Hammett plots – the most common linear free energy relationship.
It is important to know effects of substituents on chemical properties.
In particular, this contributes to understanding reaction mechanisms and to predicting
rate constants and equilibrium constants.
Hammett equation relates rates and equilibria for many reactions of compounds
containing substituted phenyl groups.
There is a relationship between the acid strengths of substituted benzoic acids
and the rates of many other chemical reactions, for instance, the rates of hydrolysis
of substituted ethyl benzoates.
CO2Et
CO2H
+ EtOH
X
X
ko: rate constant for hydrolysis of ethyl benzoate
k: rate constants for hydrolysis of substituted esters
Ko: acid dissociation constant of benzoic acid (= Keq for X = H)
K: acid dissociation constant of substituted acids (= Keq for X = substituents)
log(k/ko) = mlog(K/Ko)
DDG‡ = mDDGo
Linear free-energy relationship
DGo = -RTlogKeq
k=
kkBT
h
e
+
+
-DG /RT
Hammett linear free-energy relationship
log(k/ko) = sr
log(K/Ko) = sr
s : substituent constant
r : reaction constant (should be measured for given reactions)
-> sensitivity of a particular reaction to substituent effects
measurement of s values
r = 1 : reference reaction, the ionization of benzoic acids
CO2H
CO2+
X
H+
log(K/Ko) = sx
X
s can be determined for specific substituents (measured, known)
s values: negative, the substituted benzoic acid is less acidic than benzoic acid itself
-> electron donating groups have negative s values
positive, the substituted benzoic acid is more acidic than benzoic acid itself
-> electron withdrawing groups have positive s values
inductive effect
inductive and resonance effects
s+ : used for reactions in which there is direct resonance interaction
between an electron donor substituent and a cationic reaction center
s- : used for reactions in which there is direct resonance interaction
between an electron donor substituent and the electron-rich reaction site
s+
O
OMe
OMe
O-
O
N
sO
-O
O-
Summary using Hammett equation for a particular reaction
1. Measure kx or Kx for substituents
2. Plot log(kx/ko) vs s
3. Determine r and interpret the results
log(k/ko) = sxr
log(K/Ko) = sxr
log(k/ko)
Slope = r
s
1. When r > 1, the reaction under study is more sensitive to substituents
than benzoic acid, and negative charge is building during the reaction.
-> an electron withdrawing group stabilizes the developed negative charge.
2. When 0 < r < 1, the reaction is less sensitive to substituents than benzoic acid,
but negative charge is still building.
3. When r is equal to or close to 0, the reaction shows no substituent effects.
4. When r is negative, the reaction is creating positive charge.
-> electron donating groups increases in rates.
5. lrl large: much positive or negative charge separation
Predicting rate constants using Hammett equation
CO2-
CO2Me
k = 2 x 10-4/M s
log(km/kH) = sr = 0.70 x 2.38 = 1.69
km/kH = 101.69 = 49
CO2-
CO2Me
k=?
km = 49 x kH = 98 x 10-4/M s
NO2
NO2
Cl
OH
Which reaction is faster?
log(kp-Br/kH) = sr = -1.31 x 0.26
Br
Br
Cl
OH
log(kp-NO2/kH) = sr = -1.31 x 0.81
NO2
NO2
Cl
OH
r = -1.31
X
sm (NO2) = 0.70
X
kp-Br/kp-NO2 = 5.25
SN2; negative r
The power of Hammett plots for deciphering mechanisms
r = 2.23
not distinguished by r values
-> other technique is required
to distinguish
r = -5.09 -> SN1-like mechanism
small r =values due to
little or no change in charge
during reaction (SN2)
SN1: large negative r+
carbocation is developed
SN2
치환기에 따라 SN1에서 SN2로 바뀜
Miscellaneous experiments for studying mechanisms
Kinetic analysis, isotope effects and structure-function analysis <- reaction mechanism
Product identification
It is important to identify all the products of a reaction. Sometimes, identification of a
minor product will provide a valuable clue as to the kind(s) of mechanistic pathways.
OH
SN2
O2N
expected product
Changing the reactant structure to divert or trap a proposed intermediate
Mandelate racemase : a carbanion alpha to the carboxylate was proposed as
the intermediate formed. To test for the presence of this intermediate, the
following substrate was designed.
