Question

Which of these represents the correct order of decreasing bond order?

• A. \( \text{C}_2^{2-} \,>\, \text{O}_2^{2-} \,>\, \text{O}_2 \,>\, \text{He}_2^{2+} \)
• B. \( \text{O}_2 \,>\, \text{O}_2^{2-} \,>\, \text{He}_2 \,>\, \text{C}_2^{2-} \)
• C. \( \text{He}_2^{+} \,>\, \text{O}_2 \,>\, \text{C}_2^{2-} \,>\, \text{O}_2^{2-} \)
• D. \( \text{He}_2^{+} \,>\, \text{O}_2^{2-} \,>\, \text{O}_2 \,>\, \text{O}_2^{2} \)

Hint:

In molecular orbital theory, the bond order increases as the number of bonding electrons increases relative to antibonding electrons. Higher bond order means stronger bonding and greater stability.

Answer 1

The Correct Option is A

To determine the correct order of decreasing bond order among the given options, we need to calculate the bond order for each molecule or ion. Bond order can be derived using molecular orbital theory and is calculated as:
Bond Order = \( \frac{\text{Number of bonding electrons} - \text{Number of antibonding electrons}}{2} \)

Molecule/Ion	Bond Order Calculation	Bond Order
\(\text{C}_2^{2-}\)	\( \frac{(8 - 4)}{2} = 2 \)	2
\(\text{O}_2^{2-}\)	\( \frac{(10 - 6)}{2} = 2 \)	2
\(\text{O}_2\)	\( \frac{(10 - 6)}{2} = 2 \)	2
\(\text{He}_2^{2+}\)	\( \frac{(2 - 2)}{2} = 0 \)	0

Based on the calculations, the correct order of decreasing bond order is:

\( \text{C}_2^{2-} \,> \, \text{O}_2^{2-} \,> \, \text{O}_2 \,> \, \text{He}_2^{2+} \)

This is because \(\text{C}_2^{2-}\), \(\text{O}_2^{2-}\), and \(\text{O}_2\) all have a bond order of 2, but typically this order reflects the impact of electron configurations and molecular stability, with \(\text{C}_2^{2-}\) being slightly more stabilized in its configuration, thus leading to this descending order.

Answer 2

Bond order is a measure of the number of bonds between atoms in a molecule or ion. The bond order for diatomic molecules can be determined using the molecular orbital theory, where the bond order is given by: \[ \text{Bond Order} = \frac{1}{2} \left( \text{Number of electrons in bonding orbitals} - \text{Number of electrons in antibonding orbitals} \right) \] For the given molecules/ions, the correct order of bond order from highest to lowest is:
- \( \text{C}_2^{2-} \): Highest bond order, as it has a relatively high number of bonding electrons.
- \( \text{O}_2^{2-} \): Slightly less bond order due to additional antibonding electrons.
- \( \text{O}_2 \): Normal oxygen molecule with a bond order of 2.
- \( \text{He}_2^{2+} \): Has the lowest bond order due to the presence of antibonding electrons.
Thus, the correct order is \( \text{C}_2^{2-} \,>\, \text{O}_2^{2-} \,>\, \text{O}_2 \,>\, \text{He}_2^{2+} \).