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 Arrhenius equation: Interpretation: e -Ea/RT = "energy factor": fraction of molecules having enough energy for the reaction. A = "frequency factor": collision frequency * probability that, given enough energy, the reaction happens.

Arrhenius equation at low temperature T small -E a /RT large and negative e -Ea/RT close to 0 Number of molecules with sufficient energy grows nearly exponentially.

Arrhenius equation at high temperature Region of exponential growth. Every molecule has enough energy. Frequency factor determines rate. T large -E a /RT close to 0 e -Ea/RT close to 1 k  A

Dependence of rate on temperature Plot ln k vs 1/T: straight line with slope -E a /R and intercept ln A ("Arrhenius plot"). Doing an Arrhenius plot

Energy diagrams ("reaction profiles")

Cyclobutene to butadiene

Hexadiene to hexadiene

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

Not every collision results in reaction ? ?