Chapter 9

Explain how doping silicon with either phosphorus or gallium increases the electrical conductivity over that of pure silicon.

Explain how a p-n junction makes an excellent rectifier.

Selenium is a semiconductor used in photocopying machines. What type of semiconductor would be formed if a small amount of indium impurity is added to pure selenium?

The Group 3 A/Group 5 A semiconductors are composed of equal amounts of atoms from Group \(3 \mathrm{A}\) and Group \(5 \mathrm{A}-\) for example, InP and GaAs. These types of semiconductors are used in light-emitting diodes and solid- state lasers. What would you add to make a p-type semiconductor from pure GaAs? How would you dope pure GaAs to make an n-type semiconductor?

The band gap in aluminum phosphide (AIP) is 2.5 electronvolts \(\left(1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{J}\right) .\) What wavelength of light is emitted by an AlP diode?

An aluminum antimonide solid-state laser emits light with a wavelength of \(730 . \mathrm{nm} .\) Calculate the band gap in joules.

Cobalt fluoride crystallizes in a closest packed array of fluoride ions with the cobalt ions filling one-half of the octahedral holes. What is the formula of this compound?

The compounds \(\mathrm{Na}_{2} \mathrm{O},\) CdS, and \(\mathrm{ZrI}_{4}\) all can be described as cubic closest packed anions with the cations in tetrahedral holes. What fraction of the tetrahedral holes is occupied for each case?

What is the formula for the compound that crystallizes with a cubic closest packed array of sulfur ions, and that contains zinc ions in \(\frac{1}{8}\) of the tetrahedral holes and aluminum ions in \(\frac{1}{2}\) of the octahedral holes?

A certain metal fluoride crystallizes in such a way that the fluoride ions occupy simple cubic lattice sites, while the metal ions occupy the body centers of half the cubes. What is the formula of the metal fluoride?

The structure of manganese fluoride can be described as a simple cubic array of manganese ions with fluoride ions at the center of each edge of the cubic unit cell. What is the charge of the manganese ions in this compound?

In solid KCl the smallest distance between the centers of a potassium ion and a chloride ion is \(314 \mathrm{pm} .\) Calculate the length of the edge of the unit cell and the density of KCl, assuming it has the same structure as sodium chloride.

The CsCl structure is a simple cubic array of chloride ions with a cesium ion at the center of each cubic array (see Exercise 69 ). Given that the density of cesium chloride is \(3.97 \mathrm{g} / \mathrm{cm}^{3},\) and assuming that the chloride and cesium ions touch along the body diagonal of the cubic unit cell, calculate the distance between the centers of adjacent \(\mathrm{Cs}^{+}\) and \(\mathrm{Cl}^{-}\) ions in the solid. Compare this value with the expected distance based on the sizes of the ions. The ionic radius of \(\mathrm{Cs}^{+}\) is \(169 \mathrm{pm},\) and the ionic radius of \(\mathrm{Cl}^{-}\) is \(181 \mathrm{pm}\).

What type of solid will each of the following substances form? a. \(\mathrm{CO}_{2}\) b. \(\mathrm{SiO}_{2}\) c. \(\mathrm{Si}\) d. \(\mathrm{CH}_{4}\) e. \(\mathbf{R} \mathbf{u}\) f. \(\mathrm{I}_{2}\)

What type of solid will each of the following substances form? a. \(\mathrm{diamond}\) b. \(\mathrm{PH}_{3}\) c. \(\mathrm{H}_{2}\) d. \(\mathrm{Mg}\) e. \(\mathrm{KCl}\) f. quartz g. \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) h. \(\mathrm{SF}_{2}\) i. \(\mathrm{Ar}\) j. \(\mathrm{Cu}\) k. \(\mathrm{C}_{6} \mathbf{H}_{12} \mathbf{O}_{6}\)

The memory metal, nitinol, is an alloy of nickel and titanium. It is called a memory metal because after being deformed, a piece of nitinol wire will return to its original shape. The structure of nitinol consists of a simple cubic array of Ni atoms and an inner penetrating simple cubic array of Ti atoms. In the extended lattice, a Ti atom is found at the center of a cube of Ni atoms; the reverse is also true. a. Describe the unit cell for nitinol. b. What is the empirical formula of nitinol? c. What are the coordination numbers (number of nearest neighbors) of Ni and Ti in nitinol?

