{ Warning - these notes have not been edited to give correct subscripts, superscripts, or Greek characters, so beware of some ambiguities, e.g., H* should be (delta H*) and k2[A]2 means k(sub2)[A](squared) }
(on the other hand, they're very complete, and I hope, helpful)
mechanism - a step-by-step account of how a reaction occurs
overall reaction sequence is broken down into elementary steps
ideally includes orientation of all atoms and energy as a function of time
determining reaction mechanisms requires thinking at two levels:
molecular level - what are the molecules doing (and why) ?
experimental level - what observable behavior will provide evidence for the molecular behavior ?
e.g. for the SN2 reaction:
- nucleophile attacks backside of carbon, displacing leaving group
- an appropriate optically active substrate will give an optically active product with inversion of configuration
(requires availability of substrate and the ability to correlate absolute configuration of both compounds)
Mechanistic Classifications (see also the IUPAC recommendations, Paper 5)
for elementary steps:
associative - bond-forming
dissociative - bond-breaking
homolytic - one electron to each component
heterolytic - electron pair goes with one component
concerted - bond-forming and bond-breaking occur together
for overall reactions:
substitution, addition, elimination, redox, rearrangement
for intermediates:
cation, anion, radical, radical ion, carbene, excited state
for reagents:
electrophile, nucleophile, radical
for stereochemistry:
retention or inversion, syn or anti addition, con- or disrotatory
overall description of a reaction mechanism - examples
Diels-Alder: concerted cycloaddition without any intermediates
Friedel-Crafts: electrophilic substitution with cation intermediate (sigma-complex)
ester hydrolysis: nucleophilic substitution with cation (acid-cat.) or anion (base-cat.) intermediate (tetrahedral intermediate)
Reaction Intermediates
direct spectroscopic identification:
fast kinetics - stopped-flow, flash photolysis, temperature-jump
- if possible, follow the reaction at its usual rate - femtosecond spectroscopy is now possible
- or adjust the reaction conditions so that the intermediate is stable enough to observe at leisurematrix isolation - low temp., inert solid matrix prevents further reactions
e.g. observation of the IR spectrum of s-cis-1,3-butadieneindependent synthesis
indirect evidence:
trapping of intermediates - specific reactions expected for a given intermed.
e.g. Diels-Alder adducts from benzynecrossover experiemnts
isotopic labeling studies
Thermodynamics
G = H - T S compares reactants and products, gives no info on mechanism
however, calculated H values (from Hf° or DH° data tables) can suggest whether a given step or intermediate is possible
Kinetics
rate laws - observed reaction rate as a function of concentration(s)
a A + b B + ..... -----> x X + y Y + .....
Rate = - (1/a) d[A]/dt = - (1/b) d[B]/dt = + (1/x) d[X]/dt = + (1/y) d[Y]/dt
(measure one or more products or reactants, as convenient)
zero-order rate law:
Rate = - d [A] / dt = ko ( ko units of M sec-1 )
integrated form: [A] = [A]o - ko t
first-order rate law:
Rate = - d [A] / dt = k1 [A] ( k1 units of sec-1 )
integrated form: ln [A] = ln [A]o - k1 t
or [A] = [A]o exp(- k1 t)
half-life: t1/2 = ln 2 / k1 = 0.693 / k1 (time to drop to 50%)
natural lifetime: t = 1 / k1 (time to drop to 1/e = 36.8%)
second-order rate law:
Rate = - d [A] / dt = k2 [A]2 ( k2 units of M-1 sec-1 )
integrated form: 1 / [A] - 1 / [A]o = k2 t
(note - the concept of half-life or lifetime doesn't apply except for first-order rates)
mixed second-order rate law:
Rate = - d [A] /dt = k2 [A] [B] ( k2 units of M-1 sec-1 )
general integrated form: ( [A]o - [B]o )-1 ln( [B]o [A] / [B] [A]o ) = k2 t
(for [A]o [B]o ) requires knowledge of both [A] and [B] with time
simplifications:
1) develop known relationship between [A] and [B]
e.g. if the balanced reaction is A + B ---> C and [A]o = [B]o ,
then [A] = [B] at all times and the behavior is like second-order in [A]
