Questions: Bimolecular Reaction Dynamics: Collisions, Cross Sections, and Scattering

Question 1

In a crossed molecular beam experiment, products from a bimolecular reaction are detected predominantly scattering backward — toward the direction of the incoming reactant beam. What does this angular distribution indicate about the reaction mechanism?

• A. The reaction is endothermic, so products have less kinetic energy and scatter backward
• B. The reaction proceeds by a direct rebound mechanism: a brief, hard collision where the new bond forms and old bond breaks in one concerted step
• C. A long-lived collision complex formed and decayed, distributing products symmetrically in forward and backward directions
• D. The mass asymmetry between reactants forces products to scatter backward regardless of mechanism

Answer: (B)

Backward scattering is the signature of a direct rebound mechanism — analogous to two billiard balls bouncing head-on. The collision is brief, dominated by short-range repulsion, and the product flies off in the backward hemisphere. Option C (long-lived complex) would produce forward-backward symmetric scattering: the complex survives long enough to rotate and lose memory of the initial collision geometry, making all scattering directions equally likely. Option A confuses energetics with dynamics — reaction enthalpy does not determine scattering angle. Option D is incorrect; mass asymmetry affects velocity magnitudes, not the mechanistic signature.

Question 2

For F + D₂ → DF + D, experiments show that the DF product is born predominantly in highly excited vibrational states, with relatively little energy in translation. According to Polanyi's rules, this indicates what feature of the potential energy surface?

• A. A late barrier in the exit channel: the transition state occurs after significant D-D bond extension, channeling energy into product translation
• B. An early barrier in the entrance channel: the transition state occurs before significant D-D bond extension, and the energy released as the new F-D bond forms is channeled into product vibration
• C. An early barrier that channels energy into product translation rather than vibration
• D. A deep potential well (stable complex) that distributes energy equally among all product modes

Answer: (B)

Polanyi's rules connect energy disposal to PES topology. An 'early' barrier means the transition state is in the entrance channel — the D-D bond has barely stretched when the barrier is reached. Most energy is released as the new F-D bond forms along the exit channel, and this late energy release is channeled preferentially into vibration of the new DF bond. A 'late' barrier (exit channel transition state) would instead channel energy into product translation. F + D₂ → DF + D is the textbook case of highly vibrationally excited products arising from an early barrier.

Question 3

The steric factor p in simple collision theory fully accounts for most of the reasons why the observed rate constant falls below the hard-sphere collision rate, including quantum tunneling and orbital symmetry constraints.

• T. True
• F. False

Answer: False

The steric factor p is explicitly a fudge factor — a single number between 0 and 1 inserted to make the equation match experiment. It cannot disentangle geometric orientation requirements from quantum mechanical effects like tunneling (which can increase rates beyond classical predictions), orbital symmetry rules (Woodward-Hoffmann), or electronic factors. Molecular beam experiments reveal these contributions separately and show that p can sometimes exceed 1 when tunneling is important. Simple collision theory uses p precisely because it lacks a molecular-level description of what happens during the collision.

Question 4

A reaction that produces products with forward-backward symmetric angular scattering in a molecular beam experiment most likely proceeded through a long-lived collision complex.

• T. True
• F. False

Answer: True

When a collision complex forms and survives for many rotational periods, it loses all memory of the initial collision direction. When the complex eventually breaks apart, it ejects products with equal probability in the forward and backward directions, producing a symmetric angular distribution. A direct mechanism (rebound or stripping) is far too brief for significant rotation, so it produces an asymmetric distribution peaked either in the backward hemisphere (rebound) or forward hemisphere (stripping). Forward-backward symmetry is therefore the diagnostic signature of complex formation.

Question 5

What is the difference between a 'direct rebound' and a 'complex-mediated' bimolecular reaction mechanism, and what experimental observable most clearly distinguishes them?

Model answer: In direct rebound, the reaction occurs in a single brief collision dominated by short-range repulsion; the product flies off backward. In a complex-mediated mechanism, the collision forms a long-lived intermediate that survives many rotational periods before decomposing, losing directional memory and scattering products with forward-backward symmetry. The differential cross section — the angular distribution of products measured in a crossed molecular beam experiment — is the observable that most directly distinguishes them.

The Newton diagram from a crossed molecular beam experiment maps product scattering in velocity-angle space. Backward-peaked distributions fingerprint direct rebound; forward-backward symmetric distributions indicate complex formation. This experimental signature connects directly to the potential energy surface: reactions with deep wells (stable intermediates) favor complex formation, while reactions with high early barriers and no well favor direct rebound. The shape of the distribution also correlates with product energy disposal, linking angular dynamics to Polanyi's rules.