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

The linear structures are in (b) (ii), (iii) and (iv).

Step 1: Identify Linear Molecules

A linear molecule is one where the atoms are arranged in a straight line, often resulting in bond angles of 180 degrees. For example, molecules like carbon dioxide (CO2) are linear.

Step 2: Examine SnCl₂

SnCl₂ has a bent structure due to the presence of a lone pair on the central Sn atom, resulting in a bond angle of less than 180 degrees.

Step 3: Examine NCO⁻ Ion

The NCO⁻ ion has a linear structure as the atoms are in a straight line due to sp hybridization, giving it a bond angle of 180 degrees.

Step 4: Examine NO₂⁺ Ion

NO₂⁺ (nitronium ion) is also linear due to sp hybridization of the nitrogen atom, which leads to bond angles of 180 degrees.

Step 5: Examine CS₂

CS₂ is linear because the central carbon is sp hybridized, resulting in bond angles of 180 degrees.

Step 6: Determine the Correct Answer

Based on the linear structures identified, NCO⁻, NO₂⁺, and CS₂ are linear. Therefore, the correct choice is those molecules listed under option (b) - (ii), (iii) and (iv).

Key Concepts

Linear Molecules

Linear molecules are those in which atoms are arranged in a straight line. This geometric arrangement leads to a bond angle of exactly 180 degrees, producing a distinct straight-line appearance. Molecules achieve this structure when specific conditions like symmetrical charge distribution across the molecule are met.
Understanding linear molecules is crucial as they are one of the simplest molecular formations, often serving as a foundation for more complex molecular geometry learning. For instance:

• In the NCO⁻ ion, the atoms are aligned linearly, forming a bond angle of 180 degrees, cementing its classification as a linear molecule.
• The nitronium ion, NO₂⁺, also follows a linear structure due to the ideal bonding conditions produced by its electronic configuration.
• In compounds like CS₂, the central carbon atom aligns with surrounding atoms in a linear arrangement.

Recognizing these traits will make it easier to identify other linear molecules in more complex chemistry problems.

sp Hybridization

sp hybridization is a fundamental concept explaining how atoms form linear molecules. It's a process where one s orbital and one p orbital combine to create two new equivalent orbitals known as sp hybrid orbitals. Each of these orbitals can form a bond, explaining the linear alignment of atoms.

For instance, in the NCO⁻ ion and CS₂ molecule, the central atoms utilize sp hybridization:

• This allows the orbitals to arrange themselves in a linear fashion, minimizing electron pair repulsions and leading to 180-degree bond angles.
• sp hybridization is directly linked to creating the linear geometry, significantly impacting how these molecules interact and react with other substances.
  

Understanding how sp hybridization works is essential for predicting and explaining the behavior of linear molecules.

Bond Angles

Bond angles are the angles between adjacent lines representing bonds. They are significant as they dictate the molecule's spatial arrangement and directly influence the molecule's chemical properties.

In linear molecules such as NO₂⁺, NCO⁻, and CS₂, the bond angles are crucial:

• Each of these molecules has a bond angle of exactly 180 degrees—a hallmark feature of linear geometry.
• Bond angles help distinguish between different molecular geometries, such as linear, bent, or trigonal planar, by providing insight into how atoms are spaced in a molecule.
  

A clear grasp of bond angles helps in understanding the steric and electronic considerations that lead to particular molecular forms, making them a vital aspect of molecular geometry.