Thermokinetic Determination of Gas-Phase Basicities. Application to Ketene, Methylketene, and Formaldimine

Article abstract of DOI:10.1021/jp960761h

Rate constants have been determined for proton transfer reactions of the type (1+) + B ->/<- M + (1+), where M is ketene, methylketene, and formaldimine and B is a reference base.A quantitative relationship between the rate constant and the free energy (or enthalpy) of the reaction allows the determination of the gas-phase basicity, GB, (or proton affinity, PA) of M.This thermokinetic method gives results comparable to that obtained from equilibrium constant measurements.The values derived for ketene, methylketene, and formaldimine follow: GB(ketene) = 788 +/- 3 kJ/mol, PA(ketene) = 817 +/- 3 kJ/mol; GB(methylketene) = 809 +/- 3 kJ/mol, PA(methylketene) = 842 +/- 3 kJ/mol; GB(formaldimine) = 830 +/- 3 kJ/mol and PA(formaldimine) = 860 +/- 5 kJ/mol.Heats of formation of methylketene and of formaldimine that may be deduced from a combination of these results with literature data are as follows: ΔH_f⁰₃₀₀(CH3CHCO) = -97 +/- 5 kJ/mol and ΔH_f⁰₃₀₀(CH2=NH) = 75 +/- 5 kJ/mol.

Full text of DOI:10.1021/jp960761h

J. Phys. Chem. 1996, 100, 16555-16560
16555
Thermokinetic Determination of Gas-Phase Basicities. Application to Ketene,
Methylketene, and Formaldimine
Guy Bouchoux* and Jean-Yves Salpin
Laboratoire des Me´canismes Re´actionnels, UA CNRS 1307, Ecole Polytechnique,
91128 Palaiseau Cedex, France
ReceiVed: March 12, 1996; In Final Form: July 8, 1996X
Rate constants have been determined for proton transfer reactions of the type [MH]+ + B / M + [BH]+,
where M is ketene, methylketene, and formaldimine and B is a reference base. A quantitative relationship
between the rate constant and the free energy (or enthalpy) of the reaction allows the determination of the
gas-phase basicity, GB, (or proton affinity, PA) of M. This thermokinetic method gives results comparable
to that obtained from equilibrium constant measurements. The values derived for ketene, methylketene, and
formaldimine follow: GB(ketene) ) 788 ( 3 kJ/mol, PA(ketene) ) 817 ( 3 kJ/mol; GB(methylketene) )
809 ( 3 kJ/mol, PA(methylketene) ) 842 ( 3 kJ/mol; GB(formaldimine) ) 830 ( 3 kJ/mol and
PA(formaldimine) ) 860 ( 5 kJ/mol. Heats of formation of methylketene and of formaldimine that may be
deduced from a combination of these results with literature data are as follows: ∆Hf°300 (CH3CHCO) ) -97
( 5 kJ/mol and ∆Hf°300 (CH2dNH) ) 75 ( 5 kJ/mol.
Introduction
A more qualitative technique, the “bracketing method”,
consists of the appreciation of the occurrence/nonoccurrence
Gas-phase acidities and basicities of molecules provide
important keys to the understanding of ion/molecule chemistry,
both in the gas phase and in solution. Their precise determi-
nation is consequently of interest, and several methods are
currently used whereby these thermochemical quantities may
be obtained, each of them possessing its proper advantages and
limits.
A large amount of the presently available data1-4 is coming
from the measurement of the equilibrium constant of the proton
transfer reaction:
of the proton transfer reaction (I) when the base B is varied.
This method was first expected to give a bracketing of the proton
affinity of M, but it seems more likely that it provides
information on the gas-phase basicity.6,7
Finally, we recently7 observed that the correlation between
the experimental rate constant for the proton transfer reaction
I, kexp, and its free enthalpy change, ∆G°I, may be described
by a relationship of the type
kexp
kcoll
1
)
(1)
1 + e(∆G° +∆G° )/RT
I
a
[MH]+ + B / M + [BH]+
(I)
where kcoll is the collision rate constant and ∆G°a an apparent
energy barrier for reaction I. It has been demonstrated7 that
the reaction efficiency RE ) kexp/kcoll may be fitted by the
parametric function
The equilibrium constant for reaction I, KI, directly leads to
the corresponding free enthalpy change which is also equal to
the gas-phase basicity difference: ∆G°I ) -RT ln KI ) GB(M)
- GB(B). When the entropy variation ∆S°I can be reasonably
estimated, a value for the enthalpy change ∆H°I ) ∆G°I +
T∆S°I, i.e., the proton affinity difference ∆H°I ) PA(M) - PA-
(B), may be also deduced. Moreover, if the equilibrium constant
can be measured at various temperatures, both ∆H°I and ∆S°I
may be obtained from a van’t Hoff plot of ln KI against 1/T.
