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Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
Chapter 7 Kinetics: Rates of Chemical Reactions
vs.Thermodynamics Kinetics
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
Concepts
• Collision – dependence on concentrations of reactants and temperature
• Factors influencing (chemical) reaction rate- Concentrations of reactants and products, temperature, solvent environment, salts, metal ions, pH, light, electricity, pressure etc.
• Reaction mechanism(반응메카니즘) and elementary reaction (단일단계반응)
elementary rx의종류 -mechanism –
cf. stoichiometric reaction
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
Kinetics
• Chemical kinetics (화학속도론) – the study of rates of reactions
•한화학반응의속도(rate)는 “단위시간당농도변화(a change in concentration per unit time)”로정의됨.
reaction of rate==dtdcv
Rate Law - rate expressed as a function of the concentrations
- contains information about the mechanism of the process
reactantsproducts
intermediates
catalysta steady-state intermediates
buffered componentssolvents
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
Order of a Reaction
- describes the way in which the rate of the reaction depends on the concentration.
PBA ⎯→⎯+
a general form of the reaction law is given by, qP
nB
mA cckcv =
overall order = m + n + q
“no simple relation between the stoichiometry and the rate law”
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
Experimental Rate Data
• flow method
“the location of the spectrometer corresponds to different times”
• stopped-flow method
- for samples of small amounts- timescale : ms ~ s
• quenched-flow method
- length of the delay line and flow rate determines reaction time- timescale : ms ~ s
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
Zero-Order Reactions
constantkdtdcv === 0 (unit of k0 : M/s)
dtkdc 0=
적분 ( t: t1 → t2 and c: c1 → c2 )
∫∫ =2
1
2
10
t
t
c
cdtkdc ∫=
2
10
t
tdtk
( )12012 ttkcc −=−
if at t=0, c=c0
0323 CHO]CH[OH]CHCH[
kdt
ddt
dv ==−=
+
+
++
⎯⎯ →⎯+
H NADH CHOCH
NAD OHCHCH
3
LADH23예.
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
First-Order Reactions
ckdtdcv 1== (unit of k1 : s-1)
BA ⎯→⎯ For
rate law = ][][][1 Ak
dtBd
dtAdv ==−=
dtkAAd
1][][=−
if t = 0, [A] = [A]0t = t, [A] = [A]
∫∫ =−tA
Adtk
AAd
01
][
][ 0 ][][ tk
AA
10][][ln −=
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
예. penicillin 항생제의안정성
R NH
ON
O
H HS
HCOOH
CH3
CH3
tkAA
10][][ln −=
tkeAA 10][][ −=
01 ]ln[]ln[ AtkA +−=
(The penicillin is in a well-buffered solution at pH 7 kept at 25°C)
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
• half-life (반감기), t1/2
- the time required for half the initial concentration to react
tkAA
10][][ln −=
- for 1st order reaction
021 ][][ AA =
2/1tt = 2/1121ln tk−=
• relaxation time (이완시간), τ, for 1st order reaction- the time required for the concentration to decrease to 0.3679 (= e-1) times its initial concentration
τ11 kee −− =tkeAA 10][][ −=
01 ][][ AeA −=
τ=t
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
Penicillin의가수분해반응
N
O R
R NH
ON
O
H HS
HCOOH
CH3
CH3 N
O R
≡
O O_
NRH2
++ H2O
(Proposed Mechanism)
N
O R
+ OH-
_ NO R
OH
“slow”
NO R
OH
H2O
OOH
NRH OH-+_
+“fast”
OOH
NRH
OO
NRH2
_+
“fast”
OH- : catalyst
[OH-] = const
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
Second-Order Reactions BAcckvckdtdcv 2
22 or === (unit of k2 : M-1 s-1)
Class I (A + A → P)
- rate law depends only on the second power of a single component
예. 2 proflavin → [proflavin]2 ; v = k2[proflavin]2
NH4OCN → NH2CONH2 ; v = k2[NH4OCN]2
2 A-A-G-C-U-U → A-A-G-C-U-U
U-U-C-G-A-A
… … … … … … ; v = k2[A-A-G-C-U-U]2
N NH2H2N
dtkA
Ad22][
][−= tk
AA 20][
1][
1=−2
2 ][][ AkdtAdv =−=
적분속도법칙
반감기
2/12002
1 ][1
][1 tk
AA=−
022/1 ][
1Ak
t =
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
Class II (A + B → P)
- a reaction that is second order overall may be first order with respect to each of the two reactants.
