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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
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
O 2
+^
O + Cl 2
CH^ -C^3^ key intermediate
CH
3 CH
3
O + Cl 2
(CH
)^ COH 33
Bond Heterolysis
slow step
TS 1
ΔG
1
RDS
fast^ TS 2^ Δ
G^2
TS 3^ + H
+O (^3)
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
.
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
+^
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