The second source of thermochemical information concerning
acidities and basicities of gaseous molecules is given by the
so-called “kinetic method”.5 In these experiments the dissocia-
tion of a series of proton bound bimolecular clusters [M‚‚‚H‚‚‚B]+
a
RE )
(2)
1 + e[b(-GB(B)+c)]
with a being a normalizing factor, c ) GB(M) + ∆G°a, and b
) 1/RT* (T* is the “effective” temperature of the system). After
examination of several series of proton transfer reactions, it has
been observed that ∆G°a is of the same order of magnitude as
the term RT*. Consequently the gas-phase basicity of M may
be approximated by GB(M) ≈ c - 1/b. It has been shown that
the preceding relationship allows the determination of unknown
gas-phase basicities with good precision ((5 kJ/mol), either by
fitting of the experimental data and extraction of the parameters
a-c or by an extrapolation procedure.7
MH+ + B
[M•••H•••B]+
BH+ + M
Relation 2 may be extended to the proton affinity determi-
nation by using eq 3, with again b ) 1/RT* but, that time, c′ )
PA(M) + ∆G°a - T∆S°I.
is examined in order to deduce the relative basicities (or proton
affinities) through the relationship:
a
RE )
(3)
1 + e[b(-PA(B)+c′)]
ln([MH]+/[BH]+) ≈ ∆GB/RT (or ∆PA/RT)
The proton affinity of M may thus be approximated by PA(M)
≈ c′ - 1/b + T∆S°I. The precision of this latter relationship is
X Abstract published in AdVance ACS Abstracts, September 1, 1996.
S0022-3654(96)00761-7 CCC: $12.00 © 1996 American Chemical Society

16556 J. Phys. Chem., Vol. 100, No. 41, 1996
Bouchoux and Salpin
TABLE 1: Summary of the Experimental Determinations
of the Gas-Phase Basicity of Ketene
limited by the range of ∆S°I values; clearly a good precision is
obtained only in the cases where a set of reactions (I) possessing
similar entropic variations ∆S°I is considered.
Another way to use expression 2 or 3, which avoids the
approximation ∆G°a ≈ RT*, consists of comparing the relative
efficiency curve of the unknown M with that of a standard;
this procedure will be used later on in this paper.
Each of these four methods of determination of gas-phase
basicity possesses their domain of applicability. The “equilib-
rium method” needs the equilibration of [MH]+ and [BH]+ ions
in a mixture of neutrals M and B; this procedure obviously
necessitates that the two latter molecules are stable species but
also that the structures of M and B are conserved during the
protonation/deprotonation process. Thus, the equilibrium method
is not appropriate if an isomerization or a dissociation process
is induced by the protonation. The “kinetic method” is subjected
to the formation of the primary proton bound cluster which may
also depend upon the stability of M and B and the possibilities
of unwanted isomerization or dissociation processes.
ref
12
method
base B
acetone
isobutene
tetrahydrofuran +5.0
methyl acetate -1.7
acetone
acetone
isobutene
ethyl formate
diethyl oxide
dimethyl oxide
isopropanyl
alcohol
∆G° a GB(B)b GB(CH2CO)c
equilibrium
(ICR)
equilibrium
(ICR)
+0.8
-6.6
783.3
776.3
(795.2)
788.2
783.3
783.3
776.3
782.5
782.8
790.2
789.9
789.6
784.1
783.4
786.3
785.5
767 ( 2
13
14
-6.3
-0.8
-7.1
equilibrium
(HPMS)
-15.1 771.2
+15.0 800.5
15
bracketing
-
+
766.2
769d
this
work
thermokinetic see Table 2
788 ( 3
a ∆G° (kJ/mol) of the reaction [CH3CO]+ + B f CH2CO + [BH]+.
b GB values (kJ/mol) from GB(B) ) PA(B) + T[∆S°1/2(B) - S°H ],
+
+
with T ) 300 K and S°H ) 109 kJ/mol. PA(B) and ∆S°1/2(B) are
taken from ref 3. c GB(CH2CO) ) GB(B) - ∆G° (kJ/mol). d From ref
1a. GB(i-C3H7OH) ) GB(NH3) - 49 ) 769 kJ/mol.
The “bracketing” and the “thermokinetic” methods are not
subjected to the above mentioned constraints intrinsic to the
equilibrium or the kinetic techniques. In particular thermo-
chemical information on unstable neutral species, or simply of
neutrals hardly amenable to experiments, may be obtained.
Moreover, the basicity of a neutral corresponding to the
deprotonated form of a fragment ion may be also established
by these methods as it will be illustrated thereafter.
