Question

The correct increasing order of bond length among the following is

• A. O$_2$$^{+}$, O$_2$, O$_2$$^{-}$, O$_2$$^{2-}$
• B. O$_2$$^{+}$, O$_2$, O$_2$$^{-}$, O$_2$$^{2-}$
• C. O$_2$$^{2-}$, O$_2$, O$_2$$^{-}$, O$_2$$^{+}$
• D. O$_2$, O$_2$$^{-}$, O$_2$$^{+}$, O$_2$$^{2-}$

Hint:

The higher the bond order, the shorter the bond length.

Answer 1

The Correct Option is A

Step 1: Molecular Orbital Theory Basics According to Molecular Orbital (MO) theory, the bond order of a molecule determines its stability and bond length. Bond order is calculated as (Electrons in Bonding orbitals - Electrons in Antibonding orbitals) / 2. Bond length is inversely proportional to the bond order.

Step 2: Calculating Bond Orders for Oxygen Species For a neutral O$_2$ molecule (16 electrons), the electronic configuration results in a Bond Order of 2. When O$_2$ loses an electron to form O$_2^{+}$, the electron is removed from an antibonding orbital, increasing the Bond Order to 2.5. When O$_2$ gains one electron to form O$_2^{-}$, the electron enters an antibonding orbital, decreasing the Bond Order to 1.5. When O$_2$ gains two electrons to form O$_2^{2-}$, the Bond Order further decreases to 1.

Step 3: Determining Bond Length Order Since Bond Length \(\propto 1 / \text{Bond Order}\), the species with the highest Bond Order (O$_2^{+}$) has the shortest bond length, and the species with the lowest Bond Order (O$_2^{2-}$) has the longest bond length. Order of Bond Order: O$_2^{+}$ (2.5)>O$_2$ (2.0)>O$_2^{-}$ (1.5)>O$_2^{2-}$ (1.0). Order of Bond Length: O$_2^{+}$<O$_2$<O$_2^{-}$<O$_2^{2-}$.