rate law
provides the stoichiometry of the transition state structure relative to the ground state
rate law
shows only steps before and up to the rate determining step
k
proportional rate constant --> rates must be concentration/time
rate
the change in concentration of product or starting material over time
zeroth order kinetics
[A] = -kt + [A]?
first order kinetics
[A] = [A]?exp(-kt)
second order kinetics
1/[A] - 1/[A]? = kt
half life
t(1/2) = ln(2)/k
pseudo first order treatment
simplify by using a large excess of one reactant and assume that its concentration remains constant over the course of the reaction
steady state approximation
[I] is very small relative to [A], rate of change in [I] will also be very small --> d[I]/dt = 0 (first step fast uphill, second step slow downhill)
quasi equilibrium model
if reaction is practically in equilibrium through reaction then you can treat it as a true equilibrium (first step and second step downhill)
saturation kinetics
mechanism change as a function of concentration (first order to zeroth order)
steady state approximation
rate = (all forward rate constants and concentrations multiplied)/(sum of k's and concentrations for steps that I can react through)
initial rate kinetics
at low conversion, concentrations are constant
global kinetic analysis
track product concentration vs. time for entire length of reaction, fit higher order reaction to the curve, plot df(t)/dt vs. concentration
laser flash photolysis
pump/probe", flash light on starting materials to form intermediate, measure product formation, k = 10?-10�?
stopped flow kinetics
flash mix in mixing chamber and monitor via spectrometer, k = 10�-10?
catalysis
catalysts speed things up, kinetic feature, catalyst does not change thermodynamics
Pauling Paradigm
a catalyst binds the transition state more strongly than the starting material ground state (Kcat(TS) > Kcat)
stoichiometric reactions
concentrations of intermediates scale with the concentrations of substrates
catalytic reactions
catalyst is not consumed, concentrations of intermediates relative to concentrations of substrate changes over the course of the reaction
catalytic kinetics
apply steady state approximation to [cat�A]
Michaelis Menten kinetics
rate = kcat[E][S]/(Km+[S]) = vmax[S]/(Km + [S])
reaction progress kinetic analysis (RPKA)
workflow: find in situ method for data generation, do best fit to arbitrary polynomial, analytically differentiate, plot rate (d[ ]/dt vs. [ ])
excess
difference in concentration between reactants
same excess experiment
overlay = well-behaved (catalyst not dying, not product inhibition)
no overlay = catalyst decomposition, product inhibition
different excess experiment
plot: rate vs. [A], rate/[A] vs. [B] --> rate/[B] = [A]
different excess experiment
plot rate/[B] vs. [A], shape and overlay tells you about order in A and B
flat line
if you see this in a different excess graph of rate/[B] vs. [A], overlay means first-order in B and zeroth order in [A]
logarithmic curve
if you see this in a different excess graph of rate/[B] vs. [A], overlay means first order in B, saturation in A
straight line
if you see this in a different excess graph of rate/[A] vs. [B], overlay means first order in A and B
linear free energy relationships
substituent effects, effects on rate and equilibria and selectivity
substituent effects
field effects, resonance, induction, sterics
linear free energy relationships
two requirements:
1. hold all variables constant but one
2. variable of choice must have a proportional effect on the reaction relative to a reference function
Hammett plots
relationship between reaction rates and the pKa's of model carboxylic acids
Hammett plots
log K(x)/K(H) = sigma
rho
sensitivity factor, = sigma'/sigma
Hammett plots
relate rates to thermochemistry
electron donating groups
negative sigma values
electron withdrawing groups
positive sigma values
negative rho
positive charge build up in rate determining step
positive rho
negative charge build up in rate determining step
rho
> 1, reaction is more sensitive than benzoic acid pKa variance with substituent
rho
< 1, reaction is less sensitive than benzoic acid pKa variance with substituent
sigma-
for negative charge
sigma+
for positive charge
broken Hammett plots
mechanism or rds has changed
concave up
broken Hammett plot, mechanism changed
concave down
broken Hammett plot, rds changed
??G= rho(??G')
3 scenarios:
1. ??H' is same as ??H, ??S varies linearly with ??S'
2. ??S' is same as ??S, ??H varies linearly with ??H'
3. ??H + ??S are linearly correlated with each other in both reaction
?H = f(?S)
unusual situation, enthalpy-entropy compensation, extra-thermodynamic relationship, assume linear relationship between ?H(TS) and ?S(TS) for same reaction with different substituents
isokinetic temperature
slope of ?H(TS) vs. ?S(TS) when they are correlated
A-values
?G� for ring flip from equatorial to axial
Taft method
for ketone + water to aldehyde + methanol
Taft method
key assumption - under H+ or OH-, sterics are constant
Taft method
basic pathway: neutral substrate ? anionic tetrahedral intermediate, sensitive to electronic perturbation
acidic pathway: protonation of carbonyl followed by nucleophilic attack by water, not sensitive to electronic substituents
Taft method
log(K(S)/K(Me) = rho*sigma* + ?Es
? = proportionality factor
Es = steric substituent constant
Charton values
Van der Waals radii Taft treatment, treat groups as spheres
v = substituent constants
psi = proportionality
Sterimol
computation approach to the Taft method
Swain-Scott
parameterize nucleophilicity in terms of the reference reaction: CH3-I + H2O ? CH3-OH + I
Swain-Scott
log(k) = s(N+E) predict rates of nucleophilic and electrophilic reactions
photochemistry
photons can be quanta - defined energy
Jablonski diagram
energy wells for electronic singlet ground and excited state, triplet excited state with vibrational states
absorption
single photon promotes an electron, resulting in an electronic excited state
absorption
considerations: energy of photon must match energy gap between states, spin states of initial and final states must be identical
Beer's law
log(I?/I) = A= ?lc
allowed transition
? ? ?*, orbitals are spatially coextensive, ? > 10�
forbidden transition
n ? ?*, orbitals are not spatially coextensive (orthogonal), ? < 10�
absorption
is much faster than molecular vibrations
Franck-Condon principle
timescale of absorption too fast for nuclear motion ? during absorption geometry is constant
Franck-Condon principle
little to no change in geometry for S? to S?, v? ? v? transition is most probable
Kasha's rule
all photochemistry takes place from ground vibrational states of S? or T?
