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In which of the following pairs, both the species have the same bond order? (1) \(\mathrm{N}_{2}, \mathrm{~N}_{2}^{21}\) (2) \(\mathrm{O}_{2}, \mathrm{~F}_{2}\) (3) \(\mathrm{C}_{2}, \mathrm{O}_{2}\) (4) \(\mathrm{C}_{2}, \mathrm{~N}_{2}\)

Short Answer

Expert verified
Pair 3 (\text{C}_2 and \text{O}_2) both have bond orders of 2.

Step by step solution

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01

- Calculate the bond order of \(\text{N}_2\)

The bond order of a molecule can be calculated using Molecular Orbital (MO) theory. For \( \text{N}_2 \), the total number of bonding electrons is 10 and the number of anti-bonding electrons is 4. Bond order is calculated as: \[\text{Bond Order} = \frac{(\text{Number of Bonding Electrons - Number of Anti-Bonding Electrons})}{2} = \frac{(10 - 4)}{2} = 3\].
02

- Determine the bond order of \(\text{N}_2^{2+}\)

For \( \text{N}_2^{2+} \), remove two electrons from the bonding orbitals. There will be 8 bonding electrons and 4 anti-bonding electrons. Using the bond order formula again: \[\text{Bond Order} = \frac{(8 - 4)}{2} = 2\].
03

- Calculate the bond order of \(\text{O}_2\)

The \( \text{O}_2 \) molecule has 10 bonding electrons and 6 anti-bonding electrons. Therefore, the bond order is: \[\text{Bond Order} = \frac{(10 - 6)}{2} = 2\].
04

- Determine the bond order of \(\text{F}_2\)

For \( \text{F}_2 \), there are 10 bonding electrons and 8 anti-bonding electrons. The bond order is thus: \[\text{Bond Order} = \frac{(10 - 8)}{2} = 1\].
05

- Calculate the bond order of \(\text{C}_2\)

In \( \text{C}_2 \), there are 8 bonding electrons and 4 anti-bonding electrons. The bond order is: \[\text{Bond Order} = \frac{(8 - 4)}{2} = 2\].
06

- Determine the bond order of \(\text{O}_2\)

Already calculated in Step 3, the bond order of \( \text{O}_2 \) is 2.
07

- Calculate the bond order of \(\text{C}_2\)

Already calculated in Step 5, the bond order of \( \text{C}_2 \) is 2.
08

- Determine the bond order of \(\text{N}_2\)

Already calculated in Step 1, the bond order of \( \text{N}_2 \) is 3.
09

- Compare the bond orders

From the steps above, the bond orders of \( \text{N}_2 \) and \( \text{N}_2^{2+} \) are different: 3 and 2, respectively. \( \text{O}_2 \) and \( \text{F}_2 \) have bond orders of 2 and 1. \( \text{C}_2 \) and \( \text{O}_2 \) both have bond orders of 2, and \( \text{C}_2 \) and \( \text{N}_2 \) have bond orders of 2 and 3, respectively.

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molecular Orbital Theory
Molecular Orbital Theory (MO Theory) is a method for describing the electronic structure of molecules. Unlike simpler models, MO theory considers electrons to be delocalized over the entire molecule rather than localized between individual atoms. In this theory, atomic orbitals combine to form molecular orbitals, which can be bonding or anti-bonding. Bonding orbitals lower the energy of the molecule and hence increase stability, while anti-bonding orbitals have the opposite effect. The difference in the number of electrons in these orbitals helps in determining various properties of the molecule, including bond order.
Bonding Electrons
Bonding electrons are those that occupy bonding molecular orbitals. These orbitals are formed by the constructive interference of atomic orbitals, which helps stabilize the molecule. In simpler terms, more bonding electrons usually mean a stronger bond. For example, in the molecule \( \text{N}_2 \), there are 10 bonding electrons, leading to a high bond order and a very stable molecule. Bonding electrons are counted as part of the equation used to determine bond order.
Anti-Bonding Electrons
Anti-bonding electrons are found in anti-bonding molecular orbitals. These orbitals result from the destructive interference of atomic orbitals, causing instability in the molecule. When anti-bonding electrons are present, they counteract the stabilizing influence of bonding electrons. For instance, in \( \text{F}_2 \), there are 8 anti-bonding electrons, making the bond weaker. Like bonding electrons, anti-bonding electrons are also used in the bond order equation, but they decrease the bond order.
Calculation of Bond Order
The bond order is a key indicator of the stability and strength of a bond in a molecule. It is calculated using the formula: \[ \text{Bond Order} = \frac{\left( \text{Number of Bonding Electrons} - \text{Number of Anti-Bonding Electrons} \right)}{2} \]. This formula shows the difference between the number of bonding and anti-bonding electrons, divided by two. For example, in \( \text{O}_2 \), there are 10 bonding and 6 anti-bonding electrons, giving a bond order of 2, which signifies a double bond. The higher the bond order, the stronger the bond, and hence greater the stability of the molecule.

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