Question

Which of the following statement is INCORRECT ?

• A. Bond length of O₂ > Bond length of \(O^{2+}_2\)
• B. Bond order of \(O^{+}_2\) < Bond order of \(O^{2-}_2\)
• C. Bond length of O₂ < Bond order of \(O^{2-}_2\)
• D. Bond order of O₂ > Bond order of \(O^{2-}_2\)

Answer 1

The Correct Option is B

Bond Length: The distance between the nuclei of two bonded atoms.

Bond Order: A measure of the number of chemical bonds between a pair of atoms; the formula is \( \text{Bond Order} = \frac{\text{Number of Bonding Electrons} - \text{Number of Antibonding Electrons}}{2} \).

The incorrect statement is:

1. Bond length of \( \text{O}_2 \) < Bond length of \( \text{O}_2^{2-} \)
2. Bond order of \( \text{O}_2 \) > Bond order of \( \text{O}_2^{2-} \)
3. Bond length of \( \text{O}_2 \) > Bond length of \( \text{O}_2^{2+} \)
4. Bond order of \( \text{O}_2^+ \) < Bond order of \( \text{O}_2^{2-} \)

The correct answer is that statement 2 is incorrect because the bond order of \( \text{O}_2^+ \) is equal to the bond order of \( \text{O}_2^{2-} \), not less than it.

Answer 2

To determine which statement is incorrect, we will evaluate the bond order and bond lengths of the oxygen molecules in the different oxidation states: 1. Bond order can be calculated using the formula: \[ \text{Bond order} = \frac{1}{2} \left( \text{number of electrons in bonding molecular orbitals} - \text{number of electrons in anti-bonding molecular orbitals} \right) \] 2. O$_2$ (molecular oxygen): The molecular orbital diagram for O$_2$ shows that there are 12 electrons in bonding orbitals and 8 in anti-bonding orbitals, so the bond order of O$_2$ is: \[ \text{Bond order of O}_2 = \frac{1}{2} \left( 12 - 8 \right) = 2 \] 3. O$_2^{2-}$ (peroxide ion): For O$_2^{2-}$, there are 14 electrons in bonding orbitals and 8 electrons in anti-bonding orbitals, so the bond order is: \[ \text{Bond order of O}_2^{2-} = \frac{1}{2} \left( 14 - 8 \right) = 3 \] 4. O$_2^{2+}$ (superoxide ion): For O$_2^{2+}$, there are 10 electrons in bonding orbitals and 8 electrons in anti-bonding orbitals, so the bond order is: \[ \text{Bond order of O}_2^{2+} = \frac{1}{2} \left( 10 - 8 \right) = 1 \] From these bond order values, we can deduce the following: - Bond length comparison: A higher bond order typically means a shorter bond length. Therefore: \[ \text{Bond length of O}_2 > \text{Bond length of O}_2^{2+} \quad (\text{Statement A is correct}) \] \[ \text{Bond length of O}_2 < \text{Bond length of O}_2^{2-} \quad (\text{Statement C is correct}) \] \[ \text{Bond order of O}_2 > \text{Bond order of O}_2^{2-} \quad (\text{Statement D is correct}) \] - Incorrect statement: According to bond orders: \[ \text{Bond order of O}_2 = 2 \quad \text{and} \quad \text{Bond order of O}_2^{2-} = 3 \] So, the bond order of O$_2$ is less than that of O$_2^{2-}$, which makes statement B incorrect.

Thus, Statement B is the incorrect one.