In the present study, we report the data obtained using the
thermokinetic method to determine the basicity of ketene,
methylketene, and formaldimine. Experiments were conducted
in a Fourier transform ion cyclotron resonance (FT-ICR) mass
spectrometer equipped with an external ion source. The [MH]+
ions are produced in the external ion source by dissociative
ionization of a suitable neutral and then allowed to react in the
ICR cell with the reference bases B.
time. The concentration of the neutral was determined from
its indicated pressure (PB) after calibration of the ionization
gauge with the reaction [CH3OH]•+ + CH3OH f [CH3OH2]+
+ •OCH3 (k ) 2.53 × 10-9 cm3‚molecule-1‚s-1 9). The relative
gauge sensitivity was corrected by taking into account the
polarizability, R, of the neutrals.10 The accuracy of the so
derived experimental rate constant values is ca. (10%. The
collision rate constants, kADO, were calculated using the average
dipole orientation theory.11 Tables 2-4 contain the kexp and
kADO so determined for the reactions [MH]+ + B / M + BH]+
under investigation together with the polarizability and the dipole
moment of B. Since only relative values of the reaction
efficiencies are of interest here, these quantities are normalized,
for each set of data, by defining the relative efficiency as RE
) (kexp/kADO)/(kexp/kADO max
)
.
Experimental Section
Results and Discussion
Three sets of proton transfer reactions have been studied
which involved (i) acetyl cation, (ii) propanoyl cation, and (iii)
immonium [CH2NH2]+ cation with several reference bases B.
Experiments were performed on a Bruker Spectrospin CMS 47X
FT-ICR mass spectrometer equipped with an external ion
source.8 The acetyl cation, propanoyl cation, and [CH2NH2]+
cations were generated by dissociative ionization of acetone,
3-pentanone, and propylamine, respectively, in the external ion
source (typical conditions were as follows: filament current, 4
A; electron energy, 30-70 eV; ionizing pulse duration, 10 ms).
All of the ions resulting from electron ionization were transferred
to the reaction cell located inside the 4.7 T superconducting
magnet. Selection of the ion of interest was done by ejection
of unwanted ions by a combination of chirp and soft radio
frequency (rf) pulses. The reactants were relaxed to thermal
energy (T ) 300 K) by introducing argon inside the ICR cell
at a pressure approximatively 1 order of magnitude greater than
the pressure of the neutral reactant and by imposing a relaxation
delay of 2-6 s after selection of the reacting ions.
Ketene. Protonation of the ketene molecule is expected to
occur preferentially on the terminal carbon atom. Accordingly,
the acetyl cation [CH3CO]+ is predicted by molecular orbital
calculations, at the MP3/6-31G**/HF/4-31G + ZPE level,28 to
lie 181 kJ/mol below the oxygen protonated form [CH2COH]+;
these two structures are the most stable in the [C2H3O]+ system.
The protonation thermochemistry of ketene has been inves-
tigated experimentaly by several groups in 1977-1978.12-15
A
brief survey of these studies will be done before considering
the effects due to the reevaluation of the standards in the basicity
scale.
Ausloos and Lias studied12 the equilibrium involving proto-
nated acetone and ketene in a pulsed ICR spectrometer. From
the equilibrium constant measurement and estimate of the ∆S°
correction they concluded that PA(ketene) ) PA(acetone) +
0.7 kJ/mol. The authors further reevaluate the PA value of
acetone from the proton transfer equilibrium between acetone
and isobutene, and they finally propose PA(ketene) ) 811 ( 4
kJ/mol. In a comparable experiment using a trapped ICR
spectrometer, Vogt et al.13 explored the equilibria involving
ketene and (i) protonated tetrahydrofuran or (ii) protonated
methyl acetate to deduce GB(ketene) ) 790 kJ/mol and PA-
(ketene) ) 820 ( 8 kJ/mol. In the same study, and in contrast
with Ausloos and Lias,12 it is found that ketene is more basic
than acetone. High-pressure mass spectrometry was also used
to measure the proton affinity of ketene.14 Proton transfer
equilibria involving ketene with acetone, ether, isobutene, and
ethyl formate lead to a proton affinity value of PA(ketene) )
Next, the ions were allowed to react for a variable time with
neutral bases B. Experiments were conducted at a constant
pressure in the range of 10-8 to 10-7 mbar, as indicated by the
ionization gauge (Balzers-IMR-132) located between the high-
vacuum pump and the cell housing. The intensities of the peaks
were determined in the frequency domain after Fourier trans-
formation of the corresponding time domain signal.
