Testing second year seminar webpage to make website

3. General Reaction:
aA + bB k cC + dD where k is a the Wait!! k is contant? NOT TRUE!!!
“rate constant”
Obviously k = f(T)
General Rate Equations:
1) Separate variables
2) Apply approximations if
necessary
3) Integrate over relevant
limits ([A]o, ([B]o)
4) Algebreically solve for
variable of interest ([A](t))
Upadhyay

4. Jacobus Henricus van’t Hoff Svante August Arrhenius
Proposed in 1884: Proposed in 1889:
where A is the
“pre-exponential
factor” (A(T)) and
Ea is the energy of
activation.
Awarded Nobel Prize in Chemistry in Awarded Nobel Prize in Chemistry in
1901: “in recognition of the 1903: "in recognition of the
extraordinary services he has rendered by extraordinary services he has rendered to
the discovery of the laws of chemical the advancement of chemistry by his
dynamics and osmotic pressure in electrolytic theory of dissociation".
solutions".
Nobelprize.org

5. Max Trautz (1916)
William Lewis (1918)
Objective:
To develop a model describing how the rate constant of a reaction varies with
changing temperature considering energetic collisions.
General Assumptions:
1) Molecules are hard spheres in temperature dependent translation.
2) The molecules undergo collisions, and any collision with sufficient energy
(E*) will result in a reaction.
3) Concentration affects reaction rate due to it’s effects on collision rate.

6. b = “impact parameter” Impact Parameter:
bmax = r1 + r2 Distance of closest possible approach of the
center of the species involved in a collision.
Reactant A
-There exists some maximum impact parameter
b above which a collision will not occur (bmax). Ie:
r2
b > bmax no collision no reaction
bmax r1
Reactant B b < bmax collision occurs
reaction may occur
if sufficient energy
is transferred

7. Area of collision = π b2max =
“hard-sphere cross section”
v
V (bmax, Δt) = (vΔt)π
-Collision frequency (Z) per unit time and volume is given by: Z = π b2max<v>n1n2
where n1 and n2 are proportional to the number of collision partners present (concetration).
-Reactive cross section(σ) is the sum of the hard sphere cross sections of collision over time
and depends on the probability of a reaction having sufficient energy for a reaction to occur.

8. Maxium Energy Transfer in
Collision
b=0
v
b > bmax
v No Energy Transfer in Collision

9. -The energy transfer of a collision (Et) depends
v on the velocity of approach relative to the line of
α centers of the collisional partners.
b bmax
vlc α -Relationships allow determination of vlc:
The energy along the line of centers is given by (KE=1/2mv2):
where μ is the reduced mass of the system.

10. -The energy transfer of a collision (Et) depends
v on the velocity of approach relative to the line of
α centers of the collisional partners.
b bmax
vlc α -Relationships allow determination of vlc:
The energy along the line of centers is given by (KE=1/2mv2):
where μ is the reduced mass of the system.

11. db
Solve
b
Physical limits provide limits of integration
P(Et,b) = 1
> E*
Elc > E* Elc < E*
REACTION!
P(Et,b) = 0

12. The Maxwell-Boltzmann energy distribution:
Reaction rate = k(Et)n1n2
where
k(Et) = σ(Et)vt
Mathematical relationship: and
vt = (2Et/μ)1/2
Integrate & solve for k

13. -Rates predicted by collision theory trend higher
than experimental evidence indicates Non-reactive
approach zone
At least partially due to the “steric factor”:
compensated for by introducing a constant (p): Reactive
approach
zone
-Also, what about reaction order?
Reactive 2 3 4 n
Species:
Possible 1 3 6
Collisions:
Rate ≈ Z = π b2max<v>n1n2

14. Three Steps to Reaction:
Activation: Dectivation: Decomposition:
k1 k -1 k2
A+A A + A* A + A* A+A A* P
Apply steady state conditions with
respect to [A*] and then solve for
rate of reaction:
Reduce
based on
two
pressure
k -1 [A] >> k 2
limits.
k 2 >> k -1 [A]

15. Four Steps to Reaction:
Activation/Deacivation:
k1
A+A A + A*
k -1
Decomposition 1& 2:
k2
A* A≠ A≠ P
Adapted from R. A. Marcus, J. Chem. Phys. 43, 2658 (1965)
Awarded
Nobel Prize in Fraction of molecules with energy between E and
Chemistry in E+dE is given by
1956: "for [his]
researches into
the mechanism Consider multiple internal degrees of
of chemical freedom (s):
reactions.”
Cyril N. Hinshelwood

16. Differentiate for
Integrate over limits range of energies
between E and E + dE
Replace to get expression of
equilibrium proportion of
molecules with energy
between E and E + dE

