The kinetics and thermodynamics of ion solvation applicable to ion ...

IJIMS 5(2002)2,19-41, p. 19
The kinetics and thermodynamics of ion solvation applicable to ion
mobility spectrometry
John A. Stone, Chemistry Department, Queen’s University, Kingston, Ontario,
Canada K7L 3N6
It is a truism that an ion cannot react with a molecule unless they collide and there
are now well-accepted theories that allow the calculation of rate constants for collisions
between small ions and molecules.[1-4] After the formation of the collision complex
there are many different types of reaction that may occur, for example electron transfer
from molecule to ion, proton transfer, hydrogen atom transfer, the stabilization of the
complex etc. In all cases the system of ions and molecules moves in the direction of
decreasing free energy and, given sufficient time, will attain a state of equilibrium. This
paper describes the kinetics and thermodynamics pertinent to some of the ion chemistry
that occurs in an ion mobility spectrometer. Emphasis is placed on the formation of
ion/molecule complexes that are sometimes called cluster ions or solvated ions. The
hydration of ions by reaction with gaseous water molecules and its influence on ion
mobility will be emphasized.
Ion/molecule kinetics
There is always a long range attractive potential between an ion and a neutral
molecule which, provided that ion and molecule are not particularly large, leads to a
radius for the collision cross section which is greater than the sum of ion and molecule
radii. The rate constants, k c , for ion/molecule collisions are therefore in general
considerably larger than are those for neutral molecule/neutral molecule collisions.
Theoretical values of k c are often obtained using the Average-Dipole-Orientation (ADO)

IJIMS 5(2002)2,19-41, p. 20
theory shown in Eq.1 which treats the ion as a point charge q that is interacting with a
molecule of average polarizability α and dipole moment µD.[1,2] In the equation, µ is the
2
reduced mass of the reacting pair and C, a parameter that is a function of µ D /α , is a
measure of the average angle of the dipole with respect to the line of centres of ion and
dipole. A C value of unity signifies that the dipole has locked on to the ion. For a dipolar
molecule interacting with a positive ion this means that the ion and dipole are co-linear
with the negative end of the dipole nearest the ion. C has been parameterized for different
temperatures.[5] Over the range of ion mobility spectrometer operating temperatures the
value of C is considerably smaller than unity due to thermal motion and the value
decreases with increasing temperature. If the molecule has no permanent dipole the
second term of Equation 1 vanishes and k c = k L , the Langevin collision rate constant
which is determined by ion/induced dipole forces and is independent of temperature.[6]
1
⎛ 1
⎞
2πq
⎜ ⎛ 2 ⎞2
2
⎟
k
c
= kADO
= ⎜ α + Cµ
1
D⎜
⎟ ⎟
(1)
⎝ πkT
⎠
2
µ ⎝
⎠
Water, which is ubiquitous in ion mobility spectrometers operating at atmospheric
pressure, has a relatively large dipole moment but is not very polarizable compared with
most analyte molecules. Table 1 shows the physical properties of typical molecules
required for computation of their collision rate constants at 350K. The last column shows
the computed collision rate constant for each of the molecules with the proton-bound
acetone dimer ion of mass 117 u. It can be seen that as a rough rule of thumb one can
take the second order rate constant for the collision of an ion with a molecule as being
about 1 x 10 -9 cm 3 molecule -1 s -1 . Molecules with large dipole moments will have slightly
1

