Reaction Dynamics: Trajectories Across a Potential Energy Surface · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Reading a surface and following trajectories

Science · Chemistry · ages 23-24
Name ______________________   Date ____________

  1. On a potential energy surface for A + BC -> AB + C, where does the reactant valley lie?

    • Short A-B distance, long B-C distance
    • Long A-B, and B-C at bond length
    • Both at their bond lengths

  2. In classical dynamics, the transmission coefficient cannot be larger than 1.

    Circle one:   True   False

  3. Transition state theory gives a rate constant of 4.0 x 10^5 per second, and trajectories give kappa = 0.5. What is the true rate constant?

    • 2.0 x 10^5 per second
    • 8.0 x 10^5 per second
    • 4.5 x 10^5 per second

  4. On a surface for A + BC, the saddle point sits late, close to the product valley. Which reactant energy best helps the reaction over it?

    • Faster approach (translation)
    • Spin of the whole molecule
    • Vibration of the B-C bond

  5. What does transition state theory assume about systems that cross the dividing surface toward products?

    • Most of them come back
    • They never come back
    • Half of them come back

  6. Many trajectories reach the top but fall back to reactants. What does this do?

    • Lowers the true rate below prediction
    • Leaves the rate unchanged
    • Raises the true rate above prediction

  7. A product ratio set by downhill shape rather than barrier heights supports statistical control.

    Circle one:   True   False

  8. The measured product ratio contradicts the computed barriers. What should you inspect?

    • The barrier heights, recomputed more carefully
    • The reactant concentrations
    • The surface shape past the transition state
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Reading a surface and following trajectories W1-mt_6ctTUYqYtS-s1

  1. Long A-B, and B-C at bond length · Before reaction A is far from BC, so the A-B distance is long, and B-C is still bonded, so its distance sits near the bond length.
  2. True · Kappa is the share of barrier crossings that go on to products. A share cannot exceed 1, and recrossing can only lower it.
  3. 2.0 x 10^5 per second · The true rate constant is kappa times the transition state theory rate: 0.5 x 4.0 x 10^5 = 2.0 x 10^5 per second.
  4. Vibration of the B-C bond · A late barrier is reached after the B-C bond has stretched a long way, so energy already in B-C vibration helps most.
  5. They never come back · Transition state theory counts every crossing toward products as reactive, so it assumes none come back.
  6. Lowers the true rate below prediction · Recrossers were counted as products but never arrive.
  7. False · That signature points to dynamic, not statistical, control.
  8. The surface shape past the transition state · Downhill steering can skip the expected valley and set the ratio.
Worksheet · LightMySky