Modern Physical Organic Chemistry; Chemistry; Organic Physical Modern Reference: Lead 2006; Chapter 7 Chapter 2006;

and their Application to Organic Chemistry Application and their A Discussion of Reaction Kinetics of Reaction A Discussion MacMillan Group Meeting Anslyn E. V., Dougherty, D., E. V., A.; Univ Anslyn Dougherty, June 11, 2007 Diane Carrera ersity Science Books: Sausalito, ersity Sausalito, Science Books:

Kinetics experiments Kinetics Basics The

– Bringing it All Together, a Kinet Together, All it – Bringing Approximation) (Steady-State Reactions – Multi-Step Reactions – Elementary Constants Rate and – Rates and Postulates – Principles Diagrams Coordinate – Reaction Surfaces – Energy kinetics? – What is Overview ic Analysis of Selectivity Trends Selectivity ic Analysis of andhow the concentration of product and reac

not matter
Kinetics: the experimental measurement of the macroscopic properties of a reaction mixture mixture reaction a of properties macroscopic the of measurement experimental the Kinetics: Dynamics:molecular the scale analysis of reactionrates Thermodynamics: concerned onlythe with final st How fast does a molecule of A and B go to a molecule of C and what does this tell us about the mechanism? the us about tell this does what and of C molecule to a B go and of A molecule a does fast How the mechanism?the of a solution A and B at a How fast does concentration given

AB AB What Do We Mean When What is [A], [B] and [C] when the system is at equilibrium? the when [C] [B] and What is [A], AB C C

tants changes over time, ie, reaction rate reaction ie, time, over changes tants Talk About Reaction Kinetics? ate of a system, mechanismsystem, aate of of transformation does go to a solution of C and what does this tell us about us about tell this does what and C of solution a to go MgBr C Me O Me Me Ph OH Me – highest energy points that must be traversed during the the during traversed must be that points energy – highest structures t energy – high (valleys) products and reactants – stable


TheX and Y-axes represent a continuum of The unit alongthe Z-axis is energy Energyway Surfaces are a to visualize the peak, high energy structure peak, energy high hat are seldom obtained (peaks) obtained seldom hat are valley, reactants and products reactants and valley,

saddle point, transition state transition point, saddle Energy Surfaces molecular structures that encompasses: energy involved in a chemical transformation transformation of reactant transformation energy to product (saddle point) (saddle product to changes in molecular in changes structure

the GaAs surface
plotted against adsorbatepositionthewithin surface unit cell
The potential energy surface explains why they why explains surface energy potential The Modelling the growth of Fe on Modelling A B a GaAs surface using density fu

Erwin, S.C.; Lee, S- S.C.; Erwin, Energy Surfaces symmetrical distribution As As As As observenon-symmetrical depositionon of Fe nucleated growth nucleated Ga Ga Ga Ga As As As As Ga Ga Ga A Ga B H.; Scheffler; H.; Scheffler; M. As As As As Ga Ga Ga Ga nctional theory,

As As As As Physical Review Physical

E t total energy (E total position of Fe on Ga Ga on Fe of position = Fe , 2002 unit cell unit

, 65

, 205422 t ) while "activated complex" refe while "activated complex"

Though often used interchangeably "transition state" refers to the point on the energy surface surface energy the on point the to refers state" "transition interchangeably used often Though

The activated complex activated A is the molecular struct the molecular is B rs to the molecular structure molecular rs to the C

Erwin, S.C.; Lee, M. S-H.; Lee, Scheffler; S.C.; Erwin, Energy Surfaces symmetrical distribution symmetrical As As As As ure that exists at the at the exists that ure nucleated growth nucleated Ga Ga Ga Ga As As As As Ga Ga Ga A Ga B As As As As Ga Ga Ga Ga

As As As As

transition state transition Physical Review As As activated complex activated Ga Ga = As As Fe Ga , C 2002 Ga As As

,

Ga Ga 65 , 205422 As As happening during a chemical reaction chemical a during happening
related to the width of the channels leading from one energy well to another to well energy one from leading channels the of width the to related


Thinking about the energy surfacepotentia as Onenergy an surface, enthalpy can be relate The energy coordinate is the Gibbs free energycomprised (G) is of two components, enthalpy (H) and entropyrelatedby: (S)
G = G

