Problem 110 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following are isoelectronic and isostructural? \(\mathrm{NO}_{3}^{-}, \mathrm{CO}_{3}^{-2}, \mathrm{ClO}_{3}-\mathrm{SO}_{3}\) (a) \(\mathrm{NO}_{3}^{-}, \mathrm{CO}_{3}^{-2}\) (b) \(\mathrm{SO}_{3}, \mathrm{NO}_{3}^{-}\) (c) \(\mathrm{ClO}_{3}^{-}, \mathrm{CO}_{3}^{-2}\) (d) \(\mathrm{CO}_{3}^{-2}, \mathrm{SO}_{3}\)

Step-by-Step Solution

Answer

(a) \( \mathrm{NO}_{3}^{-}, \mathrm{CO}_{3}^{-2} \) are isoelectronic and isostructural.

Step 1: Understanding Isoelectronic and Isostructural

Isoelectronic refers to molecules or ions that have the same number of electrons, while isostructural means they have the same shape or structure. To determine whether the given ions are both isoelectronic and isostructural, we need to consider both the electron count and the molecular geometry.

Step 2: Calculate Electron Count

Let's calculate the total number of electrons for each species:1. **\( \mathrm{NO}_{3}^{-} \)**: Nitrogen (7) + Oxygen (3 x 8) + 1 extra electron for the charge = 32 electrons2. **\( \mathrm{CO}_{3}^{-2} \)**: Carbon (6) + Oxygen (3 x 8) + 2 extra electrons = 32 electrons3. **\( \mathrm{ClO}_{3}^{-} \)**: Chlorine (17) + Oxygen (3 x 8) + 1 extra electron = 50 electrons4. **\( \mathrm{SO}_{3} \)**: Sulfur (16) + Oxygen (3 x 8) = 40 electronsFrom this, we see that \( \mathrm{NO}_{3}^{-} \) and \( \mathrm{CO}_{3}^{-2} \) have the same number of electrons (32), which means they are isoelectronic.

Step 3: Determine Molecular Geometry

Next, let's check the geometry of each species:1. **\( \mathrm{NO}_{3}^{-} \)**: The geometry is trigonal planar due to three regions of electron density around the nitrogen atom and no lone pairs.2. **\( \mathrm{CO}_{3}^{-2} \)**: This ion also has a trigonal planar geometry because carbon is surrounded by three oxygens with no lone pairs.3. **\( \mathrm{ClO}_{3}^{-} \)**: Has a trigonal pyramidal geometry, which differs from the others.4. **\( \mathrm{SO}_{3} \)**: It has a trigonal planar geometry with no lone pairs around the sulfur atom.Here, \( \mathrm{NO}_{3}^{-} \) and \( \mathrm{CO}_{3}^{-2} \) share the same geometry.

Step 4: Conclusion

Both \( \mathrm{NO}_{3}^{-} \) and \( \mathrm{CO}_{3}^{-2} \) are isoelectronic (same number of electrons) and isostructural (same geometry - trigonal planar). Therefore, they meet the criteria laid out in the question.

Key Concepts

Molecular Geometry

Molecular geometry is the three-dimensional arrangement of atoms within a molecule. It is determined by the number of bonds and lone pairs surrounding the central atom. Understanding molecular geometry is crucial because it affects the physical and chemical properties of a molecule, such as reactivity, polarity, and interactions with other molecules.
For example, in the case of trigonal planar geometry, this shape arises when a central atom forms three bonds arranged in a planar, symmetrical manner, often with bond angles of approximately 120 degrees. This geometry is a hallmark of molecules like nitrate (\( \mathrm{NO}_{3}^{-} \)) and carbonate (\( \mathrm{CO}_{3}^{-2} \)), where the central atom has no lone pairs of electrons affecting its shape.
By identifying the molecular geometry, Chemists can predict a molecule's behavior during chemical reactions and interactions.

Electron Count

The electron count is a crucial concept in determining whether different species are isoelectronic. Isoelectronic species have the same number of valence electrons, ensuring similar stability and potentially similar chemical behaviors.
To calculate the electron count:

• Count the number of valence electrons for each atom in the molecule or ion.
• Add any additional electrons resulting from negative charges (or subtract electrons for positive charges).

For instance, in the case of nitrate (\( \mathrm{NO}_{3}^{-} \)) and carbonate (\( \mathrm{CO}_{3}^{-2} \)), both have an electron count of 32, making them isoelectronic. The number includes all the valence electrons from the atoms and considers the charge on the species. This information helps identify species likely to have similar structures or bonding capabilities.

Trigonal Planar

The concept of trigonal planar geometry is vital for understanding the shape and characteristics of some ionic and molecular species. A trigonal planar molecule has a central atom bonded to three others in a single plane, forming an equilateral triangle around the central atom. This configuration leads to bond angles close to 120 degrees.
An example is the carbonate ion (\( \mathrm{CO}_{3}^{-2} \)), where the carbon atom is centrally located with bonds extending outward to each oxygen atom evenly spaced around it. The absence of lone pairs on the central atom allows for this symmetric arrangement, which significantly influences the molecule's interaction with other substances.
In the context of isoelectronic and isostructural comparisons, recognizing trigonal planar geometry helps distinguish between species with similar electron counts but differing in spatial structures.