IJIMS 5(2002)2,19-41, p. 21
higher rate constants that decrease with increasing temperature. Molecules with no dipole
moments will have slightly lower rate constants that are independent of temperature.
After an ion/molecule collision, the colliding pair will form an association
complex that contains the energy of interaction as internal energy - vibrational and
rotational. The lifetime of the complex is dependent on many factors including, in
particular, the depth of the attractive well on the potential energy surface and the
molecular complexity.[7] For example, the association complex formed by an ion and a
molecule for which a highly exothermic proton transfer reaction is possible, may have a
lifetime less than the time between collisions at atmospheric pressure (~10 -10 s) whereas a
reaction which is almost thermoneutral may yield a much longer-lived complex. If the
lifetime of the complex is greater than 10 -10 s and the pressure is 1 atmosphere then
collisional stabilization may occur and the complex is trapped in a potential well. The ion
can be regarded as having been solvated by the molecule. The depth of the well depends
on the strength of the ion/molecule interaction and involves the polarizability of ion and
neutral molecule, dipolar and higher polar forces, degree of electron transfer, etc.
Consider an ion/molecule reaction in which a stable complex may be formed. If
every collision between ion and molecule (M) leads to association, then the lifetime of an
ion, i.e. the time between its formation and its association with the gaseous molecule,
may be estimated using ADO theory. Assuming that the concentration of the ions is far
less than that of the neutral molecules, then the ion disappears in a pseudo-first order
reaction. By definition, the ion lifetime is the time for the ion concentration to decrease
to 1/e of its initial value. This time is equal to 1/(k c [M]), where [M] is the concentration
+
of the neutral molecule. Take for example the possible fate of N 2 formed in an ion

IJIMS 5(2002)2,19-41, p. 22
source containing one atmosphere of nitrogen and 10 ppm of water. Assume also that the
+
only competing reactions for the ion are formation of N 4 by collision with N 2 and
formation of [N 2·OH 2 ] + by collision with water. At 350K, the lifetime with respect to
association with N 2 is 6 x 10 -11 s and that with respect to water is 3 x 10 -6 s. The collision
rate with N 2 is of course orders of magnitude larger than the collision rate with water
because the respective neutral molecule concentrations are so disparate. The collision rate
constants are however of the same order of magnitude. N + 2 will therefore initially
associate with N 2 and even if the reaction efficiency with N 2 to form N + 4 was very much
less than 100%, the reaction forming N4 + will still occur before there is a collision with a
water molecule. N + 4 , having no reaction with N 2 other than N 2 exchange, which does not
change its identity, can only disappear by collision and reaction with water. The lifetime
+
of N 4 with respect to collision and association with water is almost identical to that
calculated for N + 2 viz. 3 x 10 -6 s. If the initially formed complex, [N 4·OH ]·+ 2 , then collides
and reacts with another water to give, probably, N 2 + H 3 O + + ·OH, the half life for this
efficient reaction is computed, using the appropriate ADO collision rate constant, to be 5
x 10 -6 s. Further consecutive associative/reactive reactions with the water will have
essentially the same half life, the final ions being (H 2 O) n H + , the normal reactant ion(s) in
ion mobility spectrometry. Since the time between formation of ions in the ion source and
their gating into the drift region is of the order of milliseconds then the (H 2 O) n H + ions
will be in equilibrium with the ambient water molecules before they arrive at the shutter.
The corollary is that very reactive, high energy ions such as N + 2 and N + 4 under normal
circumstances will not even enter the drift region and certainly will not be observed at the
detector.

IJIMS 5(2002)2,19-41, p. 23
All association reactions proceed to an equilibrium state in which the flux of
reactants to products is equal in magnitude to the reverse flux. The kinetic visualization
of the equilibrium process is usually set out as in Equations 2 and 3. X is any gas
molecule present in the system.
k c
A + + M (A +·M) * (2)
k b
k f
(A +·M) * + X A +·M + X (3)
k r
The complex (A +·M) * contains all the energy of association between ion and
molecule, some of which it must lose if a stable complex is to be formed. At atmospheric
pressure this occurs by collision with any neutral molecule, X. k c is the second order
collision rate constant for ion and molecule and k b is the unimolecular dissociation rate
constant for the complex. k b can be calculated by RRKM theory [8] if the geometry and
the vibrational modes of the complex are known, or can be approximated. kf is the second
order rate constant for the stabilization of the complex by collision with X. If it is
assumed that a single collision carries away sufficient energy so that return to reactants is
not possible then k f is the rate constant for collision between complex and X, which can
also be calculated by ADO theory. An empirical efficiency factor β, whose value is less
than unity, is sometimes used to signify that a single collision is insufficient to stabilize
the complex. If the reaction is sufficiently exothermic, the reverse thermal activation of

