Chapter 10

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.)

Consider the following melting point data: Account for the trends in melting points in terms of interparticle forces

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?

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?

Mn crystallizes in the same type of cubic unit cell as Cu. Assuming that the radius of Mn is 5.6\(\%\) larger than the radius of \(\mathrm{Cu}\) and the density of copper is \(8.96 \mathrm{g} / \mathrm{cm}^{3},\) calculate the density of Mn.

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?

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.

Rubidium chloride has the sodium chloride structure at normal pressures but assumes the cesium chloride structure at high pressures. (See Exercise \(71 . )\) What ratio of densities is expected for these two forms? Does this change in structure make sense on the basis of simple models? The ionic radius is 148 \(\mathrm{pm}\) for \(\mathrm{Rb}^{+}\) and 181 \(\mathrm{pm}\) for \(\mathrm{Cl}^{-} .\)

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 \((296 \mathrm{J} / \mathrm{g} \text { ) and the vapor pressure of mercury }\) at \(25.0^{\circ} \mathrm{C}\left(2.56 \times 10^{-3} \text { torr), what is the vapor pressure of the }\right.\) 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 \(\mathrm{-L}\) 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 \(4 \mathrm{g} \pm 1 \mathrm{g} .\) He dropped this sample into water contained in a \(25-\mathrm{mL}\) 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?