Chapter 5

Identify the kinds of intermolecular forces that might arise between molecules of each of the following substances: (a) \(\mathrm{NH}_{2} \mathrm{OH}\); (b) \(\mathrm{CBr}_{4}\); (c) \(\mathrm{H}_{2} \mathrm{SeO}_{4}\); (d) \(\mathrm{SO}_{2}\).

Identify the kinds of intermolecular forces that might arise between molecules of each of the following substances: (a) \(\mathrm{NF}_{3}\); (b) \(\mathrm{PH}_{3}\); (c) \(\mathrm{HI}\); (d) \(\mathrm{HIO}\) (O is the central atom).

For which of the following molecules will dipole-dipole interactions be important: (a) \(\mathrm{O}_{2} ;\) (b) \(\mathrm{O}_{3} ;\) (c) \(\mathrm{CO}_{2}\); (d) \(\mathrm{SO}_{2}\) ?

Suggest, giving reasons, which substance in each of the following pairs is likely to have the higher normal melting point (Lewis structures may help your arguments): (a) \(\mathrm{HCl}\) or \(\mathrm{NaCl}\); (b) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OC}_{2} \mathrm{H}_{5}\) (diethyl ether) or \(\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{OH}\) (butanol); (c) \(\mathrm{CH}_{3}\) or \(\mathrm{CHF}_{3} ;\) (d) \(\mathrm{C}_{2} \mathrm{H}_{4}\) or \(\mathrm{CH}_{3} \mathrm{OH}\).

Suggest, giving reasons, which substance in each of the following pairs is likely to have the higher normal boiling point: (a) \(\mathrm{H}_{2} \mathrm{~S}\) or \(\mathrm{H}_{2} \mathrm{O}\); (b) \(\mathrm{NH}_{3}\) or \(\mathrm{PH}_{3}\); (c) \(\mathrm{KBr}\) or \(\mathrm{CH}_{3} \mathrm{Br}\); (d) \(\mathrm{CH}_{4}\) or \(\mathrm{SiH}_{4}\).

Using the VSEPR model, predict the shapes of each of the following molecules and identify the member of each pair with the higher boiling point: (a) \(\mathrm{PBr}_{3}\) or \(\mathrm{PF}_{3} ;\) (b) \(\mathrm{SO}_{2}\) or \(\mathrm{CO}_{2} ;\) (c) \(\mathrm{BF}_{3}\) or \(\mathrm{BCl}_{3}\).

Place the following types of molecular and ion interactions in order of increasing magnitude: (a) ion-dipole; (b) induceddipole-induced-dipole; (c) dipole-dipole in the gas phase; (d) ion-ion; (c) dipole-dipole in the solid phase.

In each pair, indicate which substance has the stronger intermolecular forces and explain your reasoning: (a) Ne, Ar; (b) \(\mathrm{NF}_{3}, \mathrm{BF}_{3} ;\) (c) \(\mathrm{SiH}_{4}, \mathrm{GeH}_{4}\); (d) \(\mathrm{NaF}, \mathrm{HF}\).

Which of the following molecules are likely to form hydrogen bonds: (a) \(\mathrm{PH}_{3}\); (b) \(\mathrm{HBr}\); (c) \(\mathrm{C}_{2} \mathrm{H}_{4}\); (d) \(\mathrm{HNO}_{2}\) ?

Which of the following molecules are likely to form hydrogen bonds: (a) \(\mathrm{CH}_{3} \mathrm{OCH}_{3}\); (b) \(\mathrm{CH}_{3} \mathrm{COOH}\); (c) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\); (d) \(\mathrm{CH}_{3} \mathrm{CHO}\) ?

Account for the following observations in terms of the type and strength of intermolecular forces. (a) The melting point of solid xenon is \(-112^{\circ} \mathrm{C}\) and that of solid argon is \(-189^{\circ} \mathrm{C}\). (b) The vapor pressure of diethyl ether \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OC}_{2} \mathrm{H}_{5}\right)\) is greater than that of water. (c) The boiling point of pentane, \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{3} \mathrm{CH}_{3}\), is \(36.1^{\circ} \mathrm{C}\), whereas that of 2,2 -dimethylpropane (also known as neopentane \(), \mathrm{C}\left(\mathrm{CH}_{3}\right)_{4}\), is \(9.5^{\circ} \mathrm{C}\).

We have been using "intermolecular interaction" and "intermolecular force" almost interchangeably. However, it is important to distinguish the force from the potential energy of interaction. In classical mechanics, the magnitude of the force, \(F\), is related to the distance dependence of the potential energy, \(E_{\mathrm{P}}\), by \(F=-\mathrm{d} E_{\mathrm{p}} / \mathrm{d} r\). How does the intermolecular force depend on separation for a typical intermolecular interaction that varies as \(1 / r^{6}\) ?

Predict how each of the following properties of a liquid varies as the strength of intermolecular forces incrcases and explain your reasoning: (a) boiling point; (b) viscosity; (c) surface tension.

