CH3G9 Catalysis

what does a catalyst do and how

a catalyst increases the rate of a chemical reaction without being consumed by lowering the effective activation energy of a reaction

• can do this by either modifying the slowest step in the reaction or by providing an alternative pathway that bypasses this rate determining step

give comparisons of homogenous, heterogenous and biocatalysts

do catalysts appear in the overall rate equation and rate law

not in rate equation but can appear in the rate law

how do catalysts affect thermodynamics

they don’t - only changes the kinetics not the amount of product formed

what is an elementary reaction

a single step reaction, with no intermediates and involving one or two reactants (3 in rare occasions)

what is a complex reaction

a series of elementary reactions connected together to represent the overall reaction outcome

how to determine the rate equation of elementary reactions

the chemical equation can be directly used to write the rate equation as the rate equation directly represents the change occurring at the molecular level

what determines which elementary reactions form part of the overall rate equation

the rate determining step

what factors influence kinetics

• concentration

• temperature

• solvent

• catalysis

how do you determine the rate of reaction at a given time point

the gradient of the line at that point (the derivative)

what are the 3 types of rate equations and give examples of types of reactions

first order reaction - v = k [reactant]

• monomolecular reactions - SN1, rearrangements

• spontaneous change

second order reaction - v = k [reactant1][reactant2]

• most fundamental reactions - carbonyl chemistry, SN2, eliminations

zeroth order reaction - v = k

• catalytic reactions - heterogenous metal catalysis, enzymes

• (no reaction is true zeroth order in all reactants/catalysts/reagents)

what is the Arrhenius equation

k = Ae^-Ea/RT

• A = pre-exponential factor

• Ea = activation energy (J/mol)

• R = molar gas constant

• T = temperature (K)

what is the Eyring equation

k = (κk_BT / h) exp(-∆G^‡ / RT)

• ∆G^‡ = Gibbs free energy of activation

• κ = transmission coefficient

• k_B = Boltzmann constant

• h = planck constant

• R = molar gas constant

• T = temperature

when is the Eyring equation more useful than the Arrhenius equation

when rigorous kinetic theory is needed

• i.e. to determine activation parameters such as enthalpy and entropy of activation

what is a reaction profile

a plot showing how potential energy changes during each step of the reaction

• the progress of the reaction (reaction coordinates) is plotted on x axis and the potential energy of the system is plotted on the y axis

what is an energy barrier

the minimum energy required for a reaction to occur

what is the rate-determining step

the slowest elementary step in a complex reaction sequence

• the step with the highest energy barrier

what is a substrate

the starting material used in a catalytic reaction

what is catalyst stability

the performance of a catalyst over time

what is the turn over number (TON)

the number of substrates that a catalyst can convert before becoming inactivated

what is the turn over frequency (TOF)

the number of substrate molecules converted to product per active site per unit of time

what determines the overall turnover frequency

the rate determining step

fill in the blanks:

• catalysts 1 and 2 are of similar initial __(1)__ but of very different __(2)__

• the order of initial activity is __(3)__

• what can we say about the comparative productivity of 3 and 4? __(4)__ because __(5)__

1. activity

2. stability

3. 4 > 1,2 > 3

4. nothing

5. the graph doesn’t show the full reaction

fill in the blank

• catalyst 4’ has an _____

induction period

what are the two major working modes for catalysis and give examples

transition state stabilisation

• most of biocatalysts

• general acid catalysis

• lewis acid catalysis

new mechanistic pathways

• heterogenous catalysis

• transition metal catalysis

• covalent catalysis/organocatalysis

what determines the observed rate law for a generic catalytic mechanism

the events between the resting state up to and including the transition state (TS) of the rate determining step (RDS)

what is the rate law and RDS of this reaction profile

2nd step has the highest energy barrier so is the RDS

rate law:

• d[P] / dt = k [S₁-cat] [S₂] = k [S₁] [cat] [S₂] = k’ [S₁] [S₂]

  • k’ = k [cat]

in a catalytic cycle, what is the rate of product formation determined by?

