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Atkins & de Paula:
Atkins’ Physical Chemistry 9e
Chapter 22: Reaction Dynamics
Chapter 22: Reaction Dynamics
REACTIVE ENCOUNTERS22.1 Collision theory rate constant, kr encounter rate minimum energy requirement steric requirement.
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RTEr
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r
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a
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[A][B]P B A
NN
22.1(a) Collision rates in gases collision density, the number of (A,B) collisions in a region of the sample in an interval
of time divided by the volume of the region and the duration of the interval:
22
2122
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),(,[A][B]8
21
21
AA
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Nm
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Chapter 22: Reaction Dynamics
22.1(b) The energy requirement
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Chapter 22: Reaction Dynamics
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Chapter 22: Reaction Dynamics
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Chapter 22: Reaction Dynamics
22.1(c) The steric requirement steric factor, P = σ*/σ. reactive cross-section, σ*, the area within which a molecule must approach another
molecule for reaction to occur. rate constant from collision theory, harpoon mechanism, a process in which electron transfer precedes atom extraction.
RTEAr
aeNkT
Pk /
2/18
(Exercise Example 22.2!)
Chapter 22: Reaction Dynamics
22.1(d) The RRK model The Rice–Ramsperger–Kassel model (RRK model), a model that takes into account
the distribution of energy over all the bonds in a molecule.
collision in the availableenergy ; breakage, bond for the requiredenergy ; motion, of modes of # the;
for1)(111
EEs
EEkE
EEk
E
EP b
s
b
s
RRK model
Lindemann-Hinshelwood mechanism
Exp. data for unimolecular isomerization of trans-CHD=CHD
s
Chapter 22: Reaction Dynamics
22.2 Diffusion-controlled reactions cage effect, the lingering of one molecule near another on account of the hindering
presence of solvent molecules.
Chapter 22: Reaction Dynamics
22.2(a) Classes of reaction diffusion-controlled limit, a reaction in which the rate is controlled by the rate at which
reactant molecules encounter each other in solution. activation-controlled limit, a reaction in solution in which the rate is controlled by the
rate of accumulating sufficient energy to react.
limit controlled-activation:When
limit controlled-diffusion:When
,[A][B][AB]]P[
[A][B]]AB[0[AB][AB][A][B]
[AB]
process activated :a[AB]PAB
[AB]BAAB
diffusion :d pair,encounter :AB[A][B]ABBA
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Chapter 22: Reaction Dynamics
22.2(b) Diffusion and reaction
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ABABB
B
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rrr
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Chapter 22: Reaction Dynamics
22.3 The material balance equation
3
84
medium) ofviscosity ; radius, ichydrodynam ;,(66
equation;Einstein -Stokes usingBy
21 RT
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Chapter 22: Reaction Dynamics
TRANSITION STATE THEORY transition state theory (or activated complex theory, ACT), a theory of rate constants
for elementary bimolecular reactions. transition state, the arrangement of atoms in an activated complex that must be
achieved in order for the products to form.
22.4 The Eyring equation
‡‡θ
‡‡‡
‡θ
‡]J[
臇
[A][B]
]C[PC
[A][B]]C[
CBA‡
Kkp
RTkkv
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ppK
rr
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BA
C
J
Our task!!
Chapter 22: Reaction Dynamics
22.4(a) The rate of decay of the activated complex transmission coefficient, κ, the constant of proportionality between the rate of passage
of the complex (k‡) through the transition state and the vibrational frequency along the reaction coordinate (‡); k‡ = κ‡.
22.4(b) The concentration of the activated complex
discarded) C of mode al vibrationonewith ; (
complex. theof modesother theallfor function partition thedenotes where
11
11
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)B()A()C(&bar 1where
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Chapter 22: Reaction Dynamics
22.4(c) The rate constant
difficult!very complex activated of structure and shape, size, theknow tohave we,For
equation Eyring ;
θ
C
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22.4(d) The collision of structureless particles
02
8
/22
/2
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BA
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RTaEAr
r
rr
Chapter 22: Reaction Dynamics
22.4(e) Observation and manipulation of the activated complex Na+I- decay
Photoreaction of IH∙∙∙OCO van der Waals complex IH∙∙∙OCO HOCO resembles the activated complex of H + CO2[HOCO] ‡ HO+CO
Chapter 22: Reaction Dynamics
22.5 Thermodynamic aspects22.5(a) Activation parameters
RSRS
RTERSr
ar
aRTE
r
RTHRSr
STHGRTGr
steric
a
a
ePBeeA
eBeek
RTHET
kRTEAek
p
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h
kTBeBeke
p
RT
h
kTk
KRTG
//2
//2
‡2/
θ// termS into absorbed is /
θ
‡‡
‡‡
‡
‡‡‡‡‡‡
2ln
ln ,activation ofenergy Gibbs
correlation analysis, a procedure in which ln K (=-ΔrGθ/RT) is plotted against ln k (proportional to -Δ‡G /RT).
