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

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

  1. Water has one C2 axis, two vertical mirror planes and no other nonidentity symmetry operations. What is its point group?

    • D3h
    • C2v
    • C3v

  2. What makes a transformation a symmetry operation of a fixed molecular geometry?

    • Every atom reaches an equivalent atom position
    • At least one bond breaks but atom numbers stay fixed
    • Only the formula stays fixed while the shape changes

  3. An isolated BF3 molecule in its trigonal planar equilibrium geometry has a permanent dipole.

    Circle one:   True   False

  4. A fixed molecular geometry has a mirror plane. Can that geometry be chiral?

    • Yes, because a mirror plane counts as a proper rotation
    • No, because reflection is an S1 operation
    • Yes, because vertical mirrors do not affect chirality

  5. Ammonia has a C3 axis, three vertical mirror planes and no perpendicular C2 axes. Its N-H dipoles do not cancel. Which description fits?

    • C2v, with a nonzero dipole
    • D3h, with a zero net dipole
    • C3v, with a nonzero dipole

  6. A point group allows a permanent dipole along one axis. What follows from symmetry alone?

    • A dipole is allowed, but not guaranteed
    • A nonzero dipole must exist along every rotation axis
    • A permanent dipole must be zero in every direction

  7. A fixed molecular geometry has proper rotation axes but no Sn operation of any order, including reflection and inversion. What follows?

    • Its fixed geometry is chiral
    • Its proper rotations make the geometry achiral
    • Its chirality depends on having a permanent dipole

  8. A student assigns bent water to D3h because its atoms lie in a plane. Which check rules out that assignment?

    • Planarity requires every molecule to belong to D3h
    • Water's molecular plane removes its twofold rotation
    • Water has no threefold rotation axis
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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 · Its main axis has order 2 and its mirror planes contain that axis. This gives C2v.
  2. Every atom reaches an equivalent atom position · At each final position, the atom type must match the atom type originally there. Identical atoms may exchange positions.
  3. False · Its three equal B-F bond dipoles are separated by 120 degrees and sum to zero.
  4. No, because reflection is an S1 operation · A chiral fixed geometry has no Sn operation. Mirror reflection is S1, so the geometry is achiral.
  5. C3v, with a nonzero dipole · The stated elements give C3v. The uncancelled bond dipoles give a nonzero permanent dipole.
  6. A dipole is allowed, but not guaranteed · Symmetry restricts allowed directions. The charge distribution determines whether the dipole along an allowed direction is nonzero.
  7. Its fixed geometry is chiral · The absence of all improper operations is the fixed-geometry chirality criterion. A permanent dipole is not required.
  8. Water has no threefold rotation axis · D3h requires a C3 axis. Bent water has C2 symmetry about its main axis, so planarity alone cannot justify D3h.
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