IJIMS 5(2002)2,19-41, p. 24
the stabilized complex, rate constant k r , may be ignored and the rate constant k + for stable
complex formation is given by Equation 4.
kckf
[X]
k+ =
(4)
k + k [X]
b
f
At atmospheric pressure and reasonable temperatures kb can be very small
compared with k r [X] and then k + = k c . This is usual for activated complexes having a
large number of degrees of freedom and/or for which the depth of the potential well
confining the complex is sufficiently large. A stabilized association complex is then
formed at every collision between ion and molecule. Such might be the case for example
for the association of H 2 O with H 3 O + at room temperature for which the measured
enthalpy of association is –132 kJ mol -1 .[9] However, if the association enthalpy between
ion and molecule is only a few kJ mol -1 then the complex may have a very short lifetime
and no long lived, stabilized complex may be formed. This might be the case for example
for the association of N 2 with an ion such as protonated benzene in which the charge is
delocalized over much of the ring. The enthalpy changes for such weak interactions are
very difficult to determine experimentally but they are important in defining ion
mobilities and will be very important in influencing mobilities in mixed drift gases. A
knowledge of association reaction kinetics (and thermodynamics) will certainly be
important in explaining the mechanism of operation of the new segmented field detectors
where the lifetime of weak association complexes will be very dependent on electric
field.
The thermodynamics of ion/molecule associations
The thermodynamic formulation of the equilibrium constant is well understood.
For the overall association reaction 5 leading to a stabilized complex, the associated

IJIMS 5(2002)2,19-41, p. 25
thermodynamic parameters, the equilibrium constant K, and the standard enthalpy,
entropy and free energy changes are given in Equations 6-8.
A + + M A·M + (5)
K
+
o
[A ⋅ M] P
•
[A ] P
=
+
M
(6)
∆G
o
−
RT
K = e
(7)
∆G o = ∆H o -T∆S o (8)
A compilation of early thermodynamic data for the association of many neutrals
and ions is available.[9] Most of the data in the compilation were obtained using high
pressure mass spectrometry, one of the few techniques which allows the study of
association reactions over the necessary wide temperature range.
The equilibrium constant is related by Equation 9 to the forward, k+, and
backward k - rate constants for the overall reaction. P o is the standard pressure of one
atmosphere.
k
K =
k
⋅P
+ o
(9)
−
Representative enthalpies for the association of water, acetone and acetonitrile
with four different ions are shown in Table 2 and standard enthalpy and entropy changes
for the hydration of some positive and negative ions are shown in Table 3. To be noted is
the fact that while the enthalpy of association varies widely with the nature of each ionmolecule
pair, the entropy change shows much less variation. This is because the major
contribution to ∆S o is the loss of three degrees of translational freedom when two

IJIMS 5(2002)2,19-41, p. 26
particles combine. Table 2 illustrates the fact that water is not energetically the most
strongly held molecule in the first solvation shell of an ion. Molecules with larger dipole
moments or which are more polarizable than water are preferentially held.
The role of association equilibria in ion mobility spectrometry can be considered
from the point of view of two extreme cases. (a) When the associating neutral molecule is
present throughout the whole system and (b) when the molecule is confined to the source
region and does not enter the drift region. Examples of the first case are the hydration of
ions by ubiquitous water in the drift and source gases, and the doping the whole system
with, for example, acetone. If the neutral molecule is present only in the source region,
then unimolecular decomposition of the complex will occur in the drift region with a rate
constant given by Equation 10 and an associated lifetime τ given by Equation 11.
k
k
K
o
= +
− ⋅ P
(10)
K 1 = ⋅
o
k P
τ
+
(11)
The larger the value of the equilibrium constant K, the less the decomposition that
will occur in the time that the complex spends in the drift region. This type of behaviour
will not be considered further in this paper.
An ion has the possibility of associating with more than one molecule. Table 4
shows the changes in standard enthalpy and entropy for the association of successive
solvating molecules with several ions: protonated water, H 3 O + , with water; protonated
acetone, (CH 3 ) 2 CO·H + , with water; protonated, C 5 H 5 N·H + , pyridine with water; and
protonated acetone with acetone. The enthalpy change becomes less negative for the
addition of each successive associating molecule, whereas the associated entropy changes