The bimolecular rate constants kexp were deduced from the
slope of the logarithmic plot of reactant ions versus reaction

Thermokinetics of Gas-Phase Basicities
J. Phys. Chem., Vol. 100, No. 41, 1996 16557
TABLE 2: Efficiencies of Proton Transfer Reactions Involving [CH3CO]+ and Several Bases B
PA(B)
(kJ/mol)
GB(B)c
(kJ/mol)
∆S°1/2(B)d
(J/(mol K))
PB
(mbar)
Re (Å3)
µ (D)
kexp
kADO
REi
h
h
base B
dimethyl ether
isobutene
isopropylcyanide
acetone
methyl acetate
ethyl acetate
3-pentanone
diisopropylketone
793.3a
802.1a
808.3a
810.4a
815.9a
828.9a
833.9a
852 ( 1b
766.2
776.3
775.6
783.3
788.2
800.6
804.3
821.1
18.8
23.0
0
18.8
16.7
14.6
10.5
(6)
5.16
7.92
8.05
6.37
6.81
8.62
9.93
13.53
1.31f
0.50f
4.04g
2.88f
1.71f
1.78f
2.72g
2.67g
1 × 10-7
0.6
15.59
13.81
30.50
24.07
17.13
18.05
23.28
23.68
0.0004
0.014
0.015
0.078
0.301
0.827
0.974
1
1 × 10-7
0.16
0.38
1.48
4.19
12.2
18.4
19.3
8 × 10-8
1 × 10-7
2.0 × 10-8
1.14 × 10-8
1.0 × 10-8
1.8 × 10-8
a From ref 3; the more recent value PA(isobutene) ) 801.7 ( 1.4 kJ/mol 36 fully confirms the anchoring of this basicity scale. b From ref 33.
c GB(B) ) PA(B) + T[∆S°1/2(B) - S°H ], with T ) 300 K and S°H ) 109 J/(mol‚K). d From ref 3. ∆S°1/2(B) is the standard entropy difference
+
+
+
between the protonated and the neutral form of B. When the experimental data are not available, as ∆S°1/2(B) equal to R ln(σB/σBH ) (where σ is
the relevant symmetry number) has been assigned; this estimate is indicated in parentheses. e Polarizabilities from ref 10b. f Dipole moment from
ref 33. g Dipole moment calculated by the AM1 semiempirical procedure.35 ×10-10 cm-3‚molecule-1‚s-1
.
i Relative reaction efficiency: RE )
h
(kexp/kADO)/(kexp/kADO
)
max
.
816 ( 2 kJ/mol. The ion chemistry of ketene was studied using
an ion trap device.15 The proton affinity of ketene was estimated
to lie between PA(CH3OCH3) and PA(CH3OCH3) and PA(C3H7-
OH) by the bracketing technique, thus leading to PA(ketene)
) 798 ( 5 kJ/mol.
The range of published values for the proton affinity of ketene
(798-820 kJ/mol) must be now reconsidered in view of the
most recent anchoring of the basicity scale. Table 1 summarizes
the various experimental, objective data and the GB(ketene)
values that may be deduced using the GB scale of Szulejko
and McMahon.3
It may be seen that the GB values derived from the published
data are in fact situated in the range 767-790 kJ/mol.
Significantly enough, a mean value of GB(ketene) ) 786 ( 3
kJ/mol is obtained if one considers only the nine results obtained
by the equilibrium technique.12-14 The value of 767 kJ/mol
deduced using the bracketing technique from ion trap experi-
ments15 appears to be seriously underestimated.
The thermokinetic method has been applied to the ketene
molecule by considering the deprotonation reactions:
[CH3CO]+ + B f CH2CO + [BH]+
(II)
occurring into the ICR cell of the Bruker FT-ICR spectrometer.
The acetyl cation has been produced in the external source of
the instrument by dissociative ionization of acetone, and various
bases B have been used for reaction II. The experimental rate
constant, kexp, and the theoretical rate constant, kcoll, are collected
in Table 2 together with the relevant thermochemical data.
The curve corresponding to the relative efficiency of reaction
II with respect to GB(B) is reported in Figure 1. The fit is
characterized by a normalizing factor a of 1.01 ( 0.05 and by
values of parameters b and c of 0.22 ( 0.07 kJ-1‚mol and 792.6
( 0.8 kJ/mol respectively. Using the observation7 that GB(M)
≈ c - 1/b, we derive GB(ketene) ) 788.1 kJ/mol.
Figure 1. Representative curves of proton transfer reaction efficiency
versus GB(B) for reaction [MH]+ + B / M + [BH]+ (M ) ketene,
methylketene, and formaldimine).
GB(acetone) ) 783.3 kJ/mol and GB(isobutene) ) 776.3 kJ/
mol,3 we conclude that GB(ketene) ) 787.9 ( 2.5 kJ/mol.
