Chem 1310: Introduction to physical chemistry

Part 2d: rate laws and mechanisms

Unimolecular vs bimolecular reactions

Unimolecular reactions happen within one molecule.

The molecule needs to acquire enough energy to overcome the barrier to its reaction.

Molecules collide all the time and so exchange energy.

At any time only a small fraction of them may have enough energy, most will not.

Even if they have enough energy, the reaction does not always happen.

To react or not?A game of chance

Lower barrier higher probability higher rate

Higher temperature higher average energy higher rate

Note: this figure is not to scale !!!

Dependence of rate on temperature

RT

EAk

eAk

a

RT

Ea

lnln

Arrhenius equation:

Interpretation:e-Ea/RT = "energy factor":

fraction of molecules havingenough energy for the reaction.

A = "frequency factor":collision frequency * probability that,given enough energy, the reaction happens.

Arrhenius equationat low temperature

0

10

20

30

40

50

60

70

0 200 400 600 800 1000

T (K)

k (L

mo

l-1

s-1)

T small-Ea/RT large and negativee-Ea/RT close to 0

Number of moleculeswith sufficient energygrows nearly exponentially.

Arrhenius equationat high temperature

0

500

1000

1500

2000

2500

3000

3500

4000

0 5000 10000 15000 20000

T (K)

k (L

mo

l-1

s-1)

Region ofexponentialgrowth.

Every molecule hasenough energy.Frequency factordetermines rate.

T large-Ea/RT close to 0e-Ea/RT close to 1k A

Dependence of rate on temperature

Plot ln k vs 1/T: straight line with slope -Ea/R and intercept ln A ("Arrhenius plot").

RT

EAk

eAk

a

RT

Ea

lnln

Doing an Arrhenius plot

Energy diagrams("reaction profiles")

Av molecular kinetic energy at RT

Ea

Erxn

Ea

Ea

Erxn

N CH CN H

Cyclobutene to butadiene

Ea

Erxn

Cyclobutene to butadiene

Hexadiene to hexadiene

Ea

Hexadiene to hexadiene

HNC to HCN

N CH

CN H

Ea

Erxn

Ea(reverse)

HNC to HCN

Unimolecular vs bimolecular reactions

Bimolecular reactions happen when two molecules meet.

The "encounter complex" also needs to have enough energy to overcome the barrier to its reaction.

At any time only a small fraction of the colliding pairs will have enough energy, most will not.

Even if they have enough energy, the reaction does not always happen.

Termolecular and higher reactions?

"They don't happen."

It is just too improbable for three molecules to meet each other simultaneously, with enough energy and the correct alignment.Even bimolecular reactions tend to be slower than

unimolecular ones with the same Ea.

But two molecules might meet each other, "stick", then meet a third one and finally undergo the "real" reaction.

Not every collisionresults in reaction

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