Chapter 13

Calcium metal crystallizes in a face-centered cubic unit cell. The density of the solid is \(1.54 \mathrm{g} / \mathrm{cm}^{3} .\) What is the radius of a calcium atom?

The density of copper metal is \(8.95 \mathrm{g} / \mathrm{cm}^{3} .\) If the radius of a copper atom is \(127.8 \mathrm{pm},\) is the copper unit cell primitive, body-centered cubic, or face-centered cubic?

Considering only the molecular orbitals formed by combinations of the \(2 s\) atomic orbitals, how many molecular orbitals can be formed by 1000 Li atoms? In the lowest energy state, how many of these orbitals will be populated by pairs of electrons and how many will be empty?

Conduction of an electric current is a general property associated with metals. How does the theory for metallic bonding explain conductivity?

Most metals are shiny, that is, they reflect light. How does the bonding theory for metals explain this characteristic?

Elemental silicon and carbon (in the diamond allotropic form) have the same solid-state structure. However, diamond is an insulator and silicon is a semiconductor. Explain why there is a difference.

Define the terms intrinsic semiconductor and extrinsic semiconductor. Give an example of each.

Explain the conductivity that occurs in an aluminumdoped silicon semiconductor. Is this material a p-type or an \(n\) -type semiconductor?

List the following compounds in order from least negative to most negative lattice energy: LiI, LiF, CaO, RbI.

To melt an ionic solid, energy must be supplied to disrupt the forces between ions so the regular array of ions collapses. If the distance between the anion and the cation in a crystalline solid decreases (but ion charges remain the same), should the melting point decrease or increase? Explain.

Which compound in each of the following pairs should have the higher melting point? (See Study Question 21.) (a) NaCl or RbCl (b) \(\mathrm{BaO}\) or \(\mathrm{MgO}\) (c) \(\mathrm{NaCl}\) or \(\mathrm{MgS}\)

We have identified five types of solids (metallic, ionic, molecular, network, amorphous). What particles make up each of these solids and what are the forces of attraction between these particles?

List the general properties of each type of solid.

Benzene, \(\mathrm{C}_{6} \mathrm{H}_{6},\) is an organic liquid that freezes at \(5.5^{\circ} \mathrm{C}(\text { 4 Figure } 12.1)\) to form beautiful, feather- like crystals. How much energy is evolved as heat when \(15.5 \mathrm{g}\) of benzene freezes at \(5.5^{\circ} \mathrm{C} ?\) (The enthalpy of fusion of benzene is \(9.95 \mathrm{kJ} / \mathrm{mol} .\) ) If the \(15.5-\mathrm{g}\) sample is remelted, again at \(5.5^{\circ} \mathrm{C},\) what quantity of energy is required to convert it to a liquid?

The specific heat capacity of silver is \(0.235 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}\) Its melting point is \(962^{\circ} \mathrm{C},\) and its enthalpy of fusion is \(11.3 \mathrm{kJ} / \mathrm{mol} .\) What quantity of energy, in joules, is required to change \(5.00 \mathrm{g}\) of silver from a solid at \(25^{\circ} \mathrm{C}\) to a liquid at \(962^{\circ} \mathrm{C} ?\)

Liquid ammonia, \(\mathrm{NH}_{3}(\ell),\) was once used in home refrigerators as the heat transfer fluid. The specific heat capacity of the liquid is \(4.7 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}\) and that of the vapor is \(2.2 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}\). The enthalpy of vaporization is \(23.33 \mathrm{kJ} / \mathrm{mol}\) at the boiling point. If you heat \(12 \mathrm{kg}\) of liquid ammonia from \(-50.0^{\circ} \mathrm{C}\) to its boiling point of \(-33.3^{\circ} \mathrm{C},\) allow it to evaporate, and then continue warming to \(0.0^{\circ} \mathrm{C},\) how much energy must you supply?

If your air conditioner is more than several years old, it may use the chlorofluorocarbon \(\mathrm{CCl}_{2} \mathrm{F}_{2}\) as the heat transfer fluid. The normal boiling point of \(\mathrm{CCl}_{2} \mathrm{F}_{2}\) is \(-29.8^{\circ} \mathrm{C},\) and the enthalpy of vaporization is \(20.11 \mathrm{kJ} / \mathrm{mol} .\) The gas and the liquid have molar heat capacities of \(117.2 \mathrm{J} / \mathrm{mol} \cdot \mathrm{K}\) and \(72.3 \mathrm{J} / \mathrm{mol} \cdot \mathrm{K},\) respec- tively. How much energy is evolved as heat when \(20.0 \mathrm{g}\) of \(\mathrm{CCl}_{2} \mathrm{F}_{2}\) is cooled from \(+40^{\circ} \mathrm{C}\) to \(-40^{\circ} \mathrm{C} ?\)

Construct a phase diagram for \(\mathrm{O}_{2}\) from the following information: normal boiling point, \(90.18 \mathrm{K} ;\) normal melting point, \(54.8 \mathrm{K} ;\) and triple point, \(54.34 \mathrm{K}\) at a pressure of \(2 \mathrm{mm}\) Hg. Very roughly estimate the vapor pressure of liquid \(\mathrm{O}_{2}\) at \(-196^{\circ} \mathrm{C},\) the lowest temperature easily reached in the laboratory. Is the density of liquid \(\mathrm{O}_{2}\) greater or less than that of solid \(\mathrm{O}_{2} ?\)

Silver crystallizes in a face-centered cubic unit cell. Each side of the unit cell has a length of \(409 \mathrm{pm} .\) What is the radius of a silver atom?

