Problem 167 - A Complete Resource Book in Chemistry for JEE Main

Question

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

Step-by-Step Solution

Answer

Set (c) does not contain isoelectronic species.

Step 1: Define Isoelectronic Species

Isoelectronic species are atoms, ions, or molecules that have the same number of electrons. This means they will have identical electron configurations.

Step 2: Calculate Electrons in Set (a)

For the set (a):\(\text{PO}_4^{3-}\), \(\text{SO}_4^{2-}\), and \(\text{ClO}_4^{-}\):- \(\text{P} = 15\), \(\text{O}_4 = 4 \times 8\), charge = -3; Total: \(15 + 32 + 3 = 50\)electrons.- \(\text{S} = 16\), \(\text{O}_4 = 4 \times 8\), charge = -2; Total: \(16 + 32 + 2 = 50\)electrons.- \(\text{Cl} = 17\), \(\text{O}_4 = 4 \times 8\), charge = -1; Total: \(17 + 32 + 1 = 50\)electrons.All species have 50 electrons.

Step 3: Calculate Electrons in Set (b)

For the set (b):\(\text{CN}^-\), \(\text{N}_2\), and \(\text{C}_2^{2-}\):- \(\text{C} = 6\), \(\text{N} = 7\), charge = -1; Total: \(6 + 7 + 1 = 14\)electrons.- \(\text{N}_2: 2 \times 7 = 14\)electrons.- \(\text{C}_2^{2-}\): \(2 \times 6\), charge = -2; Total: \(12 + 2 = 14\)electrons.All species have 14 electrons.

Step 4: Calculate Electrons in Set (c)

For the set (c):\(\text{SO}_3^{2-}\), \(\text{CO}_3^{2-}\), and \(\text{NO}_3^{-}\):- \(\text{S} = 16\), \(\text{O}_3 = 3 \times 8\), charge = -2; Total: \(16 + 24 + 2 = 42\)electrons.- \(\text{C} = 6\), \(\text{O}_3 = 3 \times 8\), charge = -2; Total: \(6 + 24 + 2 = 32\)electrons.- \(\text{N} = 7\), \(\text{O}_3 = 3 \times 8\), charge = -1; Total: \(7 + 24 + 1 = 32\)electrons.\(\text{SO}_3^{2-}\) is not isoelectronic with the others.

Step 5: Calculate Electrons in Set (d)

For the set (d):\(\text{BO}_3^{3-}\), \(\text{CO}_3^{2-}\), and \(\text{NO}_3^{-}\):- \(\text{B} = 5\), \(\text{O}_3 = 3 \times 8\), charge = -3; Total: \(5 + 24 + 3 = 32\)electrons.- \(\text{C} = 6\), \(\text{O}_3 = 3 \times 8\), charge = -2; Total: \(6 + 24 + 2 = 32\)electrons.- \(\text{N} = 7\), \(\text{O}_3 = 3 \times 8\), charge = -1; Total: \(7 + 24 + 1 = 32\)electrons.All species have 32 electrons.

Key Concepts

Electron configuration

Understanding electron configuration is crucial to grasp the idea of isoelectronic species. Electron configuration refers to the distribution of electrons of an atom or molecule in atomic or molecular orbitals. It's like addressing the seating arrangement for electrons around the nucleus of an atom.
The electron configuration is typically noted in a sequence of numbers and letters that represent the energy levels and sublevels. For instance, the configuration of oxygen, using the Aufbau principle, is presented as:

• 1s² 2s² 2p⁴

This configuration tells us that in oxygen, there are two electrons in the first energy level's s-orbital, followed by two electrons in the second energy level's s-orbital, and four in the p-orbital.

When two species have the same electron configuration, they have a similar arrangement of electrons, and often, similar physical and chemical properties. This forms the base for defining isoelectronic species.

ISElectronic calculation

Isoelectronic species are those which have the same number of electrons. Calculating this is relatively straightforward, but it requires careful attention. Here's how you proceed:

• Write down the atomic numbers of the constituent atoms.
• Account for all electrons in the atoms or ions, considering any charges.

Take, for instance, the sulfate ion ( ext{SO}_{4}^{2-} ) . The atomic number of sulfur is 16, and each oxygen atom has 8 electrons. The charge of 2- means there are 2 extra electrons. Therefore, the total count becomes:

• Sulfur: 16 electrons
• Oxygen: 4 × 8 = 32 electrons
• Additional due to charge: 2 electrons

This adds up to a total of 50 electrons.

By summarizing this process, you can determine if a set of species are isoelectronic by checking if their total electron number matches.

Atomic and Molecular structure

The atomic and molecular structure gives insight into the stability and reactivity of elements and compounds. An electronic structure, which includes the electron configuration and total electron count, determines much about how a substance will behave chemically.
When analyzing the atomic and molecular structures of isoelectronic species, these entities share not only the same total number of electrons but often similar bonding patterns and molecular shapes. For instance, suppose we consider ions like ( ext{PO}_{4}^{3-} ) and ( ext{SO}_{4}^{2-} ) :

• Both have tetrahedral geometry due to four coordinating oxygen atoms.
• They illustrate the impact of electron count on molecular geometry.

Thus, observing atomic and molecular structure helps us predict the behavior of isoelectronic species in different environments, enhancing our understanding of chemical interactions between these entities.