Chapter 12

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

Imagine the primitive cubic lattice. Now imagine grabbing the top of it and stretching it straight up. All angles remain ${90}^{\circ }.$ What kind of primitive lattice have you made?

Imagine the primitive cubic lattice. Now imagine grabbing opposite corners and stretching it along the body diagonal while keeping the edge lengths equal. The three angles between the lattice vectors remain equal but are no longer ${90}^{\circ }$ . What kind of primitive lattice have you made?

Which of the three-dimensional primitive lattices has a unit cell where none of the internal angles is ${90}^{\circ }$ ? (a) Orthorhombic, (b) hexagonal, (c) rhombohedral, (d) triclinic, (e) both rhombohedral and triclinic.

Besides the cubic unit cell, which other unit cell(s) has edge lengths that are all equal to each other? (a) Orthorhombic, (b) hexagonal, (c) rhombohedral, (a) triclinic, (e) both rhombohedral and triclinic.

What is the minimum number of atoms that could be contained in the unit cell of an element with a body-centered cubic lattice? (a) $1,(\mathbf{b})2,(\mathbf{c})3,(\mathbf{d})4,(\mathbf{e})5$

The densities of the elements $\mathrm{K},\mathrm{Ca},\mathrm{Sc},$ and Ti are $0.86,1.5$ , $3.2,$ and 4.5 $\mathrm{g}/{\mathrm{cm}}^3$ , respectively. One of these elements crystallizes in a body-centered cubic structure; the other three crystallize in a face-centered cubic structure. Which one crystallizes in the body-centered cubic structure? Justify your answer.

For each of these solids, state whether you would expect it to possess metallic properties: (a) TiCl_ ${}_4,(\mathbf{b})$ NiCo alloy, $(\mathbf{c})\mathrm{W}$ $(\mathbf{d})\mathrm{Ge},(\mathbf{e})\mathrm{ScN}$

Sodium metal (atomic weight 22.99 $\mathrm{g}/\mathrm{mol}$ ) adopts a body- centered cubic structure with a density of 0.97 $\mathrm{g}/{\mathrm{cm}}^3$ . (a) Use this information and Avogadro's number $(N_{\mathrm{A}}=6.022\times {10}^{23}/\mathrm{mol})$ to estimate the atomic radius of sodium. $(\mathbf{b})$ If sodium didn't react so vigorously, it could float on water. Use the answer from part (a) to estimate the density of Na if its structure were that of a cubic close packed metal. Would it still float on water?

Iridium crystallizes in a face-centered cubic unit cell that has an edge length of 3.833 $\dot{A}$. (a) Calculate the atomic radius of an iridium atom. (b) Calculate the density of iridium metal.