Molecular Symmetry: Elements, Operations and Point Groups · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Moves that leave molecules unchanged

Science · Chemistry · ages 18-19
Name ______________________   Date ____________

  1. Water is bent with one twofold axis and two mirror planes. What is its point group?

    • D3h
    • C2v
    • C3v

  2. What counts as a symmetry operation?

    • A move that leaves the molecule looking unchanged
    • Any twist that breaks at least one bond
    • A vibration that warms the molecule

  3. Boron trifluoride is polar.

    Circle one:   True   False

  4. A molecule owns a mirror plane. Can it be chiral?

    • Yes, mirrors never matter
    • No, any improper axis forbids it
    • Yes, if the mirror is vertical

  5. Ammonia is pyramidal. What is its point group, and is it polar?

    • C2v and nonpolar
    • D3h and nonpolar
    • C3v and polar

  6. Why is boron trifluoride nonpolar despite its polar bonds?

    • Its three dipoles cancel by symmetry
    • It has no bond dipoles at all
    • Its bonds are purely ionic

  7. A molecule has rotation axes but no mirror, inversion, or improper axis. Can it be chiral?

    • Yes, it can be chiral
    • No, rotations alone forbid it
    • Only if it is also polar

  8. A student labels water D3h, the group of boron trifluoride. What is the error?

    • C2v also fits water fine
    • Water has a threefold axis
    • Water owns no threefold axis or three planes
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Answer key

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

Moves that leave molecules unchanged W1-mt_KcofGO11tm-s1

  1. C2v · One twofold axis plus two planes earns the C2v label.
  2. A move that leaves the molecule looking unchanged · Rotations, reflections, inversion, and combined moves all qualify.
  3. False · Its three bond dipoles cancel exactly in the flat triangle.
  4. No, any improper axis forbids it · Chirality needs the absence of every improper axis.
  5. C3v and polar · The pyramid keeps a threefold axis and stays polar.
  6. Its three dipoles cancel by symmetry · Symmetry alone predicts the zero dipole.
  7. Yes, it can be chiral · Only rotations means no improper axis, which is the chirality condition.
  8. Water owns no threefold axis or three planes · Decision sequences beat recognition.
Worksheet · LightMySky