In summary the experimental data coming from the thermo-
kinetic method point to a gas-phase basicity of ketene being
GB(ketene) ) 788 ( 3 kJ/mol in excellent agreement with the
results of the equilibrium method, but higher by no more than
21 kJ/mol from the value obtained by ion trapping experi-
ments.15
The determination of the proton affinity, PA(ketene), may
be similarly done by considering relationship 3. It has been
pointed out that a good correlation of RE with PA(B) is expected
only for a series of reactions characterized by a comparable
T∆S°I term. This is indeed the case for the data collected in
Table 2 if one excludes the isopropylcyanide molecule (see
Table 2 and ref 7 for acetone and isobutene). The resulting
curve is presented in Figure 2. The parameters a-c are equal
to 1.01 ( 0.02 and 0.21 ( 0.02 kJ-1‚mol and 820.6 ( 0.7 kJ/
As already mentioned in the Introduction, another way to use
the relative efficiency curve consists of comparing the unknown
to a standard. The fitted curves RE versus GB(B) corresponding
to isobutene and acetone have been reported earlier.7 For these
two compounds the parameters a-c are equal to 0.95/0.96 (
0.03 and 0.27/0.22 ( 0.03 kJ-1·mol and 782.4/785.9 ( 0.7 kJ/
mol, respectively. If, as is the case here, the parameters a and
b are nearly identical to one fit to another, the difference in c
values represents the difference in gas-phase basicities; it appears
thus that GB(ketene) ) GB(acetone) + 6.7 kJ/mol (i.e., precisely
the relationship obtained by Beauchamp and co-workers13) and
that GB(ketene) ) GB(isobutene) + 9.4 kJ/mol (i.e., a difference
comparable to that observed in refs 12 and 14). Thus, using

16558 J. Phys. Chem., Vol. 100, No. 41, 1996
Bouchoux and Salpin
The protonation of methylketene, prepared by pyrolysis of
propionic anhydride, has been studied using an ion trap mass
spectrometer.19 The equilibrium constant determination of
reaction
(AcOMe)H+ + CH3CHCO / AcOMe + [CH3CH2CO]+
(III)
leads to ∆G°III ) -6.5 ( 3.2 kJ/mol. With use of PA (AcOMe)
) 839 kJ/mol and with the assumption, justified by the
conservation of the symmetry number upon protonation, that
∆S°1/2 ) 0 for the couple [CH3CH2CO]+/CH3CHCO, the authors
then deduced that PA(methylketene) ) 845 kJ/mol but with
use of PA(MeOAc) ) 839 kJ/mol. With the more recent
basicity determination for methyl acetate: GB(MeOAc) ) 788.2
kJ/mol and PA(MeOAc) ) 815.9 kJ/mol,3 the GB(methylketene)
and PA(methylketene) values must be shifted downward to
794.7 ( 3.2 kJ/mol and 822.4 ( 3.2 kJ/mol, respectively.
We investigate the following reactions involving propanoyl
cation, produced by ethyl loss from ionized diethylketone,30 and
various bases B in FT-ICR experiments:
[CH3CH2CO]+ + B / [BH]+ + CH3CHCO (IV)
The relevant data are gathered in Table 3, and the relative
efficiency curves as a function of either GB(B) or PA(B) are
reported in Figures 1 and 2. The parameter values a-c of eq
2 are 0.99 ( 0.03/0.98 ( 0.02 kJ-1‚mol, 0.16 ( 0.02/0.19 (
0.03 kJ/mol, and 814.0 ( 1.1/847.0 ( 0.5 kJ/mol for GB-
(methylketene)/PA(methylketene), respectively.
Figure 2. Representative curves of proton transfer reaction efficiency
versus PA(B) for reaction [MH]+ + B f M + [BH]+ (M ) ketene,
methylketene, and formaldimine).
From these data, by reference to acetone and isobutene, one
obtains GB(methylketene) ) 807.7 ( 2.1 kJ/mol and PA-
(methylketene) ) 840.8 ( 2.7 kJ/mol. On the other hand one
may deduce a gas-phase basicity GB(methylketene) ) 807.9
kJ/mol and a proton affinity PA(methylketene) ) 844.1 kJ/mol
using the approximations GB(M) ) c - 1/b and PA(M) ) c′
- 1/b + T∆S°I.7 We can thus confidently propose that the most
meaningful experimental values are GB(methylketene) ) 808
( 2 kJ/mol and PA(methylketene) ) 842 ( 3 kJ/mol. One
may note that the T∆S° difference associated with the GB and
PA values of methylketene (34 kJ‚mol) is very close to what is
calculated for the couple [CH3CH2CO]+/CH3CHCO when
taking ∆S° equal to zero (i.e., 33 kJ/mol), as expected from a
simple consideration of the symmetry number of both species.
It is noteworthy that, again, our estimates for GB or PA are
greater by no less than 16 kJ/mol than the values deduced from
the ion trapping experiments,19 as also observed above for the
ketene itself in similar experiments.
