Problem 114 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following pair (s) represent (s) the isoelectronic species? (a) \(\mathrm{S}^{2-} \& \mathrm{Sc}^{3+}\) (b) \(\mathrm{SO}_{2} \& \mathrm{NO}_{3}^{-}\) (c) \(\mathrm{N}_{2} \& \mathrm{CN}^{-}\) (d) \(\mathrm{NH}_{3} \& \mathrm{H}_{3} \mathrm{O}^{+}\)

Step-by-Step Solution

Answer

Isoelectronic pairs are (a), (c), and (d).

Step 1: Understanding Isoelectronic Species

Isoelectronic species are atoms, molecules, or ions that have the same number of electrons and identical electron configurations.

Step 2: Determine Electrons in Each Species

Calculate the total number of electrons in each species by considering atomic numbers and charges. For anions, add the charge to the atomic number; for cations, subtract the charge from the atomic number.

Step 3: Pair (a) Analysis: \(\mathrm{S}^{2-} \& \mathrm{Sc}^{3+}\)

Sulfur (S) has 16 electrons and gains 2 electrons in \(\mathrm{S}^{2-}\), giving 18 electrons. Scandium (Sc) has 21 electrons and loses 3 electrons in \(\mathrm{Sc}^{3+}\), leaving 18 electrons. Thus, \(\mathrm{S}^{2-}\) and \(\mathrm{Sc}^{3+}\) are isoelectronic.

Step 4: Pair (b) Analysis: \(\mathrm{SO}_{2} \& \mathrm{NO}_{3}^{-}\)

\(\mathrm{SO}_{2}\) has a total of 16 (S) + 2 \times 8 (O) = 32 electrons. \(\mathrm{NO}_{3}^{-}\) has 7 (N) + 3 \times 8 (O) + 1 (charge) = 32 electrons. Hence, \(\mathrm{SO}_{2}\) and \(\mathrm{NO}_{3}^{-}\) are not isoelectronic.

Step 5: Pair (c) Analysis: \(\mathrm{N}_{2} \& \mathrm{CN}^{-}\)

\(\mathrm{N}_{2}\) has 2 \times 7 = 14 electrons. Cyanide ion (\(\mathrm{CN}^{-}\)) has 6 (C) + 7 (N) + 1 (charge) = 14 electrons. Thus, \(\mathrm{N}_{2}\) and \(\mathrm{CN}^{-}\) are isoelectronic.

Step 6: Pair (d) Analysis: \(\mathrm{NH}_{3} \& \mathrm{H}_{3} \mathrm{O}^{+}\)

\(\mathrm{NH}_{3}\) has 7 (N) + 3 = 10 electrons. \(\mathrm{H}_{3} \mathrm{O}^{+}\) has 8 (O) + 3 - 1 (charge) = 10 electrons. Therefore, \(\mathrm{NH}_{3}\) and \(\mathrm{H}_{3} \mathrm{O}^{+}\) are isoelectronic.

Step 7: Concluding Isoelectronic Pairs

Based on the above analysis, the pairs that are isoelectronic are (a) \(\mathrm{S}^{2-} \& \mathrm{Sc}^{3+}\), (c) \(\mathrm{N}_{2} \& \mathrm{CN}^{-}\), and (d) \(\mathrm{NH}_{3} \& \mathrm{H}_{3} \mathrm{O}^{+}\).

Key Concepts

Electron Configuration

Electron configuration describes how electrons are distributed within an atom or ion's orbitals. Understanding electron configurations allows us to predict the behavior and reactivity of atoms and ions. When writing an electron configuration, we start from the lowest energy level to the highest, filling the orbitals according to the Aufbau principle.

• Writing Electron Configurations: Begin with occupying the 1s orbital, and follow with 2s, 2p, 3s... until you have placed all electrons.
• Aufbau Principle: Orbitals are filled from the lowest to highest energy.
• Pauli Exclusion Principle: Each orbital can hold a maximum of two electrons with opposite spins.
• Hund's Rule: Electrons fill degenerate orbitals singly before pairing up.

For example, in the electron configuration of sulfur, \[ \text{S} : 1s^2 2s^2 2p^6 3s^2 3p^4 \,\text{for } \text{S}^{2-} : 1s^2 2s^2 2p^6 3s^2 3p^6 \], we fill the orbitals in this sequential order considering the additional two electrons.

Ions

Ions are charged species formed when neutral atoms gain or lose electrons. This process results in the formation of cations and anions. Understanding the concept of ions is crucial in the exploration of isoelectronic species.

• Cations: Positively charged ions formed by the loss of electrons (e.g., \( \text{Sc}^{3+} \)).
• Anions: Negatively charged ions formed by the gain of electrons (e.g., \( \text{S}^{2-} \)).

When atoms form ions, they adjust their electron clouds to achieve the nearest noble gas configuration. This is why understanding electron configuration is vital to determining if two species are isoelectronic.

Atomic Number

The atomic number, denoted by the symbol Z, is the number of protons in an atom's nucleus. Each element in the periodic table has a unique atomic number, which determines its identity and properties.

• Importance of Atomic Number: It defines the element and its position in the periodic table.
• Calculating Electrons: In a neutral atom, the number of electrons equals the atomic number. However, for ions, we adjust this number by adding (for anions) or subtracting (for cations) the charge.

Understanding how the atomic number relates to the electron count is essential when identifying isoelectronic species. For instance, sulfur with atomic number 16 gains two electrons when forming \( \text{S}^{2-} \), resulting in 18 electrons, which makes it isoelectronic with \( \text{Sc}^{3+} \, \text{which has 18 electrons after losing three electrons from its atomic number of 21}. \)