Concept: Bond order is a measure of the number of chemical bonds between two atoms. It can be calculated using Molecular Orbital Theory (MOT) as half the difference between the number of electrons in bonding molecular orbitals and antibonding molecular orbitals.

Why (C) is correct: We need to calculate the bond order for each species in the given pairs using the formula: Bond Order = $\frac{1}{2}$(Number of electrons in bonding MOs - Number of electrons in antibonding MOs). Alternatively, for diatomic species with up to 20 electrons, we can use the total number of electrons to determine the bond order based on the MOT electron configuration.

Option Analysis:

• A) N${}_2$ and CN${}^{-}$
  • N${}_2$: Total electrons = 7 + 7 = 14. Bond order = 3.
  • CN${}^{-}$: Total electrons = 6 + 7 + 1 = 14. Bond order = 3.
  • This pair has the same bond order.
• B) O${}_2$${}^{+}$ and NO
  • O${}_2$${}^{+}$: Total electrons = 8 + 8 - 1 = 15. Bond order = 2.5.
  • NO: Total electrons = 7 + 8 = 15. Bond order = 2.5.
  • This pair has the same bond order.
• C) F${}_2$${}^{-}$ and O${}_2$${}^{2-}$
  • F${}_2$${}^{-}$: Total electrons = 9 + 9 + 1 = 19. Bond order = 0.5.
  • O${}_2$${}^{2-}$: Total electrons = 8 + 8 + 2 = 18. Bond order = 1.
  • This pair does NOT have the same bond order.
• D) B${}_2$${}^{2-}$ and CN${}^{+}$
  • B${}_2$${}^{2-}$: Total electrons = 5 + 5 + 2 = 12. Bond order = 2.
  • CN${}^{+}$: Total electrons = 6 + 7 - 1 = 12. Bond order = 2.
  • This pair has the same bond order.

Therefore, the pair that does not have the same bond order is F${}_2$${}^{-}$ and O${}_2$${}^{2-}$.

Correct Answer: (C)