IJIMS 5(2002)2,19-41, p. 27
do not show the same monotonic change, but remain fairly constant for the addition of
the second and succeeding molecules. In the next section, the thermodynamic
information in Table 4 will be used to determine the relative equilibrium concentrations
of the ion/molecule complexes in the four systems over a range of temperature.
Temperature/distribution diagrams for solvated ions
(H 2 O) n H + is often the reactant ion in an ion mobility spectrometer operating in the
positive ion mode and at a given temperature n will not be single valued but will have a
range of values. If the reasonable assumption is made that the various (H2O)nH + ions are
in equilibrium with each other via ambient water before the ions leave the source region,
then the relative populations of the various hydrates will remain constant in the drift
region. The thermodynamic data in Table 4 allows the distribution of the hydrates to be
computed at any temperature for a fixed ambient water concentration. Figures 1 and 2
show the calculated relative amounts of the proton hydrates at different temperatures for
water concentrations of 2 and 10 ppm. Only the first five hydrates are present with
significant intensities over the temperature range 298-568 K. At 298K, with both 2 ppm
and 10 ppm water, the reactant ion peak will consist mainly of (H 2 O) 4 H + while at 550 K,
a relatively high temperature for the operation of an ion mobility spectrometer, (H 2 O) 2 H +
will be the major ion. A change in water concentration from to 2 ppm to 10 ppm does not
change the nature of the important ions in the temperature range of the figure. The higher
hydrates are slightly more favoured by the higher water concentration at any temperature.
A molecule of water associates via hydrogen bonding with protonated
molecules, such as pyridine and acetone. For example, protonated pyridine forms a
complex with a water molecule, which may be described as C 5 H 5 N·H +···OH 2 . The

IJIMS 5(2002)2,19-41, p. 28
enthalpy change for the addition of the first water molecule depends on the difference in
proton affinity between the molecule and water. The larger this difference, the smaller the
hydration enthalpy. Water has an evaluated proton affinity of 691 kJ mol -1 and nitrogen
compounds have some of the highest proton affinities (PA = 800 - 1000 kJ mol -1 ) and so
have low hydration enthalpies.[10] Pyridine (PA = 930 kJ mol -1 ) will behave in a very
similar manner in this respect to 1,4-lutidine which is often used as a standard with an
accepted reduced mobility value. Since pyridine holds a proton very strongly, there is not
significant charge delocalization over an associated first water molecule and so the
tendency for hydrogen bonding with a second and a third water molecule is considerably
reduced compared with that seen for H 3 O + (Table 4). Figures 3 and 4 show the
distributions with temperature of the relative amounts of the hydrates of protonated
pyridine and protonated acetone for a water concentration of 10 ppm.
Figure 3 shows that the monohydrate is the only hydrate of significance for
protonated pyridine, and even so its concentration relative to that of the bare ion is
negligible above 400 K. The relative concentration of the dihydrate is negligible over the
whole temperature range. The mono-, di- and trihydrates of protonated acetone are all
present in significant relative concentrations at 298K but the second and third waters are
rather weakly bound and rapidly become insignificant with increasing temperature.
However, the monohydrate persists to a much higher temperature than does the
monohydrate of pyridine.
A protonated molecule MH + can be solvated quite strongly by the same molecule
M. The proton affinity difference is of course zero and the proton is shared equally by the
two molecules, M···H +··· M. The proton-bound dimer of acetone has a dissociation