H – T – H What Comprises the Energy
S potential energy potential enthalpy: entropy: d to the height of the surface while entropy is l energy helps us think think us helps l energy of the system, it's Gibb'ssystem, of the free energy

motions can it undergo it can motions internal and translational of rotational, sort what fr of degrees the describes properties affect the ov these in changes how and states strength, vibrational associ energy the describes on an Energy Surface? erall energy of the system of the energy erall about what is really eedom of a molecule, i.e., i.e., molecule, of a eedom ated with conformation, bond bond conformation, ated with
of the activated complex, the collis activated complex, of the
Reactions occur due to molecular col to molecular due occur Reactions two molecules moving in solution two molecules moving in Stage 1: If the energy of the collision is If the energy of collision Me H Me E OH O 3 is converted to potential energy to potential converted is Stage 2: E Me O energy exists primarily as kinetic energy, energy, kinetic as primarily exists energy 1 Me

Me Thinking About a Reaction in molecules collide and distort, kinetic energy energy distort, kinetic and collide molecules Stage 3: H O O Me H H new molecule moves off with a new kinetic energy kinetic new a off with moves molecule new E O 2 H high enough and di ion leads to a chemical reaction leads to a ion

lisions, for example, carbonyl hydrolysis Terms of Energy Transformations Terms stortion is severe stortion is Potential energy Stage 1 enough to achi Stage 2 eve the structure Stage 3 Stage follow to molecule a for path energy lowest the of curve a giving pathways reaction the all of picture

differentially populated vibrational modes of the molecules
pathways possible all of rates the of average weighted a actually is rate reaction a thus product, to reactant

Reaction coordinate diagrams are used to si to used are diagrams coordinate Reaction There are also multiple path Something that cannot represented be thein three dimensional energy surface below is the Energy Surfaces vs. Reac ways across the energy surfac energy the across ways

mplify the situation, they represent a composite tion Coordinate Diagrams

Potential Energy e for molecules to take from to take for molecules e Reaction Coordinate Reaction
G
and products
postulates and principlesorusing more rigorous alongthe energy surface, molecules can "turn" within a valley but not atsaddle a point
Reactioncoordinate diagrams show the energies Reaction coordinate diagramscan be drawn The peaks andof valleysa reaction coordinate diagramare necessarily nota in straight line reactant transition state Reaction Coordinate Reaction

intermediate Reaction Coordinate Diagrams product rds using eitherinuition according to classic methods such as computation and Marcus theory step (rds) rate-determining of transition states, states, transition of intermediate 10 the time of a typical bond vibration, 10 of bond vibration, the time a typical than longer lasts that structure chemical any approximation) state (steady dependent concentration state also energy transition but highest formation, the observed rate of determines product rate whose reaction of the step the -14 s intermediates, reactants reactants intermediates, usually the step containing the the the step containing -13 to complexes, assumes that structural changes occur along a continuum along occur changes structural that assumes complexes,
exothermic reaction


The most widely used physical organic princi The postulate is most clearly demonstrated by comparing an endothermic reaction with an an with reaction endothermic an comparing by demonstrated clearly most is postulate The G G "If two states, as for example a transition state and state transition a example for as states, "If two

reaction process and have nearly the same energy content, their interconversion will involve only a small small a only involve will interconversion their content, same energy the nearly have and process reaction

endothermic exothermic x x y y reorganization of the molecular structures" molecular the of reorganization

late transition state early transition state early transition The Hammond x > y x < y ple for estimating the structures of activated of activated structures the for estimating ple

an unstable intermediate, occur consecutively during a during occur consecutively intermediate, unstable an Postulate transition state shifts towa shifts state transition as the cation becomes more stabilized, the the more stabilized, becomes cation the as RX S N 1 transition states 1 transition rds the starting material starting rds the CH 3
energy or exothermic

Hydrogen abstraction by Cl• is exothermic while abstraction by Br• is endothermic is Br• by abstraction while is exothermic Cl• by abstraction Hydrogen in higher means reactive" "more where postulate Hammond the of application an just Really X• Classic example: Free Radical Halogenation Radical Free example: Classic
G H X = Cl H "The more reactive a compound is, the less selective it will be" will it selective less the is, compound a reactive more "The

HX Reactivity vs. Sele
G X = Br X = X X

2 2 ctivity Principle X X Br, the bet Br, the differences due to the late transition state when X = X when state transition late the to due X• X• stabilities has a greater effect on on greater effect a has stabilities product distribution product when X when = Br 80 : 1 1600: X when = Cl 5 : 4 : 1 ween alkylradical 3 ˚ : 2 : ˚ : 1 : ˚ to product formation to product