CO2H
OH
mandelic acid
Trapping and competition experiments
A common method for intermediate identification is trapping of the
intermediate with an added reagent.
never seen at room temperature
Phosphoranes: are proposed
intermediates in the hydrolysis
of RNA and DNA
trapping this intermediate
Checking for a common intermediate
possible intermediate
Similar ratio
of products
However, quite
different ratio
Stereochemical anlaysis
SN2
SN1
Double inversion
-> retention of stereochemistry
Isotope scrambling
O
OH
O
H
Claisen rearrangement
Allyl fragment may be
formed during reaction
50 : 50
Techniques to study radicals: clocks and traps
Radical clocks are one experimental technique that has received considerable use
in the analysis of radical reactions. Most radical clocks involve an intramolecular free
radical rearrangement that proceeds with a well-defined rate constant.
photolosis
ring opening rate constant ~ 108/s
-> life time: 1 to 4 ns
Three products are formed
O
CH3
H
O.
O
hv
O
.
O
O
CH3
OH
.
O
.
O
CH3
H
The use of a spin strap: the addition of a free radical to a nitroso or nitrone group creates
a relatively stable spin adduct that can be detected by EPR
(electron paramagnetic resonance) spectroscopy.
a relatively stable spin adduct
that can be detected by EPR
CH3CH2.
N (I = 1) ->
2H (I = 1/2) ->
3H
JCH3
->
JCH2
+
N
O.
N
CH2CH3
O
1
:
1
1:2:1
:
1:2:1
1:3:3:1
: 1:3:3:1
:
1
:
1:2:1
:
1:3:3:1
JN
Catalysis
General principles of catalysis
Turnover number: the average number of reactants that a catalyst acts on before the
catalyst loses its activity.
The catalyst increases rate of reaction (decreases activation energy).
The thermodynamics of a catalyzed reaction are unaffected by the catalyst.
A heterogeneous catalyst: one that does not dissolve in the solution. eg) Pd/C
A homogeneous catalyst: one that dissolves in the solution.
All calaysts operate by the same general principle – that is, the activation energy of
the rds must be lowered in order for a rate enhancement to occur.
Binding the transition state better than the ground state
Substrate: any material (reactant) used in a catalytic reaction
Activated complex: simply referred to as the transition state
Rate enhancement: the ratio of the rate constant for the catalyzed reaction to that
for the uncatalyzed one (kcat/kuncat).
To achieve catalysis, the catalyst must stabilize the transition state more than it stabilizes
the ground state. That is, the transition state must be bound better than the ground state.
A spatial temporal approach
To achieve catalysis, the catalyst must stabilize the transition state more than it stabilizes
the ground state. That is, the transition state must be bound better than the ground state.
Another explanation for catalysis: spatial temporal postulate, many intramolecular reactions
are often much faster than corresponding intermolecular reactions.
-> the rate of reaction between functionalities A and B is proportional to the time
that A and B reside within a critical distance. The longer that A and B spend together in
the correct geometry for reaction, the greater that probability.
When bound to the catalyst, the distance between A and B is closer than when they are free
in solution, and inherently the transition state brings A and B close because bonds are
beginning to form.
In summary, binding is the key element in the most widely accepted theory of
how catalysis is achieved. Greater binding of the transition state relative to the ground state
is all that needs to be invoked to give a rate enhancement.
Forms of catalysis
Proximity as binding phenomenon
Intermolecular aminolysis (k1; 1/M·s)
1.3 x 10-4 /M·s
Intramolecular cyclization (k2; 1/s)
0.17/s
-> a rate enhancement of 1200
Effective molarity (E.M.) or intramolecularity; ratio of the first order
to second order rate constants for the analogous reactions.
-> tell us the effective concentration of one of the components
in the intramolecular reaction
Entropies of translation and rotation
Gem-dimethyl effect: sterically compress two groups together and preorganize
two reactants in proximity
close
decrease of angle
R
R
An angle for R = H is greater than an angle for R = alkyl.
E.M. = 1011-1012
Tetrahedral intermediate
-> infinitely stable
not isolated
Twisted amide
-> very reactive
Electrophilic catalysis
Electrophilic catalysis includes simple electrostatics, hydrogen bonding, acid catalysis,
and electrophilic metal coordination.
