Chemical kinetics and thermodynamics of tin ionization in H2-O2-N2 flames and the proton affinity of SnO

Article abstract of DOI:10.1139/v98-172

A small amount (≤10^-6 mol fraction) of tin was introduced into five, fuel-rich, H₂-O₂-N₂ flames in the temperature range 1820-2400 K at atmospheric pressure. Ions in a flame were observed by sampling the flame along its axis through a nozzle into a mass spectrometer. The major neutral tin species in these flames were SnO (>97%) and Sn (<3%). The principal tin ions observed were SnOH⁺ and Sn⁺. Thermodynamic functions for SnOH⁺, Sn⁺, SnO, and Sn were calculated by statistical mechanics using published data from ab initio calculations and spectroscopy. The SnOH⁺ ion was formed initially by proton transfer to SnO by H₃O⁺, a natural flame ion, with which it is in equilibrium. It was also produced by chemi-ionization of SnO reacting with H; SnOH⁺ rapidly equilibrates with Sn⁺. Ion ratio measurements of SnOH⁺/H₃O⁺ led to the proton affinity PA₂₉₈/(o) (SnO) = 911 ± 21 kJ mol^-1 (218 ± 5 kcal mol^-1). A calculated equilibrium constant provided the SnOH⁺/Sn⁺ ion ratio. When electron-ion recombination of SnOH⁺ with free electrons was made dominant by the addition of CH₄ and K, the measured recombination coefficient of SnOH⁺ was (0.116 ± 0.065)T^- ((1.66±0.16)) cm³ molecule^-1 s^-1; the temperature dependence is in good agreement with the T-^1.5 dependence predicted by simple theory. The rate constant for chemi-ionization could not be measured due to impurity ions from potassium and sodium, but the equilibrium constant for chemi- ionization/recombination was calculated to be 0.004 863 exp (-52 070/T). Assuming detailed balance and the experimental recombination coefficient, the relatively small rate constant for chemi-ionization was given by 3.27 x 10^{- 10} exp (-48 630/T) cm³ molecule^-1 s^-1. Finally, calculated values were obtained for the bond energy D₀/(o)(HO-Sn⁺) = 408 ± 21 kJ mol^-1, and the standard zero-point enthalpy of formation Δ(f)H₀/(o)(SnOH⁺) = 637 ± 21 kJ mol^-1.

Full text of DOI:10.1139/v98-172

1437
Chemical kinetics and thermodynamics of tin
ionization in H2-O2-N2 flames and the proton
affinity of SnO
John M. Goodings and QingFeng Chen
Abstract: A small amount (≤10–6 mol fraction) of tin was introduced into five, fuel-rich, H2-O2-N2 flames in the
temperature range 1820–2400 K at atmospheric pressure. Ions in a flame were observed by sampling the flame along
its axis through a nozzle into a mass spectrometer. The major neutral tin species in these flames were SnO (>97%) and
Sn (<3%). The principal tin ions observed were SnOH+ and Sn+. Thermodynamic functions for SnOH+, Sn+, SnO, and
Sn were calculated by statistical mechanics using published data from ab initio calculations and spectroscopy. The
SnOH+ ion was formed initially by proton transfer to SnO by H3O+, a natural flame ion, with which it is in
equilibrium. It was also produced by chemi-ionization of SnO reacting with H; SnOH+ rapidly equilibrates with Sn+.
+
+
–1
°
Ion ratio measurements of SnOH /H3O led to the proton affinity PA298 (SnO) = 911 ± 21 kJ mol (218 ± 5 kcal
mol–1). A calculated equilibrium constant provided the SnOH+/Sn+ ion ratio. When electron-ion recombination of
SnOH+ with free electrons was made dominant by the addition of CH4 and K, the measured recombination coefficient
of SnOH+ was (0.116 ± 0.065)T–(1.66±0.16) cm3 molecule–1 s–1; the temperature dependence is in good agreement with
the T–1.5 dependence predicted by simple theory. The rate constant for chemi-ionization could not be measured due to
impurity ions from potassium and sodium, but the equilibrium constant for chemi-ionization/recombination was
calculated to be 0.004 863 exp (–52 070/T). Assuming detailed balance and the experimental recombination coefficient,
the relatively small rate constant for chemi-ionization was given by 3.27 × 10–10 exp (–48 630/T) cm3 molecule–1 s–1.
+
–1
°
Finally, calculated values were obtained for the bond energy D0 (HO—Sn ) = 408 ± 21 kJ mol , and the standard
zero-point enthalpy of formation ∆f H0 (SnOH ) = 637 ± 21 kJ mol .
+
–1
°
Key words: flame ionization, chemi-ionization, proton affinity, mass spectrometry, tin.
Résumé : On a introduit de faibles quantités (fraction molaire ≤10–6) d’étain dans cinq flammes de H2-O2-N2 riches en
combustible, à des températures allant de 1820 à 2400 K et à la pression ambiante. On a observé les ions dans les
flammes en procédant à un échantillonnage de la flamme le long de son axe à l’aide d’une canule de spectromètre de
masse. L’espèce principale d’étain dans ces flammes est le SnO (>97%) accompagnée de Sn (<3%). Les ions
principaux observés sont le SnOH+ et le Sn+. Faisant appel à des méthodes de mécanique statistique et utilisant des
données publiées de calculs ab initio et de spectroscopie, on a calculé les fonctions thermodynamiques du SnOH+, Sn+,
SnO et Sn. L’ion SnOH+ se forme initialement par un transfert de proton de H3O+ à SnO, un ion naturel de la flamme
avec lequel il est en équilibre. Il se forme aussi par chimi-ionisation du SnO réagissant avec H; le SnOH+ s’équilibre
rapidement avec le Sn+. Des mesures de rapports ioniques SnOH+/H3O+ permettent de déterminer l’affinité protonique
PA298(SnO) = 911 ± 21 kJ mol–1 (218 ± 5 kcal mol–1). On a obtenu un rapport ionique SnOH+ à l’aide de la constante
°
d’équilibre calculée. Lorsque l’addition de CH4 et de K fait que la recombinaison électron-ion du SnOH+ avec des
électrons libres devient la réaction dominante, le coefficient de recombinaison mesuré du SnOH+ est égal à (0,116 ±
(–1,66±0,16)
0,065) T
cm3 molécule–1 s–1; la relation avec la température est en bon accord avec la dépendance T–1,5 qui
est prédite par la théorie simple. Il n’a pas été possible de mesurer la constante de vitesse de la réaction de chimi-
ionisation à cause de la présence d’ions de potassium et de sodium à l’état d’impuretés; on a toutefois calculé que la
constante d’équilibre chimi-ionisation/recombinaison est égale à 0,004 863 exp (–52 070/T). Si l’on fait l’hypothèse
qu’il existe une balance détaillée et que l’on utilise le coefficient de recombinaison expérimental, on peut établir que la
relativement faible constante de vitesse de la réaction de chimi-ionisation est donnée par l’équation 3,27 × 10–10 exp (–
–1
+
48 630/T) T cm3 molécule–1 s . Finalement, on a obtenu des valeurs calculées pour l’énergie de liaison, D0 (HO—Sn )
°
–1
–1
+
°
= 408 ± 21 kJ mol , et l’enthalpie de formation au point zéro standard, ∆f H0 (SnOH ) = 637 ± 21 kJ mol .