Allows us to predict the Allows us to predict Curtin-Hammett applieswhen onlythe barrier to E a nuc addn >> E >> addn nuc determined by the relative heights of the hi of the heights relative the by determined pathways there are competing "When
G L M AB O R

a bond rotation bond G P S Nu 1 Situation Situation 1 stereochemistry of nucleophilic I 1 A I 2

will predominate because the trajectory is lower in energy energy in lower is trajectory the because predominate will Curtin–Hammett Principle due to minimized steric steric interactions due to minimized

P G 2 2 leading from interconverting interm from interconverting leading Nu ghest energy barriers leading to the products" to the barriers leading energy ghest S L interconversion is much

O R

relativeof stabilitiesthe intermediates does not matter M addition in production of P of production

to carbonyls G 1 < ediates, the product ratio is is ratio product the ediates,

1 less than the barrier less G will be the favored pathway favored the be will Nu 2 M S C O R L

Organic chemists often use this principle without realizing it realizing without principle this use often chemists Organic Understandingthis principle via reactioncoordinate diagrams O O P
G O OMe "The pathway for conversion of the product back to product back of the for conversion pathway "The of nucleophile addition axial P

OH principle of microscopic reversibility nucl reversibility of microscopic principle As leaving group departure occurs solely from the axial position, according to the the to according position, axial the from solely occurs departure group leaving As I 2 I 1 O O OH P OMe O

R Microscopic Reversibility Conversely, Conversely, Assume the forward pathway" the forward HO

O eophile addition must occur axially as well as occur axially must addition eophile OH P R is converted to to is converted OMe O

P

The same transition states are formed in states in the are formed The same transition Westheimer, F. H. Westheimer, both along forward and reverse pathways direction the reactant is the exact microscopic reverse of reverse microscopic exact the reactant is the is converted to is P via R O via

I J. Am.J. Chem . Soc. 1 O OMe P I OH 2 O axial departure departure axial of LG OMe 1969 O O

, 91 P O OH , 6066 interconvert viaa second chemicalpathway
temperature.
Thermodynamic control occurs only when the reaction is easily reversible or the products can can products the or reversible easily is reaction the when only occurs control Thermodynamic The best way to partitiona reaction between kinetic the and thermodynamic product is through higher temps higher lower temps lower and thermodynamic product thermodynamic and 1: Case A heights of the transition states transition of the heights "When a reaction is under under is a reaction "When B is both the kinetic kinetic both the is R B are determined by the relative relative by the are determined under kinetic control kinetic under B for preference small

thermodynamic control thermodynamic large preference for B under

Kinetic vs. Thermo kinetic irreversible reaction . When a reaction is under is under reaction a . When reversible reaction

control

, product ratios are determined by the relative barrier relative the by are determined product ratios , stabilities of the of the products" stabilities dynamic Control

Case 2: Case B is the product thermodynamic control thermodynamic A A is the kinetic product while while product is the kinetic

R thermodynamic product thermodynamic

B kinetic product kinetic , product ratios ratios , product kinetic control kinetic under for A preference thermodynamic control thermodynamic under for B preference enolates

stable thermodynamicenolate A synthetically useful example of kinetic vs. thermodynamic control is the selective formation of of formation selective the is control thermodynamic vs. kinetic of example useful A synthetically Working at low temps favo less substituted enolate enolate substituted less is higher in energy in higher is no unfavorable steric no unfavorable facile deprotonation, deprotonation, facile

interactions Kinetic vs. Thermodynamic kinetic enolate kinetic O rs the kinetic enolate as Me B H H O Me

O Control: Enolate Geometry the system cannot equilib Me thermodynamic enolate thermodynamic O H Me O B Me due to unfavorable steric to unfavorable due difficult deprotonation deprotonation difficult enolate stabilized by stabilized enolate interactions rate to form the more alkyl substitution the
is at a maximum, leading to diffe is at a maximum,
Reaction rates are dependenton reactant concentrationand a proportionality constant called Dependence on [R] implies that reaction order

molecularity rate constant(k

reaction order reaction k max )

the number of molecules involved in the in involved of molecules number the the mathematical dependence of the rate law on reactant concentration reactant on law rate the of dependence mathematical the can be used to describe a complicated reaction involving several steps steps but several involving a reaction can complicated be used to describe rate = = rate

time

molecularity k

rential rate equations known as known equations rate rential [R] Rates and Rate Constants

rates are time dependent with th dependent are time rates

[R] [P]

applies only to elementary reactions to elementary only applies k temperature of an energy surface and height represents the barrier transition state of elementary reactions elementary state of transition A + B + C + B + A

rate = – = rate rate laws e rate being greatest when [R] when [R] greatest being rate e

