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) \(\mathrm{CO}_{3}^{2-}, \mathrm{SO}_{3}\)

Short answer

The answer is (a) \(\mathrm{NO}_{3}^{-}, \mathrm{CO}_{3}^{2-}\).

Step-by-step solution

Defining Isoelectronic and Isostructural

Isoelectronic species are molecules or ions that have the same number of electrons. Isostructural species have the same shape or molecular geometry.

Calculate Total Electrons in Each Species

Determine the total number of electrons in each species:1. For \(\mathrm{NO}_{3}^{-}\): \(7 + 3\times8 + 1 = 32\)2. For \(\mathrm{CO}_{3}^{2-}\): \(6 + 3\times8 + 2 = 32\)3. For \(\mathrm{ClO}_{3}^{-}\): \(17 + 3\times8 + 1 = 32\)4. For \(\mathrm{SO}_{3}\): \(16 + 3\times8 = 40\) Thus, \(\mathrm{NO}_{3}^{-}, \mathrm{CO}_{3}^{2-}, \mathrm{ClO}_{3}^{-}\) are isoelectronic.

Determine the Shape of Each Species

Identify the geometry of each species:1. \(\mathrm{NO}_{3}^{-}\) is trigonal planar.2. \(\mathrm{CO}_{3}^{2-}\) is trigonal planar.3. \(\mathrm{ClO}_{3}^{-}\) is trigonal pyramidal.4. \(\mathrm{SO}_{3}\) is trigonal planar.\(\mathrm{NO}_{3}^{-}, \mathrm{CO}_{3}^{2-}, \mathrm{SO}_{3}\) are isostructural.

Determine Isoelectronic and Isostructural Pair

The pair that is both isoelectronic and isostructural is \(\mathrm{NO}_{3}^{-}\) and \(\mathrm{CO}_{3}^{2-}\), as they both have the same number of electrons and trigonal planar geometry.

Key concepts

Electron Count

The concept of electron count plays a crucial role in identifying whether species are isoelectronic. Isoelectronic species are those that possess an identical number of electrons, regardless of their chemical composition. This feature facilitates comparisons between different ions or molecules based on their electronic configuration rather than structural differences.

To determine the electron count, sum up the valence electrons of each atom within the species and consider any additional electrons due to charges. For instance:

• In \(\mathrm{NO}_{3}^{-}\), the count is obtained by adding electrons from nitrogen (7), oxygen atoms (3×8), and the extra electron from the negative charge, totaling 32 electrons.
• For \(\mathrm{CO}_{3}^{2-}\), add carbon's electrons (6) and those of oxygen and the charge, also totaling 32 electrons.
• \(\mathrm{ClO}_{3}^{-}\) follows a similar process: chlorine (17) plus three oxygens and one charge electron, again resulting in 32 electrons.
• \(\mathrm{SO}_{3}\), however, counts up to 40 electrons, differing from the others.

This analysis is essential in confirming \(\mathrm{NO}_{3}^{-}\), \(\mathrm{CO}_{3}^{2-}\), and \(\mathrm{ClO}_{3}^{-}\) as isoelectronic species due to their identical electron counts.

Molecular Geometry

Understanding molecular geometry is vital in classifying species as isostructural. It refers to the 3D arrangement of atoms within a molecule, which can be predicted using the VSEPR (Valence Shell Electron Pair Repulsion) theory. This theory states that repulsion between electrons in the valence shell of the central atom dictates the shape of a molecule.

For the species given:

• \(\mathrm{NO}_{3}^{-}\) assumes a trigonal planar geometry, as does \(\mathrm{CO}_{3}^{2-}\), owing to the presence of three electron domains around a central atom.
• \(\mathrm{ClO}_{3}^{-}\) is trigonal pyramidal, because one of the electron domains is a lone pair, altering symmetry.
• \(\mathrm{SO}_{3}\)'s symmetry makes it trigonal planar as well.

Thus, the molecular geometry aids in ascertaining that \(\mathrm{NO}_{3}^{-}\), \(\mathrm{CO}_{3}^{2-}\), and \(\mathrm{SO}_{3}\) are isostructural, sharing the same geometric shape.

Trigonal Planar

The term 'trigonal planar' pertains to one specific type of molecular geometry, where a central atom is connected to three surrounding atoms, all lying in the same plane. This geometry results in a 120-degree bond angle between surrounding atoms, ensuring minimal electron pair repulsion. It is commonly associated with molecules that have no lone pairs on the central atom, permitting a flat structure.

In our context, species such as \(\mathrm{NO}_{3}^{-}\), \(\mathrm{CO}_{3}^{2-}\), and \(\mathrm{SO}_{3}\) exhibit this trigonal planar structure. Each shares a similar bond angle, reflecting their comparable electron pair repulsions and symmetry. Recognizing this structure is indispensable for students, as it frequently appears in both theoretical and practical problems involving molecular geometry.

• This geometry is simple yet key to understanding complex chemical behavior.
• It provides insights into how electrons influence the overall molecular planarity.

Becoming familiar with this shape is often the first step in mastering more complex geometrical arrangements.

Problem Solving

Successfully tackling problems related to isoelectronic and isostructural species prepares students for more sophisticated chemistry challenges. Problem-solving involves systematic steps such as calculating electron counts and determining molecular geometry. Both areas require a keen understanding of chemical principles and analytical skills.

When confronting such problems:

• Always start with electron count calculations, being precise with each element and charge.
• Use VSEPR theory to deduce the molecular geometry, visualizing where electrons are most likely located.
• Comparing geometries and electron counts across species helps identify those that are both isoelectronic and isostructural, much like solving complex puzzles.

These exercises not only test knowledge comprehension but also enhance analytical thinking. Remember, practice is crucial. This methodical approach equips students for both theoretical applications and real-world chemical analyses.