The heat of formation of the propanoyl cation has been
determined from photoionization experiments ∆Hf°300[CH3CH2-
CO]+ ) 591.2 ( 2.3 kJ/mol.20 Combining this value with
∆Hf°[H]+ ) 1530 kJ/mol and PA(methylketene) ) 842 ( 3
kJ/mol, we deduce a heat of formation for neutral methylketene
of ∆Hf°300(CH3CHdCdO) ) -97 ( 5 kJ/mol. The tabulated
value for this quantity22 is -105 kJ/mol, and, recently, a very
different value of -65 kJ/mol has been suggested on the basis
of theoretical G2 calculations.21 This point may be commented
on further. First the tabulated ∆Hf°300(CH3CHCO) value of
-105 kJ/mol 22 is only an estimate based on the observation
that reactions involving redistribution of substituents at an sp2
carbon are nearly thermoneutral. For example the reaction
CH2O + (CH3)2CO f 2CH3CHO is associated with a ∆H° of
only -6 kJ/mol. The authors thus assume that the reaction CH2-
CO + CH3CHO f CH3CHCO + CH2O is essentially thermo-
neutral, and, using the heats of formation values of -48, -166,
and -109 kJ/mol for CH2CO, CH3CHO, and CH2O, respec-
mol for ketene and 0.96/0.96 ( 0.02 and 0.21/0.20 ( 0.02
kJ-1‚mol and 808.9 ( 0.9/813.4 ( 0.7 kJ/mol for isobutene
and acetone, respectively.
When the two standards, isobutene and acetone, are consid-
ered, a mean value of PA(ketene) ) 817 ( 3 kJ/mol is obtained.
The proton affinity may be also deduced from the GB value
and the usual entropic correction:
PA(M) ) GB(M) - T[∆S1/2(M) - S°H
]
+
+
+
where ∆S1/2(M)) S°MH - S°M and S°H being the translational
entropy of the proton. In the case of the couple [CH3CO]+/
CH2CO the ∆S1/2(M) term may be approximated by ∆S1/2(M)
≈ R ln σM/σMH ) -3.4 J‚mol-1‚K-1. Consequently, with S°H
+
+
) 109.0 J‚mol-1‚K-1 at 300 K, we deduce PA(ketene) ) GB-
(ketene) + 34 kJ/mol ) 822 kJ/mol. Finally, the direct use of
the approximation PA(ketene) ) c′ - 1/b + T∆S°I leads to
PA(ketene) ) 820.9 ( 5.0 kJ/mol. These two estimates,
subjected to the uncertainties inherent in the derivation of
∆S1/2(M) and to the range of ∆S°I values are, however, in
reasonable agreement with the experimental determination of
817 ( 3 kJ/mol.
To conclude this part, one must mention that these PA values
are comparable to, but slightly lower than, the proton affinity
value, PA(ketene) ) 825 ( 3 kJ/mol, which may be deduced
from the presently accepted 300 K heats of formation of [CH3-
CO]+ (657 ( 1.5 kJ/mol;16 a comparable theoretical evaluation
of 658 kJ/mol has been proposed17), CH2CO (-47.7 ( 1.6 kJ/
mol 18), and [H]+ (1530 kJ/mol).
Methylketene. The most stable protonated form of meth-
ylketene is the propanoyl cation, [CH3CH2CO]+; the two other
possible structures, namely, [CH3CHCOH]+ and [CH3CHCHO]+,
are higher in energy by 170 and 250 kJ/mol, respectively,
according to correlated molecular orbital calculations.29

Thermokinetics of Gas-Phase Basicities
J. Phys. Chem., Vol. 100, No. 41, 1996 16559
TABLE 3: Efficiencies of Proton Transfer Reactions Involving [CH3CH2CO]+ and Several Bases B
PA(B)
(kJ/mol)
GB(B)c
(kJ/mol)
∆S°1/2(B)d
(J/(mol K))
PB
(mbar)
base B
acetone
3-pentanone
benzylacetone
diisopropylketone
cyclohexenone
mesityl oxide
tert-butylamine
Re (Å3)
µ (D)
kexp
kADO
REj
i
i
810.4a
833.9a
845.6a
852 ( 1b
862 ( 2b
879b
783.3
804.3
809.7
821.1
829.3
845.9
899.5
18.8
10.5
-10.5
(6)
(0)
(0)
6.37
9.93
16.0
13.53
10.89
9.12
2.88f
2.72g
2.72g
2.67g
3.75f
3.9h
1 × 10-7
0.14
0.85
7.91
22.21
21.28
22.03
21.46
26.07
26.15
15.65
0.007
0.048
0.429
0.727
0.885
0.984
1
4.4 × 10-8
6.4 × 10-8
2.8 × 10-8
7.3 × 10-8
1.6 × 10-8
4.1 × 10-8
13.1
19.3
22.2
43.1
934.7a
-8.4
9.51
1.29f
a From ref 3. b From ref 34. c GB(B) ) PA(B) + T[∆S°1/2(B) - S°H ], with T ) 300 K and S°H ) 109 J/(mol‚K). d From ref 3. ∆S°1/2(B) is
the standard entropy difference between the protonated and the neutral form of B. When the experimental data are not available, a ∆S°1/2(B) equal
+
+
to R ln(σB/σBH ) (where σ is the relevant symmetry number) has been assigned; this estimate is indicated in parentheses. e Polarizabilities from ref
+
10b. f Dipole moment from ref 33. g Dipole moment calculated by the AM1 semiempirical procedure.35 h Dipole moment of mesityl oxide has been
considered equal to that of 3-penten-2-one. ×10-10 cm-3‚molecule-1‚s-1
.