2) use large excess of [B]o , so effectively [B] = [B]o at all times,
then the rate behaves as if first-order in [A] (pseudo-first-order), where kobs = k2 [B]o
3) monitor initial rates at very low conversion,
where Rate = k2 [A]o [B]o (effectively zero-order)
vary initial concentrations of [A]o and [B]o
(method of initial rates - works in all cases, more accurate than judging the linearity of a rate plot to determine kinetic order)
Mechanistic Implications from Kinetic Data:
1) for any elementary step, the kinetic order is the same as the molecularity
2) the overall rate of a reaction will be determined by the slowest step
(the rate-determining step, RDS)
3) steps after the RDS will not affect the observed rate
4) steps prior to the RDS will affect the observed rate
for a two-step reaction with an intermediate:
Reactant --(k1)--> Intermediate --(k2)--> Product
Rate (1) = - d [R] / dt = k1 [R]
Rate (2) = + d [P] / dt = k2 [I]
Rate (1) does not necessarily equal Rate (2)
case 1: k1 and k2 comparable in magnitude
intermediate builds up then disappears
case 2: k1 >> k2 (very stable intermediate)
intermediate builds up quickly, disappears slowly
case 3: k2 > k1 (unstable intermediate)
intermediate builds up to low conc., disappears quickly
case 4: k2 >> k1 (reactive intermediate)
intermediate conc. very low at all times
(steady-state concentration, approximately constant)
Steady-state Approximation:
· a reactive intermediate quickly develops a low, steady-state
concentration
that is maintained during most of the reaction, for which the change in
concentration of the intermediate can be considered negligible
- d [I] / dt = 0 or k1 [R] = k2 [I] or [I] = (k1/k2) [R]
or Rate (1) = Rate (2) or - d [R] / dt = + d [P] / dt
Rate-Determining Step:
Step 1 RDS: case 4 (above) k2 >> k1 (reactive intermediate)
Rate = - d [R] / dt = + d [P] / dt = k1 [R]
Step 2 RDS: case 2 (above) k1 >> k2 (very stable intermediate)
- d [R] / dt + d [P] / dt
Rate = - d [R] / dt = k1 [R]
Rate = + d [P] / dt = k2 [I]
First Step Reversible :
most commonly, the intermediate can go back to reactant as well as on to product
Reactant <---(k1, k-1)---> Intermediate ---(k2)---> Product
apply the SSA to the intermediate (a reactive intermediate, where ( k2 + k-1 ) >> k1 ) :
d [I] / dt = k1 [R] - k-1 [I] - k2 [I] = 0
[I] = k1 [R] / ( k-1 + k2 )
observed rate is the rate of product formation:
Rate = + d [P] / dt = k2 [I] = k1 k2 [R] / ( k-1 + k2 )
(general expression, regardless of which step is the RDS)
rearranged slightly: Rate = k1 [R] { k2 / ( k-1 + k2 ) }
= (rate of formation of I) x (fraction of I that forms product)
Limiting Cases:
Step 1 RDS: k2 >> k-1 (intermediate goes forward frequently, backward rarely)
(k-1 negligible, just like irreversible cases above)
Rate = - d [R] / dt = + d [P] / dt = k1 [R]
Step 2 RDS: k-1 >> k2 (intermediate goes backward frequently, forward rarely)
Rate = - d [R] / dt = + d [P] / dt = ( k1 k2 / k-1 ) [R]
Rate = k2 K [R] where K = [I] / [R] = k1 / k-1 (preequilibrium)
(if k-1 and k2 are of comparable magnitude, use the general expression above)
example - Diels-Alder reaction of 1,3-butadiene requires preequilibrium
formation of the s-cis diene conformation, then cycloaddition
- cyclopentadiene and other cyclic dienes are much better Diels-Alder adducts because they do not have any unfavorable preequilibrium
Arrhenius Equation:
k = A exp(-Ea/RT) or ln k = ln A - (Ea/RT)
(strong temperature dependence of the rate "constant")
A - frequency factor ~ 10E11 - 10E13 sec-1 for unimolecular rxns (vibrations)
~ 10E7 - 10E10 M-1 sec-1 for bimolecular rxns (collisions)
Ea - activation energy minimum energy required (from Boltzmann distribution)
Transition State Theory:
treatment of "activated complex" as a state in preequilibrium with reactants
and appropriate for the steady-state approximation (step 2 RDS):
A + B <---(k1, k-1)---> X* ---(k2)---> Product
Rate = + d [Prod] / dt = k2 [ X*] = k2 K* [A] [B]
k2 - a "universal" rate constant for a transition state
(~6x10E12 sec-1 at room temp.)