Mots clés : ionisation de flamme, chimi-ionisation, affinité protonique, spectrométrie de masse, étain.
[Traduit par la Rédaction] Goodings and Chen 1446
Received April 2, 1998.
J.M. Goodings1 and Q.F. Chen. Department of Chemistry, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada.
1Author to whom correspondence may be addressed. Telephone: (416) 736–2100, ext. 33852. Fax: (416) 736–5936.
E-mail: goodings@turing.sci.yorku.ca
Can. J. Chem. 76: 1437–1446 (1998)
© 1998 NRC Canada

1438
Can. J. Chem. Vol. 76, 1998
Table 1. Properties of the hydrogen–oxygen–nitrogen flames.
Flame number
3
Property
2
25
4
5
Equivalence ratio φ
1.5
1.5
1.5
1.5
1.5
H2/O2/N2
Total unburnt gas flow (cm3 s–1)
2.74/1/2.95
300
3.0/1/3.5
250
3.18/1/4.07
250
3.09/1/4.74
200
3.12/1/5.77
150
Measured flame temperature (K)
Rise velocity in burnt gas (m s–1)
2400
19.8
2230
18.6
2080
15.6
1980
11.4
1820
8.4
Equilibrium burnt gas composition (mol fractions)
H2O
0.3460
0.3063
0.2754
0.2553
0.2249
H2
0.1286
0.1527
0.1622
0.1390
0.1259
O2
H
OH
O
0.000 105 7
0.006 019
0.003 084
0.000 094 69
0.5157
0.000 007 90
0.002 650
0.000 795 1
0.000 009 35
0.5375
0.000 000 72
0.001 077
0.000 213 0
0.000 000 99
0.5610
0.000 000 18
0.000 500 8
0.000 088 90
0.000 000 23
0.6052
0.000 000 01
0.000 141 5
0.000 017 54
0.000 000 01
0.6490
N2
Percentage SnO/Sn (%)
97.1/2.9
96.9/3.1
97.0/3.0
97.6/2.4
98.1/1.9
tion were compromised by the presence of K+ and Na+ im-
purity ions. However, values of the rate constant were ob-
tained by calculating the equilibrium constant for chemi-
ionization/recombination and multiplying it by the experi-
mental recombination coefficient with the assumption of de-
tailed balance.
In a short note in 1969, Jensen (1) reported on the forma-
tion of tin ions when 10–3–10–4 mol fraction of Sn(CH3)4, a
rather high concentration, was introduced into a pair of H2-
O2-N2 flames at 2020 and 2475 K and atmospheric pressure.
Using a microwave cavity resonator to measure the free
electron concentration [e–] and a mass spectrometer to sam-
ple the ions, he first showed that the SnOH+ and Sn+ ions
observed were linked by a balanced (equilibrated) reaction.
Further experiments indicated that the rather strongly endo-
thermic chemi-ionization reaction of SnO with H to form
SnOH+ was not equilibrated in these flames. Aided by statis-
tical thermodynamic calculations, values were obtained for
Five premixed, laminar, H2-O2-N2 flames of fuel-rich
composition (equivalence ratio φ = 1.5) at atmospheric pres-
sure were employed for this work spanning a temperature
range 1820–2400 K. Their properties, including the calcu-
lated compositions of the equilibrium burnt gas based on the
JANAF tables (5), are given in Table 1. These flames have
been used extensively by Hayhurst and Kittelson who have
measured their temperatures, rise velocities and free-radical
compositions (6). The concentrations of free radicals over-
shoot their equilibrium values in the flame reaction zone and
then decay downstream towards equilibrium in the burnt
gas. The actual concentration is obtained using Sugden’s dis-
equilibrium parameter γ (7), defined as the ratio of the local
concentration of a radical at a given position in the flame to
its final equilibrium value given in Table 1; γ can achieve
large values (>100) close to the reaction zone of the cooler
flames before decaying downstream in the burnt gas towards
unity. For fuel-rich flames where H2O and H2 are major
product species, γH = γOH ϵ γ and γO = γ2. Plots of γ versus
axial distance z are available (6) for the five fuel-rich flames
listed in Table 1; thus, the radical concentrations are known
at all points in the flames. These pseudo-one-dimensional
(flat) flames were stabilized on a water-cooled brass burner
previously described (8), consisting basically of a circular
bundle of 151 stainless-steel hypodermic needle tubes. The
fuel-rich flames in plug flow were cylindrical in shape with
a diameter of about 12 mm.
°
°
the zero-point standard energy change ∆E0 (= ∆H0 ) for both
reactions and the standard internal energy of formation
+
°
∆fE0 (SnOH ).
Very recently, Hopkinson and co-workers (2) carried out
ab initio calculations of the group 14 monoxides for C, Si,
Ge, and Sn to obtain their proton affinities. For tin, these
were conducted at the B3LYP level of theory with wave
functions optimised using density functional theory. In par-
ticular, two calculations designated A (B3LYP/DZVP) and B
(B3YP/Sadlej) each provided a set of rotational and vibra-
tional temperatures for SnOH+ for statistical thermodynamic
calculations. Combined with the thermodynamic data and ta-
bles for SnO from Pedley and Marshall (3) and the spectro-
scopic data for Sn and Sn+ from Moore (4), this provided us
with the impetus to re-examine the ionization of tin in
flames.
The objectives of this study were to measure the proton
affinity PA of SnO, the electron-ion recombination coeffi-
cient for SnOH+ and the rate constant for chemi-ionization
of SnO reacting with H using our flame-ion mass spectrome-
ter to sample flames in the temperature range 1820–2400 K.
