Question

Of the following sets which does not contain isoelectronic species? (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) \(\mathrm{PO}_{4}{ }^{3-}, \mathrm{SO}_{4}^{2-}, \mathrm{ClO}_{4}\)

Short answer

Set (d) is not isoelectronic.

Step-by-step solution

Understand Isoelectronic Species

Isoelectronic species are atoms, molecules, or ions that have the same number of electrons. This typically means they have the same electronic configuration.

Calculate Total Electrons for Set (a)

For each molecule in set (a), calculate the total number of electrons:- \( \mathrm{SO}_{3}^{2-} \): Sulfur (S) has 16 electrons, and each oxygen (O) has 8 electrons. There are three oxygen atoms. With a 2- charge, add 2 extra electrons: \[16 + 3(8) + 2 = 16 + 24 + 2 = 42 \]- \( \mathrm{CO}_{3}^{2-} \): Carbon (C) has 6 electrons, and each oxygen has 8 electrons. With a 2- charge, add 2 extra electrons: \[6 + 3(8) + 2 = 6 + 24 + 2 = 32 \]- \( \mathrm{NO}_{3}^{-} \): Nitrogen (N) has 7 electrons, each oxygen has 8 electrons. With a 1- charge, add 1 extra electron: \[7 + 3(8) + 1 = 7 + 24 + 1 = 32 \]The molecules in this set do not all have the same number of electrons.

Calculate Total Electrons for Set (b)

For each molecule in set (b), calculate the total number of electrons:- \( \mathrm{CN}^{-} \): Carbon (C) has 6 electrons, Nitrogen (N) has 7 electrons. With a 1- charge, add 1 extra electron: \[6 + 7 + 1 = 14 \]- \( \mathrm{N}_{2} \): Each nitrogen has 7 electrons: \[2(7) = 14 \]- \( \mathrm{C}_{2}^{2-} \): Each carbon has 6 electrons. With a 2- charge, add 2 extra electrons: \[2(6) + 2 = 12 + 2 = 14 \]All species in this set have 14 electrons each, so they are isoelectronic.

Calculate Total Electrons for Set (c)

For each molecule in set (c), calculate the total number of electrons:- \( \mathrm{BO}_{3}^{3-} \): Boron (B) has 5 electrons, each oxygen has 8 electrons. With a 3- charge, add 3 extra electrons: \[5 + 3(8) + 3 = 5 + 24 + 3 = 32 \]- \( \mathrm{CO}_{3}^{2-} \): As calculated before: \[6 + 3(8) + 2 = 32 \]- \( \mathrm{NO}_{3}^{-} \): As calculated before: \[7 + 3(8) + 1 = 32 \]All species in this set have 32 electrons each, so they are isoelectronic.

Calculate Total Electrons for Set (d)

For each molecule in set (d), calculate the total number of electrons:- \( \mathrm{PO}_{4}^{3-} \): Phosphorus (P) has 15 electrons, each oxygen has 8 electrons. With a 3- charge, add 3 extra electrons: \[15 + 4(8) + 3 = 15 + 32 + 3 = 50 \]- \( \mathrm{SO}_{4}^{2-} \): Sulfur (S) has 16 electrons, each oxygen has 8 electrons. With a 2- charge, add 2 extra electrons: \[16 + 4(8) + 2 = 16 + 32 + 2 = 50 \]- \( \mathrm{ClO}_{4} \): Chlorine (Cl) has 17 electrons, each oxygen has 8 electrons: \[17 + 4(8) = 17 + 32 = 49 \]The species in this set have different electron counts, so they are not isoelectronic.

Key concepts

Electron Configuration

Electron configuration refers to the arrangement of electrons in an atom or molecule. This arrangement follows specific principles, such as the Pauli exclusion principle and Hund's rule, to minimize energy. Electrons fill up orbitals starting from the lowest to the highest energy level. Isoelectronic species have the same electron configuration, meaning they possess the same number of electrons, distributed in the same way across orbitals. For example, noble gases often serve as benchmarks for stable electron configurations because their outermost shells are full, leading to high stability. By understanding electron configurations, one can predict the chemical properties and reactivity of atoms and molecules.

Charge Calculation

Charge calculation is essential when determining if species are isoelectronic. The charge of an ion affects its total electron count. For negative ions or anions, extra electrons equivalent to the negative charge are added to the atom's electron count. Conversely, for positive ions or cations, electrons are subtracted from the atom's electron count. For example:

• In \(\mathrm{SO}_3^{2-}\), the 2- charge means adding 2 electrons to the total electron count.
• In \(\mathrm{CN}^{-}\), 1 electron is added for the negative charge.

These additional or missing electrons are crucial for checking the total electron count and ensuring it matches across species to qualify them as isoelectronic.

Molecular Ions

Molecular ions are charged particles composed of two or more atoms bonded together. They play an important role in many chemical reactions and physical processes. Ions can be monatomic (single atom) like \(\mathrm{Cl}^-\), or polyatomic, like \(\mathrm{NO}_3^{-}\), which consists of one nitrogen and three oxygen atoms. The overall charge of a molecular ion is determined by the sum of the charges of its constituent atoms. Molecular ions may interact differently compared to neutral molecules due to their charge, which affects their solubility, interactions with electric fields, and reactivity. Understanding the behavior of molecular ions helps in predicting the outcome of reactions, especially in aqueous solutions where ions are often prevalent.

Electron Count

The electron count of a species determines its identity as an isoelectronic species with others. Counting electrons precisely involves considering both the atomic numbers of the elements involved and their charges. This process is a key step in comparing groups of species for isoelectronic properties. To calculate electron count:

• Determine the number of electrons from the atomic number of each atom present in the species.
• Adjust the count according to the ion's charge by adding electrons for negative charges and subtracting electrons for positive charges.

For example, in the set \(\mathrm{CO}_3^{2-}\), calculate as follows: carbon contributes 6 electrons, each oxygen contributes 8, and the 2- charge adds 2 extra electrons, totaling 32 electrons.