]][[][][2 BAk
dtBd
dtAdv =−=−=
예. CH3COOC2H5 + OH- → CH3COO- + C2H5OH; v = k2[CH3COOC2H5][OH-]
H2O2 + 2Fe2+ + 2H+(excess) → 2H2O + 2Fe3+; v = k2[H2O2][Fe2+]
case 1. A와 B의초기농도가다를때, 즉 [A]0 ≠ [B]0
& 두반응물의 stoichiometry coefficient가같다고가정하자
각반응물이각각 x 만큼반응했다면,[A] = [A]0 – x; [B] = [B]0 –x; d[A]=d[B]= -dx이성립하므로,
적분속도법칙
( )( )xBxAkdtdx
−−= 002 ][][ ( )( ) dtkxBxA
dx2
00 ][][=
−−tk
BAAB
BA 20
0
00 ][][][][
ln][][
1=
−
case 2. A와 B의초기농도가같을때, 즉 [A]0 = [B]0
& 두반응물의 stoichiometry coefficient가같을때 22 ][][ Ak
dtAdv =−=
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
Renaturation of DNA as an Example of a Second-Order Reaction
“DNA reassociation rate is inversely proportional to the sequence complexity of the DNA.”
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
1. C0 : the total conc. of nucleotides in all the single strands before any renaturation occurs.
2. [A]0 : the initial conc. of a fragment A (⇔A’)
3. [A]0 = [A’]0 ≈ C0 /Nwhere N is the number of different fragments after sonication (i.e. complexity)
4. N ≈ the length of single strand fragment
여기서, N = 106–400 ≈ 106
따라서, [A]0 = [A’]0 ≈ C0 /N
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
여기서, N = 2
따라서,[A]0 = [A’]0 ≈ C0 / 2
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
2][]'][[]'[][ AkAAkdtAd
dtAd
==−=−
the rate of renaturation
- 2nd order reaction
therefore, the half-life of the reaction is
02/1 ][
1Ak
t =[A]0 = [A’]0 ≈ C0 /N
02/1 kC
Nt ≈ or NtC ∝2/10
“the half-life of renaturation times the total initial denatured strand concentration is proportional to the sequence complexity of the DNA”
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
Reactions of Other Orders
for nth order reaction nAkdtAdv ][][
=−=
ktAAn nn =
⎥⎥⎦
⎤
⎢⎢⎣
⎡−
− −− 10
1 ][1
][1
11
(for n ≠ 1)적분속도법칙 :
반감기 : ( ) 10
1
2/1 ][112
−
−
−−
= n
n
Aknt
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
Reaction Mechanisms and Rate Laws
• Mechanism – a set of elementary reactions
Rate Law Reaction Mechanism
“more than one mechanism can be written consistent with a given rate law”
• ________________ :단일단계반응에 대한 속도식은 각 반응물에 대한 반응계수의 멱수에 비례한다.
• _______________ : the number of reactant particles involved in the elementary reaction.
“The form of the rate law alone cannot predict the mechanism but the mechanism directly provides the rate law.”
일분자 단일단계반응(unimolecular elementary rx)
이분자 단일단계반응(bimolecular elementary rx)
삼분자 단일단계반응(termolecular elementary rx)
• Elementary reaction의종류
예) N2O5‡ → NO2 + NO3, rate = k [N2O5
‡ ]
예) NO(g) + O3(g) → NO2 (g) + O2(g) : rate = k [NO] [O3 ]
예) I2 분자의 Ar 분자에 의한 안정화
I + I + Ar → I2 + Ar, rate = k [ I ]2 [ Ar ]
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
• The simplest mechanism of a reaction : elementary
rate law = ][][ 2 BAkv =
productsB 2 ⎯→⎯+Aif elementary
Parallel Reactions
k1
k2
이경우, A, B, C에대한 rate law를써보면,
=−dtAd ][
- (1)
=dtBd ][
- (2)
=dtCd ][
- (3)
(1)에대응하는적분속도법칙은
( ) ][][21 Akk
dtAd
+=− ( )dtkkAAd
21][][
+−= ( )tkkAA
210][][ln +−=
- (4)
(4)식을 (2), (3)식에대입하고, B, C에대한적분속도법칙을구해보면,
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
][][1 Ak
dtBd
= - (2)
( )tkkeAA 210][][ +−=
( )tkkeAkdtBd
2101 ][][ +−=
( )∫∫ +−=t tkkB
dteAkBd0
01][
021][][
변수분리& 적분
( )
( )
ttkk
kkeAkB
02101
21
][][⎥⎥⎦
⎤
⎢⎢⎣
⎡
+−=
+−
마찬가지로,
( )( ){ }tkke
kkAk
C 211][
][21
02 +−−+
=
여기서, [B]/[C]가주어진온도에서항상일정함을알수있다.