Experimental values for PA°(SnO) by proton transfer with
H3O+ and the recombination coefficient were obtained. For
the very fast equilibrated reaction linking SnOH+ and Sn+,
ion ratio measurements were falsified by cooling of the sam-
ple in the nozzle of the mass spectrometer but the equilib-
rium constant was calculated by statistical methods. Direct
measurements of the relatively weak chemi-ionization reac-
Tin was introduced into the flames by spraying an aque-
ous solution of SnCl4·5H2O (Aldrich, 98+%) as an aerosol
derived from an atomizer described previously (9) into the
nitrogen supply of the premixed flame gas. This salt con-
tained very small amounts of potassium and sodium as im-
purities. Spraying a 0.1 M solution introduced 9.5 × 10–7
© 1998 NRC Canada

Goodings and Chen
1439
mol fraction of total tin into the unburnt flame gas. A small
amount of a grey solid, presumably metallic tin, condensed
onto the cooled sampling nozzle and mounting plate placed
in front of the flame. The usual very pale blue colour of the
flames developed a slightly stronger whitish luminosity with
tin present. No evidence was observed for the formation of
solid particles.
As an alternative to individual ions, total positive ion
(TPI) profiles can be measured by switching off the dc volt-
ages to the quadrupole rods. Still with the dc voltages
switched off and the spectrometer’s mass dial set to a given
mass number, all of the ions above that mass number are
collected; e.g., TPI100 designates total positive ions above
100 u which includes just the tin ions whereas TPI12 in-
cludes all the ions (since no measureable flame ions occur
below 12 u). This technique is useful in separating total tin
ions from ions of low mass number such as H3O+, K+, and
Na+ if present. However, the sensitivity of the mass spec-
trometer is different for individual ions and TPI because the
former are measured at fairly high resolution whereas total
ion collection amounts to zero resolution. The former sensi-
tivity is approximately one half of the latter. Since a flame is
a quasi-neutral plasma, [TPI12] is equal to [e–], the concen-
tration of free electrons. It should be pointed out that no
negative tin ions were detected in the FR flames.
A second method of measuring total ion signals was em-
ployed, which has a bearing on calibration procedures. With
an appropriate voltage bias on the sampling plate, the total
current of positive ions passing through the orifice was col-
lected on the ion lens and nose-cone in the first vacuum
chamber; it was measured with a sensitive picoammeter.
This method is appealing when absolute ion concentrations
must be measured because tuning errors and mass discrimi-
nation of individual ions are avoided. The total ion current
was calibrated using the known rate for electron-ion recom-
bination of H3O+ with e–. With the atomizer turned off, 0.25
mol% of CH4 was admitted. From the slope of a second-
order recombination plot together with Butler and
Hayhurst’s rate coefficient k = (3.6 ± 0.5) T –2.1±0.7 cm3 mol-
ecule–1 s–1 (10), a calibration factor was obtained for con-
verting ion current (µA) into ion concentration
(molecule cm–3). The same procedure was employed with
the mass spectrometer for calibrating ion signal (mV) in
terms of ion concentration (molecule cm–3). The calibration
was routinely done for each flame when absolute ion densi-
ties were needed.
On occasion, it was noted that the ion signal slowly and
steadily decreased over a period of several minutes. The
worst cases occurred for the hot flames 2 and 25 when the
burner was moved in close to the sampling nozzle; in these
circumstances, the nozzle can become red hot. A possible
explanation involves the formation of a thin layer of dielec-
tric oxide which coats the orifice rim and subsequently ac-
quires a positive charge which repels incoming positive ions
as they approach the nozzle. Accordingly, the calibration
procedure with CH4 addition was carried out at the begin-
ning and end of each set of tin experiments with each flame,
and the results were accepted only if the calibration factor
remained constant. Calibration procedures for the atomizer
delivery of tin into the flame gas have been given previously
(11, 12).
When the gas is sampled through the nozzle, it cools in
two regions: in the thermal boundary layer surrounding the
orifice and in the near-adiabatic expansion downstream of
the nozzle throat. This can cause a shift of fast equilibrium
reactions in the exothermic direction during sampling. In
particular, ion hydrates can be enhanced with respect to the
parent ion. These sampling problems have been discussed in
The five flames described in Table 1 exhibit only a low
level of natural ionization. It was sometimes advantageous
to add 0.25 mol% of CH4 to the premixed flame gas to pro-
duce a high initial concentration of H3O+ ions stemming
from the chemi-ionization of CH + O near the flame reac-
tion zone; these ions subsequently decay downstream by
electron-ion recombination. With the simultaneous addition
of tin, H3O+ can produce tin ions by chemical ionization
(CI) processes. The addition of CH4 was small enough, how-
ever, so that the flame composition and temperature re-
mained essentially unchanged. In other cases, it was
occasionally desirable to add a small amount of KNO3 to the
tin solution sprayed by the atomizer to produce K+ and free
electrons e– in the flame by collisional (thermal) ionization.
By this means, the electron–ion recombination rate of the tin
ions could be increased; there was no evidence for any di-
rect reaction of K+ with the tin ions. Thus, tin ionization
could be enhanced early in the flame by methane and (or)
suppressed later in the flame by potassium.
The burner is mounted horizontally on a motorized car-
riage with calibrated drive coupled to the X-axis of an XY-re-
corder. The flame axis z is accurately aligned with the
sampling nozzle of the mass spectrometer. The apparatus has
been described in detail previously (8) so only a brief de-
scription will be given here. Flame gas containing ions is
sampled through an orifice in the tip of a conical nozzle pro-
truding from a water-cooled sampling plate. The nozzles
were fabricated by swaging a tiny electron microscope lens
of Pt/Ir alloy into the tip of a 60° stainless-steel cone; orifice
diameters of 0.17 and 0.20 mm were employed. Alterna-
tively, a 60° electroformed nickel nozzle of diameter
0.20 mm exhibited less cooling of the sample in the bound-
ary layer and was used when it was desired to minimize the
formation of ion hydrates. The ions enter a first vacuum
chamber maintained at 0.04 Pa (3 × 10–4 Torr), and are fo-
cused into a beam by an electrostatic lens. The beam then
passes through a 3 mm orifice in the tip of a nose-cone into
a second vacuum chamber pumped to a pressure below
0.003 Pa (2 × 10–5 Torr). The ions traverse a second ion lens
into a quadrupole mass filter in which they have an axial ion
energy of 15 eV. They are detected by a Faraday collector
connected to a vibrating-reed electrometer having a grid-
leak resistance of 1010 ohm; the ion signal is applied to the
Y-axis of the XY-recorder. Thus, ion signal magnitudes
quoted in the figures below as a voltage (in mV) refer to the
collected ion current passing through 1010 ohm. By driving
the flame towards the sampling nozzle, profiles may be ob-
tained of an individual ion signal versus distance along the
flame axis z. The zero on the X-axis distance scale (z = 0) is
defined experimentally where the pressure abruptly rises
when the sampling nozzle pokes through the flame reaction
zone into the cooler unburnt gas upstream. The pressure is
measured with an ionization gauge mounted on the second
vacuum chamber.
