Chapter 9

Solid lithium has a body-centered cubic unit cell with the length of the edge of \(351 \mathrm{pm}\) at \(20{ }^{\circ} \mathrm{C}\). Calculate the density of lithium at this temperature.

Tungsten has a body-centered cubic unit cell and an atomic radius of \(141 \mathrm{pm} .\) Calculate the density of solid tungsten.

Explain how two-dimensional and three-dimensional network solids differ on the nanoscale.

Explain why diamond is an electrical insulator and graphite is an electrical conductor.

Taking the middle of the visible spectrum to be green light with a wavelength of \(550 \mathrm{nm}\), calculate how many aluminum atoms (radius \(=143 \mathrm{pm}\) ) touching their neighbors would make a straight line \(550 \mathrm{nm}\) long. Using this result, explain why an optical microscope using visible radiation will never be able to detect an individual aluminum atom (or any other atom, for that matter).

The second-order Bragg reflection \((n=2)\) from a copper crystal for X-rays with a wavelength of \(166 \mathrm{pm}\) is \(27.35^{\circ}\). Calculate the spacing between the planes of copper atoms.

The first-order Bragg reflection \((n=1)\) from a \(\mathrm{NaCl}\) crystal with a spacing of \(282 \mathrm{pm}\) is seen at \(23.0^{\circ} .\) Calculate the wavelength of the \(\mathrm{X}\) -ray radiation used.

Identify three items you use daily that have been developed recently using the principles of materials science.

In terms of band theory, what is the difference between a conductor and an insulator? Between a conductor and a semiconductor?

Name three properties of metals, and explain them by using a theory of metallic bonding.

Which substance has the greatest electrical conductivity? The smallest electrical conductivity? Explain your choice briefly. (a) Si (b) Ge (c) \(\mathrm{Ag}\) (d) \(\mathrm{P}_{4}\)

Which substance has the greatest electrical conductivity? The smallest electrical conductivity? Explain your choices briefly. (a) \(\mathrm{RbCl}(\ell)\) (b) \(\mathrm{NaBr}(\mathrm{s})\) (c) \(\mathrm{Rb}\) (d) Diamond

Define the term "superconductor." Give the chemical formulas of two kinds of superconductors and their associated transition temperatures.

Extremely high-purity silicon is required to manufacture semiconductors such as the memory chips found in calculators and computers. If a silicon wafer is \(99.99999999 \%\) pure, approximately how many atoms of some other element are present per gram of high-purity silicon?

Explain why Group \(3 \mathrm{~A}\) and Group \(5 \mathrm{~A}\) elements are used to dope silicon to improve its semiconducting properties.

Explain the difference between \(n\) -type semiconductors and \(p\) -type semiconductors.

Define the term "amorphous."

What makes a glass different from a crystalline solid such as \(\mathrm{SiO}_{2}\) ? Under what conditions could \(\mathrm{SiO}_{2}\) become glass-like?

A typical cement contains, by weight, \(65 \% \mathrm{CaO}, 20 \%\) \(\mathrm{SiO}_{2}, 5 \% \mathrm{Al}_{2} \mathrm{O}_{3}, 6 \% \mathrm{Fe}_{2} \mathrm{O}_{3},\) and \(4 \% \mathrm{MgO} .\) Determine the mass percent of each type of atom present. Then, determine an empirical formula of the material from the percent composition, setting the subscript of the least abundant element to 1.00 .

Give two examples of (a) silicate ceramics, (b) oxide ceramics, and (c) nonoxide ceramics.

Explain why, when you boil water in a pan, the water boils much faster when the pan has a lid on it than when it does not.

Will a closed container of water at \(70^{\circ} \mathrm{C}\) or an open container of water at the same temperature cool faster on a cold winter day? Explain why.

Given these properties: Camphor: colorless needles; density \(=0.900 \mathrm{~g} / \mathrm{cm}^{3}\) at \(25^{\circ} \mathrm{C}\); sublimes at \(204{ }^{\circ} \mathrm{C} ;\) insoluble in water; very soluble in ethanol or ether. Praseodymium chloride: blue-green needle crystals; density \(=4.02 \mathrm{~g} / \mathrm{cm}^{3}\) at \(25^{\circ} \mathrm{C}\); melting point \(786^{\circ} \mathrm{C}\); boiling point \(1700^{\circ} \mathrm{C}\); solubility \(103.9 \mathrm{~g} / 100 \mathrm{~mL}\) cold water, very soluble in hot water. (a) Is camphor an ionic or covalent compound? Explain your answer. (b) Is praseodymium chloride an ionic or covalent compound? Explain your answer.

