Problem 121 - A Complete Resource Book in Chemistry for JEE Main

Question

The linear structure is seen in (i) \(\mathrm{SnCl}_{2}\) (ii) \(\mathrm{NCO}^{-}\) (iii) \(\mathrm{NO}_{2}\) (iv) \(\mathrm{CS}_{2}\) (a) (i), (ii) and (iii) (b) (ii), (iii) and (iv) (c) (i), (iii) and (iv) (d) none of these

Step-by-Step Solution

Answer

Option (b) includes the correct linear structures: NCO⁻ and CS₂.

Step 1: Understand the Concept of Linear Structures

Molecules with linear geometry have bond angles of 180 degrees. This often occurs in molecules of the type AX2, where the central atom A has no lone pairs, or when sp hybridization takes place with two substituents.

Step 2: Analyze the Structure of Each Compound

Let's analyze: 1. **SnCl₂**: Has a bent structure due to lone pairs on Sn, thus not linear. 2. **NCO⁻**: The ion is linear because the central N atom is sp hybridized. 3. **NO₂**: Typically bent due to lone electron pairs on nitrogen. 4. **CS₂**: The structure is symmetrical around C, creating a linear shape.

Step 3: Determine Which Compounds Are Linear

Based on our analysis: - **NCO⁻** is linear. - **CS₂** is also linear. **SnCl₂** and **NO₂** are not linear due to electron lone pairs.

Step 4: Choose the Correct Answer Based on Options

The linear structures are found in NCO⁻ and CS₂. Any option containing these: Looking at the options, (b) includes both **NCO⁻** and **CS₂** along with **NO₂**, which, however, doesn't affect the linearity aspect required in the right choice.

Key Concepts

Bond Angles

Bond angles are crucial in determining the shape of a molecule. For linear molecular geometries, a classic bond angle of 180 degrees is formed. This results in the atoms aligning in a straight line.
The bond angle reflects how the atoms in a molecule are spaced relative to one another. In the case of a linear molecule, no other angles can divide the 180 degrees that form between three atoms in a straight configuration.
For instance, in the case of the molecule \(NCO^{-}\), the central nitrogen atom allows the adjacent carbon and oxygen atoms to sit directly opposite each other, ensuring the molecule stretches out in a linear fashion due to the 180-degree bond angles. Thus, understanding bond angles helps predict the overall shape of the molecule and its geometric configuration.

sp Hybridization

Hybridization helps explain the geometrical arrangements of atoms in a molecule. Specifically, sp hybridization results in a linear structure with a bond angle of 180 degrees.
This occurs when one atom, like the central atom in \(NCO^{-}\) or \(CS_{2}\), has hybridized orbitals formed by the mixing of one s orbital and one p orbital. This combination forms two equivalent sp orbitals.

• sp hybridization is a hallmark for linear geometry, as the two sp orbitals align at opposite ends of the atom when bonding.
• Only two electron domains around the central atom lead to a linear shape.

Overall, sp hybridization is key to understanding why certain molecules adopt a linear structure, as seen in the compounds from the exercise.

Lone Pairs

Lone pairs are pairs of valence electrons that are not shared with another atom. They reside on the central atom of a molecule and can influence molecular shape.
Lone pairs can cause repulsion that affects bond angles and molecular geometry, often making structures bent instead of linear.
In molecules like \(SnCl_{2}\) and \(NO_{2}\), the presence of lone pairs on the central atom alters the expected geometry, prompting the molecules to take on a bent shape rather than a linear one.

• SnCl₂: Lone pairs on Sn push the bonded atoms closer, resulting in a bent geometry.
• NO₂: The single lone pair on N creates an uneven distribution of electron regions, leading to a bent structure.

Recognizing the presence and effect of lone pairs is essential for accurately predicting molecular shapes.

Molecular Shapes

Molecular shapes describe how atoms in a molecule are arranged spatially. Understanding these shapes involves considering factors like hybridization, bond angles, and lone pairs.
Linear molecular geometry is characterized by atoms arranged in a straight line. There's minimal repulsion when only bonding pairs are present, as observed in molecules like \(NCO^{-}\) and \(CS_{2}\).

• For linear shapes, the central atom is often sp hybridized, supporting a geometry where bonds emerge in opposite directions.
• Molecules may not always be linear if lone pairs create extra repulsion, causing them to adopt a bent geometry instead.

Identifying molecular shapes helps in predicting reactivity and physical properties, thus making it a vital aspect in the study of chemistry.