Problem 153 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following species have bond order \(3 ?\) (a) \(\mathrm{CN}^{-}\) (b) \(\mathrm{O}_{2}^{-}\) (c) \(\mathrm{NO}^{+}\) (d) \(\mathrm{CO}\)

Step-by-Step Solution

Answer

The species with bond order 3 are \(\mathrm{CN}^{-}\), \(\mathrm{NO}^{+}\), and \(\mathrm{CO}\).

Step 1: Understand Bond Order

Bond order is the number of chemical bonds between a pair of atoms. It can be determined using molecular orbital theory by calculating the difference between the number of bonding and antibonding electrons, divided by two: \(\text{Bond Order} = \frac{\text{Number of bonding electrons} - \text{Number of antibonding electrons}}{2}.\)

Step 2: Bond Order of CN^-

For \(\mathrm{CN}^{-}\), the molecular orbital configuration is similar to \(\mathrm{N}_{2}\) due to similar electronic structures, adding an extra electron. The electron configuration is \((\sigma_{1s})^2(\sigma_{1s}^*)^2(\sigma_{2s})^2(\sigma_{2s}^*)^2(\pi_{2p})^4(\sigma_{2p})^2\). This gives: \(10\) bonding electrons and \(4\) antibonding electrons. Thus, bond order is \(\frac{10-4}{2} = 3\).

Step 3: Bond Order of O2^-

\(\mathrm{O}_{2}^{-}\) has an extra electron compared to \(\mathrm{O}_{2}\). The molecular configuration becomes \((\sigma_{1s})^2(\sigma_{1s}^*)^2(\sigma_{2s})^2(\sigma_{2s}^*)^2(\sigma_{2p_z})^2(\pi_{2p_x})^2(\pi_{2p_y})^2(\pi_{2p_x}^*)^2(\pi_{2p_y}^*)^1\). This configuration results in \(10\) bonding electrons and \(7\) antibonding electrons, giving a bond order of \(\frac{10-7}{2} = 1.5\).

Step 4: Bond Order of NO^+

For \(\mathrm{NO}^{+}\), remove one electron from the neutral \(\mathrm{NO}\) system. The electron configuration is \((\sigma_{1s})^2(\sigma_{1s}^*)^2(\sigma_{2s})^2(\sigma_{2s}^*)^2(\sigma_{2p})^2(\pi_{2p})^4\). Counting gives: \(10\) bonding electrons and \(4\) antibonding electrons. Thus, bond order is \(\frac{10-4}{2} = 3\).

Step 5: Bond Order of CO

\(\mathrm{CO}\) has an electron configuration similar to \(\mathrm{N}_{2}\): \((\sigma_{1s})^2(\sigma_{1s}^*)^2(\sigma_{2s})^2(\sigma_{2s}^*)^2(\sigma_{2p})^2(\pi_{2p})^4\). Here we have \(10\) bonding electrons and \(4\) antibonding electrons, resulting in a bond order of \(\frac{10-4}{2} = 3\).

Key Concepts

Molecular Orbital Theory

The Molecular Orbital Theory is a fundamental concept in understanding the behavior of electrons in molecules. It helps us determine the bond order of a molecule, which indicates the strength and stability of the chemical bond.
This theory combines atomic orbitals to form new orbitals called molecular orbitals. These are either lower in energy (bonding orbitals) or higher in energy (antibonding orbitals) than the original atomic orbitals. Each of these molecular orbitals can hold a maximum of two electrons, just like atomic orbitals, but the orbitals now are spread over the entire molecule rather than being confined to a single atom.

• Bonding orbitals increase electron density between atoms and stabilize the molecule.
• Antibonding orbitals, identified with an asterisk (*), decrease electron density between atoms and destabilize the molecule.

The bond order, calculated by subtracting the number of electrons in antibonding orbitals from those in bonding orbitals and dividing by two, provides insight into the number of chemical bonds and the stability of a molecule.
A higher bond order generally means a more stable and stronger bond.

Chemical Bonding

Chemical bonding is the force that holds atoms together to form molecules or compounds. It is crucial in determining the properties and behaviors of substances.
There are several types of chemical bonds, with covalent and ionic bonds being the most common. But Molecular Orbital Theory enables us to explore chemical relationships beyond the simplicity of individual bonds. By examining how electrons are distributed over molecular orbitals, we better understand not only how atoms link but also how their bonds compare in terms of strength and stability.

• Covalent bonds form when two atoms share one or more pairs of valence electrons, resulting in a stable balance of attractive and repulsive forces.
• Molecular Orbital Theory helps to quantify these interactions via the bond order metric.

In the case of the exercises given, analyzing molecules like CN^-, O₂^-, NO⁺, and CO, using the bond order concept allows us to predict molecular properties and reactivity.

Electron Configuration

Electron configuration is a method used to describe the distribution of electrons in an atom or molecule according to the principles of quantum mechanics. For molecules, it plays a critical role in determining chemical properties, including bond order.
In molecular systems, the electron configuration extends beyond individual atoms to the molecular level, where we determine how electrons fill available molecular orbitals. The filling order of these orbitals was shown in the exercise examples:

• The CN^- ion closely resembles N₂, except for one added electron that results in a bond order of 3.
• For O₂^-, adding an electron to O₂ shifts the electron configuration to lower the bond order to 1.5.
• Both NO⁺ and CO demonstrate bond orders of 3, showing similar electronic environments.

Applying these configurations helps students understand how atoms form bonds and predict the stability of those bonds in molecules.