© 1998 NRC Canada

1440
Can. J. Chem. Vol. 76, 1998
Table 2. Calculated parameters of the SnOH+ ion (2).
might indicate that SnOH+ is linear.2 The ground electronic
state is nondegenerate, and there is no evidence of a low-
lying excited state. For calculations A and B, the sum of the
rotational and vibrational contributions to the thermody-
namic functions had very similar magnitudes. Since there
was no reason to prefer one calculation over the other, the
results of the two calculations were simply averaged.
Largely for reasons of conformity with the JANAF tables
(5), a standard state for pressure of 0.1 MPa rather than 1
atm, designated by ° on thermodynamic quantities, was em-
ployed for the statistical calculations. Any differences,
which only arise for functions involving the entropy, are
small and well within the error limits.
Calculation A
Calculation B
Parameter
(B3LYP/DZVP) (B3LYP/Sadlej)
Sn—O bond length (Å)
O—H bond length (Å)
Bond angle (degrees)
1.931
0.973
154.1
1.885
0.969
167.9
Rotational temperatures (K)
150.590 11
0.409 83
0.408 72
669.578 11
0.426 47
0.426 20
120.53
Vibrational temperatures (K) 339.01
989.66
5427.05
1039.94
5521.94
considerable detail (13–15). In general, if the relaxation time
τ of an equilibrium reaction is greater than the sampling
time of roughly 1 µs, it may be assumed that the reaction
does not shift during sampling. In the present study, the
problem arising from hydrates of the tin ions, such as
SnOH+·H2O and Sn+·H2O which are probably not genuine
flame ions, is obviated by measuring TPI100 such that hy-
drate contributions are included with the SnOH+ and Sn+
parent ion signals. At the other extreme, consider for exam-
ple flame 3 in Table 1 with a rise velocity in the burnt gas of
15.6 m s–1. Appreciable air entrainment is minimal for ap-
proximately the first 2.5 flame diameters downstream of the
reaction zone; i.e., 30 mm, equivalent to a time of 1.9 ms.
For a reaction to reach equilibrium within the time-scale of
the flame, clearly τ must be small compared with 1.9 ms.
Available spectroscopic evidence indicates that tin is pres-
ent in flames only as Sn and SnO; the total concentration of
tin ions is negligible in comparison. The percentage of each
neutral species was found by calculating the equilibrium
constant K1 for the reaction
[1]
Sn + H2O = SnO + H2
°
°
The free energy function –(GT − H298)/T over a wide tem-
perature range is available for H2O and H2 from the JANAF
tables (5) and for SnO from the tables of Pedley and Mar-
°
shall (3). At any temperature T, K1 is obtained from ∆GT [1]
°
°
°
°
= –RT ln K1 with ∆GT = ∆H298 − T∆{–(GT − H298)/T} for
reaction [1]; ∆H298[1] = –D298(SnO) + D298(OH) + D298(H-
°
°
°
°
OH) – D298(H2) = –42.2 kJ mol–1 (16) based on D0 (SnO) =
528 ± 13 kJ mol–1 (3). A plot of ln K1 versus 1/T gives a
very good straight line over the whole temperature range
298.15–2500 K, yielding K1 = 1.665 exp (5140/T) from a
least-squares fit; specifically over the temperature range
1820–2400 K of the five flames, K1 = 1.015 exp (6064/T).
The percentage SnO/Sn ratio for the five flames is given in
Table 1; in all cases, SnO > 96.9% of the total tin present
and SnOH is negligible.
°
°
For some of the reactions involving tin, some of their
properties could not be measured experimentally. Tables of
thermodynamic data for many of the ancilliary species in-
volved are listed in the JANAF tables over a wide tem-
perature range (5); for SnO, the free-energy function
°
°
°
°
−(GT − H298)͞T and enthalpy function (HT − H298) are tabu-
lated by Pedley and Marshall (3) up to 4000 K. Such data
are not available for Sn, Sn+, and SnOH+, and it was neces-
°
sary to calculate third-law absolute entropies ST , free en-
ergy, and enthalpy functions for some of these species by
standard statistical methods. A good summary of the rele-
vant formulae is given in the introduction to the JANAF ta-
bles (5). For the Sn neutral atom, Moore (4) lists three low-
lying electronic states below 10 000 cm–1 with correspond-
ing electronic temperatures θe (and degeneracies, g values)
of 2002.5 K (g1 = 3), 4931.7 K (g2 = 5), and 12 392.3 K (g3
= 5); for the ground state, g0 = 1. For Sn+ (4), g0 = 2, and
there is one low-lying state with θe = 6116.9 K (g1 = 4).
The calculation of thermodynamic functions for SnOH+
was made possible by the ab initio calculations of Rodriquez
et al. (2). Two of the calculations designated here as A
(B3LYP/DZVP) and B (B3YP/Sadlej) each provided a set of
rotational and vibrational temperatures, and also structural
parameters given in Table 2. Both calculations depict SnOH+
as a bent asymmetric-top molecule with one low vibrational
temperature and two very low, nearly equal, rotational tem-
peratures; conceivably, an even higher level calculation
The tin atom has 10 stable isotopes (16) with mass num-
bers u and natural abundances (%) of 112 (0.97), 114 (0.65),
115 (0.36), 116 (14.53), 117 (7.68), 118 (24.22), 119
(8.58),120 (32.59), 122 (4.63), and 124 (5.79). With the at-
omizer spraying a 0.1 M aqueous solution of SnCl4·5H2O
into flame 3, a mass spectrum measured at high resolution
showing all of the tin ions present downstream at z = 30 mm
is given in Fig. 1. With increasing mass number, these in-
clude H3O+, Na+, a hydrate contribution from H5O2 , 39K+,
+
41K+, and three groups of isotopic tin peaks above 100 u in-
volving Sn+, SnOH+ (including a small contribution from
Sn+·H2O), and SnOH+·H2O; sodium and potassium are pres-
ent in the tin salt as impurities.
