Chapter 12

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?

Predict the trend in lattice energy, from least negative to most negative, for the following compounds based on the ion charges and ionic radii: LiI, LiF; \(\mathrm{CaO}, \mathrm{RbI}\)

To melt an ionic solid, energy must be supplied to disrupt the forces between ions so the regular array of ions collapses. Predict (and explain) how the melting point is expected to vary as a function of the distance between cation and anion.

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

Considering only the molecular orbitals formed by combinations of the \(2 s\) atomic orbitals, how many molecular orbitals can be formed by \(1000 \mathrm{Li}\) 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 band theory for metallic bonding explain conductivity?

Most metals are shiny, that is, they reflect light. How does the band 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.

Is aluminum-doped silicon a \(p\) -type or an \(n\) -type semiconductor? Explain how conductivity occurs in this semiconductor.

Which of the following allotropes of carbon is not a network solid? (a) graphite (c) buckyballs \(\left(\mathrm{C}_{60}\right)\) (b) diamond (d) graphene

A soft, white waxy solid melts over a temperature range from \(120^{\circ} \mathrm{C}\) to \(130^{\circ} \mathrm{C}\). It doesn't dissolve in water and it doesn't conduct electricity. These properties are consistent with its identity as (a) a network solid (c) an amorphous solid (b) an ionic solid (d) a metallic solid

We have identified six types of solids (metallic, ionic, molecular, network, amorphous, alloys). 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.

Classify each of the following materials as falling into one of the categories listed in Table \(12.2 .\) What particles make up these solids and what are the forces of attraction between particles? Give one physical property of each. (a) gallium arsenide (b) polystyrene (c) silicon carbide (d) perovskite, \(\mathrm{CaTiO}_{3}\)

Benzene, \(\mathrm{C}_{6} \mathrm{H}_{6},\) is an organic liquid that freezes at \(\left.5.5^{\circ} \mathrm{C} \text { (Figure } 11.1\right)\) 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 \(72.3 \mathrm{J} / \mathrm{mol} \cdot \mathrm{K},\) respectively. 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 \(-40^{\circ} \mathrm{C} ?\)

Silver crystallizes in a face-centered cubic unit cell. Each side of the unit cell has a length of 409 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, bodycentered cubic, or face-centered 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 face-centered cubic lattice of \(\mathrm{Ca}^{2+}\) ions. The edge of the 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.

A 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.

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.

Consider the three types of cubic units cells. (a) Assuming that the spherical atoms or ions in a primitive cubic unit cell just touch along the cube's edges, calculate the percentage of occupied 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.) (b) Compare the percentage of occupied space in the primitive cell (pc) with the bcc and fcc unit cells. Based on this, will a metal in these three forms have the same or different densities? If different, in which is it most dense? In which is it least dense?

The solid-state structure of silicon is shown below. (a) Describe this crystal as \(\mathrm{pc}, \mathrm{bcc},\) or fcc. (b) What type of holes are occupied in the lattice? (c) How many Si atoms are there per unit cell? (d) Calculate the density of silicon in \(\mathrm{g} / \mathrm{cm}^{3}\) (given that the cube edge has a length of \(543.1 \mathrm{pm}\) ). (e) Estimate the radius of the silicon atom. (Note: The Si atoms on the edges do not touch one another.

Spinels are solids with the general formula \(\mathrm{AB}_{2} \mathrm{O}_{4}\) (where \(A^{2+}\) and \(B^{3+}\) 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 \(\left.\left(\mathrm{Fe}^{2+}\right)\left(\mathrm{Fe}^{3+}\right)_{2} \mathrm{O}_{4}\right] .\) Another example is the mineral often referred to as spinel, \(\mathrm{MgAl}_{2} \mathrm{O}_{4}\) (IMAGE CAN'T COPY)

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?

Molecular solids, network solids, and amorphous solids all contain atoms that are joined together by covalent bonds. However, these classes of compounds are very different in overall structure, and this leads to different physical properties associated with each group. Describe how the overall structures of these classes of solids differ from each other.

Potassium bromide has the same lattice structure as NaCl. Given the ionic radii of \(\mathrm{K}^{+}(133 \mathrm{pm})\) and \(\mathrm{Br}^{-}(196 \mathrm{pm}),\) calculate the density of KBr.

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 facecentered cubic lattice of X anions with 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.)