The very dense metal iridium has a face-centered cubic unit cell and a density of \(22.56 \mathrm{g} / \mathrm{cm}^{3} .\) Use this information to calculate the radius of an atom of the element.

Vanadium metal has a density of \(6.11 \mathrm{g} / \mathrm{cm}^{3} .\) Assuming the vanadium atomic radius is \(132 \mathrm{pm},\) is the vanadium unit cell primitive cubic, body-centered cubic, or facecentered cubic?

Calcium fluoride is the well-known mineral fluorite. Each unit cell contains four \(\mathrm{Ca}^{2+}\) ions and eight \(\mathrm{F}^{-}\) ions. The \(\mathrm{F}^{-}\) ions fill all the tetrahedral holes in a facecentered cubic lattice of \(\mathrm{Ca}^{2+}\) ions. The edge of the \(\mathrm{CaF}_{2}\) unit cell is \(5.46295 \times 10^{-8} \mathrm{cm}\) in length. The density of the solid is \(3.1805 \mathrm{g} / \mathrm{cm}^{3} .\) Use this information to calculate Avogadro's number.

Iron has a body-centered cubic unit cell with a cell dimension of \(286.65 \mathrm{pm} .\) The density of iron is \(7.874 \mathrm{g} / \mathrm{cm}^{3} .\) Use this information to calculate Avogadro's number.

Assuming that in a primitive cubic unit cell the spherical atoms or ions just touch along the cube's edges, calculate the percentage of empty space within the unit cell. (Recall that the volume of a sphere is (4/3) \(\pi r^{3},\) where \(r\) is the radius of the sphere.)

Spinels are solids with the general formula \(\mathrm{AB}_{2} \mathrm{O}_{4}\) (where \(\mathrm{A}^{2+}\) and \(\mathrm{B}^{3+}\) are metal cations of the same or different metals). The best-known example is common magnetite, \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) [which you can formulate as \(\left(\mathrm{Fe}^{2+}\right)\) \(\left.\left(\mathrm{Fe}^{3+}\right)_{2} \mathrm{O}_{4}\right] .\) Another example is the mineral often referred to as spinel, \(\mathrm{MgAl}_{2} \mathrm{O}_{4}\) (IMAGE CANNOT COPY)The oxide ions of spinels form a face-centered cubic lattice. In a normal spinel, cations occupy \(1 / 8\) of the tetrahedral sites and \(1 / 2\) of the octahedral sites. (a) In \(\mathrm{MgAl}_{2} \mathrm{O}_{4},\) in what types of holes are the magnesium and aluminum ions found? (b) The mineral chromite has the formula \(\mathrm{FeCr}_{2} \mathrm{O}_{4}\) What ions are involved, and in what types of holes are they found?

The band gap in gallium arsenide is \(140 \mathrm{kJ} / \mathrm{mol}\). What is the maximum wavelength of light needed to excite an electron to move from the valence band to the conduction band?

The conductivity of an intrinsic semiconductor increases with increasing temperature. How can this be rationalized?

Which will show the highest conductivity at \(298 \mathrm{K}\) silicon or germanium?

Identify the following as either \(p\) or \(n\) -type semiconductors. (a) Germanium doped with arsenic (b) Silicon doped with phosphorus (c) Germanium doped with indium (d) Germanium doped with antimony

Diamond-based semiconductors are currently of enormous interest in the research community. Although diamond itself is an insulator, the addition of a dopant will narrow the band gap. One semiconductor system has diamond with boron as a dopant. Is this a \(p\) - or an \(n\) -type semiconductor?

Boron phosphide, BP, is a semiconductor and a hard, abrasion-resistant material. It is made by reacting boron tribromide and phosphorus tribromide in a hydrogen atmosphere at high temperature \(\left(>750^{\circ} \mathrm{C}\right)\) (a) Write a balanced chemical equation for the synthesis of BP. (Hint: Hydrogen is a reducing agent.) (b) Boron phosphide crystallizes in a zinc-blend structure, formed from boron atoms in a face-centered cubic lattice and phosphorus atoms in tetrahedral holes. How many tetrahedral holes are filled with P atoms in each unit cell? (c) The length of a unit cell of BP is 478 pm. What is the density of the solid in \(\mathrm{g} / \mathrm{cm}^{3} ?^{-}\) (d) Calculate the closest distance between a \(\mathrm{B}\) and a P atom in the unit cell. (Assume the B atoms do not touch along the cell edge. The \(\mathrm{B}\) atoms in the faces touch the \(\mathrm{B}\) atoms at the corners of the unit cell.)

Why is it not possible for a salt with the formula \(\mathrm{M}_{3} \mathrm{X}\) \(\left(\mathrm{Na}_{3} \mathrm{PO}_{4}, \text { for example }\right)\) to have a face-centered cubic lattice of \(\mathrm{X}\) anions with \(\mathrm{M}\) cations in octahedral holes?

Two identical swimming pools are filled with uniform spheres of ice packed as closely as possible. The spheres in the first pool are the size of grains of sand; those in the second pool are the size of oranges. The ice in both pools melts. In which pool, if either, will the water level be higher? (Ignore any differences in filling space at the planes next to the walls and bottom.)