It is probably helpful to list all of the ionic reactions rele-
vant to this paper in one place. These include
[2]
H + H +OH
H3O+ + e–
2 A.C. Hopkinson. Personal communication.
© 1998 NRC Canada

Goodings and Chen
1441
Fig. 1. Mass spectrum at high resolution measured at z = 30 mm downstream in flame 3 with the atomizer spraying a 0.1 M solution
of SnCl4·5H2O.
Fig. 2. Ion profiles measured at low resolution in flame 3 with
where M is a third body. Here, the = sign refers to a fast bal-
the atomizer spraying a 0.1 M solution of SnCl4·5H2O, where
anced reaction at equilibrium whereas
refers to a reaction
TPI12 denotes total positive ions, and TPI100 is total ions of tin.
The flame reaction zone is located near z = 0.
proceeding in both directions which is not necessarily bal-
anced. From this list, it is clear how the ions observed in the
mass spectrum arise. The ion hydrates are not included,
since they are assumed to form during sampling and are not
genuine flame ions.
5.1 The SnOH+/H3O+ equilibrium
In H2-O2-N2 flames, the degree of natural ionization is
measureable but small, produced by the chemi-ionization re-
action [2] with a rate coefficient k2 = (3.3 ± 1.6) × 10–36 exp
(–13 800/T) cm6 molecule–2 s–1 (17) and a reverse recombina-
tion coefficient already given as k–2 = (3.6 ± 0.5)T −2.1± 0.7 cm3
molecule–1 s–1 (10). With the atomizer spraying distilled wa-
ter (or turned off — the same signal is measured) in each of
the five flames, an H3O+ profile is obtained (not shown; see
(6)) which rises rapidly near the flame reaction zone to a
constant plateau value that persists downstream; the magni-
tude increases with increasing flame temperature. The rapid
rise reflects the γ3-dependence of the three radical concen-
trations in reaction [2]. When tin is added to a flame, SnOH+
is produced from H3O+ by the chemical ionization (CI) reac-
tion [3] involving fast proton transfer, supplemented by the
chemi-ionization reaction [4]. Atomic Sn+ ions are also
formed immediately by the fast balanced reaction [5].
Figure 2 presents profiles for the individual ions in flame
3 measured at low resolution with the atomizer spraying a
0.1 M solution of SnCl4·5H2O. For a given tin ion, low reso-
lution effectively blended all the tin isotopes into a single
peak and yielded higher sensitivity. The total positive ions
TPI12 and the total tin ions TPI100 are also shown; the differ-
ence of these two profiles is the sum of the H3O+, Na+,
[3]
[4]
[5]
[6]
[7]
[8]
[9]
H3O+ + SnO = SnOH+ + H2O
SnO + H
SnOH+ + e–
SnOH+ + H = Sn+ + H2O
Sn+ + e– + M → Sn + M
K + M → K+ + e– + M
Na + M → Na+ + e– + M
+
H5O2 , and K+ profiles. The important point at issue is that,
downstream near z = 30 mm, the SnOH+ (+ hydrate) and
H3O+ profiles are constant, indicative of equilibrium for the
fast proton transfer reaction [3] between SnO and H2O. Even
H3O+ + K
K+ + H2O + H
Na+ + H2O + H
[10] H3O+ + Na
© 1998 NRC Canada

1442
Can. J. Chem. Vol. 76, 1998
Fig. 3. Ion profiles measured at high resolution in flame 2 with
the atomizer spraying a 0.01 M solution of SnCl4·5H2O. The
flame reaction zone is located near z = 0.
Fig. 4. Van’t Hoff plot for the equilibrium constant of the proton
transfer reaction [3] involving H3O+ and SnOH+ measured in
five flames over the temperature range 1820–2400 K with the
atomizer spraying aqueous solutions of SnCl4·5H2O of
concentrations 0.1 M (open circles) and 0.01 M (closed circles).
though the reaction is strongly exoergic, the large concentra-
tion ratio [H2O]/[SnO] ≈ 3 × 105 can still bring the H3O+ and
SnOH+ ions into equilibrium in flames. Furthermore, the re-
laxation time τ3 = 1/(k3[SnO] + k–3[H2O]) is of the order of
100 µs, appreciably greater than the sampling time of
roughly 1 µs, such that the equilibrium reaction [3] does not
shift during sampling. For this estimate, a typical value of k3
for a proton transfer reaction of the order of 10–9 cm3 mole-
cule–1 s–1 was assumed (k3 would be somewhat higher at
flame temperature than room temperature). A value for k–3
for the reverse reaction was estimated to be that for k3 re-
duced by an exponential factor corresponding to the approx-
imate endothermicity of the back reaction.
120SnOH+ was measured, and [H3O+] > [120SnOH+] at the
lower tin concentration. For plotting purposes, the 120Sn iso-
topic signals were multiplied by 100/32.59 to give 100% Sn
signals. Figure 4 presents a van’t Hoff plot of ln K3 versus
1/T for the two runs with the 0.1 and 0.01 M solutions
sprayed into five flames. From the slope of the straight line
°
fitted by least squares, ∆H2100[3] = –218.0 ± 10.5 (standard
deviation) kJ mol–1 over the flame temperature range 1820–
2400 K centred on the average temperature of 2100 K.
The objective of this aspect of the study was to measure
the ion ratio [SnOH+]/[H3O+] to get the equilibrium constant
K3 giving ∆H°[3] from the slope of a van’t Hoff plot of ln
K3 versus 1/T where ∆H°[3] = PA°(H2O) – PA°(SnO), the
difference of the proton affinities. There is another important
feature of this method involving the measurement of K3 in
five flames spanning nearly 600 K. Suppose the two ion sig-
nals are subject to mass discrimination leading to an incor-
°
°
°
To obtain PA298(SnO) = PA298(H2O) – ∆H298[3], the reac-
°
tion enthalpy at 298.15 K is required, derived from ∆H298
=
°
°
°
∆H2100 – ∆ (H2100 − H298) where the standard enthalpy func-
tion (H2100 − H298) is available for H3O+, H2O (5), and SnO
(3) but not for SnOH+. Accordingly, it was calculated by sta-
tistical methods at the average flame temperature of 2100 K.
For reaction [3], the temperature correction is small;
°
°
∆(H2100 − H298) = 1.82 kJ mol–1 giving ∆H298[3] = –219.8 ±
′
°
°
°
rect value of K3 = f × K3 where f is a constant factor which
–1
°
10.5 kJ mol . Based on the current value of PA298(H2O) =
is independent of temperature. The slope of the van’t Hoff
plot will still yield the correct value of ∆H°[3] although the
intercept will be (∆S°[3]/R + ln f). It will be shown in the
next section that reaction [5] producing Sn+ shifts to the
right during sampling such that measured values of [SnOH+]
are slightly small by a nearly constant factor f which is only
very weakly dependent on temperature. This is similar to the
case of mass discrimination, and good values of ∆H°[3] are
still obtained.
