Problem 2 - Chemistry in 30 days

Question

Non-isostructural pair among the following is (a) \(\mathrm{XeF}_{2}, \mathrm{Br}_{3}^{-}\) (b) \(\mathrm{XeF}_{4}, \mathrm{PF}_{4}^{+}\) (c) \(\mathrm{CO}_{2}, \mathrm{I}_{3}^{-}\) (d) \(\mathrm{MnO}_{4}^{-}, \mathrm{ClO}_{3}^{-}\)

Step-by-Step Solution

Answer

The non-isostructural pair is (b) \( \mathrm{XeF}_{4}, \mathrm{PF}_{4}^{+} \).

Step 1: Understanding Isostructural Compounds

Compounds are isostructural if they have the same number of atoms and similar structural arrangement. Even if they have different chemical compositions, their molecular geometry (shape) should be identical.

Step 2: Analyze Structure for XeF2 and Br3-

Both \( \mathrm{XeF}_{2} \) and \( \mathrm{Br}_{3}^{-} \) are linear molecular structures. \( \mathrm{XeF}_{2} \) has a linear structure due to five electron pairs around Xe (3 lone pairs, 2 bond pairs). Similarly, \( \mathrm{Br}_{3}^{-} \) has three lone pairs and two bonding pairs, making it linear.

Step 3: Analyze Structure for XeF4 and PF4+

\( \mathrm{XeF}_{4} \) has a square planar structure, which results from four bond pairs and two lone pairs (octahedral electron geometry, but square planar molecular geometry). \( \mathrm{PF}_{4}^{+} \), on the other hand, has a tetrahedral structure due to its four bond pairs. These structures differ, making them non-isostructural.

Step 4: Analyze Structure for CO2 and I3-

\( \mathrm{CO}_{2} \) has a linear shape due to its two double-bonded oxygen atoms. Similarly, \( \mathrm{I}_{3}^{-} \) is linear due to its three lone pairs and two bonding pairs.

Step 5: Analyze Structure for MnO4- and ClO3-

\( \mathrm{MnO}_{4}^{-} \) displays a tetrahedral structure because of its four bonded oxygen atoms with no lone pairs on the central atom. Similarly, \( \mathrm{ClO}_{3}^{-} \) also approximates a tetrahedral geometry with three bonded oxygens and one lone pair.

Step 6: Identify the Non-Isostructural Pair

From the analysis, \( \mathrm{XeF}_{4} \) and \( \mathrm{PF}_{4}^{+} \) are structurally different, as \( \mathrm{XeF}_{4} \) is square planar, while \( \mathrm{PF}_{4}^{+} \) is tetrahedral, making them the non-isostructural pair.

Key Concepts

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. It is crucial to understanding the properties and reactivities of different molecules. The shape of a molecule is determined by how its atomic nuclei and electron clouds are spatially oriented. Basic shapes include linear, tetrahedral, square planar, and more, depending on the type of bonds and lone pairs present.

• Linear: Atoms are arranged in a straight line. For example, \( \mathrm{CO}_{2} \) has a linear shape due to symmetric double bonding with oxygen.
• Tetrahedral: Atoms form a shape like a pyramid with a triangular base.\( \mathrm{CH}_{4} \) is a classic example.
• Square Planar: Atoms form a flat, square-like shape, as seen in \( \mathrm{XeF}_{4} \).

Understanding these geometries helps predict molecular behavior and interactions.

Valence Shell Electron Pair Repulsion (VSEPR) Theory

Valence Shell Electron Pair Repulsion (VSEPR) theory is a model used to predict the geometry of individual molecules. The principle is simple: electron pairs surrounding a central atom repel each other and will therefore arrange themselves as far apart as possible to minimize repulsive forces.
This theory helps to determine molecule shapes:

• Lone pairs are unshared electrons that can affect the shape more strongly than bonding pairs.
• For example, in \( \mathrm{XeF}_{2} \), the VSEPR model predicts a linearly arranged geometry due to five electron pairs—two for bonds and three as lone pairs.
• In contrast, \( \mathrm{PF}_{4}^{+} \) has no lone pairs, resulting in a tetrahedral shape.

Using VSEPR theory allows chemists to predict molecular structures even before they are empirically established. It is an invaluable tool in understanding complex molecules.

Electron Pairs

Electron pairs are groups of two electrons occupying the same orbital but having opposite spins. They play a crucial role in determining a molecule's structure by influencing its shape and stability. They can be categorized mainly into two types:

• Bonding Pairs: Electrons shared between two atoms that form a covalent bond. These pairs determine the directional geometry of the molecule, such as in \( \mathrm{Br}_{3}^{-} \), where two bonding pairs shape it.
• Lone Pairs: Electrons not involved in bonding but still repel other electron pairs. They can be found on the central atom and influence the overall shape of the molecule. \( \mathrm{XeF}_{4} \) has two lone pairs, giving its square planar shape.

Understanding the placement and role of electron pairs aids in predicting molecular geometry effectively.

Chemical Bonding

Chemical bonding is the process by which atoms combine to form molecules. It leads to stability, as atoms achieve lower energy states through bonds. Different types of bonds contribute to the molecular geometry and properties:

• Covalent Bonds: In these bonds, atoms share electrons to fill their valence shells. This type of bonding is prevalent in organic molecules like \( \mathrm{CO}_{2} \), which has strong polar covalent bonds with oxygen atoms.
• Ionic Bonds: Result from electrostatic attractions between oppositely charged ions. Typically found in salts, not directly covered in the given exercise but crucial for understanding broader chemistry.
• Metallic Bonds: These bonds involve delocalized electrons that are free to move throughout the metallic lattice. Not directly related to the exercise at hand but offer a complete understanding of bonding.

Chemical bonding's role is fundamental in determining the type and strength of interaction among molecules. It provides the basis for understanding molecular shapes and stability as seen in compounds like \( \mathrm{MnO}_{4}^{-} \).