Question

In calcium fluoride structure, the coordination numbers of calcium and fluoride ions are, respectively, (a) 8 and \(\overline{4}\) (b) 6 and 8 (c) 4 and \(\overline{4}\) (d) 4 and 8

Short answer

The coordination numbers of calcium and fluoride ions in calcium fluoride are, respectively, 8 and 4, which is represented by option (a) 8 and \(\overline{4}\).

Step-by-step solution

Understand the Structure of Calcium Fluoride

Calcium fluoride (CaF2) crystallizes in a face-centered cubic lattice. Each calcium ion is surrounded by 8 fluoride ions at the corners of a cube, which means the coordination number of calcium is 8.

Determine the Coordination Number of Fluoride Ions

Each fluoride ion is surrounded by 4 calcium ions in the structure of calcium fluoride. Therefore, the coordination number of fluoride is 4.

Choose the Correct Option

Based on the structure, the coordination number of calcium is 8 and that of fluoride is 4. The correct coordination numbers match with option (a) 8 and \(\overline{4}\).

Key concepts

Calcium Fluoride Structure

The structure of calcium fluoride, often known by its mineral name 'fluorite', is crucial for understanding various aspects of solid-state chemistry. Each unit cell of calcium fluoride (CaF2) is made up of calcium ions (Ca2+) and fluoride ions (F-) in a specific ratio, which is dictated by the ionic charges and size. In this structure, calcium ions are positioned at the faces of the cube, leading to each calcium ion being surrounded by eight fluoride ions.

This arrangement forms the basis of the coordination number, which in the context of CaF2, refers to the number of oppositely charged ions that surround a given ion in the crystal lattice. For calcium ions in CaF2, this number is 8, due to each one being surrounded by eight fluoride ions at the vertices of a cube.

Understanding this geometric configuration helps learners grasp the stoichiometry and predict properties such as density and stability of the ionic compound. The strategically arranged ions explain why calcium fluoride is known for its high melting point and low solubility in water, characteristics that are useful in a range of industrial applications.

Face-Centered Cubic Lattice

The face-centered cubic (FCC) lattice is a common type of crystal structure found in many metal and ionic solids, including calcium fluoride. In an FCC lattice, ions are positioned at each corner of the cube and at the center of each face of the cube, hence the term 'face-centered'. This arrangement leads to high packing efficiency and low void space between the ions.

For students, visualizing an FCC lattice can be simplified by imagining a dice, with ions at every corner and on every face's center, excluding the top and bottom faces. This structure affects various physical properties, such as the density and melting points of substances. Due to the closeness of the ions and the efficient use of space, FCC structures tend to be quite dense and have high coordination numbers.

Coordination Numbers in the FCC Lattice

Within the FCC lattice of calcium fluoride, as mentioned, the coordination number of the calcium ions is 8. For fluoride ions, the coordination number is 4 because each fluoride ion is surrounded by four close calcium ions. This coordination plays a direct role in determining the strength of the bonding and overall stability of the solid.

Chemical Bonding in Solids

In solid structures, such as calcium fluoride, the chemical bonding holds the lattice together and determines many of the compound's properties. There are various types of bonding in solids, but ionic bonding is the most relevant for compounds like calcium fluoride.

Ionic bonding occurs when electrons are transferred from one atom to another, resulting in a lattice of positively and negatively charged ions. In CaF2, each calcium ion loses two electrons and becomes positively charged (Ca2+), while each fluoride ion gains an electron to become negatively charged (F-). These opposite charges attract each other, forming a strong and stable ionic bond.

Impact on Properties

The arrangement of ions and the nature of the ionic bonds have a profound impact on the physical characteristics of the substance. For instance, the strength of these ionic bonds gives calcium fluoride its notable high melting point and hardness. Understanding these bonds provides insights into the behaviors of materials and informs their applications in areas like ceramics and optics.