R i M h iReaction MechanismA detailed sequence of elementary steps for a reaction

R bl h iReasonable mechanism:

1. Elementary steps sum to the overall reaction

2. Elementary steps are physically reasonable

3 M h i i i t t ith t l d th3. Mechanism is consistent with rate law and other experimental observations(generally found from rate limiting (slow) step(s)

A mechanism can be supported but never proven

R i R CReaction Rate ConstantConsider the elementary reaction A + B Products

Rate = k [A] [B][ ] [ ]

1. Generally higher concentrations mean faster rates.No T dependence in [X] beyond thermal expansionNo T dependence in [X] beyond thermal expansion

2. Properties of the rate constant k: k does not depend on concentrationsk does not depend on concentrations k can have major T dependence dynamical and mechanistic information in k(T)

3. What qualitative things can we say about k?

A + B C + Dk

an elementary reaction

k h ld b ti l tk 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 thefraction with that energy contained in the appropriate degrees of freedom for rxnmultiplied byfraction of collisions that occur with a geometry appropriate for rxn

h i h i h b b i d hi k bThere might or might not be a barrier. How do we think about this?

Arrhenius EquationqThe 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.He constructed a physical picture.

Temperature Dependence of kp p f

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

E*/RTk AeThis corresponds to the form

where A and c are simply

k Ae

empirical constants. E* has units of energy, and k has units of the rate constant.

Might A and E* have physical significance?

Arrhenius EquationqThe Temperature Dependence of k

aE /RTk Aek AeA = pre-exponentialp p

factor

Ea= activationenergy

Why is there a barrier at all?

Sample Problem (9.31)

The water flea Daphnia performs a constant number of heartbeats and then dies. The flea lives twice as long at 15 °C as at 25 °C. C l ul t th ti ti n n f th Calculate the activation energy for the reaction that controls the rate of its heartbeatheartbeat.

Answer: 49.5 kJ/molAnswer 9.5 kJ/mol

Arrhenius Equation d d f ktemperature dependence of k

E /RTk AeEa/RT

A = pre-exponential p pfactorEa= activation energy

Potential energy difference between products and reactants should be related to Hreaction

L t’ t t d l 2ndLet’s try to develop a 2nd

order rate constant alongthese lines

The Arrhenius EquationThe Arrhenius EquationInsight from Collision Theory

k AeEa/RT

A = frequency factor(collisions/s with proper orientation)( p p )

E /RT f f ti f lli i ith ffi i t aE /RTe = f = fraction of collisions with sufficient energy to surmount barrier

The Arrhenius equationh f ll hInsight from collision theory

k AeEa/RT

A = frequency factor (collisions with proper orientation)

E /RTeEa/RT = f = fraction of collisions with sufficient energy to surmount barrier

Pre-exponential Factor APre exponential Factor, A

A PZA = PZAB

ZAB = collision density (calculated earlier)

28 BAB AB

A B

k TZ dm m

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

A Bm m

molecules have the proper orientation)Values of P vary from 1 for atoms to 10–6 for biomolecules

Steric Factor, PM l l OMolecular Orientation

NO NO NO NONO + NO3 NO2 + NO2

E /RTThe Exponential Factor, eEa/RT

Remember Zeb’s F+ HCl HF + Cl reaction

E /RTThe Exponential Factor, eEa/RT

ConcepTest #1ConcepTest #1

Which of the following statements is true?

A The activation energy of a reaction depends on A. The activation energy of a reaction depends on collision frequency

B. If reactant molecules collide with greater energy . f m g gythan the activation energy, they change into product molecules

C Th hi h th ti ti f tiC. The higher the activation energy of a reaction,the lower the reaction rate constant

D The activation energy depends on the temperatureD. The activation energy depends on the temperature

A + B C + Dan elementary reaction

id ibl i i i ( i 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/mol

A + B C + Dan elementary reaction

id ibl i i i ( i fil )Consider possible activation energies (reaction profiles)and steric effects for the following SN2 reaction:

F- + CH3Cl CH3F + Cl-

Steric hindrance: lotsSteric hindrance: lots

Activation energy: yes How much? C-X bond140 kJ/mol

A + B C + Dan elementary reaction

id ibl i i i ( i 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

Typical Arrhenius Parametersypk AeEa/RT

aERT

A h i s ABk PZ e

The form does not behave completelyArrhenius ABk PZ e does not behave completely

satisfactorily. It is not obvious how to obtain A, and we havealready learned that G drives reactions not just H! In factalready learned that G drives reactions, not just H! In fact,A looks a lot like (Scomplex – Sreactants). This led Eyring to . .

Transition State TheoryTransition State Theory

‡ ‡ 00SB

HR

TSTR Tk eTk e

h

TSTA

h

S‡ is the difference in entropy between reactantsentropy between reactantsand transition state