=

d k [R] / [A] a

[B] dt = b

[C] d [P] / [P]

c dt P
energy surfaces,

To solve for dynamical an molecular TST is a substitution leads to the the to leads substitution

A + B A K

AB ie statistical mechanics is is mechanics statistical

, rate constants Eyring

K

=

C

equation

Transition State Theory (TST)

k h

B  T

alysis for determining the energy values of barrier heights on on heights of barrier values the energy determining for alysis k = =

K ' K

the rate at which C is produced is dependent upon the rate of activated rate the of upon activated is dependent C at which is produced the rate complex decomposition

 key assumption: reactant and activated complex are equilibrium in and activated complex reactant key assumption: invoked to define the tr to define invoked

k

 K K

h B

 where T ] [AB = [B] [A]

= k rate = rate =

exp

k k

K ' d
RT [C] / G

= exp dt =

ansition state population state ansition k

[A] [B]=
RT

 G 

vibration frequency of activated complex of activated frequency vibration to product leading complex activated the of oscillation of an probability the coefficient, transmission k [AB ] parameters

The Eyring equation is most useful for experimental chemists when given in terms of activation activation of terms in given when chemists experimental for useful most is equation Eyring The note that the rate constant and activation activation and rate constant note that the

G = 4.576 T [10.319 + log (T / (T + log [10.319 T 4.576 = G k

= 2.083 x 10 k

= 2.083 x 10 2.083 = k

= 
G = = G

10 Eyring Equation

Texp

k

h B parameters are obtained fo T
10 H – T– H Texp exp
R S

RT S

G k
RT )] kcal / mol G exp 
RT

H r a given temperature given r a complexes activated for untrue definition by is this vibrations, and rotations through exchange energy

energiesfor the populationofmolecules at the transitionstate. state transition the representing point saddle the approaches it as transformation undergo to molecule
However, Boltzmann distributions assume that molecules are long lived enough to undergo full full undergo to enough lived long are molecules that assume distributions Boltzmann However, mechani statistical used We This substitution is S N 2 displacement 2 Nu Nu – – 180 175 ˚ ˚ H still valid and actually re still valid and H H H

K H H Br Br

=

cs to allow us

An Apparent Contradiction in TST

k h

B  T

K ' K differing angles of nucleophile approach leads to a distribution of leads to approach a distribution of nucleophile angles differing to solve for

presents the average of where energies of molecules as they cross over of molecules the col energies

K ' K K K assuming a Boltzmann distribution of distribution a Boltzmann assuming col = exp
RT transition state transition G all possible ways for a all energy surface energy  a function of temperature of function a 
Despite their similar forms, Eyring Eyring similar forms, Despite their

Cameout of empirical observations byArrhneiu

a microscopic rate constant for a fundamental step fundamental for a constant rate a microscopic Eyring k =

derived theoretically from TST theoretically derived

 B A +

k h B T exp

C

RT G k = A

exp The Arrhenius Rate Law and Arrhenius treatmentsthe are not same –E RT a s that reaction ratesincrease exponentially as

Arrhenius

a macroscopic rate constant for an entire for an transformation constant entire rate a macroscopic
A E derived empirically from experimental observation experimental from empirically derived a A + B A +

activation energy (barrier height) energy activation exponential factor exponential k = A = exp –E RT a C dependence on temperature on dependence
for E

The Eyring equationcanmathematically be manipulated to give the equation ofline aa with

Similar manipulation of the Arrhenius equation allows one to experimentally determine values values determine experimentally to one allows equation Arrhenius the of manipulation Similar k = ln a

and and A ln

k

ln 

= ln

k

Experimental Determinations of Ac k

= 

= A

kh

k

k B h B T T

ln A 

exp

k h exp B = T – – –E RT
– R a S RT
E RT H a
RT H exp + +

R S
RT R S H ln

ln

k



kh k

B tivation and Arr T Arrhenius plot Arrhenius 1 / T (K Eyring plot Eyring 1 / T (K 1 / T -1 )

