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

Short answer

The correct answer is (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

Identify the relationship between given factors and density

Density can be influenced by the following factors: 1. The type of atomic or molecular arrangement in the lattice (network-covalent, metallic, etc.). 2. The type of lattice (primitive cubic, face-centered cubic, etc.). 3. The size of the unit cell (larger or smaller compared to other forms). 4. The efficiency with which atoms or molecules pack in three dimensions. Keeping these factors in mind, let's analyze the given options to find the best explanation.

Analyze Option (a)

(a) states that amorphous silica is a network-covalent solid, while quartz is metallic. While this could potentially explain the differences in density, it's not accurate as both amorphous silica and quartz are network-covalent solids. Also, both are non-metallic. Therefore, this option cannot be the best explanation.

Analyze Option (b)

(b) claims that amorphous silica crystallizes in a primitive cubic lattice. While the crystal lattice may influence the density, this statement doesn't offer any comparison between quartz's lattice structure or how the diversity in their lattice structures may be responsible for the density difference. Hence, this option is not an appropriate explanation.

Analyze Option (c)

(c) says that quartz is harder than amorphous silica. Hardness doesn't directly influence density. Whilst generally, harder materials are denser, this is not a rule that holds in all cases. In this case, the statement doesn't present a clear explanation for the density difference, so we move on to the next option.

Analyze Option (d)

(d) suggests that quartz must have a larger unit cell than amorphous silica. A larger unit cell may indicate less efficient packing of atoms, resulting in lower density. However, in reality, quartz has a more ordered crystal structure and smaller unit cell than amorphous silica, which contributes to its higher density. Thus, this option is not accurate.

Analyze Option (e)

(e) states that atoms in amorphous silica do not pack as efficiently in three dimensions compared to atoms in quartz. This statement implies that the more ordered structure of quartz allows atoms to be packed more tightly, resulting in a higher density. This option provides the best explanation for the difference in density between amorphous silica and quartz. Therefore, the correct answer is: (e) The atoms in amorphous silica do not pack as efficiently in three dimensions as compared to the atoms in quartz.

Key concepts

Amorphous Silica

Amorphous silica is a form of silicon dioxide, often referred to simply as silica, where the atoms do not arrange themselves in a long-range order. This structure resembles that of a glass rather than a crystal, where the atoms are randomly packed, leading to a lack of a fixed pattern.
This randomness in amorphous silica means that its atoms are less densely packed compared to other more structured forms, giving it a density of about 2.2 g/cm³.

• Lacks long-range order
• Atoms arranged randomly
• Lower atomic packing efficiency compared to crystalline forms

The loose packing of atoms contributes significantly to its lower density compared to its crystalline equivalents. This property is crucial in understanding why amorphous silica has different characteristics such as lower mechanical strength and lower density than more ordered structures like crystalline quartz.

Crystalline Quartz

Crystalline quartz is another form of silicon dioxide that exhibits a well-ordered and repeating structure. This regularity and repeating pattern of atoms in crystalline quartz means that they are tightly packed, esulting in a higher density of about 2.65 g/cm³.
This is the main contrast between amorphous silica and crystalline quartz due to how the atoms are arranged within the solid.

• Ordered, repeating atomic structure
• Higher atomic packing efficiency
• Greater density compared to amorphous silica

Crystalline structures such as quartz often exhibit enhanced physical properties such as increased hardness and stability due to the efficient packing and strong network-covalent bonds formed between the atoms. Hence, crystalline quartz is not only denser but also generally harder than amorphous silica.

Atomic Packing Efficiency

Atomic packing efficiency is a key concept in understanding the density differences between materials like amorphous silica and crystalline quartz. It refers to how tightly atoms are packed together within a solid. The more efficiently packed the atoms, the higher the density will be.
Crystalline quartz, with its well-ordered atomic structure, denotes a higher packing efficiency than the random arrangement found in amorphous silica.

• Tightly packed atoms signify greater density
• Crystalline structures exhibit high packing efficiency
• Inefficient packing leads to lower density

This concept is crucial when analyzing how different forms of the same chemical compound, like the various forms of silica, can exhibit distinctly different physical properties due to the variations in their atomic packing configurations. Understanding atomic packing efficiency helps clarify why crystalline structures tend to possess higher density and superior mechanical properties.

Network-Covalent Solids

Network-covalent solids are a type of solid where the atoms are interconnected through covalent bonds to form a continuous network throughout the material.
Both crystalline quartz and amorphous silica belong to this category, despite their differing densities and atomic arrangements.

• Atoms connected in a giant network
• Strong covalent bonds provide stability
• Variety of structural forms, affecting properties

These covalent networks result in high thermal and chemical stability, which are characteristic of materials like quartz and silica. Even though crystalline quartz and amorphous silica are both network-covalent solids, the manner in which their atomic networks are organized leads to significant differences in physical properties such as density, structure, and hardness. In particular, the orderly and repeating network in crystalline quartz facilitates efficient atom packing that contributes to its higher density.