liner free energy relation (LFER), a linear relation obtained in correlation analysis; reaction becomes thermodynamically more favorable.
Chapter 22: Reaction Dynamics
22.5(b) Reactions between ions kinetic salt effect, the effect of a change in ionic strength on the rate constant of a reaction.
2/1
BA0
2/12BA
2B
2A
0
2/12BAC
2/12BB
2/12AA
02/1-
01 when
‡
BA
Cθ‡
BA
C‡‡
2log
)(loglog
)(log
loglog
C),25at aq.for 0.509 ,log( law limiting ckeluH-Debye From
[A][B]]P[
[A][B]
]C[]C[
]P[
‡
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‡‡
IzAzk
IzzzzAkk
IzzA
IAzIAz
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K
kk
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Kkkk
dt
d
Kc
Kaa
aKk
dt
d
r
rr
rr
Kkkrr
r
Exercise Example 22.3!
Chapter 22: Reaction Dynamics
THE DYNAMICS OF MOLECULAR COLLISIONS22.6 Reactive collisions22.6(a) Experimental probes of reactive collisions infrared chemiluminescence, a process in which vibrationally excited molecules emit
infrared radiation as they return to their ground states.IR chemiluminescence
O+CSCO+S
Chapter 22: Reaction Dynamics
laser-induced fluorescence (LIF), a technique in which a laser is used to excite a product molecule from a specific vibration–rotation level and then the intensity of fluorescence is monitored.
Chapter 22: Reaction Dynamics
multiphoton ionization (MPI), a process in which the absorption of several photons by a molecule results in ionization.
resonant multiphoton ionization (REMPI), a technique in which one or more photons promote a molecule to an electronically excited state and then additional photons are used to generate ions from the excited state.
A laser pulse excites electrons in a semiconductor surface (10 layers C 60 on a Cu(111) substrate) which in turn pass their energy to adsorbed molecules (NO). REMPI measures the motion of the desorbed molecules.
Chapter 22: Reaction Dynamics
reaction product imaging, a technique for the determination of the angular distribution of products.
Reaction products detected in the Streamer Chamber when a 1.1-GeV-per-nucleon beam of holmium-165 collided with a holmium-165 target at the Bevalac.
Chapter 22: Reaction Dynamics
22.7 Potential energy surfaces potential energy surface, the potential energy as a function of the relative positions of
all the atoms taking part in the reaction.
HA + HB-HC HA-HB + HC
Chapter 22: Reaction Dynamics
saddle point, the highest point on a potential energy surface encountered along the reaction coordinate.
HA + HB-HC HA-HB + HC
Chapter 22: Reaction Dynamics
saddle point, the highest point on a potential energy surface encountered along the reaction coordinate.
HA + HB-HC HA-HB + HC
Chapter 22: Reaction Dynamics
Example of potential energy surfaces.
Ultrafast reaction dynamics of the complete photo cycle of an indolylfulgimide studied by absorption, fluorescence and vibrational spectroscopy
Chapter 22: Reaction Dynamics
22.8 Some results from experiments and calculations
HA + HB-HC HA-HB + HC
Chapter 22: Reaction Dynamics
HA + HB-HC HA-HB + HC
Chapter 22: Reaction Dynamics
22.8(a) The direction of attack and separation
300
Chapter 22: Reaction Dynamics
22.8(b) Attractive and repulsive surfaces attractive surface, a potential energy surface in which the saddle point occurs early on
the reaction coordinate. repulsive surface, a potential energy surface in which the saddle point occurs late on the
reaction coordinate.
attractive surface repulsive surface
H + Cl2 HCl +Cl
Chapter 22: Reaction Dynamics
22.8(c) Classical trajectories direct mode process, a bimolecular process in which the switch of partners takes place
very rapidly. complex mode process, a bimolecular process in which the activated complex survives
for an extended period.
direct mode process complex mode process