IonPolar Molecule Reactions

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Ion-Polar Molecule Reactions

• rate constants measured for reactions between
  ions and polar molecules were found to be
  substantially larger relative to ion/non-polar
  molecule reaction rate constants

• Moran and Hamill (1963) showed experimentally
  that there was a complex dependence of the rate
  constant on the dipole moment. They carried out
  the first derivation of a rate constant as a
  function of dipole moment.

• ion-dipole interactions are much like
  dipole-dipole interactions (5 25 kJ mol-1)
  except very strong (40 600 kJ mol-1)

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H2O dimer
15 kJ mol-1
H2O proton-bound dimer

130 - 160 kJ mol-1
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• for polar molecules the ion-dipole term
  increases the interaction potential and increases
  the collision cross section

• in the limit that f 60 (locked-dipole) for a
  thermal system,

• a locked-dipole, however, violates the
  conservation of angular momentum and
  overestimates kcoll

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• Su and Bowers (1973) were the first to consider
  a rotating dipole model

• this involved the more realistic approach of a
  distance dependent average angle of orientation
  of the dipole moment relative to the line of
  centres of the collision

• this involved a graphical solution to equations
  of motion on a case-by-case basis

• later this approach was simplified by Su,
  Chesnavich, and Bowers then later by Su and
  Chesnavich

• the rotating dipole problem cannot be solved
  analytically but Su and Chesnavich (JCP, 76,
  1982, 5183) analyzed over 3000 trajectories of
  ion-dipole interactions which led to,

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and

• this leads to accurate collision rate constants
  for ions with polar molecules

• exothermic proton transfer to polar molecules
  usually occurs at this collision rate

Note that the collision rate constant is
proportional to the inverse of temperature, as T
increases, kcoll decreases
eg. Calculate the collision rate constant for
(CH3)2OH and (CH3)2O at 200 K and 400 K.
Dimethyl ether has a mD 1.30 D and a
5.29x10-24 cm3.

• we have developed the theory in the cgs system
  of units,

statcoulomb
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also,
in cgs
so, at 200 K
and at 400 K

• at 200 K xgt2 and at 400 K xlt2

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200 K
and at 400 K use
to obtain

• if we would have used the non-polar molecule
  expression we would have obtained

at all temperatures
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When an ion and a molecule collide, what happens?
collisional stabilization
redissociation
chemical reaction
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• ignoring chemical reaction the mechanism is,

M is a third-body (could be B)
the rate of reaction can be expressed as,
applying the steady-state approximation to
(AB),
subbing into the above rate expression
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at high pressure
which says that the reaction occurs at the
bimolecular collision rate

• these high pressure conditions are found in the
  high pressure ion source at UW

Under these conditions of high pressure (few
torr) the possibility of thermal activation of
AB must also be considered.
In which case we can write
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Now,
and
the vant Hoff equation
equating the two yields
So by measuring the temperature dependent ion
intensities, A and AB at a known partial
pressure of B in the ion source, then plotting
the logarithms of the resulting rate constants
against reciprocal temperature (vant Hoff plot),
it is possible to obtain DH and DS for the
reaction from the slope and intercept
respectively.
Exchange equilibrium can also be studied by this
method,
allowing accurate determinations of relative
proton affinities, halide affinities, methyl
cation affinities, etc.
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76.0 kJ mol-1
77.1 kJ mol-1
MP2/6-311G//B3LYP/6-311G
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DH -84.1
DH -76.0
DS -86.5
DS -83.3
DH -63.8
DS -78.8
Cl-
onto 2-chloropropionitrile
Br-
I-
DH / kJ mol-1 , DS / J K-1 mol-1
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Now looking at our mechanism and rate again,
and considering the limit where we are at very
low pressure,
therefore,
and if MB
third order kinetics
or
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if we are working under constant pressure,
a plot of lnA vs t gives a slope,
and a pseudo first order rate constant
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• at low P

A B
(AB)
AB
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• a plot of kapp vs B yeilds a slope

and an intercept of 0!

• clustering of dimethyl ether and protonated
  dimethyl ether

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kapp vs PB do not have 0 intercepts? We need a
new mechanism since the one we are working with
doesnt explain the phenomenon of a non-zero
intercept.
Using the steady state approximation on (AB),
show this!!
This is a horrible expression, but, if we express
it as a series (ie. perform a Taylor series
expansion)
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Taylor series expansion,
only use 0th and 1st order expansion terms
xM xo0
Maclaurin series
if kra ltlt kb
intercept
slope
non-zero
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Su Chesnavich or Langevin
(AB)
A B
AB
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m/z 75
m/z 121
1800 s
1200 s
600 s
0 s
70
130
100
80
90
110
120
m/z
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(24 s-1)
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• using calculated vibrational frequencies and
  geometries for AB, A and B, statistical methods
  are employed to model kb as a function of Do
• the dissociation energy is that used to obtain a
  theoretical kb which matches the experimental kb

A B
(AB)
Do
AB
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