Problem 18 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following species has a linear shape? (a) \(\mathrm{NO}_{2}^{+}\) (b) \(\mathrm{O}_{3}\) (c) \(\mathrm{NO}_{2}^{-}\) (d) \(\mathrm{SO}_{2}\)

Step-by-Step Solution

Answer

\( \mathrm{NO}_{2}^{+} \) has a linear shape.

Step 1: Understanding VSEPR Theory

VSEPR (Valence Shell Electron Pair Repulsion) theory is used to predict the shape of molecules. The premise is that electron pairs around a central atom will arrange themselves to be as far apart as possible to minimize repulsion.

Step 2: Determine Electron Domains for Each Species

Calculate the electron domains (bonding and non-bonding pairs) for each molecule to determine their shape according to VSEPR theory. Electron domains include both bonding pairs (bonds to neighboring atoms) and lone pairs on the central atom.

Step 3: Analyze \\( \mathrm{NO}_{2}^{+} \\\)

The \( \mathrm{NO}_{2}^{+} \) ion has a nitrogen atom as its central atom. It forms double bonds with two oxygen atoms, resulting in two bonding domains and no lone pairs on the nitrogen atom, thus having a linear shape.

Step 4: Analyze \\( \mathrm{O}_{3} \\\)

The \( \mathrm{O}_{3} \) molecule (ozone) has three oxygen atoms. The central oxygen has one double bond, one single bond, and one lone pair. This results in a bent shape due to the lone pair.

Step 5: Analyze \\( \mathrm{NO}_{2}^{-} \\\)

In \( \mathrm{NO}_{2}^{-} \), the nitrogen is the central atom with one lone pair and two nitrogen-oxygen bonds. The lone pair causes repulsion, giving the molecule a bent shape.

Step 6: Analyze \\( \mathrm{SO}_{2} \\\)

For \( \mathrm{SO}_{2} \), the sulfur atom is central with two double bonds and one lone pair, leading to a bent molecular shape due to the lone pair repulsion.

Key Concepts

Molecular Geometry

Molecular geometry is the three-dimensional arrangement of atoms within a molecule. It plays a crucial role in determining the chemical properties and reactivity of a substance. To predict molecular geometry, we often turn to the VSEPR theory (Valence Shell Electron Pair Repulsion theory). This theory suggests that electron pairs around the central atom tend to spread out as far as possible to minimize repulsive interactions.

For instance, species like the nitrate ion \( \mathrm{NO}_{2}^{+} \) demonstrate a linear geometry. Here, the central nitrogen atom forms two bonds with oxygen atoms. The lack of lone pairs on the nitrogen allows the bonding pairs to adopt a linear arrangement, balancing out repulsion. In contrast, when lone pairs are involved, as seen in many other species such as \( \mathrm{O}_{3} \), the electron repulsion is not symmetrical. This results in distortions, leading to bent shapes.

Electron Domains

Electron domains are all the regions around the central atom where electrons are located. These regions include both bonding pairs, which are electrons shared between atoms, and lone pairs, which are electrons that are not shared and belong only to the central atom.

To determine the number of electron domains, one must consider:

• Bonding domains - each single, double, or triple bond counts as one domain regardless of how many electrons are shared.
• Lone pairs - each pair of non-bonding electrons counts as one domain.

By examining these domains, we can predict molecular geometry using the VSEPR model. For example, in \( \mathrm{SO}_{2} \), there are three electron domains around the central sulfur - two bonding pairs (from the double bonds) and one lone pair. This configuration results in a bent molecular shape.

Lone Pairs

Lone pairs are pairs of valence electrons that are not shared with other atoms and are instead localized on the central atom in a molecule. Although they don't directly participate in bonding, they are essential in shaping the geometry of a molecule due to their repulsive effects.

Lone pairs tend to occupy more space than bonding pairs because they are closer to the nucleus, and suffer fewer restraints. This increased space needed by lone pairs leads to greater repulsion upon adjacent electron domains, which can distort the shape of the molecule away from what would be expected if only bonding pairs were present.

For example, consider \( \mathrm{NO}_{2}^{-} \), which contains a lone pair on the nitrogen. Although it has two nitrogen-oxygen bonds, this lone pair's repulsion causes the geometry to deviate from linear to bent. Understanding the influence of lone pairs is crucial for accurately predicting and explaining the shape of molecules in chemistry.