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Multi-Step Reaction and Rate Determining Step - Lecture Notes | CHE 255, Study notes of Organic Chemistry

Material Type: Notes; Class: Organic Chemistry; Subject: Chemistry and Biochemistry; University: University of Southern Mississippi; Term: Unknown 1989;

Typology: Study notes

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Uploaded on 08/19/2009

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Multi-Step
R
eactions and the
R
ate-Determining Step
.
Man
y
reactions in or
g
anic chemistr
y
involve a sequence of steps,
each with an energy barrier linking starting and product states.
Each step proceeds with a unique rate constant
k1
k
2
a reaction
intermediate
ABC
Note: B is an intermediate. It is not a
transition state. This important difference is
shown in the free energy diagrams below.
Two
g
eneral cases
f
or the above two-step reaction sequence will be
examined. The relative magnitudes of rate constants k1 and k2 are
determined by the relative magnitudes of the free energies of
activation (the "energy barriers") for each step.
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pf8
pf9
pfa
pfd
pfe
pff
pf12
pf13
pf14
pf15
pf16
pf17
pf18
pf19
pf1a
pf1b
pf1c
pf1d
pf1e
pf1f
pf20
pf21

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Download Multi-Step Reaction and Rate Determining Step - Lecture Notes | CHE 255 and more Study notes Organic Chemistry in PDF only on Docsity!

Multi-Step Reactions and the Rate-Determining Step

Many reactions in organic chemistry involve a sequence of steps,each with an energy barrier linking starting and product states.Each step proceeds with a unique rate constant

k^1

k^2

a reactionintermediate

A^

B^

C

Note: B is an intermediate. It is not atransition state. This important difference isshown in the free energy diagrams below

.

Two general cases for the above two-step reaction sequence will beexamined. The relative magnitudes of rate constants k

and k 1

are 2

determined by the relative magnitudes of the free energies ofactivation (the "energy barriers") for each step.

Two General Cases

k^1

k^2

slower

faster

A^

B^

C

Case A: k

< k 1

Free EnergyProgress of Reaction

TS 1

TS 2

A^

C

B

Step 1 (A

B) is slower

than step 2 (B

C).

The free energy of activation forstep 1 is larger leading to a smallerrate constant

The overall rate of Ais controlled by step 1 whichis the rate-determing step.

C

slow step

Note: A chemical intermediate, such as B, is an energy minimum in the free energydiagram. It persists for a finite time. A transition state is an energy maximum that istransitory, existing for perhaps the time of a bond vibration, ~

-12^ s

A Proposed Mechanism with a Carbocation Intermediate

bond heterolysis

slow step

+^

t-butyl carbocationa high energy intermediate

RDS

CH

CH-C-Cl 3

3

CH

3

CH

CH-C 3

3

CH

3

  • Cl

nucleophilic addition

+^

+^

nucleophile

fast

+^ :

t-butyloxonium ion

CH

CH-C 3

3

CH

3

O-HH^

CH

CH-C 3

3

CH

O-HH 3

proton exchange

+^ :^

+^

: : base

fast

CH

CH-C 3

3

CH

O-HH 3

O-HH^

CH

CH-C 3

3

CH

O-H^3

H^3

+O

The Free Energy Diagram

Free Energy

Progress of Reaction

(CH

)^ C 33

  • Cl + 2H

O 2

+^

  • 2H

O + Cl 2

CH^ -C^3^ key intermediate

CH

3 CH

3

  • H

O + Cl 2

(CH

)^ COH 33

  • 2

Bond Heterolysis

slow step

TS 1

ΔG

1

RDS

fast^ TS 2^ Δ

G^2

TS 3^ + H

+O (^3)

  • Cl

fast^ (CH

)^ COH 33

Stereochemistry of the SBecause carbocations have a trigonal planar geometry, theypossess a plane of symmetry and are achiral. Therefore, a racemicform of a chiral product is predicted in reactions that involvecarbocation intermediates

1 ReactionN

A General Scheme

chiral achiral (plane of symmetry)

SN

chiral

C^ - -X
X
R^1 R

3 R^2

C^
O
R^1 R

3 R^2

H
H
H O:
H
R^1 C RR 23
O
H
H : :
C
O
R^1 R^2 R 3
H
H

There are equal probabilities of reaction at the two faces of thecarbocation. The two oxonium ions formed in equal amounts areenantiomers. A racemic form of the product is necessarily produced

