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? $$ \begin{array}{l}{\text { (a) Amorphous silica is a network-covalent solid, but quartz }} \\ {\text { is metallic. }} \\ {\text { (b) Amorphous silica crystallizes in a primitive cubic lattice. }} \\ {\text { (c) Quartz is harder than amorphous silica. }}\end{array} $$ $$ \begin{array}{l}{\text { (d) Quartz must have a larger unit cell than amorphous }} \\ {\text { silica. }}\end{array} $$ $$ \begin{array}{l}{\text { (e) The atoms in amorphous silica do not pack as efficiently }} \\ {\text { in three dimensions as compared to the atoms in quartz. }}\end{array} $$

Short 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 as compared to the atoms in quartz.

Step-by-step solution

Understand the properties of amorphous silica and crystalline quartz

Amorphous silica has an irregular atomic arrangement, while crystalline quartz has a highly ordered, repeating atomic arrangement. The density difference between the two forms should be related to their atomic arrangement and packing in three dimensions.

Analyze the given statements

(a) Both amorphous silica and crystalline quartz are network-covalent solids, so "quartz is metallic" is incorrect. (b) The statement about "amorphous silica crystallizes in a primitive cubic lattice" is incorrect as amorphous silica doesn't have a crystalline structure. (c) The statement saying "Quartz is harder than amorphous silica" is true but doesn't explain the density difference between the two, so this isn't the best explanation. (d) Comparing the unit cell sizes of the two materials is not enough to explain the density difference since they have different atomic packing.

Identify the best explanation

(e) "The atoms in amorphous silica do not pack as efficiently in three dimensions as compared to the atoms in quartz" is the best explanation. The difference in density can be explained by the different atomic arrangement in both materials. Quartz, being a crystalline material, has a more organized and efficient packing of atoms compared to amorphous silica. As a result, quartz has a higher density. This statement is the best choice among the given options.

Key concepts

Amorphous Silica

Amorphous silica, represented by the chemical formula \( \text{SiO}_2 \), is a fascinating material that lacks a long-range atomic order. Unlike crystalline structures, amorphous silica's atoms are not arranged in a specific, repeating pattern. This irregular atomic arrangement causes amorphous silica to have a lower density, around 2.2 \( \text{g/cm}^3 \). Its unique properties make it useful in various applications such as glassmaking and ceramics.
The lack of a regular structure means the atoms are not packed as tightly, leading to lower density. Some key points about amorphous silica include:

• Irregular atomic arrangement
• No long-range order
• Lower density compared to crystalline forms

These characteristics are crucial in understanding material properties and their applications in technology and industry.

Crystalline Quartz

Crystalline quartz is another form of \( \text{SiO}_2 \) but with a highly ordered structure. This regular arrangement of atoms creates a solid framework, contributing to its higher density of 2.65 \( \text{g/cm}^3 \). Quartz's orderly, repeating atomic structure makes it extremely stable and is responsible for its characteristic hardness and clarity.
The efficient packing of atoms in quartz results in its higher density, compared to amorphous silica. Essential features of crystalline quartz include:

• Highly ordered and repeating atomic pattern
• Higher density due to compact structure
• Stable and hard

Understanding these properties helps in applications ranging from jewelry to electronics.

Atomic Arrangement

The atomic arrangement in materials can significantly influence their density and other properties. In crystalline structures like quartz, the atoms are packed in a regular, repeating pattern, leading to efficient use of space and higher density. In contrast, amorphous structures have random, disordered atomic arrangements.
This irregular packing in amorphous materials results in a less dense structure. Here's why atomic arrangement matters:

• Determines density and material strength
• Affects thermal and electrical properties
• Influences material appearance

When comparing materials like amorphous silica and crystalline quartz, the atomic arrangement offers a clear explanation for the differences in their physical properties.