k2 = k kB T / h (from statistical mechanics)
k - transmission coefficient (usually assumed = 1)
kB - Boltzmann's constant
h - Planck's constant
Rate = + d [Prod] / dt = k2 [ X*] = k2 K* [A] [B]
K* = k1 / k-1 = [X*] / [A] [B]
K* = exp(-G*/RT) = exp(-H*/RT) exp(S*/R)
Rate = { (kB T / h) exp(S*/R) } { exp(-H*/RT) } [A] [B]
(note analogies to the Arrhenius equation)
significance of H* - represents minimum energy, H* = Ea - n R T (n is rxn order)
significance of S* - represents change in disorder from reactants to transition state
S* > 0 increased disorder (favorable)
S* < 0 increased order (unfavorable)
e.g. cyclopentadiene dimerization H* = 15.5 kcal/mole, S* = - 34 cal/mole °K (e.u.)
low H* indicates bond-forming compensates bond-breaking
very negative S* indicates highly ordered transition state
e.g. azobutane thermolysis H* = 52 kcal/mole, S* = + 19 e.u.
H* comparable to bond energies, S* indicates increased disorder
e.g. t-butyl chloride ionization (SN1) S* = - 6.6 e.u.
solvent ordering around developing charges
Potential Energy Diagrams:
visualize reaction pathways as potential energy diagrams
e.g. two-dimensional contour plot for CH3-Br + I- ---> CH3-I + Br-
using C-Br and C-I distances as the axes
More-O'Ferrall Diagrams:
arrange the axes of the diagram so that reactants start at one corner and products end at the opposite corner - difference between SN1 and SN2 mechanisms is the pathway taken:
diagonal line is a classic (symmetrical) SN2
roundabout pathway breaks one bond first (SN1)
Some General Mechanistic Principles
usually envisioned via potential energy diagrams
Principle of Microscopic Reversibility:
the lowest-energy pathway in the forward direction will be the lowest-energy pathway in the reverse direction
Thermodynamic vs kinetic control:
for a reaction that could give more than one possible product:
thermodynamic control - the more stable product is major (determined by G)
kinetic control - the product formed faster is the major product (determined by Ea)
(in the majority of cases, the same product is predicted either way - only with a
particular arrangement, easily visualized in potential energy diagrams, can the two approaches lead to different products)
e.g. formation of enolate anions from methyl isopropyl ketone
more substituted double bond is more stable (thermodynamic control)
but the less-substituted side reacts faster (kinetic control)
Hammond's Postulate:
for consecutive states in a reaction (reactants, intermediates, products, or the transition states between them), if they are similar in energy, they will be similar in structure
late transition state - similar in energy and structure to products
early transition state - similar in energy and structure to reactants
e.g. electrophilic aromatic substitution
(late transition state resembles the sigma-complex intermediate, therefore a stabilizing effect on the intermediate will be reflected in the transition state and affect the rate)e.g. late vs. early transition states in H abstraction reactions
(abstraction by fluorine is highly exothermic, early transition state, very little radical character, very little selectivity for different C-H bonds)
Curtin-Hammett Principle:
for equilibrating reactants that give rise to different products, the
product ratio will be independent of the equilibrium mixture of reactants,
as long as the interconversion of the reactants is fast
(in the opposite limit, where interconversion of reactants is slow relative
to the reactions of interest, consider as if two independent reactions)
Isotope Effects
isotopic labeling - useful means of keeping track of otherwise identical atoms
primary kinetic isotope effect - (kH/kD) for a bond broken during the reaction
typical primary KIE range is (kH/kD) = 1 - 7
