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

Step by step solution

01

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.

02

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.

03

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.

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