Xenon has a triple point of \(0.81 \mathrm{~atm}\) and \(-112{ }^{\circ} \mathrm{C}\) and a normal boiling point of \(-108^{\circ} \mathrm{C}\). If the pressure exerted on a xenon sample is \(1.75 \mathrm{~atm}\) and the temperature is \(-105^{\circ} \mathrm{C}\), in what phase (physical state) does the xenon sample likely exist at these conditions? Explain your answer.

Xenon has a triple point of \(0.81 \mathrm{~atm}\) and \(-112{ }^{\circ} \mathrm{C}\) and a normal boiling point of \(-108^{\circ} \mathrm{C}\). If the pressure exerted on a xenon sample is \(1.75 \mathrm{~atm}\) and the temperature is \(-105^{\circ} \mathrm{C}\), in what phase (physical state) does the xenon sample likely exist at these conditions? Explain your answer.

Organic compounds with structures based on benzene, \(\mathrm{C}_{6} \mathrm{H}_{6},\) can be formed by substituting an atom or a group of atoms for one of the hydrogens. Such substituted benzenes have their own properties, different from benzene and from each other. Explain the order of experimental boiling points for these four compounds. (a) \(\mathrm{C}_{6} \mathrm{H}_{6}\left(80{ }^{\circ} \mathrm{C}\right)\) (b) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Cl}\left(131{ }^{\circ} \mathrm{C}\right)\) (c) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Br}\left(156^{\circ} \mathrm{C}\right)\) (d) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\left(182{ }^{\circ} \mathrm{C}\right)\)

The chlorofluorocarbon \(\mathrm{CCl}_{2} \mathrm{~F}_{2}\) was once used in air conditioners as the heat transfer fluid. Its normal boiling point is \(-30^{\circ} \mathrm{C}\), and its vaporization enthalpy is \(165 \mathrm{~J} \mathrm{~g}^{-1}\). The gas and the liquid have specific heat capacities of \(0.61 \mathrm{~J} \mathrm{~g}^{-1}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1}\) and \(0.97 \mathrm{~J} \mathrm{~g}^{-1}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1}\) respectively. Calculate the heat energy transfer when \(10.0 \mathrm{~g} \mathrm{CCl}_{2} \mathrm{~F}_{2}\) is cooled from \(40^{\circ} \mathrm{C}\) to \(-40^{\circ} \mathrm{C}\).

Liquid ammonia, \(\mathrm{NH}_{3}(\ell)\), was used as a refrigerant fluid before the discovery of the chlorofluorocarbons and is still widely used today. Its normal boiling point is \(-33.4^{\circ} \mathrm{C},\) and its vaporization enthalpy is \(23.5 \mathrm{~kJ} / \mathrm{mol}\). The gas and liquid have specific heat capacities of 2.2 \(\mathrm{J} \mathrm{g}^{-1} \mathrm{~K}^{-1}\) and \(4.7 \mathrm{~J} \mathrm{~g}^{-1} \mathrm{~K}^{-1}\), respectively. Calculate the heat energy transfer required to raise the temperature of \(10.0 \mathrm{~kg}\) liquid ammonia from \(-50.0^{\circ} \mathrm{C}\) to \(0.0{ }^{\circ} \mathrm{C}\).

Sulfur dioxide, \(\mathrm{SO}_{2}\), is found in polluted air. What types of forces are responsible for binding \(\mathrm{SO}_{2}\), molecules to one another in the solid or liquid phase?

Using the information below, place the compounds listed in order of increasing intermolecular attractions. For each substance list all types of intermolecular forces that are important. $$ \begin{array}{lc} \hline \text { Compound } & \text { Normal Boiling Point }\left({ }^{\circ} \mathrm{C}\right) \\ \hline \mathrm{SO}_{2} & -10 \\ \mathrm{NH}_{3} & -33.4 \\ \mathrm{CH}_{4} & -161.5 \\ \mathrm{H}_{2} \mathrm{O} & 100 \\ \hline \end{array} $$

Metallic gold is very malleable; that is, it can be hammered into very thin sheets, which are sometimes called gold leaf. For example, a 1.0 -g sample of metallic gold can be hammered into a sheet with an area of \(1.0 \mathrm{~m}^{2}\). The density of gold is \(19.3 \mathrm{~g} / \mathrm{cm}^{3}\) and the radius of a gold atom is \(144 \mathrm{pm}\). Calculate how many atoms thick such a gold sheet would be.

Explain why, in general, the vaporization enthalpy of a liquid is much greater than the fusion enthalpy of its solid.

Consider this information regarding two compounds (common names are used). Orpiment: yellow solid; density \(=3.49 \mathrm{~g} / \mathrm{cm}^{3}\) at \(25^{\circ} \mathrm{C} ;\) melting point \(=573 \mathrm{~K}\); slightly soluble in hot water; soluble in basic solution. Zeaxanthin: orange-red solid; density \(=0.93 \mathrm{~g} / \mathrm{cm}^{3}\) at \(25^{\circ} \mathrm{C} ;\) melting point \(=489 \mathrm{~K} ;\) insoluble in water, soluble in benzene. (a) Is orpiment an ionic or molecular compound? Explain your answer. (b) Is zeaxanthin an ionic or molecular compound? Explain your answer.