-1 henius Parameters ) y-intercept y-intercept slope slope E
A
a H S concentration and reaction
to have any value. This is doneone either of two ways:
transformation overall for the constant
The goal of a kinetics experiment is to establish a quantitative relationship between reactant reactant between relationship a quantitative establish is to experiment a kinetics of goal The

Reactionrate changes overso rates time need to rate and law rate the find to order in determined be to needs reactant each of order The d

[P] dt A + B + C + B + A 2. Plot rate constants as a function of as function a constants 2. rate Plot kinetics rate initial Use 1. order second [A]

zero order zero Kinetics Experiments: first order rate in the hopes that rate in

P the slope of the line of d [P] / dt vs. of d line the of slope the [B], [C] kept constant kept [C] [B], concentration (pseudo-f concentration it will lend insight into

d [P] /

be compared at equivalent points for the data data the for points equivalent at compared be if a reactant is involved in a step after the the after step a in involved is a reactant if Keys to Keep in Mind dt

rds, its order will be zero order will its rds, = k [A] a irst order kinetics) [B] b

[C] the reaction mechanism [A] tells us the order of the reactant the of order the us [A] tells c

First Order Kinetics: deriving the rate law rate the deriving First Order Kinetics: Distinguishing between unimolecular andbimolecular pathways: pentyne 1 rearrange and integrate: and rearrange found to be first order in in order first be to found Br Li A A 2

[A]

a b o = starting concentration

ln [A] = ln [A] ln = [A] ln Kinetics Experiments: Li P P 1 + P Br 1 and and zero order in o –

2 k t Gilbert, J.C.; McKinley, E.G.; Hou, D.-R. D.-R. Hou, E.G.; McKinley, J.C.; Gilbert,

2

Elementary Reactions Elementary

d dt [P] Monitoring [P] instead of [A]: of instead [P] Monitoring Br = Li

pathway A is operating A is pathway d

[A] dt n= ln

= k [A]

[A] Tetrahedron o [A] – [P] o Li ,

1997 Br k t

, 53 , 9891
LG = Nucleophilic Substitution of a Thiamine Analog Thiamine a of Substitution Nucleophilic Second Order Kinetics: deriving the rate law rate the deriving Kinetics: Order Second N S rearrange and integrate: and rearrange A + B A + A

Me Kinetics Experiments: N P P Me N NH Zoltewicz, J. A.; Uray, G.; Kauffman, G. M. M. G. Kauffman, G.; Uray, J. A.; Zoltewicz, 2 LG [B] SO o – [A] 1 3

2- Elementary Reactions

o d

[P] dt ln Me [A] [B] = o o N

[B] [A] k [A] [B] [A] Me N NH

2 J. Am. Chem. Soc. Chem. J. Am.

= SO k t 3 on sulfite dependence order second

1980

, 102 , 3653

experimentally easy, people often turn to psue

LG = Nucleophilic Substitution of a Thiamine Analog Thiamine a of Substitution Nucleophilic For a bimolecular reaction, one must be able to mo one must reaction, For a bimolecular law rate the deriving Kinetics: Order Second Me N S rearrange and integrate: and rearrange A + B A + A N Me NH N 2 SO 3 LG

Me Kinetics Experiments: N P P Me N NH Zoltewicz, J. A.; Uray, G.; Kauffman, G. M. M. G. Kauffman, G.; Uray, J. A.; Zoltewicz, 2 LG SO 3 2- Me [B] do-firstkinetics order to prove bimolecularity N SO o – [A] 1 Me NH N 3 2-

2

nitor both [A] and [B]. As this is not always always is not this As and [B]. nitor both [A] Elementary Reactions o

SO d

[P] dt ln 3 SO Me [A] [B] 3 = 2- o o N

[B] [A] k [A] [B] [A] Me N NH

2 J. Am. Chem. Soc. Chem. J. Am.

= SO k t 3 Me N on sulfite dependence order second Me N NH 2

1980 SO 3 SO

, 102 3 , 3653

simplified rate expression rate simplified bimolecular or more comp or more bimolecular

Pseudo-first order kinetics are generally seen with catalytic reactions catalytic with seen generally are kinetics order Pseudo-first By using a large excess (>10of equiv)

It is important to remember that in spite of the to remember important It is

k obs A + B A + second in B second order A + B

[B Kinetics Experiments: Ps ] lex reaction mechanisms o first order in B in order first P

