Problem 39 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The molecule that has linear structure is (a) \(\mathrm{CO}_{2}\) (b) \(\mathrm{NO}_{2}\) (c) \(\mathrm{SO}_{2}\) (d) \(\mathrm{SiO}_{2}\)

Step-by-Step Solution

Answer

The linear molecule is \( \mathrm{CO}_2 \).

Step 1: Identify Molecule Structure

To determine which molecule has a linear structure, we need to analyze the molecular geometry of each given molecule based on its electron pairs and the atoms bonded to the central atom.

Step 2: Analyze Molecular Geometry of CO2

The \(\mathrm{CO}_{2}\) molecule has a central carbon atom double-bonded to two oxygen atoms. It has no lone pairs, resulting in a linear shape due to the repulsion between the double bonds, leading to a bond angle of 180°.

Step 3: Analyze Molecular Geometry of NO2

The \(\mathrm{NO}_{2}\) molecule has a central nitrogen atom bonded to two oxygen atoms with one lone electron present. This creates a bent shape due to the presence of an unpaired electron which distorts the linear geometry.

Step 4: Analyze Molecular Geometry of SO2

In \(\mathrm{SO}_{2}\), the central sulfur atom is double-bonded to two oxygen atoms and has one lone pair of electrons. This lone pair creates an asymmetry, leading to a bent shape rather than linear.

Step 5: Analyze Molecular Geometry of SiO2

The \(\mathrm{SiO}_{2}\) can be represented by multiple \(\mathrm{Si-O}\) Si-O (silicon dioxide) linkages in a network. In its simplest form, each \(\mathrm{Si}\) is surrounded by oxygen in a tetrahedral arrangement, thus not categorized as linear.

Step 6: Determine the Linear Molecule

From the analysis, \(\mathrm{CO}_{2}\) is the only molecule that exhibits a linear geometry due to its symmetrical arrangement without lone pairs affecting the bond angles.

Key Concepts

Linear Structure

Molecules that have a linear structure are those that form a straight line in their geometric shape. This occurs when a central atom is connected to two other atoms and there are no lone electron pairs skewing the structure. In a linear molecule, all atoms are positioned in a straight line, resulting in specific bond angles.
The case of \(\mathrm{CO}_2\) is a classic example. Here, the carbon atom makes double bonds with two oxygen atoms, forming a structure with 180° bond angles, without any lone electron pairs that might distort its geometry. This straight-line formation gives it its linear characteristic.
Linear structures are typically straightforward and symmetric, which allows the molecule to adopt a minimal-energy state by minimizing lone pair repulsion effects. Hence, molecules like \(\mathrm{CO}_2\) maintain a linear geometry under these conditions.

Electron Pair Geometry

The electron pair geometry of a molecule provides insight into the spatial arrangement of all electron pairs around a central atom, including both bonding and lone pairs. This concept is guided by the VSEPR (Valence Shell Electron Pair Repulsion) theory, which helps predict how electron pairs are positioned to minimize repulsion.

• For \(\mathrm{CO}_2\), the electron pair geometry is linear because it includes only the bonding electron pairs, resulting in no lone pairs affecting the spatial organization.
• However, for \(\mathrm{NO}_2\) and \(\mathrm{SO}_2\), the presence of lone pairs causes the electron pairs to repel more strongly, altering the geometry from linear to bent.

The significance of understanding electron pair geometry lies in predicting and explaining molecular shape variations and how nonbonding electrons influence the overall molecular structure.

Bond Angles

Bond angles are a crucial aspect of molecular geometry. They determine the angle formed between two adjacent bonds at an atom. In molecules with a linear structure, such as \(\mathrm{CO}_2\), bond angles are typically 180°, providing a straight path.
Unlike linear structures, molecules like \(\mathrm{NO}_2\) and \(\mathrm{SO}_2\) have smaller bond angles due to the influence of lone electron pairs. These lone pairs exert additional repulsion, causing the bonded atoms to come closer together and change the angle from the ideal 180° to a smaller value. This results in bent or angular structures.
Understanding bond angles is essential as they directly affect the shape and chemical behavior of the molecule, impacting properties like polarity and reactivity.