Chapter 10

Barium has a body-centered cubic structure. If the atomic radius of barium is 222 \(\mathrm{pm}\) , calculate the density of solid barium.

The radius of gold is \(144 \mathrm{pm},\) and the density is 19.32 \(\mathrm{g} / \mathrm{cm}^{3}\) . Does elemental gold have a face-centered cubic structure or a body-centered cubic structure?

The radius of tungsten is 137 \(\mathrm{pm}\) and the density is 19.3 \(\mathrm{g} / \mathrm{cm}^{3}\) . Does elemental tungsten have a face-centered cubic structure or a body- centered cubic structure?

What fraction of the total volume of a cubic closest packed structure is occupied by atoms? (Hint: \(V_{\text { sphere }}=\frac{4}{3} \pi r^{3} .\) ) What fraction of the total volume of a simple cubic structure is occupied by atoms? Compare the answers.

Iron has a density of 7.86 \(\mathrm{g} / \mathrm{cm}^{3}\) and crystallizes in a body-centered cubic lattice. Show that only 68\(\%\) of a body-centered lattice is actually occupied by atoms, and determine the atomic radius of iron.

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 \(\mathrm{A} /\) Group 5 \(\mathrm{A}\) 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?

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 \(\mathrm{Na}_{2} \mathrm{O}, \mathrm{CdS},\) and \(\mathrm{ZrL}_{4}\) 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?

In solid \(\mathrm{KCl}\) 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 \(\mathrm{KCl}\) , 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 71 ). 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. \(\mathrm{Ru}\) f. \(\mathrm{I}_{2}\) g. \(\mathrm{KBr}\) h. \(\mathrm{H}_{2} \mathrm{O}\) i. \(\mathrm{NaOH}\) j. \(\mathrm{U}\) k. \(\mathrm{CaCO}_{3}\) I. \(\mathrm{PH}_{3}\)

What type of solid will each of the following substances form? a. 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. Ar j. \(\mathrm{Cu}\) k. \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\)

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?

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?

Mercury is the only metal that is a liquid at room temperature. When mercury vapor is inhaled, it is readily absorbed by the lungs, causing significant health risks. The enthalpy of vaporization of mercury is 59.1 \(\mathrm{kJ} / \mathrm{mol}\) . The normal boiling point of mercury is \(357^{\circ} \mathrm{C}\) . What is the vapor pressure of mercury at \(25^{\circ} \mathrm{C} ?\)

A substance, X, has the following properties: Sketch a heating curve for substance \(X\) starting at \(-50 .^{\circ} \mathrm{C}\)

The molar heat of fusion of sodium metal is 2.60 kJ/mol,whereas its heat of vaporization is 97.0 kJ/mol. a. Why is the heat of vaporization so much larger than the heat of fusion? b. What quantity of heat would be needed to melt 1.00 g sodium at its normal melting point? c. What quantity of heat would be needed to vaporize 1.00 g sodium at its normal boiling point? d. What quantity of heat would be evolved if 1.00 g sodium vapor condensed at its normal boiling point

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 \(\mathrm{g}\) 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 \(\mathrm{kg}\) ice at \(-20.0^{\circ} \mathrm{C}\) to steam at \(250.0^{\circ} \mathrm{C} ?\) Specific heat capacities: ice, \(2.03 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C} ;\) liquid, \(4.18 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C} ;\) steam, 2.02 \(\mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C}\) \(\Delta H_{\mathrm{vap}}=40.7 \mathrm{kJ} / \mathrm{mol} ; \Delta H_{\mathrm{fus}}=6.02 \mathrm{kJ} / \mathrm{mol} .\)

What quantity of energy is needed to heat a 1.00 -mole sample of \(\mathrm{H}_{2} \mathrm{O}\) from \(-30.0^{\circ} \mathrm{C}\) to \(140.0^{\circ} \mathrm{C} ?\) (see Exercise 101\()\)

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. Br_ 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 \(200^{\circ} \mathrm{C} ?\)

The melting point of a fictional substance \(X\) is \(225^{\circ} \mathrm{C}\) at 10.0 atm. If the density of the solid phase of \(\mathrm{X}\) is 2.67 \(\mathrm{g} / \mathrm{cm}^{3}\) and the density of the liquid phase is 2.78 \(\mathrm{g} / \mathrm{cm}^{3}\) at 10.0 atm, predict whether the normal melting point of \(\mathrm{X}\) will be less than, equal to, or greater than \(225^{\circ} \mathrm{C}\) . Explain.