P + B P + k =

B, [B] can be consideredconstant, [B]

[B] k

d

obs dt [P] o if B is a catalyst, then [B] remains constant remains [B] then a catalyst, is B if name, pseudo-firstki order =

the slope the slope of of k a plot k quadratic dependence on [B] on dependence quadratic [B] on dependence linear

[A] [B] [A]

eudo-First Order Kinetics commonly used for determining kinetic order kinetic for determining used commonly

= k [A] [B]

obs a law first order rate o vs [B] = o

netics describes actually

k obs o o o is the rate constant constant rate the is , leading to a [A]

second order in B order in second first order B in k half lives or whenhalf competing lives or are pathways an issue
product or slight decreases in starting material concentration material starting in decreases slight or product

It is importantusetoanalytical It is an technique thatcan accurately measure low concentrations of comple 5-10% to followed generally are Reactions The most common technique used by organic chemists, it is used when reactions have longer longer have reactions when used it is chemists, organic by used technique common most The [P]

10% conversion

k initial [P]

time Kinetics Experiments: Initial Rate Kinetics Rate Initial Experiments: Kinetics time tion where the graph of [P] vs time is linear time vs [P] the graph of tion where half-life prevents deviations in ideal behavior due to due behavior ideal in prevents deviations [P] [A] >> while reaction the Following competing reaction pathways reaction competing [A] can be approximated as a constant a as approximated be [A] can

starting material to be consumed material starting for 50% required of the time the

k

k d

= dt [P] AB = slope slope [A] =

o – k [A] =

: in units of time units : in of M / time units : in – k [A] o -1

energy intermediates such as carbocations,radicals, carbanions and carbenes
kineticsstateto steady to determinerate laws
cannot be described by the rate rate the by described be cannot Steady state kinetics are often used when studyi Most mechanisms are comprised of more than one step involving reactive intermediates and so so and intermediates reactive involving step one than more of comprised are mechanisms Most reactants steady state approximation (SSA) approximation state steady R I

P Kinetics Experiments: laws for elementary steps given pr R O reaction SSA is valid if: valid is SSA of the reactive in the concentration and the product, ensures that [I] remains small [I] remains that ensures product, the and significantly I is of energy 4. The I P and between is irre P of I to conversion 3. The [reactants] and [P] in change to the compared small [I] is in change absolute 1. The relative to the barriers in the in the reverse direction to the barriers relative and product is 2. small of I to reactants for The barrier conversion

ng organic mechanisms as they often involve high Steady State Kinetics R

eviously. In these cases we turn cases these In eviously.

d dt [I] = 0 termediate is constant during during the is constant termediate MeO higher than that of the reactants reactants that of the than higher versible, this prevents equilibration equilibration this prevents versible, 2 C Ph

Second order intermediate formation followed by first order product fomation product order first by followed formation intermediate order Second

Solving for [I] law: for lets us the rate Solving write [I] law: for lets us the rate Solving write First order intermediate formation followed by secondproduct order formation

A +B

[I] [I] A

= =

k

k -1 k

1

+ k

k

-1 k k [A] [B] k

1

- -

1 1 +

1 1 [A] k

2 k [B] 2

IP IP

Steady State Kinetics:

k k 2 2

B

d d

dt dt [P] [P]

= =

k

k k 1

1

-1 k

k k -1 + 2 2 + [A] [B]

[A] [B] k

2 k [B]

2

d

d

dt dt

[P] [P] Possible Scenarios

=

=

on [A] and a more complicated dependence on [B] on dependence complicated more a [A] and on

In this scenario, there In is a there this scenario, first order dependence In this scenario, there In is a there this scenario, first order dependence

k

k

impossible to diffentiate kinetically between this this between kinetically to diffentiate impossible on [A] and [B]. It is import It is [B]. and on [A]

2

2 case and a second order elementary reaction elementary order second a and case

[I] [B] [I]

[I]

d d

dt dt [I] [I]

= =

k k 1 1

[A] [B] – [B] [A] – [A]

ant to realize that it is that realize ant to k -1

[I] – – [I] k -1

[I]– k 2

[I] [B]0 = k 2 [I] [I] = 0 mechanistic conclusionsbased on experimentalresults
reactant to form a second product to form a second reactant
Working out the expectedorder of each oneofscenarios reactant allows for a variety to draw

First order intermediate andproduct formation followed by a second order reactionwith another