fluorescence
emissive decay of S? ? S? with production of photon
absorption spectrum
has information about excited state geometry
emission spectrum
has info on vibrational states of S?
fluorescence
timescale: 10?-10? s?�
fluorescence lifetime
time for fluorescence intensity to fall to 1/e (36.7%) of initial value
fluorescence lifetime
allowed transition (? ? ?*): large ?, short this
forbidden transition (n ? ?*): small ?, long this
intersystem crossing
conversion of S? to T?, forbidden
spin-orbit coupling
coupling change in electronic spin to change the orbital angular momentum, allows for intersystem crossing
phosphorescence
T? ? S? with emission of photon, spin forbidden, long lived T? excited states
reactive intermediates
carbanions, carbeniums, carboniums, free radicals
?-radical
odd electron sits in a p orbital
sigma-radical
odd electron sits in hybrid orbital, no resonance/localized spin density
bond dissociation energies
energy required to break the bond homiletically, read out on radical stability, assumes ?S� = 0
bond dissociation free energy
pKa = ?Eox
bond dissociation free energy
0
BDFE determination
alternative method: measure Key for HAT where one BDFE is known
radical stability
substitution: allylic > benzylic > 3� > 2� > 1� >> Me
radical stability
hybridization: sp� > sp� > sp
radical stability
both electron withdrawing groups and electron donating groups stabilize radicals, heteroatoms with lone pairs stabilize
bond order
1/2(bonding-antibonding)
persistent radicals
ex: trityl radical, TEMPO
radical clock
powerful and simple method to estimate rates of radical reactions
clock
compounds that undergo unimolecular reaction with known/reliable rate
radical clock
assumptions: all steps irreversible, R� reacts with X-Y at similar rate to P�
radical clock
apply SSA to d[P�]/dt
KMnO4
proceeds through an HAT mechanism, linear correlation between ?H� and log(kox)
thermochemistry
can be more important than spin
bonds
next to radicals are weakened
Bell-Evans-Polanyi
Ea = alpha*?H� + c
k = Aexp(-Ea/RT)
assumptions: Arrhenius pre-exponential is constant for reaction class, must be for similar reactions
Marcus Theory
??G(TS)/??G� = 0.5 + ??G�/4?
Marcus theory
most simple organic HAT reactions: ??G� << 4? ? ??G(TS) = 0.5??G� for two similar reactions
polar effects in HAT
E = repulsive term - Q - MO
nucleophilic radicals
low IE, low EA, easier to oxidize
electrophilic radicals
high IE/EA, easier to reduce
carbenes and nitrenes
characteristics of carbenium and carbanions, powerful synthetic intermediates
singlet carbene
has electrophilic character (with electron withdrawing groups)
triplet carbene
has significant diradical character (with electron donating groups)
NHCs
formed from the deprotonation of an amidizolium salt, nucleophilic carbene
carbenes
formed by the decomposition of diazos or alkyl halide deprotonation
carbenes
can perform [2+1] cycloadditions to alkenes, lone pair interacts with the LUMO and empty p-orbital interacts with the HOMO
migrations
hydride or alkyl group moves to create more stable molecule with double bond instead of carbene
energy transfer
D* + A ? D + A*
Dexter energy transfer
sensitization, triplet excited states, spin is conserved (triplet ? triplet), collision, access triplets that you can't make by ISC, two simultaneous and coupled electron transfer events
Forster energy transfer
singlets, long-distance process via dipole-dipole coupling
Forster energy transfer
Kfret ? r^6
Forster energy transfer
requirements: overlap of absorption and emission
excited state energy transfer
excited states are typically stronger oxidants and stronger reductants than corresponding ground states
Stern-Volmer
luminescent molecules, measure rates of excited state processes
Stern-Volmer
I?/I = 1 + kqT[Q]
electronic transfer thermochemistry
?G� = -RTlnKeq = nF?E�
Marcus theory
intersecting parabolas that correspond to solvated donor-acceptor complexes
Marcus reorganization energy
?, energy needed to reorganize from the equilibrium coordinated of the reactant to that of the products
Franck-Condon principle
nuclear positions and velocities don't change during an electronic transition
Marcus Theory
eventually raise driving force and lower rate due to overlap of energy wells, should see inverted region where -?G� goes up but rate goes down
Closs-Miller
removed diffusion effect by making the energy transfer intramolecular, saw inverted region of Marcus relationship
Marcus theory
quantum correction: when HOMO and LUMO interact/mix they split just like MOs, creates gap in parabolas called H(DA)
H(DA) > kBT
reaction remains on lower surface and goes to product every time it reaches TS (adiabatic ES)
H(DA) ? 3kBT
reaction can jump onto the upper surface (non-adiabatic ET), cross TS many times to go to product
electron transfer
requires overlap between wavefunctions of donor and acceptor
Marcus-Levitch equation
H(AD) = H(AD)�exp(-?(r(DA)-r?)
? = constant