Superalloys have been made of nickel and aluminum. The alloy owes its strength to the formation of an ordered phase, called the gamma-prime phase, in which Al atoms are at the corners of a cubic unit cell and Ni atoms are at the face centers. What is the composition (relative numbers of atoms) for this phase of the nickel-aluminum superalloy?

Carbon tetrachloride, \(\mathrm{CCl}_{4},\) has a vapor pressure of 213 torr at \(40 .^{\circ} \mathrm{C}\) and 836 torr at \(80 .^{\circ} \mathrm{C} .\) What is the normal boiling point of \(\mathrm{CCl}_{4} ?\)

Diethyl ether \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OCH}_{2} \mathrm{CH}_{3}\right)\) was one of the first chemicals used as an anesthetic. At \(34.6^{\circ} \mathrm{C},\) diethyl ether has a vapor pressure of \(760 .\) torr, and at \(17.9^{\circ} \mathrm{C},\) it has a vapor pressure of \(400 .\) torr. What is the \(\Delta H\) of vaporization for diethyl ether?

The molar heat of fusion of benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) is \(9.92 \mathrm{kJ} / \mathrm{mol}\). Its molar heat of vaporization is \(30.7 \mathrm{kJ} / \mathrm{mol}\). Calculate the heat required to melt 8.25 g benzene at its normal melting point. Calculate the heat required to vaporize 8.25 g benzene at its normal boiling point. Why is the heat of vaporization more than three times the heat of fusion?

What quantity of energy does it take to convert 0.500 kg ice at \(-20 .^{\circ} \mathrm{C}\) to steam at \(250 .^{\circ} \mathrm{C} ?\) Specific heat capacities: ice, \(2.03 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C} ;\) liquid, \(4.2 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C} ;\) steam, \(2.0 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C} ; \Delta H_{\mathrm{vap}}=\) \(40.7 \mathrm{kJ} / \mathrm{mol} ; \Delta H_{\mathrm{fus}}=6.02 \mathrm{kJ} / \mathrm{mol}.\)

An ice cube tray contains enough water at \(22.0^{\circ} \mathrm{C}\) to make 18 ice cubes that each has a mass of \(30.0 \mathrm{g}\). The tray is placed in a freezer that uses \(\mathrm{CF}_{2} \mathrm{Cl}_{2}\) as a refrigerant. The heat of vaporization of \(\mathrm{CF}_{2} \mathrm{Cl}_{2}\) is \(158 \mathrm{J} / \mathrm{g} .\) What mass of \(\mathrm{CF}_{2} \mathrm{Cl}_{2}\) must be vaporized in the refrigeration cycle to convert all the water at \(22.0^{\circ} \mathrm{C}\) to ice at \(-5.0^{\circ} \mathrm{C} ?\) The heat capacities for \(\mathrm{H}_{2} \mathrm{O}(s)\) and \(\mathrm{H}_{2} \mathrm{O}(l)\) are \(2.03 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C}\) and \(4.18 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C},\) respectively, and the enthalpy of fusion for ice is \(6.02 \mathrm{kJ} / \mathrm{mol}\).

A \(0.250-g\) chunk of sodium metal is cautiously dropped into a mixture of \(50.0 \mathrm{g}\) water and \(50.0 \mathrm{g}\) ice, both at \(0^{\circ} \mathrm{C}\). The reaction is $$2 \mathrm{Na}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{NaOH}(a q)+\mathrm{H}_{2}(g) \quad \Delta H=-368 \mathrm{kJ}$$ Assuming no heat loss to the surroundings, will the ice melt? Assuming the final mixture has a specific heat capacity of \(4.18 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C},\) calculate the final temperature. The enthalpy of fusion for ice is \(6.02 \mathrm{kJ} / \mathrm{mol}\).