By way of contrast, the profiles in Fig. 3 were measured
at high resolution in the hot flame 2 with the atomizer spray-
ing a 0.01 M solution of SnCl4·5H2O. Again, the SnOH+ and
H3O+ profiles are constant downstream, indicative of equi-
librium. In this case, only the single biggest isotopic peak
691.0 kJ mol–1,3 the proton affinity of SnO has a value
PA298(SnO) = 911 ± 21 kJ mol–1 = 218 ± 5 kcal mol–1, in
°
excellent agreement with the calculated value of 215.6 kcal
mol–1 obtained by Rodriquez et al. (2).
5.2 The SnOH+/Sn+ equilibrium
The equilibration of SnOH+ and Sn+ by reaction [5] is
rapid in flames. If k5 = 10–9 cm3 molecule–1 s–1 is assumed
with k–5 reduced by a factor corresponding to the endother-
micity of the back reaction (approximately 100 kJ mol–1),
the relaxation time τ5 ≈ 0.1 µs. This means that the reaction
will shift to the right in the exothermic direction during sam-
pling, and measured [SnOH+]/[Sn+] ratios will be too small.
3 E.P. Hunter and S.G. Lias. NIST Standard Database Number 69. March 1998 release. http://webbook.nist.gov/chemistry/form-ser.html/
© 1998 NRC Canada

Goodings and Chen
1443
5.3 Recombination of SnOH+ with electrons
Fig. 5. Ion profiles measured in flame 3 with 0.25 mol% of
added CH4 and the atomizer spraying a mixed solution of
0.098 M SnCl4·5H2O and 0.001 M KNO3 such that electron–ion
recombination of SnOH+ is the dominant process downstream;
TPI12 denotes total positive ions and TPI100 is total ions of tin.
The flame reaction zone is located near z = 0.
These hydrogen flames contain a small amount of H3O+
natural ionization formed by the chemi-ionization reaction
[2], and SnOH+ is formed by chemical ionization (CI) of
SnO by H3O+ via the proton transfer reaction [3]. A further
possible source of SnOH+ is the chemi-ionization reaction
[4]. To study the recombination reaction [–4], the objectives
were to form a relatively high concentration of SnOH+ rap-
idly near the flame reaction zone and then to assure that re-
combination was dominant downstream in the burnt gas.
These conditions were achieved, first by adding 0.25 mol%
of CH4 to produce a superequilibrium level of H3O+ for CI
by reaction [3]. Then, a small amount of potassium as KNO3
was added to the atomizer solution to raise the concentration
of free electrons in the flame, thereby enhancing the rate of
recombination of SnOH+ by reaction [–4]. Potassium atoms
are chemically ionized initially by H3O+ to some extent by
reaction [9] (19) but progressively ionize further down-
stream by collisional (thermal) ionization via reaction [7]
(20). There is no evidence that potassium interacts with tin
by any process other than its effect on recombination
through [e–]. It was necessary to adjust the relative concen-
trations of both SnCl4·5H2O and KNO3 in the atomizer solu-
tion rather carefully so that (i) H3O+ disappears quite rapidly
downstream to maximize the region in which SnOH+ recom-
bination is dominant, and (ii) [SnOH+] falls to a value near
zero at z = 30 mm downstream indicating that SnOH+ ion
production by the chemi-ionization reaction [4] was negligi-
ble.
Since absolute SnOH+ concentrations were needed for the
recombination studies described below, it was necessary to
calculate the equilibrium constant K5 as a function of tem-
perature. In this way, total tin ion signals [TPI100] could be
measured and true [SnOH+] determined using K5.
Figure 5 presents profiles for flame 3 with added CH4 and
with the atomizer spraying a mixed aqueous solution of
0.098 M SnCl4·5H2O and 0.001 M KNO3. At these concen-
trations, the profiles fulfil the conditions outlined in (i) and
(ii) above. The TPI100 signal includes SnOH+, Sn+, and any
hydrates formed during sampling. Since negative ions were
not detected in these flames, the TPI12 profile which mea-
sures the sum of all positive ions gives [e–] because a flame
is a quasi-neutral plasma. From reaction [–4], –d[SnOH+]/dt
= k–4[SnOH+][e–] – (ion production term) with v = dz/dt =
15.6 m s–1 from Table 1. Differentiation of [TPI100] gives the
kinetic expression –d[TPI100]/dt = –d[SnOH+]/dt – d[Sn+]/dt
= k–4[SnOH+][e–] + k6[Sn+][e–] – k4[SnO][H]eqγ in which the
equilibrated reaction [5] does not appear. The assumptions
are made that three-body recombination of atomic Sn+ in re-
action [6] is negligible compared with reaction [–4], and that
the production term from reaction [4] can be ignored be-
cause of the experimental conditions set up; also, reaction
[3] does not contribute downstream where [H3O+] ≈ 0. Since
[SnOH+] = [TPI100]/(1 + K5[H]eqγ/[H2O]), the kinetic
expression reduces to –v(d[TPI100]/dz)(1 + K5[H]eqγ/[H2O]) =
k–4[TPI100][TPI12]. Note that the factor (1 + K5[H]eqγ/[H2O]),
which has been multiplied across to the left-hand side, is
equivalent to (1 + [Sn+]/[SnOH+]); the ion ratio is small
compared with unity, varying from 0.13 in flame 2 to 0.06 in
flame 5.
