Problem 199 - A Complete Resource Book in Chemistry for JEE Main

Question

Of the following sets which does not contain isoelectronic species? \([2005 \mid\) (a) \(\mathrm{SO}_{3}^{2-}, \mathrm{CO}_{3}^{2}, \mathrm{NO}_{3}^{-}\) (b) \(\mathrm{CN}^{-}, \mathrm{N}_{2}, \mathrm{C}_{2}^{2-}\) (c) \(\mathrm{BO}_{3}^{3}, \mathrm{CO}_{3}^{2-}, \mathrm{NO}_{3}^{-}\) (d) \(\mathrm{PO}_{4}^{3-}, \mathrm{SO}_{4}^{2}, \mathrm{ClO}_{4}^{-}\)

Step-by-Step Solution

Answer

Sets (a) and (c) are not isoelectronic, as their species have different electron counts.

Step 1: Define Isoelectronic Species

Isoelectronic species are atoms, ions, or molecules that have the same number of electrons or the same electronic structure. To determine if a set is isoelectronic, each species should have the same total number of electrons.

Step 2: Calculate Electrons for Set (a)

Count the total electrons for each species in set (a):- \( \text{SO}_3^{2-} \): S (16) + 3O (3 × 8) + 2 extra = 26 electrons- \( \text{CO}_3^{2-} \): C (6) + 3O (3 × 8) + 2 extra = 24 electrons- \( \text{NO}_3^{-} \): N (7) + 3O (3 × 8) + 1 extra = 24 electronsSince \( \text{SO}_3^{2-} \) has a different electron count, these species are not isoelectronic.

Step 3: Calculate Electrons for Set (b)

Count the total electrons for each species in set (b):- \( \text{CN}^- \): C (6) + N (7) + 1 extra = 14 electrons- \( \text{N}_2 \): N (7) + N (7) = 14 electrons- \( \text{C}_2^{2-} \): 2C (2 × 6) + 2 extra = 14 electronsAll species in this set have 14 electrons, so they are isoelectronic.

Step 4: Calculate Electrons for Set (c)

Count the total electrons for each species in set (c):- \( \text{BO}_3^{3-} \): B (5) + 3O (3 × 8) + 3 extra = 28 electrons- \( \text{CO}_3^{2-} \): C (6) + 3O (3 × 8) + 2 extra = 24 electrons- \( \text{NO}_3^{-} \): N (7) + 3O (3 × 8) + 1 extra = 24 electrons\( \text{BO}_3^{3-} \) has a different electron count, so these species are not isoelectronic.

Step 5: Calculate Electrons for Set (d)

Count the total electrons for each species in set (d): - \( \text{PO}_4^{3-} \): P (15) + 4O (4 × 8) + 3 extra = 32 electrons- \( \text{SO}_4^{2-} \): S (16) + 4O (4 × 8) + 2 extra = 32 electrons- \( \text{ClO}_4^{-} \): Cl (17) + 4O (4 × 8) + 1 extra = 32 electronsAll species in this set have 32 electrons, so they are isoelectronic.

Key Concepts

Electron Count

To understand isoelectronic species, it's crucial to grasp the concept of electron count. This refers to the number of electrons present in an atom, ion, or molecule. When we talk about isoelectronic species, we mean different chemical entities that share the same total number of electrons.

For example, to determine if \[\text{SO}_3^{2-}, \text{CO}_3^{2-}, \text{NO}_3^{-} \] are isoelectronic, we need to tally the electrons in each:

• \( \text{SO}_3^{2-} \): Sulfur has 16 electrons, each oxygen contributes 8, and we add 2 more due to the charge, totaling 26.
• \( \text{CO}_3^{2-} \): Carbon has 6 electrons, plus 3 oxygens as above, and two extra for a total of 24.
• \( \text{NO}_3^{-} \): Nitrogen has 7 electrons, the 3 oxygens are included, plus one extra electron from its charge adds up to 24.

By comparing the electron counts, we see the importance of calculating them accurately, as they help determine whether species are indeed isoelectronic.

Chemical Species

Chemical species are distinct entities such as atoms, molecules, ions, or radicals that can be identified in a chemical context. In the study of isoelectronic species, understanding the types of chemical species is key to recognizing their electronic similarities.

Isoelectronic chemical species can belong to different groups or types, yet they share the same electron count. For instance, in set (b) of the exercise:

• \( \text{CN}^- \) is a polyatomic ion composed of a carbon and a nitrogen atom.
• \( \text{N}_2 \) is a diatomic molecule consisting of two nitrogen atoms.
• \( \text{C}_2^{2-} \) is an ion made of two carbon atoms, carrying a -2 charge.

These species are chemically different—a molecule versus ions, yet they are electronically similar, each holding 14 electrons in total. This helps illustrate the principle that different chemical species can have equivalent electron configurations.

Ion Structures

Understanding ion structures is essential when analyzing isoelectronic species. Ions are atoms or groups of atoms with a net electrical charge, resulting from the loss or gain of one or more electrons. This charge affects the total electron count significantly.

When evaluating whether different ions belong to the same isoelectronic set, their structures and charges must be calculated carefully. In set (d), the ions \[\text{PO}_4^{3-}, \text{SO}_4^{2-}, \text{ClO}_4^{-} \] are analyzed:

• \( \text{PO}_4^{3-} \) involves phosphorus with 15, four oxygens, plus 3 extra from the charge, totaling 32 electrons.
• \( \text{SO}_4^{2-} \) adds sulfur with 16, the same oxygen setup, and 2 from the charge for another 32 electrons.
• \( \text{ClO}_4^{-} \) includes chlorine with 17, same four oxygens, and one extra electron due to its charge to make 32.

This illustrates how the structure of ions, together with their charges, determine if they are isoelectronic. It demonstrates the intricate balance of elements and charges in defining similar electronic arrangements across different ions.