Example: The Hydrolysis of (S)-3-Bromo-3-methylhexane(S)-3-bromo-3-methylhexane

acetone

(50%)3-methyl-3-hexanol

Racemic Form

H^ O^2
(S)
(R)
C^

Br

H^ CH^3
CH 2
C 2
HCH^3
C 2
H^ C^3
C^
OH
H^ CH^3
CH 2
C 2
HCH^3
C 2
H^ C^3
C
HO
CH
CH 2
CH 2

3

CH
CH 2

3 CH

3

CHC
CH 2
CH 2

3

CH

CH 2

3

H^ C^3

via S

2 N

achiral There is an equal probability ofattack by H

O at each face. 2

SolvolysisA nucleophilic substitution reaction where the solvent is thenucleophile is called solvolysis.When water is the solvent, the term hydrolysis is used.Methanolysis means methanol is the nucleophile/solvent.

+^

water

ROH

+ HX

RX

H^2

O

RX

+^

CH

OH 3

methanol

ROCH

+ HX 3

RX

+^

CH

CH 3

OH 2

ethanol

ROCH

CH 2

+ HX 3

RX

+^

acetic acid

ROCCH

+ HX 3

CH

COH 3

O

=O

hydrolysismethanolysisethanolysisacetolysis

Factors Influencing the Rates of the

SN

1 and S

2 ReactionsN

The S

1 and SN

2 are always potentially competitive pathways for anyN

nucleophilic substitution reaction. However, because of structural,electronic, and other factors, one pathway usually dominates.Effect of Structure on the S

1 and SN

2 ReactionsN

A change in alkyl group substitution around the reacting carboninfluences nucleophilic substitution by the S

1 and SN^

2 mechanismsN

in opposite ways.

An Example: Incorporation of isotopic bromine in RBr

isotope label

+^

R-Br

*^ Br-R

+^

Br

acetone

Br

R = CH

3

CH

CH 3

2

CH

CH 3 CH

3

CH

CH C 3

3 CH

3

CH

-C-CH 3

2 CH

3 CH

3

.

This study shows that methyl bromide reacts 25,000times faster than tert-butyl bromide, and 5 million timesfaster than neopentyl bromide, in this S

2 reactionN

Relative second-order rate constants in acetoneat 25

o C for the S

2 reactionN

relativerate

76

(1.0)

faster

The Steric Effect

.

This slowdown in the rate of the S

2 reaction with increasingN

alkyl substitution around the reaction center is attributed to asteric effect, increasing steric hindrance in approaching thereaction center by the incoming nucleophile

Nu:

The incoming nucleophile approachesthe carbon center on an axis oppositethe leaving group. Groups larger thanH attached to the carbon center screenthis line of approach.

methyl

C^

X H H H

ethyl

Nu:

-^

C^
X
CH

3 H H

isopropyl Nu:

-^

C^
X
CH

3 H CH

3

tert-butyl

Nu:

-^

X
CH

3 CH

3 CH^3

C

increasing steric hindrance

The Structure of CarbocationsCarbocations are trivalent carbonspecies with a positive charge.

R^3

+C

.

Carbocations are locally planarwith the three valences in a plane

A trigonal planar geometryis predicted by VSEPR theory

.

  • C R R

R

Relative Stabilities of CarbocationsMany experiments indicatethe stability order ofcarbocations is:

+^
+^
+^

o^3

o^2

o^1

methyl

^

^

most stable

least stable

R C
R
R
R C
R
H
H C
R
H
H C
H
H

Gas phase experiments (in the absence of solvation) provide ΔH values for simple alkanes undergoing the heterolytic process

+^

  • H:

R-H

R+

The larger the value for

ΔH,

the less stable the cation

cation

+^

+^

+^

(kJ/mol)

increasing stability

CH

3

CH

CH 3

2

CH

CH 3 CH

3

CH

C 3 CH

3

CH

3

ΔH

Hyperconjugation

.

Interaction of the sigma electrons in the C-H bond of the methyl groupwith the empty p-orbital of the carbocation disperses and stabilizes thepositive charge

H C

C

H H

hyperconjugation often is shown by

H C

H^

H C H

H C

H

H

H C H

H

The Hammond-Leffler Postulate

free energy

reaction coordinate

According to the Hammond-Leffler Postulate, since S

1 processes areN

highly endergonic, the transition state comes late along the reactioncoordinate and resembles the carbocation state. Factors that stabilizecarbocations will stabilize the TS in an S

1 reaction leading to a faster rate.N

resembles product state TS

resemblesreactant state

TS

reactant state

product state

highly exergonic step reactant state

product state highly endergonic step