Problem 20 - Chemistry: The Central Science in SI Units, Global Edition

Question

Amorphous silica, \(\mathrm{SiO}_{2}\), has a density of about \(2.2 \mathrm{~g} / \mathrm{cm}^{3}\), whereas the density of crystalline quartz, another form of \(\mathrm{SiO}_{2}\), is \(2.65 \mathrm{~g} / \mathrm{cm}^{3}\). Which of the following statements is the best explanation for the difference in density? (a) Amorphous silica is a network-covalent solid, but quartz is metallic. (b) Amorphous silica crystallizes in a primitive cubic lattice. (c) Quartz is harder than amorphous silica. (d) Quartz must have a larger unit cell than amorphous silica. (e) The atoms in amorphous silica do not pack as efficiently in three dimensions as compared to the atoms in quartz.

Step-by-Step Solution

Answer

The best explanation for the difference in density between amorphous silica and crystalline quartz is (e) - The atoms in amorphous silica do not pack as efficiently in three dimensions compared to the atoms in quartz.

Step 1: Statement (a)

Amorphous silica is a network-covalent solid, but quartz is metallic. This statement is incorrect because both amorphous silica and crystalline quartz are network covalent solids, not metallic.

Step 2: Statement (b)

Amorphous silica crystallizes in a primitive cubic lattice. This statement is incorrect because amorphous silica does not form a crystalline lattice, as it is amorphous.

Step 3: Statement (c)

Quartz is harder than amorphous silica. This statement is true, but it does not explain the difference in density between the two forms of \(\mathrm{SiO}_{2}\).

Step 4: Statement (d)

Quartz must have a larger unit cell than amorphous silica. This statement is not relevant because amorphous silica does not have a unit cell due to its amorphous structure.

Step 5: Statement (e)

The atoms in amorphous silica do not pack as efficiently in three dimensions compared to the atoms in quartz. This statement is true, and it explains the density difference between amorphous silica and crystalline quartz. In amorphous silica, the atoms are arranged in a less ordered manner, leading to less efficient packing and a lower density compared to the ordered arrangement in crystalline quartz. Therefore, the best explanation for the difference in density between amorphous silica and crystalline quartz is option (e).

Key Concepts

Amorphous Solids

Amorphous solids are materials where the atoms or molecules are arranged in a random or less ordered manner. Unlike crystalline solids, they lack a long-range repeating pattern. Amorphous solids can be thought of like a frozen liquid where the structure is disordered. This lack of order means that the structural arrangement can vary from one region of the amorphous solid to another.

In amorphous silica, the atoms do not pack efficiently, leading to lower density and mechanical properties when compared to crystalline forms. Because their atoms do not align in neat rows or layers, amorphous solids do not have regular shapes like crystals do. This structure affects various properties like hardness and melting point.

Examples of amorphous solids include:

• Glass
• Plastics
• Gels

Each of these materials exhibits the essential characteristics of lack of long-range order, which influence their physical properties and applications.

Crystalline Solids

Crystalline solids are materials where the atoms are arranged in a highly ordered repeating pattern. These solids exhibit precise geometric shapes, which are reflected in their crystal lattice structures. The ordered arrangement means that every atom is in a fixed position, relative to the others, creating a uniform structure that repeats itself in three dimensions throughout the entire solid.

Quartz is a crystalline form of silicon dioxide (\(\mathrm{SiO}_{2}\)), where its atoms are tightly packed in a regular lattice, resulting in a more dense and hard structure compared to amorphous silica. This ordered arrangement allows for efficient packing and contributes to its higher density and superior mechanical strength.

Common features of crystalline solids include:

• Regular geometric shapes
• Well-defined melting points
• Anisotropic properties, meaning they differ depending on the direction measured

Crystalline solids are essential in many applications due to their strength and stability.

Density

Density is a key physical property that defines how much mass a material has in a given volume, expressed in units like grams per cubic centimeter (g/cm³). It is calculated using the formula \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
The density of a material relates closely to how its particles are arranged. Materials with tightly packed structures tend to have higher densities because there is more mass within the same volume.

In the case of silicon dioxide, the density of crystalline quartz is higher than that of amorphous silica. This is due to the efficient packing of atoms in the crystal lattice in quartz, as opposed to the more disordered arrangement found in amorphous silica. Therefore, crystalline solids generally have higher densities than their amorphous counterparts.

Understanding density is important in various fields, such as materials science and engineering, because it impacts material choices and functionality in industrial applications.

Network Covalent Solids

Network covalent solids are a fascinating class of materials where atoms are bonded by a continuous network of covalent bonds throughout the entire material. These extensive network bonds result in unique mechanical and thermal properties, rendering these solids exceptionally hard and stable.

Both amorphous silica and crystalline quartz belong to the category of network covalent solids. However, even within this category, there are variations based on structure. In quartz, the network of covalent bonds is organized in a repeating pattern, contributing to its strength and density. Conversely, although amorphous silica also features covalent bonds, the absence of long-range order impacts its packing efficiency and density.

Common characteristics of network covalent solids include:

• High melting and boiling points due to strong bonding
• Hard and durable nature
• Non-conductivity due to the absence of free electrons

These properties make network covalent solids highly useful in a range of technological and industrial applications, from semiconductors to refractory materials.