19. 4 1 H-H eq
Energy (eV)
2
H-H (Å)
1 1.5 2.0 D-H (Å)
2
2 D-Heq
1
Houston 2

20. Henry Eyring and John Polanyi (1931)
Objective:
To develop a model describing how the rate
constant of a reaction varies with changing
temperature considering unstable transition
states.
General Assumptions:
John Polanyi
1) An eqillibrium exists between the reactants
“activated state (“transition state”) of a Awarded Nobel Prize in
chemical reaction. Chemistry in 1986: for
2) The difference in energy (Eact)between these his contributions
two states must be supplied for the to the concerning the dynamics
reaction for the it to form. of chemical elementary
3) A certain vibrational degree of freedom processes“.
exists that is necessarily active for the
transition state to dissociate

21. General Reaction: X≠ C+D
1 K≠ through
A+B X≠ C+D [X≠] = K≠ [A][B] 3
vibrational
mode v with
Evib=hv=kbT.
Gibb’s-Helmholtz
Standard Relation:
Enthalpy Change:
∆G∘ = ∆H∘ - T∆S∘
RT lnK = -∆G∘
2
∆H∘ = Eact

22. 2 Run the Reaction
1 Preparation of select
vibrational mode(s)
 Simple Infrared Excitation
 Stimulated Raman Excitation
 Infrared Multiphoton Excitation 3 Detection of Mode
 Vibrational Overtone Excitation Specific Products
 Stimulated Emission Pumping  Photoacoustic Spectroscopy
 Resonance Enhanced Multiphoton
Imaging (REMPI)

23. The selection rule for rotational state
transitions is given by:
∆J = ±1
The different energies of the allowed transitions
lead to elaborate vibrational spectrum:
Wiki

24. 1 2
Laser pulses shoot sample with
infrared or near-ir frequency Sample heats up from
radiation. the radiation, which
activates modes of
vibration and
rotation. This in
turn creates
Photoacoustic pressure waves
Spectrum in the air.
3
The pressure waves
Fourier are detected as
sound by a
microphone.
Transform
http://www.shimadzu.com/an/ftir/support/ftirta
lk/talk7/intro.html

25. Gas Flow
Cell
Window
Microphone
Buffer Gas Semipermiable Resonating
Volumes Mirrors Chamber
Braz. J. Phys. vol.32 no.2b São Paulo June 2002
Wiki PAS

26. Path A
Length = L
Wiki

27. Calculated
Two Endothermicity
1
Possible CH3 + DCl 2200 cm-1
Abstraction CH3D + Cl
CH2D + HCl 1800 cm-1
Pathways 2
Pathway 1 H Pathway 2
Cl D H Cl
H

28. Calculated Potentials: In the thermal reaction, what would we
expect the product distribution to be?
“Primary Kinetic Isotope Effect”
F
r
E
e
n
q
e
u
r
e
g
n
y
c
y
G. D. Boone, F. Agyin, D. J. Robichaud, F.-M. Tao, and On these considerations, we expect the
S. A. Hewitt, J.Phys. Chem. A 105, 1456 ~2001
major product to be CH2D in the absence of
state specific vibrational excitation.

29. 1) A molecular beam was created using a 1:1:4 mixture of CH3D,
Cl2, and He with a 660 torr backing pressure.
2) Deuteromethane was vibrationally excited with 2.3 μm (4300
cm-1) laser pulses (excitation laser).
3) Molecular chlorine was dissociated with a 355 nm laser pulse
(dissociation laser).
4) After a 200-250 ns delay, a 2+1 REMPI produces ions from
either the CH2D or CH3 product (probe laser).
5) Time-of-flight mass spectrometry detects products.
Simultaneously, the laser beam is directed through a cell containing
15 torr CH3D for collection of absorbtion spectrum to
computationally verify vibrational assignments.

30. Action Spectra
 Monitors the generation of a product of a specific product over
a range of vibrational excitation laser wavelengths.
 Provides information similar to photoacoustic spectroscopy.
 Allows determination of degree of generation of a specific
product with respect to individual vibrational modes.
REMPI Excitation Spectra
 Monitors the generation of multiple products through mass
resolved spectrometric detection after REMPI.
 Allow determination of product distributions from vibrational
mode specific reactants.

31. 6x
Stronger Signal
REMPI spectrum:
J. Chem. Phys., Vol. 119, No. 9, 1 September 2003
6x
Weaker Signal

32. 2v2 2v2
A1 E
Symmetry Symmetry
Parallel
Transition
Perpendicular
Transition
J. Chem. Phys., Vol. 119, No. 9, 1 September 2003

33. 1
Houston 2