Like most substances, bromine exists in one of the three typical phases. \(\mathrm{Br}_{2}\) has a normal melting point of \(-7.2^{\circ} \mathrm{C}\) and a normal boiling point of \(59^{\circ} \mathrm{C}\). The triple point for \(\mathrm{Br}_{2}\) is \(-7.3^{\circ} \mathrm{C}\) and 40 torr, and the critical point is \(320^{\circ} \mathrm{C}\) and 100 atm. Using this information, sketch a phase diagram for bromine indicating the points described above. Based on your phase diagram, order the three phases from least dense to most dense. What is the stable phase of \(\mathrm{Br}_{2}\) at room temperature and 1 atm? Under what temperature conditions can liquid bromine never exist? What phase changes occur as the temperature of a sample of bromine at 0.10 atm is increased from \(-50^{\circ} \mathrm{C}\) to \(200^{\circ} \mathrm{C} ?\)

Consider the following enthalpy changes: $$\begin{aligned} \mathrm{F}^{-}+\mathrm{HF} \longrightarrow \mathrm{FHF}^{-} & \Delta H=-155 \mathrm{kJ} / \mathrm{mol} \\ \left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}=\mathrm{O}+\mathrm{HF} \longrightarrow\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}=\mathrm{O}--\mathrm{HF} & \Delta H=-46 \mathrm{kJ} / \mathrm{mol} \\\ \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{HOH}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}--\mathrm{HOH}(\text { in ice }) & \Delta H=-21 \mathrm{kJ} / \mathrm{mol} \end{aligned}$$ How do the strengths of hydrogen bonds vary with the electronegativity of the element to which hydrogen is bonded? Where in the preceding series would you expect hydrogen bonds of the following type to fall?

Argon has a cubic closest packed structure as a solid. Assuming that argon has a radius of \(190 . \mathrm{pm},\) calculate the density of solid argon.

Dry nitrogen gas is bubbled through liquid benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) at \(20.0^{\circ} \mathrm{C} .\) From \(100.0 \mathrm{L}\) of the gaseous mixture of nitrogen and benzene, \(24.7 \mathrm{g}\) benzene is condensed by passing the mixture through a trap at a temperature where nitrogen is gaseous and the vapor pressure of benzene is negligible. What is the vapor pressure of benzene at \(20.0^{\circ} \mathrm{C} ?\)

A \(20.0-\mathrm{g}\) sample of ice at \(-10.0^{\circ} \mathrm{C}\) is mixed with \(100.0 \mathrm{g}\) water at \(80.0^{\circ} \mathrm{C}\). Calculate the final temperature of the mixture assuming no heat loss to the surroundings. The heat capacities of \(\mathrm{H}_{2} \mathrm{O}(s)\) and \(\mathrm{H}_{2} \mathrm{O}(l)\) are 2.03 and \(4.18 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C},\) respectively, and the enthalpy of fusion for ice is \(6.02 \mathrm{kJ} / \mathrm{mol}\).

In regions with dry climates, evaporative coolers are used to cool air. A typical electric air conditioner is rated at \(1.00 \times\) \(10^{4} \mathrm{Btu} / \mathrm{h}(1 \mathrm{Btu}, \text { or British thermal unit }=\) amount of energy to raise the temperature of 1 lb water by \(1^{\circ} \mathrm{F}\) ). What quantity of water must be evaporated each hour to dissipate as much heat as a typical electric air conditioner?

Which of the following compound(s) exhibit only London dispersion intermolecular forces? Which compound(s) exhibit hydrogen-bonding forces? Considering only the compounds without hydrogen-bonding interactions, which compounds have dipole-dipole intermolecular forces? a. \(\mathrm{SF}_{4}\) b. \(\mathrm{CO}_{2}\) c. \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) d. \(\mathrm{HF}\) e. \(\mathrm{ICl}_{5}\) f. \(\mathrm{XeF}_{4}\)

Which of the following statements about intermolecular forces is(are) true? a. London dispersion forces are the only type of intermolecular force that nonpolar molecules exhibit. b. Molecules that have only London dispersion forces will always be gases at room temperature \(\left(25^{\circ} \mathrm{C}\right).\) c. The hydrogen-bonding forces in \(\mathrm{NH}_{3}\) are stronger than those in \(\mathrm{H}_{2} \mathrm{O}\). d. The molecules in \(\mathrm{SO}_{2}(g)\) exhibit dipole-dipole intermolecular interactions. e. \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}\) has stronger London dispersion forces than does \(\mathrm{CH}_{4}.\)