for k1 ≈ k2
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
예제. 64Cu is unstable against decay, emitting either a electron or a positron.29
Cu6429
k_
k+
)( 62%6430
−+ βCu
)( 38%6429
++ βCu
64Cu 의반감기가 12.80 h 일때, k_와 k+를계산하라.29
풀이.
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
Series Reactions (Consecutive Elementary Reactions)
CBA kk ⎯→⎯⎯→⎯ 21 PuNpU 239day 35.2239min 35.2239 ⎯⎯⎯ →⎯⎯⎯⎯ →⎯예)
이경우, A, B, C에대한 rate law를써보면,
=−dtAd ][
- (1) =dtBd ][
- (2) =dtCd ][
- (3)
이제각화학종들에대한적분속도법칙을구해보자.
(i) A의경우 (easy one)
][][1 Ak
dtAd
=− dtkAAd
1][][
−= tkAA
10][][ln −=
(ii) B의경우
][][][21 BkAk
dtBd
−=
tkeAA 10][][ −= - (4)
][][][201
1 BkeAkdtBd tk −= −
(4)
“slightly more difficult to solve”
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
((a trick))
][][2 Bk
dtBd
−=
먼저다음의속도식을풀어보자.
tkeBB 20][][ −= 0][][ 2 BeB tk =
( ) ⎟⎠⎞
⎜⎝⎛ +=+= ][][][][][ 22
2222 BkdtBdeeBk
dtBdeeB
dtd tktktktk
( ) ( )tkktk eAkeBdtd
21201 ][][ −−=
][][][201
1 BkeAkdtBd tk −= −
( ) constekk
AkeB tkktk +
−= −− 212
12
01 ][][
at t=0, [B]=[B]0=0
constkk
Ak+
−=
12
01 ][0
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
constkk
Ak+
−=
12
01 ][0
12
01 ][kk
Akconst
−−=
( ) constekk
AkeB tkktk +
−= −− 212
12
01 ][][
( )
12
01
12
01 ][][][ 212
kkAk
ekk
AkeB tkktk
−−
−= −− tktk e
kkAk
ekk
AkB 21
12
01
12
01 ][][][ −−
−−
−=
- (5)
(iii) C의경우
항상 0][][][][ ACBA =++ 가성립하므로, (4)식과 (5)식을이용하면,
( ) 012
010 ][][
][][ 211 ACee
kkAk
eA tktktk =+−−
+ −−−
( )⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
−−+−
−=⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
−−
−−=−−−−−−
−
12
11120
12
10
2111211 1][1][][
kkekekekek
Akkeek
eACtktktktktktk
tk
- (6)
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
[A]/[A]0
[B]/[A]0
[C]/[A]0
maximum pt
inflection pt
( )tktk eekk
AkB 21
12
01 ][ ][ −− −
−=
⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
−−
−=−−
12
120
21
1][][kk
ekekAC
tktktkeAA 10][][ −=
Summary
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
series rx의한 elementary rx이속도결정단계(rate-determining step)인경우
(i) k1 >> k2인경우, (ii) k1 << k2인경우,
{ }tk
tktk
eA
kkekek
AC
2
21
1][
1][][
0
12
120
−
−−
−≈
⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
−−
−=
{ }tk
tktk
eA
kkekek
AC
1
21
1][
1][][
0
12
120
−
−−
−≈
⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
−−
−=
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
Wm Wm-1 Wm-2 W1 W0km km-1 k2 k1
W0
W1
W3
W2
Wm-1 Wm
t
m/z m/z
00W
01W
02W
03W
01m-W
0mW
tkim
n
oni
inii
nit e WCW +−−
=++∑=
0)(
Wi(t), : Concentration of the ith cluster at time t and 0.ki : Evaporation rate constant of the ith cluster.m : the largest size of water cluster at t=0.C : coefficients
oiW
)1(for C C 11 imnkk
k ini
nii
iini −=
−= +
++
++ L
W
WC - 1 C 0
01
1
i
ni
m-
n
ini
ii
+=
+∑=
Evaporation Kinetics of Gas Phase Water Clusters
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
Equilibrium and Kinetics
A Bk1
k-1
equilibrium constant : K
Rate law for [A]
][][][11 BkAk
dtAd
−+−=−
At equilibrium,
eqeq BkAk ][][0 11 −+−=eq
eq
AB
kk
][][
1
1 =−
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
Complex Reactions
One feature of complex reactions is that there is a considerable increase in mathematical complexities as soon as the reaction mechanism has more than a couple of steps.
