Problem 115 - A Complete Resource Book in Chemistry for JEE Main

Question

The correct order of increasing \(\mathrm{C}-\mathrm{O}\) bond length of \(\mathrm{CO}, \mathrm{CO}_{3}^{2-}, \mathrm{CO}_{2}\) is (a) \(\mathrm{CO}_{3}^{2-}<\mathrm{CO}_{2}<\mathrm{CO}\) (b) \(\mathrm{CO}_{2}<\mathrm{CO}_{3}^{2^{2}}<\mathrm{CO}\) (c) \(\mathrm{CO}<\mathrm{CO}_{3}^{2}-\mathrm{CO}_{2}\) (d) \(\mathrm{CO}<\mathrm{CO}_{2}<\mathrm{CO}_{3}^{2-}\)

Step-by-Step Solution

Answer

The correct order is (d) CO < CO2 < CO3^{2-}.

Step 1: Understanding Bond Length

Bond length is the distance between the nuclei of two bonded atoms. Generally, in molecules, single bonds are longer than double bonds, which in turn are longer than triple bonds. Therefore, when evaluating bond lengths in molecular structures, particularly for C-O bonds, it's important to consider the bond types.

Step 2: Analyzing CO Bond

The molecule CO contains a triple bond between carbon and oxygen. Triple bonds are the strongest and shortest compared to double and single bonds. Therefore, the C-O bond in CO is the shortest.

Step 3: Analyzing CO2 Bond

The molecule CO_2 contains double bonds between the carbon and each oxygen atom. Since double bonds are longer than triple bonds but shorter than single bonds, the C-O bond length in CO_2 is longer than in CO, but shorter than a single bond.

Step 4: Analyzing CO3^2- Bond

In the carbonate ion CO_3^{2-}, the C-O bonds are resonance hybrids between double and single bonds. This situation results in average bond length that is longer than a double bond, but shorter than a single bond. Thus, the C-O bond in CO_3^{2-} is the longest among the three specimens mentioned.

Step 5: Arranging the Bond Lengths

After analyzing the bond types in each molecule, the order of increasing C-O bond lengths is: CO (triple bond shortest) < CO_2 (double bond in between) < CO_3^{2-} (resonance average longest).

Step 6: Choosing the Correct Option

From the given options, the order CO < CO_2 < CO_3^{2-} matches our analysis of the increasing C-O bond lengths. Thus, option (d) is correct.

Key Concepts

Resonance Structures

Resonance structures are an important concept in understanding molecular phenomena. They represent different versions of the same molecule, showcasing how electrons can be distributed within a molecule's bonds. It's like having multiple blueprints for the same house, each looking slightly different. In actuality, the molecule doesn't switch between these structures but rather is best described as a resonance hybrid, taking characteristics from all possible structures.

In the case of the carbonate ion (\( ext{CO}_3^{2-}\)), resonance plays a key role. Instead of having fixed single or double bonds, the molecule shares its \( ext{C-O}\)bonds among three equivalent forms, resulting in a bond length that is a mix between a single and double bond. This equal distribution helps minimize the energy of the molecule, leading to a more stable structure.

Molecular Structure

Molecular structure is the three-dimensional arrangement of atoms in a molecule, influencing properties like bond length and angles. The geometry of a molecule determines how atoms are positioned relative to one another, which directly affects the molecule's chemical and physical properties.

The structure of \( ext{CO}_2\)is linear, with carbon in the middle and oxygen atoms on either side. This arrangement forms double bonds, contributing to specific bond lengths and reactivity patterns. On the other hand, the carbonate ion (\( ext{CO}_3^{2-}\)) has a planar triangular shape due to its resonance structure. These factors in molecular geometry influence not only the bond lengths but also how the molecules interact with other compounds.

Chemical Bonding

Chemical bonding refers to the interaction that holds atoms together within a molecule. There are several types of bonds, such as single, double, and triple bonds, each differing in the number of shared electron pairs. This bond strength and character significantly impact the bond length between atoms.

In the molecule \( ext{CO}\), the carbon and oxygen are joined by a triple bond, involving the sharing of three pairs of electrons. This type of bond is strong and results in a shorter bond length. Meanwhile, in \( ext{CO}_2\), double bonds exist between the carbon and oxygen atoms, leading to a relatively shorter bond length than single bonds but longer than triple bonds. Understanding these types of bonds helps clarify why different molecules have varying bond lengths.

Bond Type Analysis

Bond type analysis involves studying the nature and number of bonds within a molecule to understand the bond lengths and strengths. By analyzing the bond types, we can predict the physical properties and reactivity patterns of molecules.

For instance, considering the bond lengths in \( ext{CO}, \ ext{CO}_2, \ ext{and} \ ext{CO}_3^{2-}\), one can observe that the triple bond in \( ext{CO}\) results in the shortest bond. \( ext{CO}_2\) has double bonds, leading to intermediate bond lengths. Lastly, the \( ext{CO}_3^{2-}\) ion forms a model case for studying resonance effects. Its bonds, being a blend due to resonance, end up having longer lengths than the other two molecules. This analysis helps create a deeper understanding of molecular properties and interactions.