Problem 90 - A Complete Resource Book in Chemistry for JEE Main

Question

\(\mathrm{M}_{2} \mathrm{X}\) have a structure closely related to that of fluorite. It is actually reverse of fluorite structure hence called antifluorite structure. In such a structure (a) \(\mathrm{F}\) ions occupy all the 8 octahedral voids (b) each \(\mathrm{F}^{-}\)is surrounded by \(4 \mathrm{Ca}^{2^{+}}\)in tetrahedral arrangement (c) larger cations occupy the position of \(\mathrm{F}\) - ions and smaller anions that of \(\mathrm{Ca}^{2+}\) ions. (d) smaller cations occupy the position of fluoride ions and larger anions that of \(\mathrm{Ca}^{2^{+}}\)ions

Step-by-Step Solution

Answer

Option (d) describes the antifluorite structure accurately.

Step 1: Understanding Antifluorite Structure Basics

The antifluorite structure is the reverse of the fluorite (CaF2) structure. In the antifluorite structure, cations and anions swap their lattice positions. Thus, in antifluorite, cations occupy the sites that would typically be occupied by anions in the fluorite structure and vice versa.

Step 2: Analyze Option (a)

Option (a) suggests that F ions occupy all the 8 octahedral voids, which would not be correct for the antifluorite structure. In fact, in a fluorite structure, the cations are in the tetrahedral voids and the anions form the lattice. Thus, this option does not align with the antifluorite structure where larger anions form the lattice.

Step 3: Analyze Option (b)

Option (b) suggests each F- is surrounded by 4 Ca2+ in a tetrahedral arrangement, which describes a fluorite structure. For the antifluorite structure, smaller cations like Li+ would occupy positions like fluoride ions, and the lattice is based on larger anions. Hence, this option is incorrect.

Step 4: Analyze Option (c)

Option (c) states that larger cations occupy the positions of F- ions and smaller anions occupy positions of Ca2+. This is a reversal of what is observed in the antifluorite structure, where smaller cations occupy the positions of anions from the fluorite structure, not larger cations.

Step 5: Analyze Option (d)

Option (d) correctly indicates that smaller cations occupy positions that fluoride ions would in a fluorite structure while larger anions take the position of Ca2+ ions. This describes the antifluorite structure accurately as smaller cations fill spaces of anions and larger anions form the lattice.

Key Concepts

Fluorite Structure

The fluorite structure is an arrangement seen in compounds like calcium fluoride (CaF₂). This structure is characterized by a lattice where the larger ions (usually cations) are placed in the center at points corresponding to the unit cell, and the smaller ions (anions) fit into the spaces around them. This means the cations are surrounded symmetrically by anions, resulting in a stable configuration.

In the classic fluorite model, the calcium ions ( ext{Ca}^{2+}) occupy the face-centered cubic (FCC) positions while fluoride ions ( ext{F}^{-}) are placed in the tetrahedral holes of the FCC lattice.

• Calcium ions form a cubic lattice.
• Fluoride ions fill all the tetrahedral spaces.

This arrangement results in each ext{Ca}^{2+} being surrounded by 8 ext{F}^{-} ions, and each ext{F}^{-} being coordinated by 4 ext{Ca}^{2+} ions, creating a well-balanced structural integrity.

Cations and Anions

Cations and anions represent positively and negatively charged ions, respectively. In ionic compounds, the forces between oppositely charged cations and anions are what keep the structure intact. The roles these ions play can vary significantly depending on the type of crystal structure.

• Cations: These are typically metal ions that have lost one or more electrons, resulting in a positive charge (e.g., ext{Ca}^{2+}). They tend to be smaller and fit into specific holes or voids in the crystal lattice.
• Anions: These ions gain electrons and bear a negative charge (e.g., ext{F}^{-}). They are usually non-metal ions, larger than cations, and form the primary lattice framework within the structure.

In the antifluorite structure, the roles are inversed compared to the fluorite arrangement. Smaller cations take the lattice positions formerly held by the anions, while larger anions occupy the sites typically filled by cations.

Lattice Positions

Lattice positions refer to the specific, repetitive spots within a crystal's three-dimensional network where ions or atoms reside. In different crystal structures, ions will occupy different positions based on their size and charge.

In the fluorite structure, for example, the larger cations reside in a cubic lattice, while the smaller anions occupy the tetrahedral sites. However, in the antifluorite structure, there is an interesting swapping:

• Antifluorite Cations: The smaller cations (such as ext{Li}^{+}) occupy typical anion positions, which were the fluoride spots in a fluorite lattice.
• Antifluorite Anions: Larger anions fill the positions the cations previously held, forming the primary lattice structure.

This swapping of positions results in a reversed lattice structure from that of fluorite, maintaining the coordination but altering the tetrahedral and cubic sites.

Tetrahedral Arrangement

A tetrahedral arrangement arises when an atom or ion is positioned in the center of a pyramid-like shape, surrounded symmetrically by four other atoms or ions. This geometry is crucial in both organic and inorganic chemistry.

• In a typical tetrahedral arrangement, the central atom is equidistant from all four surrounding ions or atoms, creating angles of approximately 109.5°.
• In the fluorite structure, each fluoride ion is coordinated tetrahedrally by four calcium ions, emphasizing a stable and symmetrical configuration.

Conversely, in the antifluorite structure, this arrangement is inverted. The smaller cations take the position of the anions, and they are tetrahedrally coordinated by the adjacent larger anions in the lattice. This reverse coordination maintains the integrity of the crystal structure by ensuring that electrostatic forces are balanced, continuing its crucial role in defining the physical properties of the compound.