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 acidsand the rates of many other chemical reactions, for instance, the rates of hydrolysis of substituted ethyl benzoates.

CO2Et

X

CO2H

X

+ EtOH

ko: rate constant for hydrolysis of ethyl benzoatek: rate constants for hydrolysis of substituted estersKo: 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) G‡ = mGo

Linear free-energy relationship

Go = -RTlogKeq

kBTh

e -G /RT++

k =

log(k/ko)

log(K/Ko) = =

Hammett linear free-energy relationship

: substituent constant : reaction constant (should be measured for given reactions) -> sensitivity of a particular reaction to substituent effects

= 1 : reference reaction, the ionization of benzoic acids

CO2H

X

CO2-

X

+ H+

can be determined for specific substituents (measured, known)

log(K/Ko) = x

values: negative, the substituted benzoic acid is less acidic than benzoic acid itself -> electron donating groups have negative values positive, the substituted benzoic acid is more acidic than benzoic acid itself -> electron withdrawing groups have positive values

measurement of values

inductive effect inductive and resonance effects

+ : used for reactions in which there is direct resonance interaction between an electron donor substituent and a cationic reaction center- : used for reactions in which there is direct resonance interaction between an electron donor substituent and the electron-rich reaction site

OMe OMe

O-

N

O

O O O--O

-

+

1. When > 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 < < 1, the reaction is less sensitive to substituents than benzoic acid, but negative charge is still building. 3. When is equal to or close to 0, the reaction shows no substituent effects.4. When is negative, the reaction is creating positive charge. -> electron donating groups increases in rates. 5. ll large: much positive or negative charge separation

log(k/ko)

log(K/Ko) = x= x

log(k/ko)

Slope =

Summary using Hammett equation for a particular reaction

1. Measure kx or Kx for substituents2. Plot log(kx/ko) vs 3. Determine and interpret the results

Predicting rate constants using Hammett equation

log(km/kH) = = 0.70 x 2.38 = 1.69 m(NO2)= 0.70

km/kH = 101.69 = 49

km = 49 x kH = 98 x 10-4/M s

CO2Me CO2-

CO2Me CO2-

k = 2 x 10-4/M s

NO2 NO2

k = ?

Cl

Br

OH

Br

Cl

NO2

OH

NO2

Which reaction is faster?

log(kp-Br/kH) = = -1.31 x 0.26

Cl

X

OH

X

= -1.31

log(kp-NO2/kH) = = -1.31 x 0.81

kp-Br/kp-NO2 = 5.25

SN2; negative

The power of Hammett plots for deciphering mechanisms

not distinguished by values-> other technique is required to distinguish

= 2.23

= -5.09 -> SN1-like mechanism

small =values due to little or no change in charge during reaction (SN2)

SN1: large negative +

SN2

carbocation is developed

치환기에 따라 SN1 에서 SN2 로 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.

O2N

OH

SN2expected 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.

OH

CO2H

mandelic acid

Trapping and competition experiments

A common method for intermediate identification is trapping of the intermediate with an added reagent.

Phosphoranes: are proposed intermediates in the hydrolysis of RNA and DNA

never seen at room temperature

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

Claisen rearrangement

O O

H

OH

50 : 50

Allyl fragment may be formed during reaction

Techniques to study radicals: clocks and trapsRadical clocks are one experimental technique that has received considerable usein the analysis of radical reactions. Most radical clocks involve an intramolecular free radical rearrangement that proceeds with a well-defined rate constant.

photolosis

O

O

O

HCH3

hvO.

O

O

HCH3

.

OH

O

O

CH3

.

.

Three products are formed

ring opening rate constant ~ 108/s-> life time: 1 to 4 ns

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. +

NO N

O.

CH2CH3

N (I = 1) -> 1 : 1 : 1

2H (I = 1/2) -> 1:2:1 : 1:2:1 : 1:2:1

3H -> 1:3:3:1 : 1:3:3:1 : 1:3:3:1

JNJCH2

JCH3

Catalysis

General principles of catalysisTurnover 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/CA 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 reactionActivated complex: simply referred to as the transition stateRate 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 inthe 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 stateis all that needs to be invoked to give a rate enhancement.