Electrostatic interactions
Oxyanion hole
150-fold rate enhancement
Cation-p interactions
Metal ion catalysis
2 x 1016-fold rate enhancement
pKa of metal-bound water = 7.2 (108 more acidic than water itself)
Acid-base catalysis; see previous section
Nucleophilic catalysis
Nucleophilic catalysis arise when a nucleophile binds to a reactant and enhances its rate
of reaction. -> less common than electrostatic catalysis
NMe2
NMe2
N
H
DMAP; N,N'-dimethylaminopyridine
N
better electrophile and more reactive
than the starting acid halide or anhydride
Covalent catalysis
Iminium ion
enamine
N
H
H
N
HH
O
Iminium ion
아래로 공격
Strain and distortion
When a substrate binds to a catalyst that is more complementary in structure or electronic
characeristics to the transition state, the substrate may distort in order to optimize binding
interactions. That is, because the catalyst is designed to optimally bind the transition state,
it necessarily is not optimal for the most stable structure of the ground state.
-> distortion as a strain on the substrate -> the strain raises the energy of the substrate
-> diminish activation energy
The chair is distorted into a conformation resembling a half-chair
Brønsted acid-base catalysis
specific catalysis
The specific acid is defined as the protonated form of the solvent in which the reaction is
being performed.
eg) H3O+, CH3CNH+, CH3SO(H+)CH3
The specific base is defined as the conjugate base of the solvent.
eg) HO-, -CH2CN, CH3SOCH2The specific acid catalysis refers to a process in which the reaction rate depends upon
the specific acid, not upon other acids in the solution.
The specific base catalysis refers to a process in which the reaction rate depends upon
the specific base, not upon other bases in the solution.
kobs = k[H3O+]/KaRH+
Specific acid catalyzed reactions
added acid (AcOH in H2O)
A-는 반응에 관여하지 않음.
따라서 rate law에 포함되지 않음
KaHA = [A-][H3O+]/[HA]
KaRH+ = [R][H3O+]/[RH+]
앞과 동일
[HA] 항 없음
If the acid catalysis is involved in an equilibrium prior to the rds, and it is not involved
in rds, then the kinetics of the reaction will depend solely upon the concentration of
the specific acid. This is true even if an added acid (AcOH) is involved in protonating
the reactant.
Why? When a prior equilibrium is established, [RH+] determines the rate of the reaction.
The concentration of RH+ depends solely upon the pH and the pKa of RH+, and does not
depend upon the concentration of the acid HA that was added to solution.
Specific base catalyzed reactions
BH+는 반응에 관여하지 않음.
따라서 rate law에 포함되지 않음
KaRH =[R-][H3O+]/[RH]
kobs = kKaRH /[H3O+]
[B] 항 없음
23 page에서 다시 설명
Kinetic plots
The hallmark of specific acid or specific base catalysis is that the rate depends on the pH and not on
the concentration of various acids or bases. This always means that an equilibrium involving the
acid or base occur prior to rds, and the acid or base is not involved in rds itself.
specific acid catalysis
specific base catalysis
kobs = k[H3O+]/KaRH+
kobs = kKaRH /[H3O+]
logkobs = logk –pH-logKaRH+
logkobs = logk +pH+logKaRH+
added acid
added base
General catalysis
In case that the proton transfer is involved in rds, not in a prior equilibrium
-> general catalysis
When an acid is involved in rds, -> general acid catalysis
When a base is involved in rds, -> general base catalysis
The term ‘general’ refers to the fact that any acid or base we added to the solution
will affect the rate of the reaction.
The term ‘specific’ refers to the fact that just one acid or base, from the solvent,
affects the rate of the reaction.
General acid catalyzed reactions
HA는 반응에 관여함.
따라서 rate law에 포함
Ka = [A-][H3O+]/[HA]
kobs = k[HA] or k[H3O+][A-]/Ka
- Since the acid is always regenerated after the reaction,
its concentration never changes over the course of the reaction -> pseudo-first order
- the concentration of either HA or A- is in the rate expression.
General base catalyzed reactions
B는 반응에 관여함.
