Problem 110 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following are isoelectronic and isostructural? \(\mathrm{NO}_{3}^{-}, \mathrm{CO}_{3}^{-2}, \mathrm{ClO}_{3}^{-}, \mathrm{SO}_{3}\) (a) \(\mathrm{NO}_{3}^{-}, \mathrm{CO}_{3}^{-2}\) (b) \(\mathrm{SO}_{3}, \mathrm{NO}_{3}^{-}\) (c) \(\mathrm{ClO}_{3}^{-}, \mathrm{CO}_{3}^{-2}\) (d) \(\mathrm{CO}_{3}^{-2}, \mathrm{SO}_{3}\)

Step-by-Step Solution

Answer

(a) \(\mathrm{NO}_3^-\) and \(\mathrm{CO}_3^{2-}\) are isoelectronic and isostructural.

Step 1: Understand the Concept of Isoelectronic and Isostructural

Isoelectronic species have the same number of electrons. Isostructural species have the same structural shape or geometry. To determine isoelectronic and isostructural pairs, we need to calculate the total number of electrons and assess their geometry.

Step 2: Calculate Electrons in Each Species

- 1. **\(\mathrm{NO}_3^-\):** - Nitrogen: 7 - Oxygen: 3 x 8 = 24 - Charge (-1): +1 electron - Total: 7 + 24 + 1 = 32 electrons. 2. **\(\mathrm{CO}_3^{2-}\):** - Carbon: 6 - Oxygen: 3 x 8 = 24 - Charge (-2): +2 electrons - Total: 6 + 24 + 2 = 32 electrons. 3. **\(\mathrm{ClO}_3^-\):** - Chlorine: 17 - Oxygen: 3 x 8 = 24 - Charge (-1): +1 electron - Total: 17 + 24 + 1 = 42 electrons. 4. **\(\mathrm{SO}_3\):** - Sulfur: 16 - Oxygen: 3 x 8 = 24 - Total: 16 + 24 = 40 electrons.

Step 3: Determine Electron Matches

From Step 2, we find that both \(\mathrm{NO}_3^-\) and \(\mathrm{CO}_3^{2-}\) have 32 electrons, making them isoelectronic.

Step 4: Analyze Geometric Structures

The nitrate ion \(\mathrm{NO}_3^-\) and the carbonate ion \(\mathrm{CO}_3^{2-}\) both exhibit the same trigonal planar structure due to similar hybridization (sp^2) around the central atom (N or C), making them isostructural as well.

Step 5: Conclusion Based on Analysis

Since \(\mathrm{NO}_3^-\) and \(\mathrm{CO}_3^{2-}\) are both isoelectronic and isostructural, the correct answer is option (a).

Key Concepts

Electrons Counting

Counting electrons is a basic yet crucial step in determining the properties of molecular species. In the context of isoelectronic species, it involves ensuring that all compared molecules possess the same total number of electrons. Thus, understanding electron counting can help identify similarities in chemical properties. For instance, consider nitrate (\(\mathrm{NO}_3^- \)), carbonate (\(\mathrm{CO}_3^{2-} \)), chlorate (\(\mathrm{ClO}_3^- \)), and sulfur trioxide (\(\mathrm{SO}_3 \)). By counting the electrons in these species:

• Hydrogen has 7 electrons, and by adding 3 oxygen atoms, you get 24 more electrons. Adding one for the negative charge gives a total of 32 electrons in nitrate.
• Carbon, with 6 electrons, when combined with 3 oxygen atoms and the negative charge contribution, results in 32 electrons for the carbonate ion.
• Chlorine contributes 17 electrons, with the oxygen and negative charge adding up to 42 electrons for chlorate.
• Sulfur, with 16 electrons plus 3 oxygen atoms, gives a total of 40 electrons in sulfur trioxide.

An important point to remember here is that the shared number of electrons (32) in nitrate and carbonate ions indicates that they are isoelectronic. This characteristic is significant in identifying similarities in other properties like structure and reactivity.

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of the atoms within a molecule, which significantly influences its reactivity, polarity, phase of matter, color, magnetism, and biological activity. Understanding molecular geometry involves analyzing the spatial distribution of atoms, which rely heavily on the arrangement of electron pairs around the central atom.The geometry can be predicted using VSEPR (Valence Shell Electron Pair Repulsion) theory. For instance:

• The nitrate ion \(\mathrm{NO}_3^- \) and the carbonate ion \(\mathrm{CO}_3^{2-} \) both exhibit a trigonal planar geometry.
• Trigonal planar structures occur when there are three bonds and no lone pair on the central atom, with bond angles close to 120 degrees.
• Other ions like chlorate \(\mathrm{ClO}_3^- \) may not share this geometry due to their differing electron pair arrangements and hybridization.

Hence, understanding molecular geometry is vital for predicting interactions among molecules, which is crucial in fields such as chemistry and biochemistry.

Hybridization

Hybridization is a central concept in molecular chemistry wherein atomic orbitals mix to form new, equivalent hybrid orbitals. This process dictates the shape and bond angles of a molecule. For \(\mathrm{NO}_3^- \) and \(\mathrm{CO}_3^{2-} \), hybridization plays a key role in their trigonal planar structure.

• Both nitrate and carbonate ions undergo sp² hybridization, mixing one s orbital and two p orbitals of the central atom (Nitrogen for nitrate and Carbon for carbonate).
• The resulting hybrid orbitals form three equivalent sigma bonds with surrounding oxygen atoms, stabilizing the planar structure of the molecule.
• Due to this hybridization, bond angles in such structures typically measure 120 degrees, aligning with the trigonal planar geometry.

Understanding hybridization helps us comprehend not only the geometry but also the bonding and molecular interactions that determine the stability and reactivity of molecules in chemical reactions.

Trigonal Planar Structure

The trigonal planar structure is a simple yet fundamental geometric shape in chemistry, characterized by three atoms surrounding a central atom in a flat, triangular shape. This structure is often examined in molecules where the central atom forms three bonds and has no lone pairs. It plays a significant role in understanding molecules like \(\mathrm{NO}_3^- \) and \(\mathrm{CO}_3^{2-} \).

• In a trigonal planar structure, the three peripheral atoms create a 120-degree angle with each other, reflecting a symmetric distribution of charge and negligible molecular polarity.
• This symmetry and balance impact the properties of the molecule, such as its optical and electronic behavior.
• The characteristic flat shape of this structure can also be crucial in determining how the molecule interacts with other substances, particularly how it bonds in larger complex structures.

A clear understanding of the trigonal planar structure enables students to predict and explain the molecular characteristics and behavior of relevant chemical species, providing insightful perspectives useful in various scientific disciplines.