Substitution for [I] gives the rate law: rate the for [I] gives Substitution Rearrange to solve for [I]: for to solve Rearrange

A I

k

2 k

k In this scenario, there In is a there this scenario, first or

B -

1

1 order dependence on [B] and the reaction will be retarded by [P by retarded be will the reaction [B] and on dependence order P I + P

2 Steady State Kinetics:

1

d dt [I]

=

d

[I] k

1

dt [P der dependence on [A], a less than first first than a less [A], on dependence der [A] – [A] = 2

]

= d

k

k

-1 dt [P -1 [P

[I] [P [I] 2

Possible Scenarios

k k ] 1 1

-1 ] + k = [A]

[P

1

k 1

k k ] – ] – 1 2 2 2 ] + [A] [B]

[I] [B]

[B]

k k 2 [I] [B]0 = 2

[B]

1 ]

A

A comparison of the rate laws for the three scenarios leads to a series of interesting conclusions interesting of series a to leads scenarios three the for laws rate the of comparison A

the overall rate law overall the 1. The numerator is the numerator 1. The required to form t form to required is dependent on concentration, often ex often concentration, on dependent is 3. Termsthe in denominator are not neccesarily of co r steps are order elementary Second element order first denominator, the in terms the 2. For react

d dt

[P]

k

k - =

1

1

k k 1

-1

Case 1 Case 2 Case 3 Case Case 2 1 Case k + 2 IP

[A] [B] [A] k 2

[B] he product. The denominator is the he product. The denominator

Steady State Kinetics: Obse k 2

B product of all the forward of all rate the forward constants epresented by the product of the rate constant and concentration constant and rate the of product the by epresented

perimental can be altered conditions perimental A +B

d dt

[P]

k k

= - 1 1

mparable magnitude. If one of the denominator terms denominator the of If one magnitude. mparable sum k ary steps are represented so represented are ary steps

1

k k

-1 2 rvations about Rate Laws of terms reflecting another route by which I can by which route another reflecting terms of + [A] [B]

IP k 2

and concentrations of all reactants all of concentrations and k 2

that lead to a simplification of simplification to a lead that

d dt [P lely by lely a rate constant. 2 ] =

A I k

-1 k

[P

1 k

k

2 k k

1

B 2 - 1

1 ] +

[A] [A] [B] k 2 [B] P I + P 2 1 and a zero order dependence when [B] is large is [B] when dependence order a zero and

the reaction is now first order in is now A and B first order the reaction

This will lead to observed will lead This

Often experimental conditions can be used to simplify the rate expression forgiven a reaction

if we add excess if P

k

obs

d dt [P 2 ] = 1 I A

: k

1

k k 2 [B] -1 [A] [A] [B]

[P k

o

2 k

k saturation kinetics with a first or saturation kinetics with a first Kinetics Saturation State Kinetics: Steady

1 B - 1 1 ] P I + P I + 2 1 if we add excess if B: the reaction is now first order first now is reaction the

saturation kinetics are observed in all cases where all in observed are kinetics saturation

d dt [P B is involved 2

] d der dependence on

= dt [P 2

] k =

-1 k

[P

1

k after 1 2

] +

[A] [B] [A] k

1 k

a pre-equilibrium step pre-equilibrium a k 2 2

[B] k [A] [A] [B] 2 in A and zero order in B order in zero and A in [B] B when [B] is low

= k 1 [A]

Using Kinetics to Interpret Selectivity Trends

An interesting enantioselectivity trend in Denmark's phosphoramide catalyzed aldol reaction leads to an investigation into origin of stereoselectivity and analysis of reaction mechansim

O 1. 10 mol % cat OH OMe OSiCl3 CHCl3, CH2Cl2 Me –78 ˚C 80 – 90% yield H H OMe X X 40 – 82% ee Me Me Me 2. MeOH 3. NaHCO3

Me Cl Cl O P N O Me O Si P O O P Cl N N (CH2)3 OSiCl3 Me Me H Ph H Me Me H 2 Me catalyst ionization binding

KIE studies show that aldolization O P Cl O O is the rds for aldehydes with EWG O P aldolization Me P Ph Si P O O and EDG Cl Cl Me H Cl Si H O O Cl

Cl X Me Me Denmark, S.E.; Bui, T. J. Org. Chem. 2005, 70, 10393 withdrawing or donating substituents

