Problem 216 - A Complete Resource Book in Chemistry for JEE Main

Question

The speces in which the atom is in a state of sphybridization is? (a) \(\mathrm{NO}_{2}^{-}\) (b) \(\mathrm{NO}_{3}^{-}\) (c) \(\mathrm{NO}_{2}\) (d) \(\mathrm{NO}_{2}^{+}\)

Step-by-Step Solution

Answer

The species with \( \mathrm{sp} \) hybridization is \( \mathrm{NO}_{2}^{+} \).

Step 1: Understanding Hybridization

Hybridization involves mixing atomic orbitals to form new hybrid orbitals suitable for pairing of electrons to form chemical bonds. To find the hybridization of a molecule, we first need to determine the central atom's steric number, which is the sum of bonded atoms and lone pairs of electrons around it.

Step 2: Analyzing \( \mathrm{NO}_{2}^{-} \)

For \( \mathrm{NO}_{2}^{-} \), the central atom is nitrogen (N). It has two bonded oxygen atoms and one lone pair, making the steric number 3 (2 oxygen atoms + 1 lone pair). A steric number of 3 corresponds to \( \mathrm{sp}^2 \) hybridization.

Step 3: Analyzing \( \mathrm{NO}_{3}^{-} \)

For \( \mathrm{NO}_{3}^{-} \), nitrogen forms 3 bonds with oxygen atoms and has no lone pairs. This gives a steric number of 3 (3 oxygen atoms + 0 lone pairs), indicating \( \mathrm{sp}^2 \) hybridization.

Step 4: Analyzing \( \mathrm{NO}_{2} \)

In \( \mathrm{NO}_{2} \), nitrogen has two bonds with oxygen and one lone electron (not a lone pair), corresponding to a steric number of 2, which suggests \( \mathrm{sp} \) hybridization. However, due to the presence of a radical electron, consider that the effective hybridization can be slightly different in practice but structurally behaves like \( \mathrm{sp}^2 \).

Step 5: Analyzing \( \mathrm{NO}_{2}^{+} \)

For \( \mathrm{NO}_{2}^{+} \), nitrogen forms two bonds with oxygen and has no lone pairs. This gives a steric number of 2 (2 bonds + 0 lone pairs), indicating \( \mathrm{sp} \) hybridization.

Step 6: Conclusion

From the analysis, \( \mathrm{NO}_{2} \) and \( \mathrm{NO}_{3}^{-} \) have \( \mathrm{sp}^2 \) hybridization. \( \mathrm{NO}_{2}^{-} \) has \( \mathrm{sp}^2 \) hybridization, and \( \mathrm{NO}_{2}^{+} \) has \( \mathrm{sp} \) hybridization. Therefore, the species with \( \mathrm{sp} \) hybridization is \( \mathrm{NO}_{2}^{+} \).

Key Concepts

Atomic Orbitals

Atomic orbitals are regions around an atom's nucleus where electrons are likely to be found. These orbitals are mathematical functions that describe the wave-like behavior of single electrons or pairs of electrons around atoms. Each orbital can hold a maximum of two electrons with opposite spins.
There are several types of atomic orbitals, each with a unique shape:

• s Orbitals: Spherical in shape and can hold up to two electrons.
• p Orbitals: Dumbbell-shaped with three orientations, each holding two electrons, for a total of six electrons.
• d Orbitals: More complex shapes, with five orientations, accommodating up to ten electrons.
• f Orbitals: Even more complex, with seven orientations, holding up to fourteen electrons.

For hybridization, atomic orbitals can combine to form hybrid orbitals, which are more effective in forming chemical bonds. These hybrid orbitals better explain molecular geometry and properties of molecules.

Chemical Bonds

Chemical bonds are the links between atoms in a molecule. These bonds hold atoms together and result from the interaction of electrons between atoms. There are three primary types of chemical bonds:

• Ionic Bonds: These are formed when electrons are transferred from one atom to another, resulting in oppositely charged ions that attract each other.
• Covalent Bonds: These are the most common types in organic and biological molecules, formed when atoms share pairs of electrons.
• Metallic Bonds: These involve the sharing of electrons among a lattice of atoms, typical in metals.

Hybridization plays a significant role in covalent bonds, as the mixing of atomic orbitals allows the shared electrons to be more effectively distributed, providing stability and specific geometry to the molecule. Understanding chemical bonds is crucial for predicting the structure and reactivity of substances.

Steric Number

The steric number is an essential concept in predicting the hybridization state of atoms in molecules. It helps to determine how many hybrid orbitals an atom will use. Basically, the steric number is the sum of the number of atoms bonded to the central atom and the number of lone pairs of electrons around it.
Here's how it works:

• Steric Number of 2: Indicates the need for two orbitals, typically resulting in \( sp \) hybridization.
• Steric Number of 3: Results in three orbitals, which is \( sp^2 \) hybridization.
• Steric Number of 4: Uses four orbitals, leading to \( sp^3 \) hybridization.

By calculating the steric number, one can predict the hybridization type, which in turn informs you about the molecule's shape and bond angles. For instance, in the given solutions, the steric number guides us to understand why \( \mathrm{NO}_2^- \) adopts \( sp^2 \) hybridization and \( \mathrm{NO}_2^+ \) maintains an \( sp \) hybridization. This understanding is essential for visualizing molecular geometry accurately.