Problem 125 - A Complete Resource Book in Chemistry for JEE Main

Question

Consider the following statements: 1\. the bond order of \(\mathrm{NO}\) is \(2.5\) 2\. the bond order of \(\mathrm{NO}^{+}\)is 3 3\. the bond order of \(\mathrm{O}_{2}\) is \(1.5\) 4\. the bond order of \(\mathrm{CO}\) is 3 Which of these statements are correct? (a) 1,2 and 3 (b) 2,3 and 4 (c) 1,3 and 4 (d) 1,2 and 4

Step-by-Step Solution

Answer

Option (d) is correct: statements 1, 2, and 4 are correct.

Step 1: Understanding Bond Order

Bond order refers to the number of chemical bonds between a pair of atoms. Typically, bond order is deduced from the molecular orbital theory. For diatomic molecules or ions, bond order influences the molecule's stability: higher bond orders generally indicate more stable molecules.

Step 2: Calculate Bond Order of \(\mathrm{NO}\)

For \(\mathrm{NO}\), the electron configuration is such that the molecular orbitals filled are \(\sigma_2s^2\sigma^*_{2s}^2\sigma_{2p_z}^2\pi_{2p_x}^2=\pi_{2p_y}^2\pi^*_{2p_x}^1\). This gives a bond order of \((8-3)/2 = 2.5\). Statement 1 is correct.

Step 3: Calculate Bond Order of \(\mathrm{NO}^{+}\)

In \(\mathrm{NO}^{+}\), one electron is removed from the \(\mathrm{NO}\) molecule. The molecular orbital configuration becomes \(\sigma_2s^2\sigma^*_{2s}^2\sigma_{2p_z}^2\pi_{2p_x}^2\pi_{2p_y}^2\). This gives a bond order of \((8-2)/2 = 3\). Statement 2 is correct.

Step 4: Calculate Bond Order of \(\mathrm{O}_2\)

The electron configuration of \(\mathrm{O}_{2}\) leads to molecular orbitals being filled as \(...\pi_{2p_x}^2\pi_{2p_y}^2\pi^*_{2p_x}^1\pi^*_{2p_y}^1\). The bond order is \((10-6)/2 = 2\). Statement 3 is incorrect since it should state a bond order of 2.

Step 5: Calculate Bond Order of \(\mathrm{CO}\)

\(\mathrm{CO}\) has the electron configuration leading to a bond order of \((8-2)/2=3\). Therefore, the bond order for \(\mathrm{CO}\) is indeed 3. Statement 4 is correct.

Step 6: Review Correct Statements

From the calculations, statements 1, 2, and 4 are correct because they accurately reflect the bond orders of \(\mathrm{NO}\), \(\mathrm{NO}^{+}\), and \(\mathrm{CO}\) respectively.

Step 7: Choose the Correct Option

The correct statements are 1, 2, and 4, matching option (d). Therefore, option d is the right choice.

Key Concepts

Molecular Orbital Theory

Molecular Orbital Theory is an essential concept in understanding the formation and characteristics of molecules. Unlike the simpler Lewis structure approach, which focuses on valence electrons in fixed positions, Molecular Orbital (MO) Theory examines the combination of atomic orbitals that span across the entire molecule. These combinations create molecular orbitals, which can hold electron pairs.
Molecular orbitals are categorized into bonding and antibonding types. Bonding orbitals, denoted as low-energy, stabilize a molecule by holding the atoms together. Antibonding orbitals, on the other hand, are higher energy and can destabilize a molecule.

• Each molecular orbital can hold up to two electrons.
• Electrons fill the orbitals starting from the lowest energy levels.
• The presence of more electrons in bonding orbitals compared to antibonding orbitals typically leads to a stable molecule.

This theory is crucial for accurately predicting molecular properties such as bond order and magnetism. By analyzing how electrons fill these molecular orbitals, chemists can determine whether a molecule is likely to exist and stay intact.

Chemical Bonds

Chemical bonds are the glue that holds atoms together in molecules, forming distinct substances with unique properties. There are several types of chemical bonds, including covalent, ionic, and metallic bonds, but here we focus mainly on covalent bonds and their evaluation through bond orders.
In the realm of diatomic molecules, bond orders demonstrate the number of shared electron pairs between two atoms. For instance, a bond order of three means that the atoms are connected by a triple bond, indicating three shared pairs of electrons, as seen in carbon monoxide (CO).

• Bond order = (Number of electrons in bonding orbitals - Number of electrons in antibonding orbitals) / 2.
• Higher bond orders suggest stronger bonds and shorter bond lengths.
• Determining bond order is essential for predicting the strength and length of the bond as well as the chemical reactivity.

Chemical bonds and their characteristics are foundational in fields ranging from materials science to pharmaceuticals, affecting how substances react and interact.

Stability of Molecules

The stability of molecules is a fundamental concept in chemistry, indicating how likely a molecule is to maintain its structure without decomposing. Several factors determine molecular stability, such as bond order, electron configuration, and the presence of lone pairs of electrons.
Molecules with higher bond orders tend to be more stable due to stronger, more numerous connections between atoms. This principle reflects on molecular longevity and how molecules respond under varying conditions.

• Stability is enhanced if the molecule has filled bonding orbitals.
• Lowers the energy of the molecule, making it less reactive in some situations.
• External factors like temperature and pressure can influence stability by providing energy for potential reactions.

Understanding molecular stability helps chemists design new compounds that resist decomposition and have desired reactivity characteristics, which is especially valuable in designing drugs and materials.