IJIMS 5(2002)2,19-41, p. 29
enthalpy of 125.5 kJ mol -1 and, as seen in Figure 5, this leads to the dimer being the
predominant ion over the whole temperature range when the concentration of acetone is
100 ppm. This concentration is therefore a reasonable value if the dimer is to be the
reagent ion in the operation of an ion mobility spectrometer over quite a large
temperature range. The more highly solvated species are not significant because of steric
considerations.
The effect of hydration and clustering on ion mobilities
Because the proton hydrates are in equilibrium at all times with the water in the
source and drift gases, the reactant ion peak will always have an almost symmetrical
shape but the computed reduced mobility will be affected by the changing ion
composition at different temperatures. At low E/N the mobility, K, is related to the ion
mass via the reduced mass µ (defined in Equation 12 in which m A is the ion mass and
m X is the mass of the drift gas molecule) according to Equation 13.
µ =
m
m m
A
A
X
+ m
X
(12)
1
2
3 q ⎛ 2π
⎞ 1+ α
K = ⎜ ⎟
(13)
16 N ⎝ µ kT ⎠ ΩD(T)
Ω D (T) is defined as an average ion-neutral collision cross section that, according
to ADO theory, is independent of ion size. The proviso here is that only long-range forces
contribute to the collision cross section, and that the charge of the ion can still be
regarded as located at a point. In the limit of m A >> m M , µ reduces to m M . This means
that, not unexpectedly, the largest effect on the mobility of the ion due to changes in
reduced mass should be observed for ions of very low mass. The drift time of a group of

IJIMS 5(2002)2,19-41, p. 30
ions that are in equilibrium as they pass along a drift tube is the sum of their individual
drift times, ti , weighted by their equilibrium fractional abundances fi , i.e. t = Σ fi ti . Since
f i changes with temperature, a theoretical calculation of ion mobility should take this into
account and the effect should be acknowledged in any experimental mobility
determination. A computed reduced mobility for an ion that can participate in a clustering
reaction, with water for example, in the drift tube should not have a constant value for
data collected at different temperatures. Since all association reactions are exothermic,
the mass of the ion that is subject to association with neutral molecules will decrease with
increasing temperature and hence the contribution that the reduced mass makes to the
mobility will change. According to Equation 13, the mobility will vary as the inverse of
the square root of the reduced mass.
Since any ion will associate with water and since no ion mobility spectrometer
has a zero water content, then the mobility of any ion should be temperature dependent.
The extent of the variation of the mobility of an ion with temperature due to changing
mass will depend on the thermodynamics of its association with water. The hydrated
proton, of all the common hydrated ions, has the largest change in relative mass over the
viable temperature range of ion mobility spectrometry. The effect of hydration on the K o
values for other ions will depend on the enthalpy and entropy of association with water
and on their masses relative to that of water and the drift gas. The information present in
graphs such as those in Figures 1-5 may be used to assess the effect of ion-molecule
association on ion mobility as a function of temperature. Figure 6 shows the expected
changes in ion mobility for the systems of Figures 1-5 and for protonated pyridine and

IJIMS 5(2002)2,19-41, p. 31
protonated acetone at 2 ppm water. The relative mobilities have been normalized for each
system to the mobility of the non-hydrated ion, H 3 O + for the proton.
The largest relative change in Figure 6 is for H 3 O + , the most highly hydrated of
all the ions at any temperature. It is also to be noted that for this ion between 490K and
540K the effect of change of mass on mobility is almost independent of water
concentration over the range 2-10 ppm. Figures 1 and 2 show that this is the region where
(H 2 O) 2 H + predominates at both water concentrations. The same is true, but to a lesser
extent, around 360 K where (H 2 O) 3 H + predominates. The protonated acetone
monohydrate has maximum stability around 340 K and the dependence of the mobility on
water concentration is least at this temperature. The pyridine monohydrate exists only at
the lowest temperatures but there is a noticeable change in the mass dependence of the
mobility at these temperatures. At temperatures above ~350 K, protonated pyridine is not
hydrated to any significant extent and the constant ionic mass should make it a good
candidate, all other things being equal, as a reference mobility standard, albeit of rather
low mass and hence quite high absolute mobility.
The graph for the protonated acetone-acetone system in Figure 6 shows a large
range where there is little mass dependence of mobility. This occurs because the protonbound
dimer has a large enthalpy change for dissociation and it is therefore the dominant
ion over this very wide range of temperature.

