Problem 171 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following constitutes a group of the isoelectronic species? (a) \(\mathrm{C}_{2}^{2-}, \mathrm{O}_{2}^{-}, \mathrm{CO}, \mathrm{NO}\) (b) \(\mathrm{NO}^{+}, \mathrm{C}_{2}^{2}, \mathrm{C}^{\mathrm{N}-}, \mathrm{N}_{2}\) (c) \(\mathrm{CN}^{-}, \mathrm{N} 2, \mathrm{O}_{2}^{2-}, \mathrm{C}_{2}^{2-}\) (d) \(\mathrm{N}_{2}, \mathrm{O}_{2}, \mathrm{NO}^{+}, \mathrm{CO}\)

Step-by-Step Solution

Answer

Options (b), (c), and (d) form groups of isoelectronic species.

Step 1: Understanding Isoelectronic Species

Isoelectronic species are atoms, molecules, or ions that have the same number of electrons. To find a group of isoelectronic species, we must first determine the total electron count for each species in the options provided.

Step 2: Calculate Electrons in Each Option - (a)

Calculate electrons for each molecule or ion:- \(\text{C}_2^{2-}\): Carbon has 6 electrons, so \(2 \times 6 + 2 = 14\) electrons.- \(\text{O}_2^{-}\): Oxygen has 8 electrons, so \(2 \times 8 + (-1) = 15\) electrons.- CO: Carbon has 6 and Oxygen 8 electrons, so \(6 + 8 = 14\) electrons.- NO: Nitrogen has 7 and Oxygen 8 electrons, so \(7 + 8 = 15\) electrons.Conclusion: \(\text{C}_2^{2-}\) and CO are isoelectronic with 14 electrons each.

Step 3: Calculate Electrons in Each Option - (b)

Calculate electrons for each molecule or ion:- \(\text{NO}^+\): Nitrogen has 7 and Oxygen 8 electrons, with a positive charge removing one, so \(7 + 8 - 1 = 14\) electrons.- \(\text{C}_2^{2}\): Carbon has 6, \(2 \times 6 = 12\) electrons.- \(\text{CN}^+\): Carbon has 6 and Nitrogen 7 electrons, while a negative charge adds one, so \(6 + 7 + 1 = 14\) electrons.- \(\text{N}_2\): Nitrogen has 7, \(2 \times 7 = 14\) electrons.Conclusion: \(\text{NO}^+\), \(\text{CN}^-\), and \(\text{N}_2\) are isoelectronic with 14 electrons each.

Step 4: Calculate Electrons in Each Option - (c)

Calculate electrons for each molecule or ion:- \(\text{CN}^-\): Carbon has 6 and Nitrogen 7 electrons, while a negative charge adds one, so \(6 + 7 + 1 = 14\) electrons.- \(\text{N}_2\): Nitrogen has 7, \(2 \times 7 = 14\) electrons.- \(\text{O}_2^{2-}\): Oxygen has 8, \(2 \times 8 + 2 = 18\) electrons.- \(\text{C}_2^{2-}\): Carbon has 6, \(2 \times 6 + 2 = 14\) electrons.Conclusion: \(\text{CN}^-\), \(\text{N}_2\), and \(\text{C}_2^{2-}\) are isoelectronic with 14 electrons each.

Step 5: Calculate Electrons in Each Option - (d)

Calculate electrons for each molecule or ion:- \(\text{N}_2\): Nitrogen has 7, \(2 \times 7 = 14\) electrons.- \(\text{O}_2\): Oxygen has 8, \(2 \times 8 = 16\) electrons.- \(\text{NO}^+\): Nitrogen has 7 and Oxygen 8 electrons, with a positive charge removing one, so \(7 + 8 - 1 = 14\) electrons.- \(\text{CO}\): Carbon has 6 and Oxygen 8 electrons, so \(6 + 8 = 14\) electrons.Conclusion: \(\text{N}_2\), \(\text{NO}^+\), and CO are isoelectronic with 14 electrons each.

Step 6: Identify the Correct Group of Isoelectronic Species

From the calculations, the options (b), (c), and (d) contain isoelectronic species. Specifically, all these have species with 14 electrons.

Key Concepts

Electron Count

Understanding the electron count of different molecules and ions is crucial for determining whether they are isoelectronic. Isoelectronic species have identical numbers of electrons. Calculating electron counts involves summing the electrons of each element while considering any charges.
- Each neutral atom has a number of electrons equal to its atomic number.
- Positive charges (cations) indicate lost electrons, requiring deduction from the electron count.
- Negative charges (anions) signify gained electrons and should be added to the electron tally.
For instance, a molecule with a double negative charge, such as \( ext{C}_2^{2-}\), would mean adding two electrons to the combined count of the carbon atoms.

Molecular Ions

Molecular ions are charged species formed by gaining or losing electrons through a molecule. This alteration results in positive or negative charges impacting electron count.
- Cations are positively charged and have fewer electrons than protons, occurring when electrons are removed.
- Anions carry a negative charge, possessing more electrons due to electron acquisition.

Working with molecular ions often entails adjusting the electron count based on ion charges. Whether calculating for \(\text{NO}^+\) with its reduced electron count—due to the positive charge—or \(\text{O}_{2}^{2-}\) with increased electrons, understanding charge effects is essential. Recognizing these ions helps ensure accurate electron configuration evaluations.

Chemical Bonding

Chemical bonding refers to the interaction of atoms that enables the formation of molecules. The essence of bonding lies in electron sharing, transfer, or overlap to achieve stability, often resulting in isoelectronic species.
- Covalent bonding involves the sharing of electrons between atoms, as seen in \(\text{CO}\).
- Ionic bonding happens when electrons are transferred, leading to charged ions which can still participate in forming isoelectronic groups.

In molecules like \(\text{NO}^+\), variations in bonding result from electron dynamics, which affect their charge and electron counts. This makes understanding chemical bonding a key factor in analyzing isoelectronic species.

Electron Configuration

Electron configuration illustrates the distribution of electrons in an atom or molecule's orbitals. Knowing how to write and interpret these configurations is critical to mastering isoelectronic species analysis.
- Starting from the lowest energy level, electrons fill orbitals following the Aufbau principle.
- Isoelectronic species will share similar electron configurations owing to similar electron numbers.

For instance, analyzing \(\text{N}_2\) and \(\text{CN}^-\), both species contain 14 electrons, showing similarities in their configurations. This alignment illustrates why understanding electron configuration is key for determining isoelectronic relationships. The combination of number and arrangement allows for comprehensive evaluation of chemical reactivity and stability.