Predict which substance in each of the following pairs has the greater viscosity in its liquid form at \(0^{\circ} \mathrm{C}\) : (a) ethanol, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\), or dimethyl ether, \(\mathrm{CH}_{3} \mathrm{OCH}_{3}\); (b) butane, \(\mathrm{C}_{4} \mathrm{H}_{10}\), or propanone, \(\mathrm{CH}_{3} \mathrm{COCH}_{3}\).

Rank the following molecules in order of increasing viscosity at \(50^{\circ} \mathrm{C}: \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{SH}, \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}, \mathrm{C}_{6} \mathrm{H}_{6}\).

The following boiling points correspond to the substances listed. Match the boiling points to the substances by considering the relative strengths of their intermolecular forces. b.p. \(\left({ }^{\circ} \mathrm{C}\right)\) : $$ -162,-88.5,28,36,64.5,78.3,82.5,140,205,290 \text {; substance: } $$ \(\mathrm{CH}_{4}, \mathrm{CH}_{3} \mathrm{CHOHCH}_{3}, \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{OH}\) (has a benzene ring), \(\mathrm{HOCH}_{2} \mathrm{CHOHCH}_{2} \mathrm{OH}, \mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{3} \mathrm{CH}_{3}, \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\). Hint: The boiling point of \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CHCH}{\underline{\phantom{xx}}}_{2} \mathrm{CH}_{3}\) is \(28^{\circ} \mathrm{C}\) and that of \(\mathrm{CH}_{3} \mathrm{OH}\) is \(64.5^{\circ} \mathrm{C}\).

Chloromethane \(\left(\mathrm{CH}_{3} \mathrm{Cl}\right)\), methane, and acetic acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\) form molecular solids. (a) What types of forces hold these molecules in a molecular solid? (b) Place the solids in order of increasing melting point.

Classify each of the following solids as ionic, network, metallic, or molecular: (a) iron pyrite (fool's gold), \(\mathrm{FeS}_{2}\); (b) octane (a component of gasoline), \(\mathrm{C}_{8} \mathrm{H}_{18}\); (c) cubic boron nitride (a compound with a structure similar to that of diamond, but with alternating boron and nitrogen atoms), BN; (d) calcium sulfate (gypsum), \(\mathrm{CaSO}_{4}\); (e) the chromium plating on a motorcycle.

Iron crystallizes in a bec structure. The atomic radius of iron is \(124 \mathrm{pm}\). Determine (a) the number of atoms per unit cell; (b) the coordination number of the lattice; (c) the length of the side of the unit cell.

The metal polonium (which was named by Marie Curie after her homeland, Poland) crystallizes in a primitive cubic structure, with an atom at each corner of a cubic unit cell. The atomic radius of polonium is \(167 \mathrm{pm}\). Sketch the unit cell and determine (a) the number of atoms per unit cell; (b) the coordination number of an atom of polonium; (c) the length of the side of the unit cell.

Calculate the atomic radius of each of the following elements (b) tantalum, bcc structure, density \(16.654 \mathrm{~g} \cdot \mathrm{cm}^{-3}\).

One form of silicon has density of \(2.33 \mathrm{~g} \cdot \mathrm{cm}^{-3}\) and crystallizes in a cubic lattice with a unit cell edge of \(543 \mathrm{pm}\). (a) What is the mass of each unit cell? (b) How many silicon atoms does one unit cell contain?

Indium arsenide crystallizes in the sphalerite structure (Fig. \(5.45\) ). (a) What are the coordination numbers of the indium and arsenide ions? (b) What is the formula of indium arsenide?

An oxide of rhenium crystallizes with a cubic unit cell that has a rhenium cation at each corner and an oxide ion at the center of each edge of the crystal. (a) Determine the coordination numbers of the two ions. (b) Write the formula of the oxide.

When an oxide of uranium crystallizes the uranium cations form an expanded cubic close-packed array with an oxide ion in each tetrahedral hole. (a) Determine the coordination numbers of the two ions. (b) Write the formula of the oxide.

The molecular structures of many common liquid crystals are long and rodlike. In addition, they contain polar groups. Explain how both characteristics of liquid crystals contribute to their anisotropic nature.

Draw the Lewis structure of (a) \(\mathrm{NI}_{3}\) and (b) \(\mathrm{BI}_{3}\), name the molecular shape, and indicate whether each can participate in dipole- dipole interactions.

Draw the Lewis structure of (a) \(\mathrm{CF}_{4}\), (b) \(\mathrm{SF}_{4}\), name the molecular shape, and indicate whether each can participate in dipole- dipole interactions.

(a) Calculate the surface areas of the isomers 2,2 dimethylpropane and pentane. Assume that 2,2-dimethylpropane is spherical with a radius of \(254 \mathrm{pm}\) and that pentane can be approximated by a rectangular prism with dimensions \(295 \mathrm{pm} \times\) \(692 \mathrm{pm} \times 766 \mathrm{pm}\). (b) Which has the larger surface area? (c) Which do you expect to have the higher boiling point?