IJIMS 5(2002)2,19-41, p. 32
References
1. T. Su, W.J. Chesnavich and M.T. Bowers, Collisions in a Non-Central Field: A
Variational and Trajectory Investigation of Ion-Dipole Capture, J. Chem. Phys. 72
(1980) 2641-2645.
2. T. Su and M.T. Bowers, Theory of Ion-Polar Molecule Collisions: Comparison with
Experimental Charge Transfer Reactions of Rare Gas Ions to Geometric Isomers of
Difluorobenzene and Dichloroethylene, J. Chem. Phys. 58 (1973) 3027-3037.
3. D.P. Ridge, Capture Collision Theory, p1-13 in: P. Ausloos and S. Lias (Eds)
Structure/Reactivity and Thermochemistry of Ions, D. Reidel, Dordrecht, 1987.
4. T. Su, The Parameterization of Kinetic Energy Dependencies of Ion-Polar Molecule
Collision Rate Constants by Trajectory Calculations. J. Chem. Phys. 100 (1994) 4703.
5. T. Su and M.T. Bowers, Ion-Polar Molecule Collisions: the Effect of Ion Size on Ion-
Polar Molecular Rate Constants; the Parameterization of the Average-Dipole
Orientation Theory, Int. J. Mass Spectrom.Ion. Phys. 12 (1973) 347-356.
6. G. Gioumousis and D.P. Stevenson, Reactions of Gaseous Molecule Ions with
Gaseous Molecules. V. Theory, J. Chem. Phys. 29 (1958) 294-299.
7. M. Meot-Ner, Temperature and Pressure Effects in the Kinetics of Ion-Molecule
Reactions, p 197-271in: M.T. Bowers (Ed) Gas Phase Ion Chemistry, V1, Academic
Press New York, 1979.
8. W. Forst, Theory of Unimolecular Reactions, Academic Press, New York, 1973.
9. R.G. Keesee and A.W. Castleman, Thermochemical Data on Gas-Phase Ion-Molecule
Association and clustering Reactions, J. Phys. Chem. Ref. Data 15 (1986) 1011.

IJIMS 5(2002)2,19-41, p. 33
10. NIST Standard Reference Database Number 69, Chemistry WebBook, February
2000, The National Institute of Standards and Technology, Washington, DC.

IJIMS 5(2002)2,19-41, p. 34
Figure 1. Fractional amounts of the (H 2 O) n H + ions in equilibrium with H 2 O at 2 ppm in
Relative amount
1
0.8
0.6
0.4
0.2
nitrogen at 1 atmosphere as functions of temperature.
(H 2 O) 3 H
+
(H 2 O) 4 H +
(H 2 O) 5 H +
(H 2 O) 2 H +
H 3 O +
0
298 348 398 448 498 548
Temperature (K)

IJIMS 5(2002)2,19-41, p. 35
Figure 2. Fractional amounts of the (H 2 O) n H + ions in equilibrium with H 2 O at 10 ppm in
nitrogen at 1 atmosphere as functions of temperature.
Relative amount
1
0.8
0.6
0.4
0.2
(H 2 O) 3 H
+
(H 2 O) 4 H +
(H 2 O) 5 H +
(H 2 O) 2 H +
H 3 O +
0
298 34
8
39
8
44 49
Temperature 8 (K) 8
54
8

IJIMS 5(2002)2,19-41, p. 36
Figure 3. Fractional amounts, as functions of temperature, of protonated pyridine and its
hydrate in equilibrium with 10 ppm H 2 O in nitrogen at 1 atmosphere.
Relative amount
1
0.8
0.6
0.4
0.2
C 5 H 5 N·H +
[C 5 H 5 N·H·OH 2 ]
+
[C 5 H 5 N·H·(OH 2 ) 2 ]
+
0
298 348 398 44 49
Temperature 8 (K) 8
548