j RE ) (kexp/kADO)/(kexp/kADO
)
max
.
i
TABLE 4: Efficiencies of Proton Transfer Reactions Involving [CH2NH2]+ and Several Bases B
PA(B)
(kJ/mol)
GB(B)c
(kJ/mol)
∆S°1/2(B)d
(J/(mol K))
PB
(mbar)
Re (Å3)
µ (D)
kexp
kADO
REj
i
i
base B
cyclohexanone
diisopropylketone
diisopropyl ether
acetylacetone
pyrrole
mesityl oxide
methylamine
tert-butylamine
837 ( 2a
852 ( 1a
861 ( 1a
869.4b
804.3
821.1
828.3
838.0
843.9
845.9
864.7
899.5
(0)
(6)
(0)
4.6
4.2
(0)
-12.6
-8.4
11.11
13.53
12.37
10.11
7.94
9.12
3.98
2.87f
2.671g
1.13f
3.03f
1.74f
3.9h
2.5 × 10-8
0.9
1.6
2.4
13.3
10.7
24.2
12.4
14.1
27.45
27.15
19.51
27.79
20.62
33.76
17.44
19.23
0.045
0.080
0.166
0.663
0.703
0.973
0.969
1
3 × 10-8
6.5 × 10-8
3.3 × 10-8
2 × 10-8
875.3b
879a
2.0 × 10-8
1.5 × 10-8
2 × 10-8
901.2b
1.30f
1.29f
934.7b
9.51
a From ref 34. b From ref 3. c GB(B) ) PA(B) + T[∆S°1/2(B) - S°H ], with T ) 300 K and S°H ) 109 J/(mol‚K). d From ref 3. ∆S°1/2(B) is
the standard entropy difference between the protonated and the neutral form of B. When the experimental data are not available, a ∆S°1/2(B) equal
+
+
to R ln(σB/σBH ) (where σ is the relevant symmetry number) has been assigned; this estimate is indicated in parentheses. e Polarizabilities from ref
+
10b. f Dipole moment from ref 33. g Dipole moment calculated by the AM1 semiempirical procedure.35 h Dipole moment of mesityl oxide has been
assumed to be equal to that of 3-penten-2-one.33 ×10-10 cm-3‚molecule-1‚s-1
.
j Relative reaction efficiency: RE ) (kexp/kADO)/(kexp/kADO
)
max
.
i
tively, they deduced ∆Hf°300(CH3CHdCdO) ) -105 kJ/mol.
We believe that the thermoneutrality hypothesis must apply,
more closely, to reactions V and VI, in which the substitution
done by the bracketing technique involving immonium ion
[CH2dNH2]+ in an FT-ICR spectrometer.23 It has been
observed that the [CH2dNH2]+ cation is deprotonated by
diisopropyl ether but not by styrene, while an intermediate
situation is observed with ammonia; after considering these
results, the authors proposed a proton affinity value PA-
(CH2dNH) ) 854 ( 8 kJ/mol.
CH3CHdCH2 + CH2dCdO f
CH2dCH2 + CH3CHdCdO (V)
CH3CHdCdCH2 + CH2dCdO f
CH2dCdCH2 + CH3CHdCdO (VI)
We similarly studied the reaction
[CH2dNH2]+ + B / CH2dNH + BH+
(VII)
concerns an ethylenic sp2 carbon atom; with ∆Hf°300(CH2dCH2)
) 52 kJ/mol, ∆Hf°300(CH3CHdCH2) ) 20 kJ/mol, ∆Hf°300
-
with immonium ions produced in the external source of the
Bruker FT-ICR instrument and a set of eight bases B (Table
4). The relative efficiencies correlate satisfactorily with either
GB(B) or PA(B) as indicated in Figures 1 and 2.
