Activated complex theory
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Transcript of Activated complex theory
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Activated complex theory
• Using the concepts of statistical thermodynamics.
• Steric factor appears automatically in the expression of rate constants.
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27.4 The Eyring equation • The transition state theory pictures a reaction between A and B as proceeding
through the formation of an activated complex in a pre-equilibrium: A + B -> C‡
K‡ = ( `‡` is represented by `±` in the math style)
• The partial pressure and the molar concentration has the following relationship:pJ = RT[J]
• thus[C‡] = K‡ [A][B]
• The activated complex falls apart by unimolecular decay into products, P,
C‡ → P v = k‡[C‡] • So v = k‡ K‡ [A][B]
Define k2 = k‡ K‡v = k2[A][B]
BA
C
pp
pp
p
RT
p
RT
p
RT
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(a) The rate of decay of the activated complex
k‡ = κv
where κ is the transmission coefficient. κ is assumed to be about 1 in the absence of information to the contrary. v is the frequency of the vibration-like motion along the reaction-coordinate.
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(b) The concentration of the activated complexBased on Equation 20.54, we have
with ∆E0 = E0(C‡) - E0(A) - E0(B)
are the standard molar partition functions.
provided hv/kT << 1, the above partition function can be simplified to
Therefore we can write qC‡ ≈
where denotes the partition function for all the other modes of the complex.
RTE
BA
CAe
qNK /0
Jq
kThveq
/1
1
hv
kT
kThv
q
)( 11
1
cq
hv
kT
q
K
hv
kTRTE
BA
CA eqq
qNK /0
K‡ =
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(c) The rate constant
combine all the parts together, one gets
k2 = k‡ K‡ = κv
then we get
k2 = κ (Eyring equation)
p
RT
hv
kTp
RT
K
CK
h
kT
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(d) The collisions of structureless particles
A + B → AB
Because A and B are structureless atoms, the only contribution to their partition functions are the translational terms:
k2 = κ
k2 = κ NA
3J
mJ
Vq
212 /)( kTm
h
JJ
p
RTVm
C
mC
VIkTq
2
2
RTE
mC
BAA eIkT
V
N
p
RT
h
kT /023
33 2
RTEeru
kT //
0221
8
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Kinetics Salt EffectIonic reaction A + B → C‡ C‡ → P d[P]/dt = k‡[C‡]
the thermodynamic equilibrium constant
Then
d[P]/dt = k2[A][B]
Assuming is the rate constant when the activity coefficients are 1 ( )
Debye-Huckle limiting law with A = 0.509
log(k2) = log( ) + 2AZAZBI1/2 (Analyze this equation)
]][[
][
]][[
][
BA
CK
BA
C
aa
aK
BA
C
BA
C
K
Kkk
2
02k Kkk 02
K
kk
02
2
212 /)log( IAzJJ
02k
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Experimental tests of the kinetic salt effect
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• Example: The rate constant for the base hydrolysis of [CoBr(NH3)5]2+ varies with ionic strength as tabulated below. What cab be deduced about the charge of the activated complex in the rate-determining stage?
I 0.0050 0.0100 0.0150 0.0200 0.0250 0.0300
k/ko 0.718 0.631 0.562 0.515 0.475 0.447
Solution:
I1/2 0.071 0.100 0.122 0.141 0.158 0.173
Log(k/ko) -0.14 -0.20 -0.25 -0.29 -0.32 -0.35
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27.6 Reaction Collisions
• Properties of incoming molecules
can be controlled:
1. Translational energy.
2. Vibration energy.
3. Different orientations.
• The detection of product molecules:
1. Angular distribution of products.
2. Energy distribution in the product.
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27.7 Potential energy surface
• Can be constructed from experimental measurements or from Molecular Orbital calculations, semi-empirical methods,……
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Potential energy surfaces, pt. 2.
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Various trajectories through the potential energy surface
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27.8 Results from experiments and calculations
(a) The direction of the attack and separation
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Attractive and repulsive surfaces
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Classical trajectories