#### Phys Org Exam 2

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

[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)

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

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?�

time for fluorescence intensity to fall to 1/e (36.7%) of initial value

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

odd electron sits in a p orbital

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

substitution: allylic > benzylic > 3� > 2� > 1� >> Me

hybridization: sp� > sp� > sp

both electron withdrawing groups and electron donating groups stabilize radicals, heteroatoms with lone pairs stabilize

bond order

1/2(bonding-antibonding)

powerful and simple method to estimate rates of radical reactions

clock

compounds that undergo unimolecular reaction with known/reliable rate

assumptions: all steps irreversible, R� reacts with X-Y at similar rate to P�

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

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

low IE, low EA, easier to oxidize

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