°
°
The free energy function –(GT − H298)/T was calculated
by statistical methods for SnOH+ and Sn+ at many tempera-
tures up to 2500 K and combined with corresponding values
from the JANAF tables (5) for H and H2O to obtain
°
°
∆GT − ∆H298 for reaction [5]. Using all values at 298.15 K
(16) and our value of PA298(SnO) = 910.8 kJ mol–1,
°
°
∆H298[5] = PA°(SnO) – IE°(H) + D°(SnO) + IE°(Sn) –
–1
°
D°(OH) – D°(H-OH) = –86.3 kJ mol , giving ∆GT and thus
K5. A plot of ln K5 versus 1/T gives a very good straight line
over the range of flame temperatures 1820–2400 K with a
least-squares fit represented by K5
(11 450/T). In fact, a good straight line is obtained over the
whole temperature range of 298–2500 K fitted by K5
= 0.077 38 exp
=
0.1115 exp (10 890/T). The entropy change of reaction [5]
was calculated to be ∆S2100 = –21.2 and ∆S298 = –6.4 J mol–1
°
°
–1
°
K . The reaction enthalpy has a value ∆H2100 = –94.8 kJ
mol–1 at the average flame temperature with ∆H0 = –84.3 ±
°
20.9 kJ mol–1 (= ∆E0 ), in reasonable agreement with the
°
°
value arrived at by Jensen (1). He quotes a value ∆E0 [5] =
–100 ± 20 kJ mol–1 based on mass-spectrometric measure-
ments of the [SnOH+]/[Sn+] ratio at two flame temperatures
and a rough statistical calculation with vibrational tempera-
tures estimated from those of the alkaline earth metals. His
ion ratio measurements may not have been shifted apprecia-
bly by sampling cooling because, to the best of our knowl-
edge, he was employing low-pressure flames (P = 1–10
Torr) in his mass spectrometer (18); since the relaxation time
For the final kinetic expression, Fig. 6 presents a plot for
flame 3 of the left-hand side versus [TPI100][TPI12] in the
range z = 15–30 mm where [H O+] 0. The slope of the plot
≈
3
τ
1/P, its magnitude in his experiment may have exceeded
the sampling time of approximately 1 µs.
gives the recombination coefficient k–4 = 3.6 × 10–7 cm3
molecule–1 s–1 in this particular case. The small negative in-
© 1998 NRC Canada

1444
Can. J. Chem. Vol. 76, 1998
Fig. 6. Plot involving the kinetic expression for SnOH+ ion loss
by electron–ion recombination by reaction [–4] for the range z =
15–30 mm downstream in flame 3 using the ion profiles
presented in Fig. 5, where the slope yields the recombination
coefficient k–4.
Fig. 7. Logarithmic plot of the recombination coefficient k–4
versus temperature T in the range 1820–2400 K. The best-fit
solid line exhibits a T–1.7 dependence, for comparison with the
broken line giving the T–1.5 dependence expected from simple
theory.
reached by Jensen (1). A final consideration is that the rate
of collisional (thermal) ionization R7 ≈108 ions cm–3 s–1 even
for a tiny (unknown) potassium impurity concentration of
10–7 M in the atomizer solution (20); the rate R4 for the
chemi-ionization of tin is very comparable, and certainly not
dominant. Although the experiments were not successful,
these considerations seemed worthy of discussion because
they indicate the complete ionization picture and may apply
to other metals with small rate coefficients for chemi-
ionization.
tercept shows that ion production is small and can safely be
ignored. Similar profiles were measured and plots made to
evaluate k–4 in all five flames. The results over the tempera-
ture range 1820–2400 K are given in Fig. 7 as a plot of log
k–4 versus log T. A straight line fitted by least squares gives
the temperature variation as k–4
=
(0.116
±
0.065)T –(1.66± 0.16) cm3 molecule–1 s–1. A discussion of the
temperature dependence of electron-ion recombination coef-
ficients in flames has been given by Butler and Hayhurst
(10). Simple theory indicates a T–1.5 dependence with which
our value is in good agreement.
Accordingly, the equilibrium constant K4 for reaction [4]
was obtained by statistical methods, again involving the free
energy function –(GT − H298)/T calculated for SnOH+ and
available for SnO (3), H and e– (5). At any temperature T,
°
°
5.4 Chemi-ionization of SnO + H
° ° °
this gives ∆{–(GT − H298)/T} = R ln K4 + ∆H298/T with
Repeated attempts were made to measure the rate constant
of the chemi-ionization reaction [4] directly but were frus-
trated by the presence of tiny amounts of potassium and so-
dium in the salt sample of SnCl4·5H2O. These impurities
give rise to the K+ and Na+ peaks visible in the mass spec-
trum shown in Fig. 1 which arise initially upstream by the
electron transfer reactions [9] and [10] (19), and further
downstream by the collisional (thermal) ionization reactions
[7] and [8] (20). The initial rise of the SnOH+ profile in
Fig. 2 stems from proton transfer by reaction [3]. This
means that the growth of the SnOH+ profile in the upstream
region cannot be analysed for k4. Figure 2 also shows how
the K+ and Na+ signals grow downstream by thermal ioniza-
tion to increase [e–]. Furthermore, k4 cannot be readily eval-
uated from the constant SnOH+ profile downstream near z =
30 mm because reaction [4] is not at equilibrium. The relax-
∆H298[4] = –PA298(SnO) + IE298(H) = 407.4 kJ mol–1. Over
the temperature range 1820–2400 K of the five flames, a
plot of ln K4 versus 1/T gave a very good straight line from
which K4 = 0.004 868 exp (–52 070/T). Over the whole tem-
perature range 298.15–2500 K, a similar plot gave a good
straight line yielding K4 = 0.001 324 exp (–49 710/T).
For reaction [4], other channels in both the forward and
reverse directions are unlikely, and the assumption of de-
tailed balance is reasonable. Using K4 in the range of flame
temperatures, the rate constant for chemi-ionization is ob-
tained from k4 = k–4K4. When combined with the experimen-
tal values of k–4 in the five flames, values of k4 are obtained
ranging from 5.03 × 10–19 in flame 2 at 2400 K to 8.07 ×
10–22 cm3 molecule–1 s–1 in flame 5 at 1820 K. A plot of ln
k4 versus 1/T is shown in Fig. 8. A good straight line fitted
by least squares through the data points gives k4 = 3.27 ×
10–10 exp (–48 630/T) cm3 molecule–1 s–1 for the tempera-
ture range 1820–2400 K. Even at flame temperatures, the
values of the rate constant are small but should have been
measureable experimentally were it not for the presence of
potassium and sodium as impurities.
°
°
°
½
ation time is given by τ4 = {ln (2e – 1)}/2(k4k–4[SnO][[H])
which has a value of the order of 10 ms for a 0.1 M solution
of SnCl4·5H2O sprayed by the atomizer and k4 ≈ 10–20 cm3
molecule–1 s–1 at 2100 K (derived below); equilibrium can-
not be achieved in the time of approximately 2 ms corre-
sponding to 30 mm of flame. The same conclusion was
© 1998 NRC Canada

Goodings and Chen
1445
the electron-ion recombination coefficient of SnOH+ as a
function of temperature. Its T–1.7 temperature dependence is
close to the T–1.5 dependence predicted by simple theory.