the effect is based on higher zero-point vibrational energy for C-H
(C-H bond has a head-start over C-D in bond breaking)
theoretical maximum occurs when bond to H(D) is half broken
mechanistic implications: indicates whether C-H bond breaking is part of RDS
magnitude indicates extent of bond breaking
e.g. deprotonation of diisopropyl ketone (kH/kD) = 6.1
electrophilic aromatic substitution (kH/kD) = 1
secondary kinetic isotope effect - (kH/kD) for a bond not broken in the reaction
typical secondary KIE range is (kH/kD) = 0.7 - 1.5
the effect is based on rehybridization or other change at the given bondalpha secondary KIE - on same C as the reaction site (e.g. rehybridization)
e.g. hybridization change from sp3 to sp2 (kH/kD) > 1
(C-H bending vibration contributes favorably to the reaction)p-methylbenzyl chloride ionization (kH/kD) = 1.30
hybridization change from sp2 to sp3 (kH/kD) < 1
(C-H bending vibration must be suppressed during the reaction)formation of benzaldehyde cyanohydrin (kH/kD) = 0.73
beta secondary KIE - on next C to the reaction site (e.g. hyperconjugation)
e.g. hyperconjugation weakens C-H bond (kH/kD) > 1
Substituent Effects - The Hammett Equation
measure effect of a substituent on the acidity of benzoic acid:
define sx = pKa(H) - pKa(X) (s represents sigma in this section)
sigma x - substituent constant (classifies direction and strength of its effect)
sx > 0 (positive) - electron-withdrawing (acid-strengthening)
sx < 0 (negative) - electron-donating (acid-weakening)
Hammett discovered that the effect of a substituent correlated proportionally on many other reactions (first done with base hydrolysis of alkyl benzoates)
log [ K(X) / K(H) ]any rxn = r log [ Ka(X) / Ka(H) ]benzoic acid = r sx (r represents rho in this section)
or for rate constant data (rather than equilibrium data):
log [ k(X) / k(H) ]any rxn = r sx
these are called Linear Free-Energy Relationships (LFERs) because
log [ K(X) / K(H) ] = - [ G(X) - G(H) ] / 2.3 RT = r sx
(the correlation is actually a substituent's effect on delta G (delta delta G) )
reaction constant ( rho ) - defines a reaction's need for electron donation or withdrawal
e.g. PhCOOH acidity +1.00 (by definition)
PhNH2 basicity - 2.77
Ph3CCl ionization - 3.97
PhCH3 + Cl· - 0.66 (polar transition state)
a nonlinear Hammett plot could indicate a change in mechanism (see Paper 6)
Substituent group classifications:
electronic effects (electron donation and withdrawal)
- resonance effects: transmitted through pi bonds
- inductive effects: transmitted through sigma bonds
- field effects: transmitted through space
steric effects (based on size or shape of the substituent)
a given substituent can have either electron-donating or -withdrawing effects, depending on the type of interaction
e.g. Hammett substituent constants for -OH : spara = -0.37 but smeta = +0.12
more than one type of substituent effect can operate
e.g. compare the acidities of alcohols and phenols (pKa values)
ROH ~16-18
ArOH ~10 (resonance effect)
m(NO2)PhOH 8.3 (inductive effect)
p(NO2)PhOH 7.1 (resonance effect)
classification of substituents:
+R electron-withdrawing resonance effect
-R electron-donating resonance effect
+I electron-withdrawing inductive effect
-I electron-donating inductive effect
recognize general categories of substituents:
-R and -I (only e- donors) alkyl groups, most metals
-M but +I (electronegative but with lone pair) -X, -OR, -NR2
+M and +I (positive or partially positive) -NR3+, -NO2, -COR, -CN
Modified Hammett equations:
for reactions with strong resonance interactions, the standard Hammett
Equation doesn't correlate very well
(because the substituent is assumed to act in the same way as it did towards
benzoic acid ionization
- note there is no direct resonance connection between the substituent and