Consider the following data for xenon: $$ \begin{array}{ll}{\text { Triple point: }} & {-121^{\circ} \mathrm{C}, 280 \text { torr }} \\ {\text { Normal melting point: }} & {-112^{\circ} \mathrm{C}} \\ {\text { Normal boiling point: }} & {-107^{\circ} \mathrm{C}}\end{array} $$ Which is more dense, \(\operatorname{Xe}(s)\) or \(\operatorname{Xe}(l) ?\) How do the melting point and boiling point of xenon depend on pressure?

Which is stronger, a dipole–dipole interaction between two molecules or a covalent bond between two atoms within the same molecule? Explain.

Consider the following formulas for n-pentane and neopentane: Both compounds have the same overall formula \(\left(\mathrm{C}_{5} \mathrm{H}_{12}, \text { molar }\right.\) mass \(=72.15 \mathrm{g} / \mathrm{mol} ),\) yet \(n\) -pentane boils at \(36.2^{\circ} \mathrm{C}\) whereas neopentane boils at \(9.5^{\circ} \mathrm{C} .\) Rationalize the differences in the boiling points between these two nonpolar compounds.

Some of the physical properties of \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{D}_{2} \mathrm{O}\) are as follows: Account for the differences. (Note: D is a symbol often used for \(^{2} \mathrm{H},\) the deuterium isotope of hydrogen.)

Consider the following data for an unknown substance \(\mathrm{X} :\) $$\begin{array}{l}{\Delta H_{\mathrm{vap}}=20.00 \mathrm{kJ} / \mathrm{mol}} \\\ {\Delta H_{\mathrm{fus}}=5.00 \mathrm{kJ} / \mathrm{mol}}\end{array}$$ $$\begin{array}{l}{\text { Specific heat capacity of solid }=3.00 \mathrm{Jg} \cdot^{\circ} \mathrm{C}} \\ {\text { Specific heat capacity of liquid }=2.50 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C}} \\ {\text { Boiling point }=75.0^{\circ} \mathrm{C}} \\ {\text { Melting point }=-15.0^{\circ} \mathrm{C}} \\ {\text { Molar mass }=100.0 \mathrm{g} / \mathrm{mol}}\end{array}$$ In the heating of substance \(\mathrm{X}\) , energy (heat) is added at a constant rate of 450.0 \(\mathrm{J} / \mathrm{min}\) . At this rate, how long will it take to heat 10.0 \(\mathrm{g}\) of \(\mathrm{X}\) from \(-35.0^{\circ} \mathrm{C}\) to \(25.0^{\circ} \mathrm{C} ?\)

Consider the data for substance \(X\) given in Exercise 117 . When the temperature of 1.000 mole of \(X(g)\) is lowered from \(100.0^{\circ} \mathrm{C}\) to form \(\mathrm{X}(l)\) at \(50.0^{\circ} \mathrm{C}, 28.75 \mathrm{kJ}\) of heat is released. Calculate the specific heat capacity of \(\mathrm{X}(g)\)

Argon has a cubic closest packed structure as a solid. Assuming that argon has a radius of 190. pm, calculate the density of solid argon

Dry nitrogen gas is bubbled through liquid benzene (C. \(\mathrm{H}_{6} )\) at \(20.0^{\circ} \mathrm{C} .\) From 100.0 \(\mathrm{L}\) of the gaseous mixture of nitrogen and benzene, 24.7 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 -g sample of ice at \(-10.0^{\circ} \mathrm{C}\) is mixed with 100.0 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 \(\mathrm{kJ} / \mathrm{mol} .\)

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 \(\mathrm{CCl}_{4} ?\)

In regions with dry climates, evaporative coolers are used to cool air. A typical electric air conditioner is rated at \(1.00 \times 10^{4}\) Btu/h \((1 \mathrm{Btu}, \text { or British thermal unit }=\text { amount of energy to }\) raise the temperature of 1 \(\mathrm{lb}\) 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?

The critical point of \(\mathrm{NH}_{3}\) is \(132^{\circ} \mathrm{C}\) and \(111 \mathrm{atm},\) and the critical point of \(\mathrm{N}_{2}\) is \(-147^{\circ} \mathrm{C}\) and 34 \(\mathrm{atm}\) . Which of these substances cannot be liquefied at room temperature no matter how much pressure is applied? Explain.

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 \(\mathrm{HBr}\) . c. \(\mathrm{Cl}_{2}\) will have a higher boiling point than Ar. d. HCl is more soluble in water than in \(\mathrm{CCl}_{4}\) 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 8A, ionic, or molecular) will each of the following substances form? a. \(\mathrm{Kr}\) b. \(\mathrm{SO}_{2}\) c. \(\mathrm{Ni}\) d. \(\mathrm{SiO}_{2}\) e. \(\mathrm{NH}_{3}\) f. \(\mathrm{Pt}\)