IJIMS 5(2002)2,19-41, p. 37
Figure 4. Fractional amounts, as functions of temperature, of protonated acetone and its
hydrates in equilibrium with 10 ppm H 2 O in nitrogen at 1 atmosphere.
1
0.8
[(CH 3 ) 2 CO ·H·OH 2 ] +
[(CH 3 ) 2 CO·H] +
Relative amount
0.6
0.4
[{(CH 3 ) 2 CO} 2·H·OH 2 ] +
0.2
[{(CH 3 ) 2 CO} 3·H·OH 2 ]
+
0
298 348 398 448 498 548
Temperature (K)

IJIMS 5(2002)2,19-41, p. 38
Figure 5. Fractional amounts, as functions of temperature, of protonated acetone and its
clusters with neutral acetone in equilibrium in nitrogen at 1 atmosphere containing 100
ppm acetone.
Relative amount
1
0.8
0.6
0.4
0.2
{(CH 3 ) 2 CO} 2 H +
{(CH 3 ) 2 CO} 3 H + (CH 3 ) 2 COH +
0
29
8
34
8
39
8
44
Temperature 8 (K)
498 54
8

IJIMS 5(2002)2,19-41, p. 39
Figure 6. The expected changes in mobility, relative to the dry ion, resulting from
changes in hydration for protonated water, protonated acetone and protonated pyridine.
For each ion the bottom curve is for 10 ppm water and the top curve is for 2 ppm water.
The curve marked A/A is for protonated acetone in equilibrium with 100 ppm acetone.
1
C 5 H 5 NH +
(CH 3 ) 2 COH +
Relative mobility
0.9
0.8
A/A
H 3 O +
0.7
290 340 390 440 490 540
Temperature (K)

IJIMS 5(2002)2,19-41, p. 40
Table 1. ADO rate constants for the association reaction
{(CH 3 ) 2 CO) 2 }H + + M → {(CH 3 ) 2 CO) 2 }H +·M
M µ D (Debye) α (10 -24 cm 3 ) k (10 -9 cm 3 molecule -1 s -1)
H 2 O 1.85 1.44 1.68
NH 3 1.47 2.20 1.60
CH 3 CN 3.96 4.45 2.42
N 2 0 1.77 0.66
CO2 0 2.65 0.67
Table 2. Standard enthalpy changes (kJ mol -1 ) for the
association reaction: A + + M → A +·M
M
A + water acetone acetonitrile
K + -75 -87 -102
+
NH 4 -83 -97 -115
H 3 O + -132 -201 -195
+
CH 3 NH 3 -79 -90 -103
Table 3. Stqandard enthalpy and entropy changes for the hydration of ions:
A + + H 2 O → A + ⋅H 2 O
A +
-∆H o
(kJ mol -1 )
-∆S o
(J K -1 mol -1 )
H + 691 104
H 3 O + 132 102
Na + 102 90
Cs + 57 81
2,6-lutidine⋅H + 55 108
Cl - 55 84
OH - 94 80
NO 2
-
60 88
NO3 - 52 80

IJIMS 5(2002)2,19-41, p. 41
Table 4. Standard enthalpy (kJ mol -1 ) and entropy (J K -1 mol -1 in brackets) changes for the
reaction A.M n-1 + + M -> A + .M n (Data from Reference 7)
A + M n =1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7
H 3 O + H 2 O -150.6
(-139)
-93.3
(-121)
-71.1
(-118)
-64.0
(-136)
-54.4
(-127)
-49.0
(-124)
-43.1
(-113)
(CH 3 ) 2 CO.H + H 2 O -85.8
(-108.8)
-56.9
(-97)
-53.1
(-92)
-43.1
(-85)
-43.1
(-98)
C 5 H 5 N.H + H 2 O -62.8
(-107)
-40.2
(-82)
-34.7
(-82)
(CH 3 ) 2 CO.H + (CH 3 ) 2 CO -125.5
(-123)
-48.1
(-93)
-40.6
(-92)