The Question is from NEET guide , and it was created by the author THIRUPATHI REDDY

Question

The bond length in $O_2$ is experimentally determined to be 121 pm.  Using this information and the concept of bond order, predict the approximate bond length in $O_2^+$ (superoxide ion).

THIRUPATHI REDDY · Accepted Answer

## CORE INFORMATION
✓ **Answer**: B
## CONCEPT FRAMEWORK
 **Primary Concept**: Relationship between bond order and bond length.
 **Related Topics**: Molecular orbital theory, diatomic molecules.
 **Prerequisites**: Understanding of molecular orbital diagrams and bond order calculation.
## SOLUTION PATHWAY
**Given Information**:
  Bond length of $O_2$ = 121 pm
  We need to find the bond length of $O_2^+$
**Method & Steps**:
 1. Determine the bond order of $O_2$ and $O_2^+$.
  Reasoning: Bond order is the number of bonds between two atoms.  A higher bond order indicates a stronger bond and shorter bond length.
  Formula/Rule: Bond order = $\frac{1}{2}$(number of electrons in bonding orbitals - number of electrons in antibonding orbitals)
 2. Draw the molecular orbital diagram for $O_2$ and $O_2^+$.
  Working: For $O_2$, the electronic configuration is $(\sigma_{2s})^2 (\sigma_{2s}^*)^2 (\sigma_{2p})^2 (\pi_{2p})^4 (\pi_{2p}^*)^2$. Bond order = $\frac{1}{2}(8-4) = 2$.
  For $O_2^+$, one electron is removed from the $\pi_{2p}^*$ antibonding orbital.  The electronic configuration is $(\sigma_{2s})^2 (\sigma_{2s}^*)^2 (\sigma_{2p})^2 (\pi_{2p})^4 (\pi_{2p}^*)^1$. Bond order = $\frac{1}{2}(8-3) = 2.5$.
  Key Point: Removing an electron from an antibonding orbital increases the bond order.
 3. Relate bond order to bond length.
  Result: Since $O_2^+$ has a higher bond order (2.5) than $O_2$ (2), its bond length will be shorter.
  Verification: Higher bond order means stronger attraction between the oxygen atoms, resulting in a shorter bond length.
 ## OPTION ANALYSIS
A :x: Slightly greater than 121 pm: Incorrect because higher bond order leads to shorter bond length.
B ✓: Slightly less than 121 pm: Correct because the bond order in $O_2^+$ is higher than in $O_2$.
C :x: Approximately equal to 121 pm: Incorrect; bond order difference implies a length difference.
D :x: Significantly greater than 121 pm: Incorrect; higher bond order leads to shorter, not longer, bond length.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Confusing bond order with bond length: Remember that higher bond order implies shorter bond length.
  2.Incorrectly drawing molecular orbital diagrams:  Pay close attention to electron filling and orbital energies.
 **Quick Tips**:
  1.Remember the relationship: Higher bond order = shorter bond length.
  2.Practice drawing molecular orbital diagrams for diatomic molecules to understand the relationship between electron configuration and bond order.

THIRUPATHI REDDY · Answer

Slightly greater than 121 pm

THIRUPATHI REDDY · Answer

The correct Option is "Slightly less than 121 pm"

THIRUPATHI REDDY · Answer

Approximately equal to 121 pm

THIRUPATHI REDDY · Answer

Significantly greater than 121 pm

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