따라서 rate law에 포함
kobs = k[B] or k[HO-][HB+]/Kb
- Since the base is always regenerated after the reaction,
its concentration never changes over the course of the reaction -> pseudo-first order
- the concentration of either B or BH+ is in the rate expression.
19 page
fast
slow
실제로는 첫번째 단계가 rds
따라서 HO-는 general base로 작용
Note: ‘specific’ is used to designate the protonated or deprotonated form of the solvent
(H3O+ or HO- for water), but it is also used to designate a mechanism involving an acid or
base in an equilibrium prior to rds.
However, sometimes hydronium or hydroxide can be involved in rds.
In this case the specific acid and base are participating in general-catalysis.
Kinetic plots
Since the rate for general-acid or general-base catalysis always depends on [HA] or [B] added to the
solution, and is not soley dictated by the pH, the experimental observations are quite dufferent from
specific-acid-specific-base catalysis.
Since [HA] or [B] has been incorporated into kobs, this value is lineraly related to [HA] or [B].
However, the pH depence is more difficult to understand.
kobs = k[HA] or k[H3O+][A-]/Ka
kobs = k[B] or k[HO-][HB+]/Kb
페이지 20과 비교
general acid catalysis
general base catalysis
pH < pKa, HA로 주로 존재, 따라서 k의 변화 없음
pH ~ pKa, HA와 A- (이것은 반응에 관여하지 않음)이 공존
pH > pKa, HA가 점차적으로 A-로 바뀌어 k가 지속적으로 감소
C와 mirror image
general acid catalysis
general base catalysis
Concerted or sequential general-acid-general-base catalysis
Both a general acid and a general base catalyst are required for a reaction.
This is often the case with enzymes.
acid base
kobs = k[HA][B]
The rate dependence on pH is a combination of that observed for general-acid
The largest kobs is found at pH where
and general-base catalyst.
the product of the concentrations of
HA and B is at a maximum
Enzymatic catalysis
physical process
chemical process
Michaelis-Menten kinetics
k1
kcat
E + S ←
→ E·S → P + E
k-1
E
+ S
→
←
E·S: Michaelis complex
→
P
E·S
rate = d[P]/dt = kcat[ES]
d[ES]/dt = k1[E][S] – k-1[ES] - kcat[ES] = 0
[E]0 = [E] + [ES]
[E] = [E]0 - [ES]
k1([E]0-[ES])[S] – k-1[ES] - kcat[ES] = 0
[ES] =
[E]0[S]
Km + [S]
Km = (k-1 + kcat)/k1
rate = d[P]/dt = kcat[ES] =
kcat[E]0[S]
Michaelis-Menten equation
Km + [S]
Kinetic parameters to be determined for enzymatic reactions: kcat and Km
The meaning of Km, kcat and kcat/Km
1. kcat: catalytic constant
turnover number: the maximum number of substrate molecules converted to products
per active site per unit time or the rate constant for the conversion of the substrate to the
product within the active site of the catalyst (unit; 1/s)
-> proximity, acid-base catalysis, electrostatic consideration, covalent catalysis, and the
relief of strain will influence kcat.
2. Km : apparent dissociation constant that may be treated as the overall dissociation constants
of all enzyme-bound species.
k-1 >> kcat -> Km = k-1/k1 the dissociation constant for ES complex.
Under these circumstances, Km can provide insights into how good a receptor
the catalyst is. The smaller Km means a better receptor. -> Km reflects a
physical process (binding) rather than a chemical transformation.
k-1 << kcat -> Km = kcat/k1 (a very good catalyst) does not resemble the dissociation constant
for ES complex
3. kcat/Km (specific constant)
Km >> [S],
kcat/Km ; apparent second order rate constant
-> this is related to how well the catalyst binds the substrate and how well the catalyst turns
over the substrate to product. -> Information on both binding and catalysis
Enzyme active sites
Ricin A is a potent cytotoxin from 아주까리
Proposed mechanism
general acid
attacks ribosomes, hydrolyzing the N-glycoside linkage
of specific adenosine nucleotides in oligonucleotides
general base
-> enhances nucleophilicity of water
6-OH
3-OH
Rate enhancement: 104-105
Vmax: 2.24 x 10-5 M/s
Km: 4.69 x 10-5 M