All the alkali metals crystallize with bec structures. (a) Find a general equation relating the metallic radius to the density of a bcc solid of an element in terms of its molar mass and use it to deduce the atomic radius of each of the following elements, given the density of each \(\left(\right.\) in \(\left.\mathrm{g} \cdot \mathrm{cm}^{-3}\right): \mathrm{Li}, 0.53 ; \mathrm{Na}, 0.97 ; \mathrm{K}, 0.86 ; \mathrm{Rb}, 1.53\); Cs, 1.87. (b) Find a factor for converting the density of a bcc element into the density that it would have if it crystallized in a ccp structure. (c) Calculate what the densities of the alkali metals would be if they were ccp. (d) Which, if any, would float on water?

An oxide of niobium has a unit cell in which there are oxide ions at the middle of each edge and niobium ions at the center of each face. What is the empirical formula of this oxide?

Uranium dioxide, \(\mathrm{UO}_{2}\), can be further oxidized to give a nonstoichiometric compound \(\mathrm{UO}_{2+x}\), where \(0

Are the following statements true or false? (a) If there is an atom present at the corner of a unit cell, there must be the same type of atom at all the corners of the unit cell. (b) A unit cell must be defined so that there are atoms at the corners. (c) If one face of a unit cell has an atom in its center, then the face opposite that face must also have an atom at its center. (d) If one face of a unit cell has an atom in its center, all the faces of the unit cell must also have atoms at their centers.

A commonly occurring mineral has a cubic unit cell in which the metal cations, \(M\), occupy the corners and face centers. Inside the unit cell, anions, A, occupy all the tetrahedral holes created by the cations. What is the empirical formula of the \(\mathrm{M}_{m} \mathrm{~A}_{a}\) compound?

Tetrahedral and octahedral interstitial holes are formed by the vacancies left when anions pack in a ccp array. (a) Which hole can accommodate the larger ions? (b) What is the size ratio of the largest metal cation that can occupy an octahedral hole to the largest that can occupy a tetrahedral hole while maintaining the close-packed nature of the anion lattice? (c) If half the tetrahedral holes are occupied, what will be the empirical formula of the compound \(\mathrm{M}_{x} \mathrm{~A}_{y}\), where \(\mathrm{M}\) represents the cations and \(\mathrm{A}\) the anions?

(a) If a pure element crystallizes with a primitive cubic lattice, what percentage of the unit cell is empty space? (b) How does this percentage compare with that of empty space in an fcc unit cell?

Consider a metallic element that crystallizes in a cubic close-packed lattice. The edge length of the unit cell is \(408 \mathrm{pm}\). If close-packed layers are deposited on a flat surface to a depth (of metal) of \(0.125 \mathrm{~mm}\), how many close-packed layers are present?

Ethylammonium nitrate, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{NH}_{3} \mathrm{NO}_{3}\), was the first ionic liquid to be discovered. Its melting point of \(12^{\circ} \mathrm{C}\) was reported in 1914 and it has since been used as a nonpolluting solvent for organic reactions and for facilitating the folding of protcins. (a) Draw the Lewis structure of each ion in ethylammonium nitrate and indicate the formal charge on each atom (in the cation, the carbon atoms are attached to the \(N\) atom in a chain: \(\mathrm{C}-\mathrm{C}-\mathrm{N})\). (b) Assign a hybridization scheme to each \(\mathrm{C}\) and \(\mathrm{N}\) atom. (c) Ethylammonium nitrate cannot be used as a solvent for some reactions because it can oxidize some compounds. Which ion is more likely to be the oxidizing agent, the cation or anion? Explain your answer. (d) Ethylammonium nitrate can be prepared by the reaction of gaseous ethylamine, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{NH}_{2}\), and aqueous nitric acid. Write the chemical equation for the reaction. What type of reaction is this? (e) \(2.00 \mathrm{~L}\) of ethylamine at \(0.960\) atm and \(23.2^{\circ} \mathrm{C}\) was bubbled into \(2.50 .0 \mathrm{~mL}\) of \(0.240 \mathrm{M} \mathrm{HNO}_{3}(\mathrm{aq})\) and \(4.10 \mathrm{~g}\) of ethylammonium nitrate was produced. What were the theoretical and percentage yields of the salt? (f) Suggest ways in which the forces that hold ethylammonium nitrate ions together in the solid state differ from those that hold together salts such as sodium chloride or sodium bromide. (g) Low-melting salts in which the cation is inorganic and the anion organic have been prepared. Explain the trend in melting point seen in the following series: sodium acetate \(\left(\mathrm{NaCH}_{3} \mathrm{CO}_{2}\right)\), \(324^{\circ} \mathrm{C}\); sodium propanoate \(\left(\mathrm{NaCH}_{3} \mathrm{CH}_{2} \mathrm{CO}_{2}\right), 285^{\circ} \mathrm{C}\); sodium butanoate \(\left(\mathrm{NaCH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CO}_{2}\right), 76^{\circ} \mathrm{C}\); and sodium pentanoate \(\left(\mathrm{NaCH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CO}_{2}\right), 64^{\circ} \mathrm{C}\).