often there is no analytical solution. numerical method에의존
or approximation method에의존The Steady-State Approximation
- during the major part of the reaction, the rates of change of concentrations of all reaction intermediates are negligibly small.
CBA kk ⎯→⎯⎯→⎯ 21for
][][][21 BkAk
dtBd
−= 0][][ 21 ≈− BkAk2
1 ][][
kAk
B ≈
][][2 Bk
dtCd
= ][1 Ak≈ tkeAk 101 ][ −=
tkeAA 10][][ −=
dteAkCt tk∫ −=0
011][][ { }tkeA 11 ][ 0
−−= ((the same result as before))
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
Prior-equilibrium approximation (Pre-equilibria)
X P + Qk2 (slow)
A + B Xk1
k-1
(fast, equilibrium)- an intermediate is in equilibrium with the reactants (pre-equilibrium).
- A pre-equilibrium arises when the rates of formation of the intermediate and its decay back into reactants are much faster than its rate of formation of products.
Since A, B and X are in equilibrium,
1
1
]][[][
−==
kk
BAXK ]][[][
1
1 BAkk
X−
=
therefore the rate of formation of product is
]][[][][][
1
212 BA
kkk
XkdtQd
dtPd
−===
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
Rate Law Reaction Mechanism
Deducing a Mechanism from Kinetic Data
다음의 stoichiometric reaction에대하여,
CBA ⎯→⎯+
]][[][ −=− OHAkdtAd
속도법칙을구했더니, 이었다. 메커니즘은?
A + OH- M-k1
M- + B C + OH-k2
((mechanism 1))
A + OH- X , K (fast to equibrium)
N- P-k1 (slow, rate determining)
P- + B C + OH-k2 (fast)
((mechanism 2))
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
Temperature Dependence
- The rate constants of most reactions increase as the temperature is raised.
- Experimentally, a plot of ln k against 1/Tgives a straight line for many reactions.
Tk 1ln ∝
RTE
Ak a−= lnln
or RTaE
Aek −=((The Arrhenius equation))
where A (pre-exponential factor or frequency factor) and Ea (activation energy) are the Arrhenius parameters
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
The interpretation of the Arrhenius parameters
for an elementary (endothermic) reaction
PNM ⎯→⎯+
we get a potential energy profile like the one to the left.
• ______________ : the collection of motions, such as changes in interatomic distances and bond angles, that are directly involved in the formation of products from reactants.
OH- + CH3Br CH3OH + Br-예.
• ______________ : the minimum kinetic energy that reactants must have in order to form products.
• _____________________ : a measure of the rate at which collisions occur irrespective of their energy.• __________________ : the fraction of collisions with a kinetic energy in excess of an energy Ea (the Boltzmann distribution)
RTaE
Aek −= (“the rate of successful collisions”)
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
Transition-State Theory
• a transition state is a molecule that is stable along the reaction coordinate between reactants and products. (cf, activated complex) • lasting only a few molecular vibrations (i.e. lifetime in the range of ~ps~fs).
for every elementary reaction, M + Nk
P
][][ ≠≠= MNkdtPd
the rate of product formation is
]][[][
NMMNK
≠≠ =]][[][ NMKMN ≠≠ =
]][[][ NMKkdtPd ≠≠=
≠≠= Kkk
M + N MN kP
K
one can write as following.
