P1250095211icJhX

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Fred J. Grieman
Kinetics (4) Collision Theory and rate
constant k ZAB rate constant equal to
collision frequency?
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Rate k AmBnWhat determines k(T)?

1. Must molecules encounter each other to react?
2. Does energy of encounter matter?
3. How do these parameters affect the magnitude of
   k(T)?
4. What affects the temperature dependence of k?

• Chemical Kinetics Model (Gas Phase to start)
• Molecules must collide to react.
• What is the rate of collision?

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Kinetic Theory of Gases

• Small particles in large volume
• Constant, random motion
• No force between molecules except on collision
• Elastic collisions between molecules and walls
• (No energy transfer)
• Collision frequency is related to velocity
  (speed)
• Velocity is related to Energy
• Energy is related to Temperature

Following derivation to show Ek N ½ m u2
(3/2) nRT
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What do we have relating a gas to temperature?
Ideal gas law PV nRT (N/No)RT

• Pressure Force (molecular collisions)
• Area (with walls)
• Force
  collision with wall changes momentum
• 
  m (mass) u
  (velocity)
• Imagine container c (z)
  Volume V abc
• b
  (y)
• a (x)

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Consider 1 dimension x
mux wall area bc
A -mux a x
P F/A F ?mux/?t for one
collision ?mux mux (-mux) 2 mux ?t
distance btwn collisions/velocity
2a/ux
F 2 mux / (2a / ux ) mux2 / a For N
molecules with average average velocity ux F
N mux2/a P F/A N mux2/a /bc P N
mux2/V Velocity vector u uxi uyj uzk
u2 ux2 uy2 uz2
? ? ? ?
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u2 ux2 uy2 uz2 ux uy uz So u2
3ux2 or ux2 ?u2 Finally, P N mux2/V
? N mu2/V
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PV ? N mu2 Ek N(½mu2) PV ?Ek nRT
ideal gas law Ek (3/2) nRT ? Ek (per mole)
(3/2) RT Ek depends only on
T!!! R 8.3145 J/molK
Speed of Molecules ? rate of collisions
(need velocity as function of T from energy) Ek
N ½ m u2 (3/2) nRT u2 (3nRT/Nm)
(3RT/Nom) (3RT/M) (u2)½ urms (3RT/M)½
rms root mean square at T, molecules have
same energy, but urms decreases with mass
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Range of velocities average velocity An
average a Si niai/N fi ni/N distribution
function a Si fiai
suppose continuous not descrete
a ? f(a) a ds f is continuous
distribution function ave. velocity u u ?o8
f(u) u du f(u) 4p
(M/2pRT)3/2 u2 e-Ek/RT
Maxwell-Boltzmann Distribution
Show plot
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Maxwell-Boltzmann Distribution f(u) 4?
(M/2?RT)3/2u2e-Ek/RT From f(u) u (8RT/pM)1/2
similar to urms gt u
Also ump (2RT/M)1/2
u2e-Ek/RT causes maximum Speed falls off
exponentially at high E Ave. speed increases with
T
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Collision Frequency use Maxwell-Boltzmann
Hard-sphere approximation d rA rB
Collision Rate ZAB AB Use
Maxwell-Boltzmann volume swept out with
u Collision Freq. ZAB (8RT/pNo?)1/2pd2 ?
mAmB/(mAmB)
(Looks like average u) T 298K ZAB 1011
(L/molsec) rate constant
rA
rB
d
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• Reaction Rates
• Assume that reaction happens on every collision
• Rate constant is then collision frequency k
  ZAB
• Rate k A B example A B 0.02 mol/L
  (0.5 atm.)
• Rate 1011 .02.02 4 x 107 mol/L sec
• How fast is this?
• A/rate .02 mol/L ? 4x107 mol/Lsec 5 x 10-10
  seconds
• Too fast!!! Whats wrong???
• Reaction does not occur on every collision!

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Rate constant k ZAB (collision frequency) is
too large Reaction too fast compared to reality
(Party analogy?) Like getting a date on
every encounter!!! We know Inhibition
exists. For molecules Activation Energy exists
- EA Collision Energy EA for reaction to
occur
Chickened out asking for a date
Ecollision lt EA Ecollision gt EA Relative
velocity vector must be gt uthreshold Ass
ume k ZAB e-EA/RT k lt ZAB rxn does NOT
occur on every
collision
Activated complex or Transition State
Inhibition to asking for a date
Got courage got date!
EA, for
Maxwell-Boltzmann Distribution f(u) 4?
(M/2?RT)3/2 u2 e-Ek/RT
A BC Reactants
EA, rev
?Erxn (Thermodynamics)
AB C Products