Concept 06 / 06Chemical Kinetics
Collision Theory of Reaction Rates
Collision theory: collision frequency, effective collisions requiring threshold energy and proper orientation, the steric (probability) factor, rate = P Z e^(-Ea/RT), energy distribution of molecules and why a 10 K rise roughly doubles the rate, and limitations of the theory.
Collision theory (Arrhenius, Max Trautz and William Lewis) explains rates at the molecular level, treating reacting molecules as hard spheres.
Main ideas.
1. Molecules must collide to react. The number of collisions per second per unit volume is the collision frequency (for example for A and B).
2. Only effective collisions lead to products. A collision is effective if (a) the colliding molecules have kinetic energy at least equal to the threshold energy ( above the average), and (b) they collide with the proper orientation, so that the atoms that must bond come into contact.
3. Rate , where is the probability or steric factor (the fraction of collisions with suitable orientation), and is the fraction with enough energy. Comparing with Arrhenius, .
Orientation. In , the hydroxide must approach the carbon from the side opposite bromine; collisions at the bromine end do nothing, however energetic.
Energy distribution and temperature (see figure). The kinetic energies of molecules follow the Maxwell-Boltzmann distribution. The fraction with energy at least is the area under the curve beyond . On heating, the curve flattens and shifts to higher energy; the area beyond roughly doubles for a rise near room temperature (for typical ), which is why rate roughly doubles. The total number of collisions increases only slightly with temperature (about per ), so it is the energy factor that matters.
A catalyst lowers , which moves the threshold to the left and greatly enlarges the fraction of effective collisions at the same temperature.
Limitations. The theory treats molecules as hard spheres and ignores their structure, so it cannot predict ; calculated rates agree with experiment only for simple reactions. Transition state theory refines it.
Key Takeaways:
- Effective collisions need energy and proper orientation.
- Rate ; .
- Temperature mainly raises the fraction of energetic molecules, not the collision frequency.
- A catalyst increases the fraction of effective collisions by lowering .
- Pitfall: not every collision is a reaction; typically only a tiny fraction succeeds.
Brain-Teaser 1: For , what fraction of collisions has enough energy at , and by what factor does it increase at ?
Solution: , so the fraction is . At : , fraction . The factor is about : the rate roughly doubles.
Brain-Teaser 2: Why does increasing temperature from to increase collision frequency by only about yet nearly double the rate?
Solution: Collision frequency is proportional to average speed, which scales as : . The rate depends mostly on the exponential factor , which changes by a factor of about over the same range (see Brain-Teaser 1).
Brain-Teaser 3: A catalyst lowers from to at . By what factor does the rate increase (assuming unchanged)?
Solution: . Lowering the barrier by makes the reaction over twenty thousand times faster.
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