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
≠≠= Kkk
≠≠ −= KRTG ln∆
hTk
k B=≠ (from statistical treatment of transition-state)
≠= KhTk
k B (Eyring equation)
≠≠≠ −= STHG ∆∆∆
RTH
RS
hTk
k B≠≠
−+=∆∆lnln RT
EAk a−= lnlncf)
RTE
RTH a−≈−
≠∆ &RS
hTk
A B≠
+≈∆lnln aEH ≈≠∆ &
TkAhRSB
ln≈≠∆
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
Universal crossed molecular beams apparatus with synchrotron photoionization mass spectrometric product detection
Yang X, Lin J, Lee YT, Blank DA, Suits AG, Wodtke AM, REVIEW OF SCIENTIFIC INSTRUMENTS, 68: (9) 3317-3326 SEP 1997
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
≠≠= MNck
dtPd ][
Ionic Reactions and Salt Effects
M + N MN kP
K
for any elementary reactions,
NM
MN
NM
MN
NM
MN
ccc
aaa
K≠≠≠
⋅==≠
γγγ
NMMN
NMB ccKhTk
v≠
≠=γ
γγ or≠≠
== ≠
MN
NM
MN
NMB kKhTk
kγ
γγγ
γγ0
(k0 : rate constant for ideal solution)
∑=−=speciesall
iiiii ZcIIZ
2
212 , where51.0logγ
From Debye-Hückel limiting law, we know
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
≠
=MN
NMkkγ
γγ0
≠−++= MNNMkk γγγ logloglogloglog 0
51.0log 2 IZii −=γ
( ) IZZZZkk NMNM ][51.0loglog 2220 +−+−=
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
Isotopes and Stereochemical Properties
CH3 C
O
O C
HR
R'
H2OCH3 C
O
OHHO C
HR
R'
+ +
?
C
H3C
H
O + X- C
H3C
H
O-
X
C
O-
HX
CH3
C
O-
HCH3
X
or
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
Relaxation Methods
• relaxation? “the return of a system to equilibrium”
A + B Pk1
k-1 ]][[][
][][][
1
1
BAP
BAP
kk
Keqeq
eq ===−
• Perturbation의종류
1. Temperature jump : discharge of an electric capacitor, strike of a short laser pulse, etc.
2. Pressure jump : removing a restraining diaphragm, etc3. Flash- or laser-pulse photolysis : a short pulse of light to produce excited
molecules (ex. [H+] jump when excited state is more acidic than the ground state)
][]][[][11 PkBAk
dtPd
−−=
the rate law for P
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
A + B Pk1
k-1 ]][[][
][][][
1
1
BAP
BAP
kk
Keqeq
eq ===−
][]][[][11 PkBAk
dtPd
−−=the rate law for P :
“Due to a short and weak perturbation, the concentration of P is decreased by ∆[P].”(Assumption)
( )=
−=
dtPPd
dtPd ][][][ ∆
( )( ) ( )][][][][][][][11 PPkPBPAk
dtPd
∆∆∆∆
−−++=− −
( ){ } ( )][][][][][][]][[ 12
1 PPkPPBABAk ∆∆∆ −−+++= −
( ){ } ][][][][][][]][[ 12
111 PkPPBAkPkBAk ∆∆∆ −− ++++−=
][][][ PPP ∆−=][][][][][ PAAAA ∆∆ +=+=][][][][][ PBBBB ∆∆ +=+=
][]][[][11 PkBAk
dtPd
−−=−∆
Prof
. San
g-W
on L
ee (K
orea
Uni
vers
ity, D
epar
tmen
t of C
hem
istry
) Prof. Sang-Won Lee (K
orea University, D
epartment of C
hemistry)
( ){ } ][][][][11 PkBAk
dtPd
∆∆
−++=−
( ) 11 ][][1
−++=
kBAkτ
τ][][ P
dtPd ∆∆
=− “1st-order kinetics”
