Problem 118 - A Complete Resource Book in Chemistry for JEE Main

Question

Among the following species, identify the isostructural pairs \(\mathrm{NF}_{3}, \mathrm{NO}_{3}^{-}, \mathrm{BF}_{3}, \mathrm{H}_{3} \mathrm{O}^{+}, \mathrm{HN}_{3}\) (a) \(\left[\mathrm{NF}_{3}, \mathrm{NO}_{3}^{-}\right]\)and \(\left[\mathrm{BF}_{3}, \mathrm{H}_{3} \mathrm{O}^{+}\right]\) (b) \(\left[\mathrm{NF}_{3}, \mathrm{HN}_{3}\right]\) and \(\left[\mathrm{NO}_{3}^{-}, \mathrm{BF}_{3}\right]\) (c) \(\left[\mathrm{NF}_{3}, \mathrm{H}_{3} \mathrm{O}^{+}\right]\)and \(\left[\mathrm{NO}_{3}^{-}, \mathrm{BF}_{3}\right]\) (d) \(\left[\mathrm{NF}_{3}, \mathrm{H}_{3} \mathrm{O}^{+}\right]\)and \(\left[\mathrm{HN}_{3}, \mathrm{BF}_{3}\right]\)

Step-by-Step Solution

Answer

The isostructural pairs are (c) \(\left[\mathrm{NF}_3, \mathrm{H}_3 \mathrm{O}^+\right]\) and \(\left[\mathrm{NO}_3^-, \mathrm{BF}_3\right]\).

Step 1: Understand Isostructural Concept

Isostructural species have a similar geometry or shape, which means they share the same hybridization and arrangement of atoms. We solve the problem by determining the structure of each species and finding pairs that match.

Step 2: Determine the Structure of NF3

The structure of \(\mathrm{NF}_3\) is trigonal pyramidal. It has one lone pair of electrons on the nitrogen and three fluorine atoms bonded to nitrogen. This structure results in an \(sp^3\) hybridization.

Step 3: Determine the Structure of NO3-

The \(\mathrm{NO}_3^-\) ion has a trigonal planar structure with one nitrogen atom at the center, bonded to three oxygen atoms. It involves \(sp^2\) hybridization.

Step 4: Determine the Structure of BF3

\(\mathrm{BF}_3\) is also trigonal planar like \(\mathrm{NO}_3^-\). The boron atom is at the center, bonded to three fluorine atoms. It involves \(sp^2\) hybridization.

Step 5: Determine the Structure of H3O+

The \(\mathrm{H}_3\mathrm{O}^+\) ion has a trigonal pyramidal shape with one lone pair of electrons and three hydrogen atoms bonded to the oxygen atom, similar to \(\mathrm{NF}_3\). This results in \(sp^3\) hybridization.

Step 6: Determine the Structure of HN3

\(\mathrm{HN}_3\) has a linear structure, which involves \(sp\) hybridization. Unlike the other tetrahedral or planar forms, it does not match others in this list.

Step 7: Match Isostructural Pairs

Now, we identify species with similar structures: \(\mathrm{NF}_3\) and \(\mathrm{H}_3\mathrm{O}^+\) are both trigonal pyramidal. \(\mathrm{NO}_3^-\) and \(\mathrm{BF}_3\) are both trigonal planar.

Step 8: Choose Correct Option

From the identified pairs, the isostructural pairs are found in option (c): \(\left[\mathrm{NF}_3, \mathrm{H}_3 \mathrm{O}^+\right]\) and \(\left[\mathrm{NO}_3^-, \mathrm{BF}_3\right]\).

Key Concepts

Molecular Geometry

Molecular geometry focuses on the three-dimensional arrangement of atoms within a molecule. It is crucial because the shape of a molecule can significantly influence its properties and reactions. The VSEPR (Valence Shell Electron Pair Repulsion) theory is frequently used to predict molecular geometry. According to VSEPR, electron pairs around a central atom will arrange themselves as far apart as possible to minimize repulsion.
For instance:

• A linear geometry results when there are two regions of electron density around the central atom.
• A trigonal planar shape emerges when three regions are present.
• A trigonal pyramidal shape occurs when four regions are present, including one lone pair.

Understanding these basic geometries helps us determine the shapes of more complex molecules and predict how they might interact with other substances.

Hybridization

Hybridization is a concept that explains the mixing of atomic orbitals to form new hybrid orbitals, which are more conducive to forming chemical bonds. This helps explain the observed geometries of molecules:

• In \(sp^3\) hybridization, one s and three p orbitals mix to form four equivalent orbitals, leading to shapes like tetrahedral or trigonal pyramidal.
• In \(sp^2\) hybridization, one s and two p orbitals combine to form three equivalent orbitals, typically resulting in a trigonal planar arrangement.
• In \(sp\) hybridization, one s and one p orbital fuse, forming two equivalent orbitals aligned linearly.

Understanding hybridization allows chemists to predict the shape of a molecule and the type of bonds it can form, which is essential for understanding molecular reactivity.

Trigonal Pyramidal

The trigonal pyramidal shape is a type of molecular geometry that occurs when a molecule has one lone pair and three bonded atoms around the central atom. This geometry is often a result of \(sp^3\) hybridization. The lone pair exerts a greater repulsive force than the bonded atoms, causing the structure to become a pyramid with a triangular base.
For example:

• Ammonia (\(NH_3\)) and \(NF_3\) both exhibit trigonal pyramidal geometry.
• In each case, there is one lone pair on the nitrogen atom, resulting in the characteristic pyramid shape.
• Similar trigonal pyramidal structures are seen in \(H_3O^+\) due to its lone pair on oxygen.

This geometry is crucial because it affects not just the molecule's shape but also its polarity and interactions with other substances.

Trigonal Planar

Trigonal planar geometry is observed in molecules with three bonded atoms around the central atom, with no lone pairs, causing the atoms to lie on the same plane. This geometry is often associated with \(sp^2\) hybridization, resulting in a flat, triangular shape.
Consider the following cases:

• Boron trifluoride (\(BF_3\)) and the nitrate ion (\(NO_3^-\)) both demonstrate trigonal planar geometry.
• The central atoms (boron and nitrogen, respectively) are connected to three other atoms, leading to a \(120^\circ\) bond angle.
• This planar arrangement allows for a symmetrical distribution of charge, often leading to nonpolar molecules.

This geometry is significant for predicting the reactivity and intermolecular forces of molecules.

Linear Structure

Molecules with a linear structure have a straight-line geometry, involving atoms positioned at an angle of \(180^\circ\). This occurs when there are either two bonded atoms or linear arrangements of larger groups around a central atom, leading to \(sp\) hybridization.
Examples of linear structures include:

• The hydrogen cyanide (\(HCN\)), where carbon is bonded to nitrogen, forming a linear shape.
• The \(HN_3\) molecule also has a linear arrangement due to the resonance structure within its chain of atoms.
• Linear shapes are simple yet vital, contributing to a molecule's potential polarity and dipole moment.

Understanding linear structures is essential in predicting how these molecules will align and interact in different chemical environments.