A Hammett A that reveals plot enantioselectivity is Arrhenius study showed that the activation parameters are similar for both classes of substrates of classes both for similar are parameters activation the that showed study Arrhenius log (er / ero) E MeO MeO A (M a (kcal/mol)


G S H -1 S OMe -1 ) 1 O H –54.6 –39.0 –54.6 12.1 10.7 12.1 13.4 3.39x10 13.4 1.6 3.3 1.6 1.2 2.9 1.2

1 2 1 Using Kinetics to Interp Kinetics Using  F 3 C 4 O O 2 H H Conclusions: classes of substrates undergo the same mechanistic pathway same mechanistic the undergo of substrates classes suggest that both parameters activation in similarities 2. The state at the transition complex negative 1. Large,

greatest for substrates with strong electron with strong for substrates greatest ret Selectivity Trends

parameters is the is the source of enantiodivergence parameters in activation substrates, perhaps changes As the rds is the same for of classes both

from a change in other factors affecting selectivity factors affecting other in change from a The difference in enantioselectivies must arise must arise in enantioselectivies The difference
S indicates a highly ordered activated ordered activated a S highly indicates

diagrams to try an rationalize the observed selectivity trend. selectivity observed the rationalize an try to diagrams 
(late TS)
the more electron rich the aldehyde, the later the transition transition later the the aldehyde, the rich more electron the Case 1 Case G The authorsthe invoke Hammond postulate, Curtin-Hammettand principle reaction coordinate this scenario is under Curtin-Hammett control Curtin-Hammett under is scenario this aldehyde binding is fast (early TS) while aldolization is slow slow is aldolization while TS) (early fast is binding aldehyde

R G state for aldolization and the better the selectivity the better the and state for aldolization R : aldolization determining is stereochemistry : aldolization TC MeO MeO R OMe
G TC S

O S to Interp Kinetics Using

H S Me Me Ph H H O O TC Cl Cl Si

O

O ret Selectivity Trends P P the more electron deficient electron more the transtion state for aldehyde aldehyde for state transtion aldolization is fast (early TS) aldolization
aldehyde binding is slow (late TS) while while TS) (late slow is binding aldehyde Cl

Case 2 Case R : binding is stereochemistry determining is stereochemistry : binding F 3 binding stage binding C TC R the aldehyde, the later the the the aldehyde, binding and the better the the better the and binding O H TC

S S

G

always straightforward Eyring analysis in an Arrhenius situation

often for simplified systems As seenfrom the As previous example, applyingkine It is easy to make mistakes and use analyses that are inappropriate for the situation, ie, using an an using ie, situation, the for inappropriate are that analyses use and mistakes make to is easy It

Most organic mechanisms are complicated and cont Me
G , E Me MeO MeO a , A: can be obtained for any reaction for obtained be , A: can
OSiCl S , S , H
3 H : only for elementary reactions for elementary : only H OMe O X

H selectivity from aldolization selectivity from Using Kinetics to Interpret Selectivity Trends O H 1. 10 mol % cat CHCl 3. NaHCO 2. MeOH –78 –78 3 , CH ˚ C 2 Cl 3 2 tic analyses to multi-step organic reactionsnot is ain several steps wherea ain several steps F X 3 C this is true only for single step, for single only true is this Me OH O unimolecular reactions Me H OMe E OMe a =
selectivity from aldehyde binding from aldehyde selectivity H + RTH + s kinetic analyses are are analyses kinetic s scenarios to explain the the to explain scenarios observed selectivity observed need to invoke two to invoke need reactivity andtrends selectivity of basis mechanistic the into insight enormous lend can they techniques, LFER with conjunction
reactions to the multi-step organic transformationswe encounter every day
happening is to what actually appropriate is
and why reactions take place andchemicalpredictusto allow behavior
diagrams. coordinate and reaction surfaces
difference huge a make can phrasing of differences slight where field a in imperative
can Kinetics become very complicated very quickly as one movesfrom the realm of elementary that analysis an use always to important is it and described been have scenarios kinetic of variety A how about think to way a with us provide use we that principles and postulates organic physical The energy are kinetics reaction analyzing for basis theoretical the and energy about all are Reactions is important, usin Terminology A kinetic analysis by itself is often not enough to determine mechanism, however, when used in in used when however, mechanism, determine to enough not is often itself by analysis kinetic A

g the correct words and phrases is correct g the Conclusions key to communication and is communication key to