Problem 41 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

$$ \mathrm{CO}_{2} \text { is isostructural with : } $$ (a) \(\mathrm{HgCl}_{2}\) (b) \(\mathrm{SnCl}_{2}\) (c) \(\mathrm{C}_{2} \mathrm{H}_{2}\) (d) \(\mathrm{NO}_{2}\)

Step-by-Step Solution

Answer

(a) \(\mathrm{HgCl}_{2}\) and (c) \(\mathrm{C}_{2}\text{H}_{2}\) are isostructural with \(\text{CO}_{2}\).

Step 1: Definition of Isostructural Compounds

Two compounds are considered isostructural if they have the same molecular geometry or structure. We need to determine the molecular structure of each compound and compare it with that of \(\text{CO}_{2}\).

Step 2: Determine Structure of CO2

The molecule \(\text{CO}_{2}\) has a linear structure due to the central carbon atom forming double bonds with each oxygen atom. This gives it a bond angle of 180 degrees.

Step 3: Analyze Structure of HgCl2

The molecule \(\text{HgCl}_{2}\) is also linear. It consists of a central mercury atom bonded to two chlorine atoms, with a bond angle of 180 degrees.

Step 4: Analyze Structure of SnCl2

The molecule \(\text{SnCl}_{2}\) has a bent or angular geometry, not a linear structure. The bond angle is less than 180 degrees due to the lone pair on Sn, so it is not isostructural with \(\text{CO}_{2}\).

Step 5: Analyze Structure of C2H2

The molecule \(\text{C}_{2}\text{H}_{2}\) (also known as acetylene) is linear. It has a carbon-carbon triple bond and each carbon atom is bonded to a hydrogen atom, giving it a linear structure with 180-degree angles.

Step 6: Analyze Structure of NO2

The molecule \(\text{NO}_{2}\) is bent or angular due to the lone pair on the nitrogen atom, leading to a bond angle less than 180 degrees. Thus, it is not isostructural with \(\text{CO}_{2}\).

Step 7: Conclusion

Among the given options, \(\mathrm{HgCl}_{2}\) and \(\mathrm{C}_{2}\text{H}_{2}\) have a linear structure like \(\text{CO}_{2}\). Both are isostructural with \(\text{CO}_{2}\).

Key Concepts

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. It's crucial for determining how molecules interact and behave. The geometry can largely affect the physical and chemical properties of a compound.

• Different types of geometries include linear, bent, tetrahedral, trigonal planar, and more.
• The molecular geometry of a molecule is often predicted using the VSEPR (Valence Shell Electron Pair Repulsion) theory. This theory states that electron pairs around a central atom tend to orient themselves as far apart as possible to minimize repulsion.

The geometry is pivotal in understanding isostructural compounds, where similar arrangements indicate the same type of geometry in different molecules.

Linear Structure

A linear structure occurs when atoms are arranged in a straight line. This geometry is characterized by a bond angle of 180 degrees, meaning it is as stretched out as possible.

• Linear structures are simple yet important, as they reduce complex molecular interactions down to a straightforward model.
• Classic examples of linear molecules include carbon dioxide (\( ext{CO}_2 \)) and acetylene (\( ext{C}_2 ext{H}_2 \)).

The arrangement of bonds in these molecules allows for unique chemical properties, such as the ability of acetylene to combust easily due to its straightforward structure.

Bond Angles

Bond angles determine the positioning of atoms around a central atom. They play a crucial role in shaping the geometry of a molecule.

• A bond angle refers to the angle formed between two adjacent bonds at an atom.
• For example, a bond angle of 180 degrees results in a linear geometry.

In contrast, smaller bond angles, such as those in water (\( ext{H}_2 ext{O} \)), result in bent structures due to electron pair repulsion. Understanding bond angles helps explain why certain molecules like \( ext{SnCl}_{2} \) are not linear and thus not isostructural with \( ext{CO}_2 \).

Structural Isomerism

Structural isomerism involves compounds with the same molecular formula but different arrangements of atoms, resulting in varied structures and properties. It's important not to confuse this with isostructural compounds, which have the same geometry rather than the same formula.

• Isomers have identical molecular formulas but diverge significantly in their properties.
• Isostructural compounds like \( ext{CO}_2 \), \( ext{HgCl}_2 \), and \( ext{C}_2 ext{H}_2 \) share a linear structure, yet they can exist with different chemical behaviors if their atomic compositions differ.

While structural isomerism focuses on formulaic identity with different structures, being isostructural underscores having the same geometrical form, which is pivotal in assessing molecular behavior and interaction.