Consider this information regarding two compounds. Thallium azide: yellow crystalline solid; melting point = \(330^{\circ} \mathrm{C}\); slightly soluble in water, more soluble in hot water; insoluble in ethanol or diethyl ether. Camphene: colorless, cubic crystals; melting point \(=51{ }^{\circ} \mathrm{C}\); boiling point \(=159{ }^{\circ} \mathrm{C} ;\) insoluble in water; moderately soluble in ethanol; soluble in diethyl ether. (a) Is camphene an ionic or molecular compound? Explain your answer. (b) Is thallium azide an ionic or molecular compound? Explain your answer.

Consider liquid water in equilibrium with its vapor at \(100{ }^{\circ} \mathrm{C}\). Estimate the number of water molecules per \(\mathrm{cm}^{3}\) in (a) the liquid (density \(=0.958 \mathrm{~g} / \mathrm{cm}^{3}\) at \(\left.100{ }^{\circ} \mathrm{C}\right)\); (b) the vapor.

If you get boiling water at \(100^{\circ} \mathrm{C}\) on your skin, it burns. If you get \(100^{\circ} \mathrm{C}\) steam on your skin, it burns much more severely. Explain why this is so.

If water at room temperature is placed in a flask that is connected to a vacuum pump and the vacuum pump then lowers the pressure in the flask, we observe that the volume of the water decreases and the remaining water turns into ice. Explain what has happened.

The normal boiling point of \(\mathrm{SO}_{2}\) is \(263.1 \mathrm{~K}\) and that of \(\mathrm{NH}_{3}\) is \(239.7 \mathrm{~K}\). At \(-40^{\circ} \mathrm{C}\), would you predict that ammonia has a vapor pressure greater than, less than, or equal to that of sulfur dioxide? Explain.

Butane is a gas at room temperature; however, if you look closely at a butane lighter you see it contains liquid butane. Explain how it is possible to have liquid butane present.

While camping with a friend in the Rocky Mountains, you decide to cook macaroni for dinner. Your friend says the macaroni will cook faster in the Rockies because the lower atmospheric pressure will cause the water to boil at a lower temperature. Do you agree with your friend? Explain your reasoning.

Consider three boxes of equal volume. One is filled with tennis balls, another with golf balls, and the third with marbles. If a closest-packing arrangement is used in each box, which one has the most occupied space? Which one has the least occupied space? (Disregard the difference in filling space at the walls, bottom, and top of the box.)

Barium sulfide(s) has the \(\mathrm{NaCl}\) structure and a density of \(4.25 \mathrm{~g} / \mathrm{cm}^{3} .\) Calculate the interionic distance and compare this value with the sum of the ionic radii \(\left(\mathrm{Ba}^{2+}=\right.\) \(\left.149 \mathrm{pm} ; \mathrm{S}^{2-}=170 \mathrm{pm}\right)\)

Potassium chloride and rubidium chloride both have the sodium chloride structure (Figure 9.24 ). X-ray diffraction experiments indicate that their cubic unit cell dimensions are \(629 \mathrm{pm}\) and \(658 \mathrm{pm}\), respectively. (i) One \(m o l \mathrm{KCl}\) and \(1 \mathrm{~mol} \mathrm{RbCl}\) are ground together to a very fine powder in a mortar and pestle, and the X-ray diffraction pattern of the pulverized solid is measured. Two patterns are observed, each corresponding to a cubic unit cell-one with an edge length of \(629 \mathrm{pm}\) and one with an edge length of \(658 \mathrm{pm}\). Call this Sample 1 . (ii) One \(\mathrm{mol} \mathrm{KCl}\) and \(1 \mathrm{~mol} \mathrm{RbCl}\) are heated until the entire mixture is molten and then cooled to room temperature. A single X-ray diffraction pattern indicates a cubic unit cell with an edge length of roughly \(640 \mathrm{pm}\). Call this Sample 2 . (a) Suppose that Samples 1 and 2 were analyzed for their chloride content. What fraction of each sample is chloride? Could the samples be distinguished by means of chemical analysis? (b) Interpret the two X-ray diffraction results in terms of the structures of the crystal lattices of Samples 1 and 2 . (c) What chemical formula should you write for Sample \(1 ?\) For Sample \(2 ?\) (d) Suppose that you dissolved \(1.00 \mathrm{~g}\) Sample 1 in \(100 \mathrm{~mL}\) water in a beaker and did the same with \(1.00 \mathrm{~g}\) Sample 2\. Which sample would conduct electricity better, or would both be the same? What ions would be present in each solution at what concentrations?