The recombination reaction is the backward direction of the
chemi-ionization reaction of SnO + H. Its relatively small
rate coefficient could not be measured experimentally due to
the ionization of potassium and sodium present as impurities
in the tin salt. However, the equilibrium constant for chemi-
ionization/recombination could be calculated by statistical
methods. Assuming detailed balance, the rate coefficient for
chemi-ionization as a function of temperature was obtained
as the product of the experimental recombination coefficient
Fig. 8. Semi-logarithmic plot giving the temperature variation of
the rate constant as ln k4 versus 1/T for the chemi-ionization
reaction [4] in the range 1820–2400 K.
and calculated equilibrium constant. Finally, the bond
+
°
strength D0 (HO—Sn ) could be calculated, and also the
+
°
standard zero-point enthalpy of formation ∆fH0 (SnOH ).
This study combines experiment with theoretical calcula-
tions to give a fairly complete analysis of tin ionization.
The authors wish to thank Prof. Alan C. Hopkinson and
members of his group for helpful discussions, and for mak-
ing available to us the details of their ab initio calculations
of the SnOH+ ion. Support of this work by the Natural Sci-
ences and Engineering Research Council of Canada is grate-
fully acknowledged.
+
+
°
°
5.5 Bond energy D0(HO-Sn ) and ∆fH0(SnOH )
The standard Sn—O bond dissociation energy for the
SnOH+ ion can be found from the calculated change in the
enthalpy function for the dissociation reaction
[11] SnOH+ → Sn+ + OH
1. D.E. Jensen. J. Chem. Phys. 51, 4674 (1969).
2. C.F. Rodriquez, A. Cunje, and A.C. Hopkinson. J. Mol. Struct.
(Theochem), 430, 149 (1998).
3. J.B. Pedley and E.M. Marshall. J. Phys. Chem. Ref. Data, 12,
967 (1983).
4. C.E. Moore. Natl. Stand. Ref. Data Ser. Natl. Bur. Stand.
(U.S.) (NSRDS–NBS) 35. Vol. 3. Superintendent of Docu-
ments, U.S. Government Printing Office, Washington, D.C.
Reissued 1971 (from NBS Circ. 467, 1958).
5. M.W. Chase, Jr., C.A. Davies, J.R. Downey, Jr., D.J. Frurip,
R.A. McDonald, and A.N. Syverud. JANAF thermochemical
tables. 3rd ed. J. Phys. Chem. Ref. Data, 14 (Suppl. 1) (1985).
6. C.J. Butler and A.N. Hayhurst. J. Chem. Soc. Faraday Trans.
93, 1497 (1997).
°
°
with reference to reaction [5]; i.e., ∆{H298 − H0 }[11] = 3.49
kJ mol–1 = ∆H298[11] – ∆H0 [11] = ∆H298[5] + D298(H—OH)
°
°
°
°
+
°
– D0 (HO—Sn ). This gives a value for the bond energy
+
–1
D0 (HO—Sn ) = 408 ± 21 kJ mol (98 ± 5 kcal mol–1).
°
Finally, the standard zero-point enthalpy of formation
+
–1
°
°
∆fH0 (SnOH ) can be obtained from ∆H0 [5] = –84.3 kJ mol
+
°
°
with ∆fH0 (Sn ) = 1010.6 (21), ∆fH0 (H2O) = –238.9 and
–1
+
°
°
∆fH0 (H) = 216.0 kJ mol (5). The value is ∆fH0 (SnOH ) =
640 ± 21 kJ mol–1 (153 ± 5 kcal mol–1); at room tempera-
ture, ∆fH298(SnOH+) = 637 ± 21 kJ mol–1. It is in good
°
agreement with Jensen’s value stated as the equivalent func-
+
–1
°
tion ∆fE0 (SnOH ) = 655 ± 27 kJ mol estimated nearly 30
7. A.N. Hayhurst and D.B. Kittelson. Proc. R. Soc. London A,
338, 155 (1974).
years ago from a crude statistical model.
8. J.M. Goodings, C.S. Hassanali, P.M. Patterson, and C. Chow.
Int. J. Mass Spectrom. Ion Processes, 132, 83 (1994).
9. J.M. Goodings, S.M. Graham, and W.J. Megaw. J. Aerosol
Sci. 14, 679 (1983).
10. C.J. Butler and A.N. Hayhurst. J. Chem. Soc. Faraday Trans.
92, 707 (1996).
11. J.M. Goodings and P.M. Patterson. Int. J. Mass Spectrom. Ion
Processes, 151, 17 (1995).
12. S.D.T. Axford and A.N. Hayhurst. Int. J. Mass Spectrom. Ion
Processes, 110, 31 (1991).
13. A.N. Hayhurst, D.B. Kittelson, and N.R. Telford. Combust.
Flame, 28, 123 (1977).
14. A.N. Hayhurst and D.B. Kittelson. Combust. Flame, 28, 137 (1977).
15. N.A. Burdett and A.N. Hayhurst. Combust. Flame, 34, 119 (1979).
16. D.R. Lide (Editor). CRC handbook of chemistry and physics.
73rd ed. CRC Press, Boca Raton, Fla. 1992.
The ionization of tin was investigated in H2-O2-N2 flames
in the range 1820–2400 K by mass-spectrometric sampling.
The study was greatly aided by data for rotational and vibra-
tional temperatures of the SnOH+ ion from ab initio calcula-
tions (2) so that thermodynamic functions could be
calculated by statistical mechanics. If total tin is present
only as SnO and Sn, SnO > 97% in these fuel-rich flames.
The flame conditions are such that SnOH+ can be measured
in equilibrium with H3O+, leading to the proton affinity
PA°(SnO) relative to that of H2O. The rapid equilibration of
SnOH+ with Sn+ cannot be measured because it is shifted to
a lower unknown temperature during sampling, but its equi-
librium constant could be determined by a statistical thermo-
dynamic calculation. This provided correct values of the
SnOH+ concentration for the experimental measurement of
17. S.D.T. Axford and A.N. Hayhurst. J. Chem. Soc. Faraday
Trans. 91, 827 (1995).
© 1998 NRC Canada

1446
Can. J. Chem. Vol. 76, 1998
18. H.F. Calcote. In Ion-molecule reactions. Vol. 2. Edited by J.L.
Franklin. Plenum Press, New York. 1972. p. 673.
19. A.N. Hayhurst and N.R. Telford. Trans. Faraday Soc. 66, 2784
(1970).
20. A.F. Ashton and A.N. Hayhurst. Combust. Flame, 21, 69 (1973).
21. S.G. Lias, J.E. Bartmess, J.F. Liebman, J.L. Holmes, R.D.
Levin, and W.G. Mallard. J. Phys. Chem. Ref. Data, 17 (Suppl.
1) (1988).
© 1998 NRC Canada