(CH2dCdCH2) ) 191 kJ/mol, and ∆Hf°300(CH3CHdCdCH2)
) 162 kJ/mol, it follows that ∆Hf°300(CH3CHdCdO) ) -80
and -76 kJ/mol from reactions V and VI, respectively. This
is indeed a first argument in favor of a reevaluation of the
presently used heat of formation of methylketene. The second
evidence is that the heat of formation of neutral methylketene
we can derive from its experimental ionization energy, 8.95
eV,1b combined with the estimated heat of formation of
methylketene radical cation of 779 kJ/mol derived by Traeger
et al.31 leads to ∆Hf°300(CH3CHdCdO) ) -85 kJ/mol.
Consequently, experiments and structural thermochemical re-
lationships point to a ∆Hf°300(CH3CHdCdO) value in the range
-96/-76 kJ/mol. The higher value obtained from G2 calcula-
tions,21 ∆Hf°300(CH3CHdCdO) ) -65 kJ/mol, let an opened
question as long as this method usually gives accurate heat of
formation values ((5 kJ/mol); it may be noted for example that
the ∆Hf°300 of ketene itself is very well-estimated at the G2
level32 (-47 kJ/mol as opposed to the experimental value of
-48 kJ/mol).
From the curve fitting we derive the parameter values a-c
of 0.99 ( 0.06/0.98 ( 0.05 and 0.195 ( 0.045/0.207 ( 0.045
kJ-1‚mol and 835.4 ( 1.5/867.0 ( 1.3 kJ/mol, respectively for
GB(CH2dNH)/PA(CH2dNH). With the approximation GB-
(M) ) c - 1/b and PA(M) ) c′ - 1/b + T∆S°I 7 (and ∆S1/2(M)
) -5.8 J/(mol‚K)), we deduce GB(CH2dNH) ) 830.3 ( 1.5
kJ/mol and PA(CH2dNH) ) 862.2 ( 3 kJ/mol. Now, by
reference to acetone and isobutene, one obtains GB(CH2dNH)
) 830.0 ( 3.0 kJ/mol and PA(CH2dNH) ) 858.9 ( 2.7 kJ/
mol, leading finally to the rounded values GB(CH2dNH) )
830 ( 3 kJ/mol and PA(CH2dNH) ) 860 ( 5 kJ/mol.
Although the error limits are overlapping, our estimate is
slightly higher than that obtained by Peerboom et al. by the
bracketing method,23 PA(CH2dNH) ) 854 ( 8 kJ/mol. In fact,
this shift was expected because, according to relationship 3,
the PA(M) does not correspond to the beginning of the rising
part of the RE curves.7 In the present case the shift led to an
underestimate of the PA(M) as estimated by the bracketing
method of about 10 kJ/mol.
Formaldimine. Formaldimine is a highly unstable species
in the condensed phase and is thus not amenable to a direct
determination of its basicity by the equilibrium method. The
first tentative determination of the basicity of CH2dNH has been

16560 J. Phys. Chem., Vol. 100, No. 41, 1996
Bouchoux and Salpin
(10) (a) Bartmess, J. E.; Georgiadis, R. M. Vacuum 1983, 33, 149. (b)
Miller, K. J. J. Am. Chem. Soc. 1990, 112, 8533.
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The determination of the heat of formation of formaldimine,
CH2dNH, is still an actual question; the various estimates span
a wide range of values (69-135 kJ/mol) with seemingly a recent
consensus offered by a theoretical estimate of 86 ( 10
kJ/mol 24,25 and an experimental determination of 88 ( 8 kJ/
mol 26 based on the appearance energy measurement. Our PA-
(CH2dNH) determination, combined with the well-established
heat of formation of immonium ion, ∆Hf°300[CH2NH2]+ ) 745
kJ/mol,27 allows us to propose a heat of formation of formaldi-
mine of ∆Hf°300 (CH2dNH) ) 75 ( 5 kJ/mol. Owing to the
experimental and theoretical uncertainties, the agreement be-
tween this value and the two previously recalled most recent
estimates is excellent.
1016.
(15) Debrou, G. B.; Fulford, J. E.; Lewars, E. G.; March, R. E. Int. J.
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Conclusion
(19) Armitage, M. A.; Higgins, M. J.; Lewars, E. G.; March, R. E. J.
Am. Chem. Soc. 1980, 102, 5064.
The recently developed thermokinetic method7 has been
applied to the determination of gas-phase basicities and proton
affinities of three important neutral molecules: ketene, meth-
ylketene, and formaldimine. The method gives results with an
accuracy of (3 to (5 kJ/mol and in excellent agreement with
data obtained from the measurement of the equilibrium constant
of proton transfer reaction. Moreover, the method proves to
be useful when the neutrals are unstable or reactive species.
From a combination of the above results and literature data
we derive the following heat of formation values of neutral
methylketene and formaldimine: ∆Hf°300(CH3CHCO) ) -97
( 5 kJ/mol and ∆Hf°300(CH2dNH) ) 75 ( 5 kJ/mol.
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1980; p 155.
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