Forms of catalysisProximity as binding phenomenon

Intermolecular aminolysis (k1; 1/M·s)

Intramolecular cyclization (k2; 1/s)

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

1.3 x 10-4 /M·s

0.17/s-> a rate enhancement of 1200

Entropies of translation and rotation

Gem-dimethyl effect: sterically compress two groups together and preorganize two reactants in proximity

R R

decrease of angleclose

An angle for R = H is greater than an angle for R = alkyl.

Tetrahedral intermediate -> infinitely stable

E.M. = 1011-1012Twisted amide-> very reactive

not isolated

Electrophilic catalysis

Electrophilic catalysis includes simple electrostatics, hydrogen bonding, acid catalysis,and electrophilic metal coordination.

Electrostatic interactions

Oxyanion hole

150-fold rate enhancement

Cation- 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

N

NMe2

NH

NMe2

DMAP; N,N'-dimethylaminopyridine

better electrophile and more reactive than the starting acid halide or anhydride

Covalent catalysis

Iminium ion

enamine

NH N

H

OH

H

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 catalysisspecific 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, CH3SOCH2

-

The 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+

added acid (AcOH in H2O)

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.

앞과 동일

Specific acid catalyzed reactions

A- 는 반응에 관여하지 않음 .따라서 rate law 에 포함되지 않음

KaHA = [A-][H3O+]/[HA]KaRH+ = [R][H3O+]/[RH+]

[HA] 항 없음

kobs = kKaRH /[H3O+]

Specific base catalyzed reactions

KaRH =[R-][H3O+]/[RH]

BH+ 는 반응에 관여하지 않음 .따라서 rate law 에 포함되지 않음

[B] 항 없음

23 page 에서 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 catalysisIn case that the proton transfer is involved in rds, not in a prior equilibrium -> general catalysisWhen an acid is involved in rds, -> general acid catalysisWhen a base is involved in rds, -> general base catalysisThe 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.

HA 는 반응에 관여함 .따라서 rate law 에 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 acid catalyzed reactions

General base catalyzed reactions

B 는 반응에 관여함 .따라서 rate law 에 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.

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.

19 page

fast

실제로는 첫번째 단계가 rds따라서 HO- 는 general base 로 작용

slow

Kinetic plots

general acid catalysis general base catalysis

kobs = k[HA] or k[H3O+][A-]/Ka kobs = k[B] or k[HO-][HB+]/Kb

페이지 20 과 비교

pH < pKa, HA 로 주로 존재 , 따라서 k 의 변화 없음pH ~ pKa, HA 와 A- ( 이것은 반응에 관여하지 않음 ) 이 공존pH > pKa, HA 가 점차적으로 A- 로 바뀌어 k 가 지속적으로 감소

general acid catalysis general base catalysis

C 와 mirror image

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.

Concerted or sequential general-acid-general-base catalysisBoth 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 and general-base catalyst. The largest kobs is found at pH where

the product of the concentrations of HA and B is at a maximum

Enzymatic catalysisMichaelis-Menten kinetics

E + S E·S P + E←→k1

→k-1

kcat

E·S: Michaelis complex

SE + ←→ → 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]

k1([E]0-[ES])[S] – k-1[ES] - kcat[ES] = 0

[E] = [E]0 - [ES]

[E]0[S]Km = (k-1 + kcat)/k1

[ES] =Km + [S]

rate = d[P]/dt = kcat[ES] = kcat[E]0[S]

Km + [S]Michaelis-Menten equation

Kinetic parameters to be determined for enzymatic reactions: kcat and Km

physical process

chemical process

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],

The meaning of Km, kcat and kcat/Km

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

Proposed mechanism

Ricin A is a potent cytotoxin from 아주까리

attacks ribosomes, hydrolyzing the N-glycoside linkageof specific adenosine nucleotides in oligonucleotides

general acid

general base-> enhances nucleophilicity of water

Rate enhancement: 104-105

Vmax: 2.24 x 10-5 M/sKm: 4.69 x 10-5 M

6-OH

3-OH