzf Nz+

Nr

Ne

Nr

He

02+

02

02

02+ o=+ 0=+ 02* 02+ 02+ OZi 0=+ NO+ NO’ NO+ 0‘%+ 0;* Oz* -Nz H30+ HsOz’ H,03+ H904+ co+

01 02 HZ N2 N20 SOS Hz0 COz NO NO Hz0 02

He He He He He He He He NO NO NO He

D Estimated

N2

He

Nz Hz0 Hz0 Hz0 Hz0 co

He Nz Nz Nz 02 co

BOND DISSOCIATION

T

k x 1030

(“K)

(molecuies2 cm6 .7x- ’ )

300 280 82

83 19 120 2.8 2.4 31 G.74 19

300 200 82 s2 82

200 200 300 200 300 300 300 82 82 82 307 307 307 307 344-l

from thermochemical

52

-600 -85 23 5 30 150 -5 -10 -10 3700 2300 2400 900 140

ENERGIES FOR ION-MOLECULE

R
CLUSTERS 1 +-B

Ref_

Dc.1,.

(/cJ mole-

12 14

115 77

14 15 17 i4 17 17 17 17 17 17 19 20,21 19 17 17 17 12 12 12 18 23

37 46 32 27 7 22 105 139 109 84 54 88 119 27 12 11 169 81 63 54 140

‘)

$zoe-

95.4 95.4 95.4 43.9 43.9 43.9 620’

110130”

27.2

151 92.9 72.1 64 118&30”

‘f

13 16

17

18

16

22 22 22 22 23

data.

In?. J. Mass Spectrom. Ion Phys., 10 (1972/73)

I&SCUSSION

The results obtained are listed in Table 1, where they are compared with the available experimental data. The relevant polarisabilities and dipole moments were taken from Moelwyn-Hughes lo . The heats of formation of the various clusters may be calculated from the D-values obtained, uSing the heats of formation of ionic and neutral species as given in the National Bureau of Standards compilation”. (i) Positive ions In the cases where theory and experiment may be compared, the agreement is generally satisfactory, the only serious discrepancy arising in the value of D(Nz+ -N2) calculated from the low temperature rate constant. We may also compare these results with the data of Adams el ~1." who studied various switching reactions of the type: I’-B+C

+ I+-C+B

(51

and thus concluded that D(O,+-B) varied with 9 according to the chemical nature of B, in the sequence B = H,O > SO, > N,O > 0, > N, > Ht. This sequence is borne out by the present data except that D(Oz+-SOz) is calculated to be larger than D(02* -H?O). This discrepancy may be due to the very approximate nature (error limits > 30 %) of the experimental rate constants for 02+ - SO, and 02+ - Hz0 formation17. An error of less than 50 o? in each rate constant, for example, would be sufficient to make D(O,i-SO,) < D(O,‘-H,O). Thus it appears that, in general, the D(l?-B) values obtained in this way are fairly reliable. (ii) Negative ions The available data on negative ion clusters is rather more sparse. However the reaction of Ot - with CO, to give O2 - - CO2 has been studied, and rate constant values of 4.7 x 10m2’ (200 “K; M = He”), 9 x IO- 30 (300 “K; M = CO, (ref. 24)) and 2 x lo-” (300 “K; P/1= O2 (ref. 24)) have been reported. From this, P(02--CO?) values of 105, 88 and 96 kJ mole-’ may be calculated_ These results support the conclusion of Adams et al.", that D(OL--Cot) > -HzO). The latter quantity has been measured25 as 76.9 kJ mole-‘. At the Jw2same time, there is also reasonable agreement with the reported experimental value26 of D(0, --COz) = 76.9 i 8 kJ mole- ‘. The observed rate constant17 for the formation of 02- - N2 (200 OK; M = He)of -4x 10e3’ leads to a calculated value of D(0, ---N,) of 8 kJ mole- l. There is no experimental value with which this may be compared. However the Ink J. Mass Specirom. Ion Phys., 10 (1972173)

383

rate constant value of 4.3 x 10- 31 , measured for the formation of 04-, under the same conditions’ ‘, leads to a calculated dissociation energy of 17 kJ mole- I, which does not agree with the experimental value” of about 56.8 kJ mole-‘. Similarly the other reported value2s of 3 x lOA 31 (298 “K; M = 0,) leads to a calculated D(Ot--02) value of 25 kJ mole- r. Thus the application of eqn. (4) to negative ion clusters is not so well justified by the presently available experimental data.

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Int. J. Mass Spectrom. Ion Phys., 10 (1972/73)