the activation energy of the cycle as a whole, ∆G^‡_cycle

what is the resting state in a reaction coordinate diagram

the lowest energy combination of catalyst and reaction components

what is ∆G^‡_cycle

the energy difference between resting state and TS of the RDS

• i.e. highest energy combination of catalyst and reaction components

in these two reaction profiles, what are the resting states

top reaction profile: [cat]

bottom reaction profile: I₁

which of these has a new mechanism that is catalytic

what is a precatalyst

a stable compound from which a “catalytically active” species is generated - often irreversibly

can occur using an activator or by reaction with a substrate → induction period

what is an off-cycle species

compounds generated from catalytic intermediates not directly implicated in the productive cycle

what is the true catalyst in a catalytic cycle

any intermediate with a catalytic cycle can be considered a viable catalyst

• precatalyst

• a species obtained when the product is released

• the product itself

• an off cycle species, that forms reversible

draw a conversion-time graph to show what happens when you have an irreversible vs reversible off-cycle reaction

what is chemo and regional selectivity

selectivity determined as ratio between products (or yields)

what is stereoselectivity

selectivity often determined by the excess

• enantio- and diastereoselectivity

what is enantiomeric excess (ee)

the absolute difference between the mole fractions of each enantiomer

what is the equation to calculate enantiomeric excess

ee = | x_R - x_S|

• x_R + x_S = 1

what is enantiomeric ratio (er)

the ratio between the mole fractions of each enantiomer

er = x_R / x_S

how do you calculate an enantiomeric ratio (er) from the enantiomeric excess (ee)

• use an R enantiomer being preferred with a 76 % ee

0.76 = x_R - x_S = (1 - x_S) - x_S = 1 - 2x_S

x_S = (1 - 0.76) / 2 = 0.12

er = x_R / x_S = 88 / 12 = 7.3

for this reaction profile, what product is preferred and what does the ratio of the product depend on and why

selective for blue product

selectivity-determining step and RDS coincides

• ratio of product depends on RDS

prospects for selective catalysis are high

for this reaction profile, what product is preferred and what does the ratio of the product depend on and why

selectivity-determining step happens after RDS

• ratio of product depends on barrier with lower energy than RDS

not selective

• after going over RDS, it will be random as it has enough energy for both

for this reaction profile, how do you determine which product is formed. what kind of selectivity is this

A is the predominant adduct at equilibrium but the major product does not have to come from the major species

• conversion of B so reaction prefers pathway 2

chemoselectivity

how can you decrease the activation barrier ∆G^‡_cycle for the RDS of the reaction cycle. give an example

stabilise the ground state more than the ground state

or

destabilise the ground state more than the transition state

• solvation - in polar vs apolar solvents, transition states can (de)stabilise

what are the 7 forms of catalysis

• proximity enforcement

• electrophilic catalysis

• nucleophilic catalysis

• strain and distortion

• acid-base catalysis

• covalent catalysis

• phase transfer catalysis

what happens in proximity enforcement catalysis

when reactions happen through collisions between tow molecules, the reaction will be faster if the molecules are held closely together in space

some catalysts bind two substrates and bring them close together, forcing rate acceleration due to entropic cost of reaction already paid through binding

what is effective molarity

the concentration a second reactant would need to have to obtain the same rate constant as the equivalent intramolecular reaction

• i.e. the ratio between the intra and intermolecular rate constant

effective molarity equation

EM = k₁ / k₂

• k₁ = rate constant for intramolecular reaction

• k₂ = rate constant for intermolecular reaction

how much can a reaction be accelerated solely due to proximity effects

>10⁸

what are the chemical modifications that could be made to this molecule to increase rate of reaction due to proximity effects

what are lewis acids

chemical species which can accept electron pairs from lewis bases into empty orbitals

give examples of molecules that can be lewis acids

boron based

• BF₃

• BR₃

• BH₃

aluminium based

• AlCl₃

• AlR₃

silicon

• SiR₄

sulphur

• SO₃

what metals are good Lewis acid catalysts

alkali/alkaline earth metals

• K⁺, Ca²⁺, Mg²⁺

transition metals

• Fe³⁺, Ti⁴⁺, Sc³⁺, Zn²⁺

carbocations

• positively charged carbons (e.g. trityl ion shown)

proton

what type of synthesis are lewis acid catalysts important for and why

asymmetric synthesis/catalysis

• generally simple to equip lewis acids like transition metal ions with chiral ligands

what is lewis base catalysis

catalysis via nucleophilic binding to a reactant, with subsequent enhancement of reaction rate

draw the catalysed reaction between a generic acid chloride, alcohol and pyridine

when doing lewis base catalysis, what is important about the reactants/catalyst

the catalyst must be a better nucleophile and leaving group than the reaction nucleophile

what are good catalysts for lewis base catalysis

pyridine or more electron rich pyridines like DMAP

what is catalysis by strain or distortion

destabilisation of the ground state, rather than stabilisation of the TS, often done by inducing strain or distortion

give examples of catalysis by strain or distortion

lysozyme - strain induced biocatalysis

molecular cage catalysis - strain by confinement

what is specific bronsted acid catalysis

a process where the reaction rate only depends on the specific acid, not other acids in solution (vice versa for specific base catalysis)

what is a specific acid (bronsted acid-base catalysis)

the protonated form of the solvent in which the reaction is being performed

what is the specific base (bronsted acid-base catalysis)

the conjugate base of the solvent

what are the two main forms of bronsted acid-base catalysis

general and specific

write a generic chemical equation for a strong acid in water in specific acid base catalysis

