Draw and label the molecular orbital (MO) diagrams for C2 and C22–

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Draw and label the molecular orbital (MO) diagrams for C2 and C22–. Give the MO ground state electron configuration, the bond order, and the magnetism for each molecule. Which molecule has the stronger bond?

The correct answer and explanation is :

Molecular Orbital (MO) Diagrams and Electron Configurations

  1. C₂ Molecule (Neutral)
  • The molecular orbital diagram for the C₂ molecule can be drawn as follows:
    • Carbon (C) has 6 electrons in its valence shell, so the C₂ molecule has a total of 12 electrons.
    • For homonuclear diatomic molecules like C₂, the molecular orbitals are filled in the following order:
    • σ(1s), σ(1s), σ(2s), σ(2s), π(2px), π(2py), π(2px), π(2py)
    • The filling of electrons in the molecular orbitals (MO) will be as follows:
    σ(1s) 2 σ*(1s) 2 σ(2s) 2 σ*(2s) 2 π(2px) 2 π(2py) 2 π*(2px) 0 π*(2py) 0 Ground State Electron Configuration for C₂:
  • 2 electrons in σ(1s)
  • 2 electrons in σ*(1s)
  • 2 electrons in σ(2s)
  • 2 electrons in σ*(2s)
  • 2 electrons in π(2px)
  • 2 electrons in π(2py) Bond Order Calculation:
    Bond Order = (Number of bonding electrons − Number of antibonding electrons) / 2
    Bond Order = (2 + 2 + 2 + 2 − 2 − 2) / 2 = 2 Magnetism:
    Since there are no unpaired electrons, C₂ is diamagnetic.
  1. C₂²⁻ Molecule (C₂ with two extra electrons)
  • For C₂²⁻, two additional electrons are added to the π(2px) and π(2py) antibonding orbitals. The filling of the molecular orbitals is as follows: σ(1s) 2 σ*(1s) 2 σ(2s) 2 σ*(2s) 2 π(2px) 2 π(2py) 2 π*(2px) 1 π*(2py) 1 Ground State Electron Configuration for C₂²⁻:
  • 2 electrons in σ(1s)
  • 2 electrons in σ*(1s)
  • 2 electrons in σ(2s)
  • 2 electrons in σ*(2s)
  • 2 electrons in π(2px)
  • 2 electrons in π(2py)
  • 1 electron in π*(2px)
  • 1 electron in π*(2py) Bond Order Calculation:
    Bond Order = (Number of bonding electrons − Number of antibonding electrons) / 2
    Bond Order = (2 + 2 + 2 + 2 − 2 − 2 − 1 − 1) / 2 = 1 Magnetism:
    Since C₂²⁻ has 2 unpaired electrons, it is paramagnetic.

Comparison of Bond Strengths

  • C₂ has a bond order of 2, and C₂²⁻ has a bond order of 1.
  • A higher bond order indicates a stronger bond. Therefore, C₂ has a stronger bond than C₂²⁻.

Conclusion:

  • C₂ is diamagnetic, with a bond order of 2, and has a stronger bond than C₂²⁻.
  • C₂²⁻ is paramagnetic, with a bond order of 1, and has a weaker bond than C₂.

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