Which of the following statements is(are) true? a. LiF will have a higher vapor pressure at \(25^{\circ} \mathrm{C}\) than \(\mathrm{H}_{2} \mathrm{S}\). b. HF will have a lower vapor pressure at \(-50^{\circ} \mathrm{C}\) than HBr. c. \(\mathrm{Cl}_{2}\) will have a higher boiling point than Ar. d. HCl is more soluble in water than in CCl_. e. \(\mathrm{MgO}\) will have a higher vapor pressure at \(25^{\circ} \mathrm{C}\) than \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\)

Aluminum has an atomic radius of \(143 \mathrm{pm}\) and forms a solid with a cubic closest packed structure. Calculate the density of solid aluminum in \(\mathrm{g} / \mathrm{cm}^{3} .\)

Pyrolusite is a mineral containing manganese ions and oxide ions. Its structure can best be described as a body-centered cubic array of manganese ions with two oxide ions inside the unit cell and two oxide ions each on two faces of the cubic unit cell. What is the charge on the manganese ions in pyrolusite?

The structure of the compound \(\mathrm{K}_{2} \mathrm{O}\) is best described as a cubic closest packed array of oxide ions with the potassium ions in tetrahedral holes. What percent of the tetrahedral holes are occupied in this solid?

What type of solid (network, metallic, Group \(8 \mathrm{A},\) ionic, or molecular) will each of the following substances form? a. \(\mathrm {K r}\) b. \(\mathrm{SO}_{2}\) c. \(\mathrm {Ni}\) d. \(\mathrm{SiO}_{2}\) e. \(\mathrm{NH}_{3}\) f. \(\mathrm{Pt}\)

When 1 mole of benzene is vaporized at a constant pressure of 1.00 atm and at its boiling point of \(353.0 \mathrm{K}, 30.79 \mathrm{kJ}\) of energy (heat) is absorbed and the volume change is +28.90 L. What are \(\Delta E\) and \(\Delta H\) for this process?

You and a friend each synthesize a compound with the formula \(\mathrm{XeCl}_{2} \mathrm{F}_{2}\). Your compound is a liquid and your friend's compound is a gas (at the same conditions of temperature and pressure). Explain how the two compounds with the same formulas can exist in different phases at the same conditions of pressure and temperature.

Consider two different organic compounds, each with the formula \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}\). One of these compounds is a liquid at room conditions and the other is a gas. Write Lewis structures consistent with this observation, and explain your answer. (Hint: The oxygen atom in both structures satisfies the octet rule with two bonds and two lone pairs.)

Some ionic compounds contain a mixture of different charged cations. For example, wüstite is an oxide that contains both \(\mathrm{Fe}^{2+}\) and \(\mathrm{Fe}^{3+}\) cations and has a formula of \(\mathrm{Fe}_{0.950} \mathrm{O}_{1.00}\). Calculate the fraction of iron ions present as \(\mathrm{Fe}^{3+} .\) What fraction of the sites normally occupied by \(\mathrm{Fe}^{2+}\) must be vacant in this solid?

Some ionic compounds contain a mixture of different charged cations. For example, some titanium oxides contain a mixture of \(\mathrm{Ti}^{2+}\) and \(\mathrm{Ti}^{3+}\) ions. Consider a certain oxide of titanium that is \(28.31 \%\) oxygen by mass and contains a mixture of \(\mathrm{Ti}^{2+}\) and \(\mathrm{Ti}^{3+}\) ions. Determine the formula of the compound and the relative numbers of \(\mathrm{Ti}^{2+}\) and \(\mathrm{Ti}^{3+}\) ions.

Spinel is a mineral that contains \(37.9 \%\) aluminum, \(17.1 \%\) magnesium, and \(45.0 \%\) oxygen, by mass, and has a density of \(3.57 \mathrm{g} / \mathrm{cm}^{3} .\) The edge of the cubic unit cell measures \(809 \mathrm{pm} .\) How many of each type of ion are present in the unit cell?

