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Question:

Using MO theory, predict which of the following species has the shortest bond length?

O2+2

O+2

O⁻

O2⁻

Solution:

  1. O2+2: Valence electrons = 6 + 6 - 2 = 10 (σ2s)²(σ*2s)²(σ2p)²(π2p)⁴ BO = (10 - 4)/2 = 3;
  2. O+2: Valence electrons = 6 + 6 - 1 = 11 (σ2s)²(σ2s)²(σ2p)²(π2p)⁴(π2p)¹ BO = (10 - 5)/2 = 2.5;
  3. O⁻: Valence electrons = 6 + 6 + 1 = 13 (σ2s)²(σ2s)²(σ2p)²(π2p)⁴(π2p)³ BO = (10 - 7)/2 = 1.5;
  4. O2⁻: Valence electrons = 6 + 6 + 2 = 14 (σ2s)²(σ2s)²(σ2p)²(π2p)⁴(π2p)⁴ BO = (10 - 8)/2 = 1;
    Bond length ∝ 1/bond order ⇒ O2+2 has the highest bond order and smallest bond length. Hence, the correct option is A.