R + H₃O⁺ ←> RH⁺ —-slow→ PH⁺ —fast—> P + H₃O⁺

derive a generic rate equation for a strong acid in water in specific acid base catalysis

• R + H₃O⁺ ←> RH⁺ —-slow→ PH⁺ —fast—> P + H₃O⁺

d[P] / dt = k [RH⁺]

K_a,RH+ = [H₃O⁺] [R] / [RH⁺] => [RH⁺] = [H₃O⁺] [R] / K_a,RH+

∴ d[P] / dt = k [H₃O⁺] [R] / K_a,RH+

write a generic chemical equation for a weak acid in water in specific acid base catalysis

R + HA ←> RH⁺ + A^- —-slow→ PH⁺ + A^- —fast—> P + HA

derive a generic rate equation for a strong acid in water in specific acid base catalysis

• R + HA ←> RH⁺ + A^- —-slow→ PH⁺ + A^- —fast—> P + HA

d[P] / dt = k[RH+]

K_a = [RH⁺] [A^-] / [R] [HA] => [RH⁺] = K_a [HA] [R] / [A^-]

K_a’ = [H₃O⁺] [A-] / [HA] => [HA] / [A-] = [H₃O⁺] / K_a’

[RH⁺] = K_a / K_a’ [H₃O⁺] [R] = K_a’’ [H₃O⁺] [R]

∴ d[P] / dt = k K_a’’ [H₃O⁺] [R] = k’ [ H₃O⁺] [R]

write a generic chemical equation for when an acid is in the RDS in general acid base catalysis

R + HA ←slow→ RH+ —fast→ PH+ → P + HA

derive a generic rate equation for an acid in the RDS in general acid base catalysis

• R + HA ←slow→ RH+ —fast→ PH+ → P + HA

d[P] / dt = k [HA] [R] = k[H₃O⁺] [A^-] [R] / K_a’

• as K_a’ = [H₃O⁺] [A^-] / [HA] so [HA] = [H₃O⁺] [A^-] / K_a’

what is in all acid-base catalysis rate equations

HA or A^-

what do general and specific refer to for acid-base catalysis

general - any acid/base added to solution will affect the rate of reaction

specific - just one acid/base (that from the solvent) will affect the rate

when does the proton transfer happen for general vs specific acid-base catalysis

general

• proton transfer occurs during RDS

specific

• proton transfer occurs before RDS

what do the kinetics of general vs specific acid base catalysis depend on

general

• kinetics depend directly on catalyst concentration

specific

• kinetics only depend on solution pH, not catalyst concentration

draw the k_obs vs pH and [HA] graphs for specific acid catalysis

• log(k_obs) decreases linearly with pH

• k_obs is independent of [HA] at fixed pH

draw the k_obs vs pH and [HA] graphs for general acid catalysis

• log(k_obs) linear at low pH then sharply decrease around the pK_a of HA

• k_obs increases with increased [HA]

draw the k_obs vs pH and [HA] graphs for specific base catalysis

• log(k_obs) increase linearly with pH

• k_obs independent of [B]

draw the k_obs vs pH and [HA] graphs for general base catalysis

• log(k_obs) linear at high pH, then sharply decrease around pK_a of BH⁺

• k_obs increases with increased [B]

what method can you use to distinguish specific and general acid/base catalysis

pH plots:

• log(k_obs) vs pH

• k_obs vs [HA] or [B]

how do the pH plots of acid catalysis relate to base catalysis

they are the inverse (except general acid/base catalysis k_obs vs [HA]/[B] plot)

what is the libido rule

general-acid or general-base catalysis will occur when a thermodynamically unfavourable proton transfer in the ground state is converted to a thermodynamically favourable transfer in the transition state

when will general-acid or general-base catalysis occur

when a thermodynamically unfavourable proton transfer in the ground state is converted to a thermodynamically favourable transfer in the transition state

what potential energy surface belongs to which type of acid-base catalysis

A. specific - no proton transfer in RDS

B. general - proton transfer in RDS

C. general - goes through one TS

D. specific - proton transfer in RDS

what should you look for to determine if an acid/base catalysis is general or specific

if proton transfer happens in RDS then it is general, if not then specific