You are asked to help set up a historical display in the park by stacking some cannonballs next to a Revolutionary War cannon. You are told to stack them by starting with a triangle in which each side is composed of four touching cannonballs. You are to continue stacking them until you have a single ball on the top centered over the middle of the triangular base. a. How many cannonballs do you need? b. What type of closest packing is displayed by the cannonballs? c. The four corners of the pyramid of cannonballs form the corners of what type of regular geometric solid?

Some water is placed in a sealed glass container connected to a vacuum pump (a device used to pump gases from a container), and the pump is turned on. The water appears to boil and then freezes. Explain these changes using the phase diagram for water. What would happen to the ice if the vacuum pump was left on indefinitely?

The molar enthalpy of vaporization of water at \(373 \mathrm{K}\) and 1.00 atm is \(40.7 \mathrm{kJ} / \mathrm{mol} .\) What fraction of this energy is used to change the internal energy of the water, and what fraction is used to do work against the atmosphere? (Hint: Assume that water vapor is an ideal gas.)

For a simple cubic array, solve for the volume of an interior sphere (cubic hole) in terms of the radius of a sphere in the array.

A 0.132 -mole sample of an unknown semiconducting material with the formula XY has a mass of \(19.0 \mathrm{g}\). The element X has an electron configuration of \([\mathrm{Kr}] 5 s^{2} 4 d^{10} .\) What is this semiconducting material? A small amount of the Y atoms in the semiconductor is replaced with an equivalent amount of atoms with an electron configuration of \([\mathrm{Ar}] 4 s^{2} 3 d^{10} 4 p^{5} .\) Does this correspond to n-type or p-type doping?

One method of preparing elemental mercury involves roasting cinnabar (HgS) in quicklime (CaO) at 600.^ C followed by condensation of the mercury vapor. Given the heat of vaporization of mercury (296 J/g) and the vapor pressure of mercury at \(25.0^{\circ} \mathrm{C}\left(2.56 \times 10^{-3} \text {torr }\right),\) what is the vapor pressure of the condensed mercury at \(300 .^{\circ} \mathrm{C} ?\) How many atoms of mercury are present in the mercury vapor at \(300 .^{\circ} \mathrm{C}\) if the reaction is conducted in a closed 15.0 -L container?

General Zod has sold Lex Luthor what Zod claims to be a new copper-colored form of kryptonite, the only substance that can harm Superman. Lex, not believing in honor among thieves, decided to carry out some tests on the supposed kryptonite. From previous tests, Lex knew that kryptonite is a metal having a specific heat capacity of \(0.082 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C}\) and a density of \(9.2 \mathrm{g} / \mathrm{cm}^{3}.\) Lex Luthor's first experiment was an attempt to find the specific heat capacity of kryptonite. He dropped a \(10 \mathrm{g} \pm 3 \mathrm{g}\) sample of the metal into a boiling water bath at a temperature of \(100.0^{\circ} \mathrm{C} \pm 0.2^{\circ} \mathrm{C} .\) He waited until the metal had reached the bath temperature and then quickly transferred it to \(100 \mathrm{g} \pm 3 \mathrm{g}\) of water that was contained in a calorimeter at an initial temperature of \(25.0^{\circ} \mathrm{C} \pm 0.2^{\circ} \mathrm{C} .\) The final temperature of the metal and water was \(25.2^{\circ} \mathrm{C} .\) Based on these results, is it possible to distinguish between copper and kryptonite? Explain. When Lex found that his results from the first experiment were inconclusive, he decided to determine the density of the sample. He managed to steal a better balance and determined the mass of another portion of the purported kryptonite to be \(4 \mathrm{g} \pm 1\) g. He dropped this sample into water contained in a 25-mL graduated cylinder and found that it displaced a volume of \(0.42 \mathrm{mL} \pm 0.02 \mathrm{mL} .\) Is the metal copper or kryptonite? Explain. Lex was finally forced to determine the crystal structure of the metal General Zod had given him. He found that the cubic unit cell contained four atoms and had an edge length of \(600 . \mathrm{pm} .\) Explain how this information enabled Lex to identify the metal as copper or kryptonite. Will Lex be going after Superman with the kryptonite or seeking revenge on General Zod? What improvements could he have made in his experimental techniques to avoid performing the crystal structure determination?