benzoic acid)
s+ constants - for reactions with direct resonance interaction with a + charge
standard reaction is SN1 ionization of cumyl chloride
define r = -4.62 in 10% acetone, 90% water, so that s+meta ~ smeta
s- constants - for reactions with direct resonance interaction with a - charge
sI constants - to consider only the inductive effects of a given substituent
Yukawa-Tsuno Equation:
separates a substituent's effects into resonance and inductive components
log [ k(X) / k(H) ] = rI sI + rR sR
the different r values indicate the extent to which the reaction uses resonance and inductive effects
Solvent Effects
solvent can exert an enormous effect on reactions, mainly by stabilizing ions
HCl ------(gas phase)--------> H+ + Cl- H = + 333 kcal/mole
HCl ---(aqueous solution)-----> H+ + Cl- H = - 16 kcal/mole
specific solvation and general solvation:
measure energetics of reactions with water molecules:
R+ ---(H2O)---> R+(H2O) ---(H2O)---> R+(H2O)2 ---(etc.)---> R+(aq)
the first few solvent molecules attach to an ion with high H
(specific solvation - H depends on the nature of R+)
e.g. H+ + H2O ---> H3O+ H = - 170 kcal/mole
CH3+ + H2O ---> CH3OH2+ H = - 66 kcal/mole
the second layer of solvent attaches with lower H
(general solvation - H is mostly independent of R+)
macroscopic (bulk) properties of solvents:
polarity - measurable as a permanent dipole moment
polarizability - ease of distortion of the electron density
dielectric constant - ability to support charge separation
- a function of polarity and polarizability
- generally a measure of how well a solvent will support ionization processes and stabilize charged species
classifications of solvents:
polar/nonpolar (based on dielectric constant or dipole moment)
protic/aprotic (based on ability to donate an H-bond)
general effects of solvent polarity on reactions:
charge separation - favored by polar solvents
e.g. SN1 reactions, acid dissociationscharge combination - favored by nonpolar solvents
e.g. SN2 reactions ( Nu- + R4N+ ---> Nu-R + R3N)
( Nu- + RX ---> Nu-R + X- )
remember that rate effects reflect the difference between solvation of the reactants and the transition state
measures of solvent polarity:
Grunwald-Winstein Equation (solvent Y values or ionizing power):
for the ionization of t-butyl chloride in various solvents:
log (ksolvent / kstandard) = Y
standard solvent is 80% ethanol : 20% water
better ionizing solvents have positive Y valuesextension to other reactions gives an LFER:
log (ksolvent / kstandard) = m Y
where m is the reaction constant (the reaction's response to solvent ionizing power)
Reichardt Dye Indicators - ET(30)
based on a shift in lambda max for a visible absorption spectrum of a dye
when the electronic distribution of the excited state is very different from that of the ground state, the transition energy is raised because the solvent orientation is wrong for the excited state (assuming there can be no solvent reorientation during the absorption process, about 10-15 sec)
Reactions in the Gas Phase
in the absence of solvent, some familiar trends are reversed
acidity of alcohols (in solution):
MeOH > H2O > EtOH > iPrOH > tBuOH
acidity of alcohols (in the gas phase):
tBuOH > iPrOH > EtOH > MeOH > H2O
the gas-phase results indicate that the larger alkyl groups can stabilize a negative charge better (in contrast to the usual view of alkyl groups as electron-donating)
the effect is generally considered to be due to polarizability - larger groups can disperse charge better (either + or -)
the solution-phase order is dominated by solvation effects
(steric hindrance by the larger alkyl groups prevents good solvation)
substituent effects are generally larger in the gas phase
(solvent stabilization is removed, which often masks substituent effects)