Elementary Reactions

El l

For elementary reactions,reaction order equals molecularity

Unimolecular: A Rate = k[A]

Elementary reactions occur in a single encounter

Unimolecular: A Rate = k[A]

Bimolecular: A + B Rate = k[A][B]

T l l A B C R t k[A][B][C]Termolecular: A + B + C Rate = k[A][B][C]

Termolecular reactions are rare;hi h l l iti khigher molecularities are unknown.

Rate Laws2A

A

AA B

dk

dtd

kd

1. A + A P

2. A + B Pdt

Case 1: 1 1A A

kt 0A A

Case 2:if [B] >> [A] then [B] is essentially constant andif [B] >> [A], then [B] is essentially constant, and

- [ ] - 'k B t k tA A e A e [ ]

0 0

with '

A A e A ek k B

a “pseudo first order” reaction

Let us try to develop a physically-based model for the rate constant k, for the case that the reaction is elementary.

Arrhenius EquationTh T t D d f kThe Temperature Dependence of k

Arrhenius found experimentally that many reactions had/Tk Ae c

Arrhenius found experimentally that many reactions hada temperature dependence of the form

HC CH decomposition from 600 K to 2500 KHCCH decomposition from 600 K to 2500 KThe observed rate follows this formfor at least 11 orders of magnitudefor at least 11 orders of magnitude.

To cast this in a modern form, k = A exp(E/kBT).Fitting the data to this form gives E = 173 kJ/mol

He constructed a physical picture.

Temperature Dependence of k

Many reactions have a rate cons’t ythat shows a temperature dependence as on the left.

E*/RTk AeThis corresponds to the form

where A and c are simply empirical constants

k Aeempirical constants.E* has units of energy, and A has units of the

t t trate constant.Do A and E* have physical significance?

Arrhenius Equationtemperature dependence of ktemperature dependence of k

E /RTProducts

aE /RTk AeA = pre-exponential p pfactor

Ea= activation energy

Potential energy difference between products and

h ld b l d reactants should be related to Hreaction

Rxn might be endothermic

Let’s develop a 2nd order rate constant along these lines

Rxn might be endothermic

Arrhenius Equationtemperature dependence of ktemperature dependence of k

E /RTProducts

aE /RTk AeA = pre-exponential p pfactor

Ea= activation energy

Potential energy difference between products and

h ld b l d reactants should be related to Hreaction

Rxn might be endothermic

Let’s develop a 2nd order rate constant along these lines

Rxn might be endothermic

A + B C + Dk

an elementary reaction

k should be proportional tok should be proportional tonumber of times A and B collide per secondmultiplied byp yfraction with sufficient energy for rxnmultiplied byfraction with that energy contained in the fraction with that energy contained in the appropriate degrees of freedom for rxnmultiplied byfraction of collisions that occur with a geometry appropriate for rxnThere might or might not be a barrier. How do we think about this?There might or might not be a barrier. How do we think about this?

The point where [d(energy)/d(progress)] =0 is very special,the “Transition State”. More very soon.

The Arrhenius equationh f ll hInsight from collision theory

/aE /RTk Ae

A = frequency factor (collisions with proper orientation)

E /RTaE /RTe = f = fraction of collisions with sufficient energy to surmount barrier

Pre-exponential Factor APre exponential Factor, A

A = PZAB

ZAB = collision density (calculated earlier)

P = steric factor (the probability that collidingmolecules have the proper orientation)

Values of P vary from 1 for atomsto 10–6 for biomolecules

Steric Factor, Pmolecular orientation

NO NONO + NO3

NO2 + NO2

More in a few minutes

The Exponential FactoraE

RTe

The Exponential Factor, e

A + B C + Dan elementary reaction

C id ibl ti ti i ( ti fil )Consider possible activation energies (reaction profiles)and steric effects for the following reaction:

CH4 + D CH3D +H

Steric hindrance: not muchSteric hindrance not much

Activation energy: yes How much? C-H bond140 kJ/molWhat mi ht the TS 140 kJ/mol

(but maybe a lot less!)

What might the TSgeometry look like andstill be elementary? )

H3CDH

A + B C + Dan elementary reaction

C id ibl ti ti i ( ti fil )Consider possible activation energies (reaction profiles)and steric effects for the following reaction:

OH + D HOD

Steric hindrance: someSteric hindrance some

Activation energy: No – a radical-radical recombination

NO2 + CO NO + CO2

Observed rate = k [NO2]2Deduce a possible and reasonable mechanismDeduce a possible and reasonable mechanism

NO2 + NO2 NO3 + NO slow

NO CO NO COO ll

NO3 + CO NO2 + CO2 fast

NO2 + CO NO + CO2Overall,

Is the rate law for this sequence consistent with observation?

Yes

Does this prove that this must be what is actually happening?Does this prove that this must be what is actually happening?

No! Note the NO3 intermediate product!