13. Liquids, Solids & Intermolecular Forces

Niobium oxide crystallizes in the following cubic unit cell:

What is the formula of niobium oxide, and what is the oxidation state of niobium? (LO 12.5) (a) NbO, Nb = +2 (b) Nb2O, Nb = +2 (c) NbO2, Nb = +4 (d) Nb2O3, Nb = +3

Titanium oxide crystallizes in the following cubic unit cell:

(b) What is the formula of titanium oxide?

With the exception of helium, the noble gases condense to form solids when they are cooled sufficiently. At temperatures below 83 K, argon forms a close-packed solid whose structure is shown below. (b) Is this value larger or smaller than the bonding atomic radius estimated for argon in Figure 7.7?

What is the minimum number of atoms that could be contained in the unit cell of an element with a face-centered cubic lattice? (a) 1, (b) 2, (c) 3, (d) 4, (e) 5.

Determine the number of atoms per unit cell for each metal. (c) Nickel

Consider the unit cells shown here for three different structures that are commonly observed for metallic elements. (a) Which structure(s) corresponds to the densest packing of atoms?

Platinum crystallizes with the face-centered cubic unit cell. The radius of a platinum atom is 139 pm. Calculate the edge length of the unit cell and the density of platinum in g/cm3 .

Rhodium has a density of 12.41 g/cm3 and crystallizes with the face-centered cubic unit cell. Calculate the radius of a rhodium atom.

Copper crystallizes in a face-centered cubic unit cell with an edge length of 362 pm. What is the radius of a copper atom in picometers? What is the density of copper in g>cm3?

Aluminum has a density of 2.699 g>cm3 and crystallizes with a face-centered cubic unit cell. What is the edge length of a unit cell in picometers?

An element crystallizes in a face-centered cubic lattice. The edge of the unit cell is 4.078 Å, and the density of the crystal is 19.30 g>cm3. Calculate the atomic weight of the element and identify the element.

Titanium metal has a density of 4.506 g>cm3 and an atomic radius of 144.8 pm. In what cubic unit cell does titanium crystallize?

The atomic radius of Pb is 175 pm, and the density is 11.34 g>cm3. Does lead have a primitive cubic structure or a face-centered cubic structure?

The density of a sample of metal was measured to be 6.84 g>cm3. An X-ray diffraction experiment measures the edge of a face-centered cubic cell as 350.7 pm. What is the atomic weight, atomic radius, and identity of the metal?

Sodium hydride, NaH, crystallizes in a face-centered cubic unit cell similar to that of NaCl (Figure 12.11). How many Na+ ions touch each H- ion, and how many H- ions touch each Na+ ion?

Identify the structure of each of the two unit cells shown in Problem 48 as the rock salt structure, zinc blende structure, fluorite structure, antifluorite structure, or none of these.

If the edge length of an NaH unit cell is 488 pm, what is the length in picometers of an Na¬H bond? (See Problem 12.50.)

Tausonite, a mineral composed of Sr, O, and Ti, has the cubic unit cell shown in the drawing. (a) What is the empirical formula of this mineral?

A particular form of cinnabar (HgS) adopts the zinc blende structure. The length of the unit cell edge is 5.852 Å. (c) Which of the two substances has the higher density? How do you account for the difference in densities?

A particular form of cinnabar (HgS) adopts the zinc blende structure. The length of the unit cell edge is 5.852 Å. (b) The mineral tiemannite (HgSe) also forms a solid phase with the zinc blende structure. The length of the unit cell edge in this mineral is 6.085 Å. What accounts for the larger unit cell length in tiemmanite?

CuI, CsI, and NaI each adopt a different type of structure. The three different structures are those shown in Figure 12.26. (a) Use ionic radii, Cs+ 1r = 1.81 A 2, Na+ 1r = 1.16 A 2, Cu+ 1r = 0.74 A 2, and, I- 1r = 2.06 A 2, to predict which compound will crystallize with which structure.

Copper iodide crystallizes in the zinc blende structure. The sep- aration between nearest neighbor cations and anions is approximately 311 pm, and the melting point is 606 °C. Potassium chloride, by contrast, crystallizes in the rock salt structure. Even though the separation between nearest-neighbor cations and anions is greater (319 pm), the melting point of potassium chlo- ride is higher (776 °C). Explain.

The density of an unknown metal is 12.3 g/cm3, and its atomic radius is 0.134 nm. It has a face-centered cubic lattice. Find the atomic mass of this metal

The ionic compound CaO crystallizes with the same structure as sodium chloride (Figure 8.3). (a) In this structure, how many O2- are in contact with each Ca2+ ion (Hint: Remember the pattern of ions shown in Figure 8.3 repeats over and over again in all three directions.)

Calculate the fraction of empty space in cubic closest packing to five significant figures.

The ionic substance strontium oxide, SrO, forms from the reaction of strontium metal with molecular oxygen. The arrangement of the ions in solid SrO is analogous to that in solid NaCl:

(c) The density of SrO is 5.10 g>cm3. Given your answer to part (b), how many formula units of SrO are contained in the cube shown here?

The ionic substance strontium oxide, SrO, forms from the reaction of strontium metal with molecular oxygen. The arrangement of the ions in solid SrO is analogous to that in solid NaCl:

(b) Based on the ionic radii in Figure 7.8, predict the length of the side of the cube in the figure (the distance from the center of an atom at one corner to the center of an atom at a neighboring corner).

Pure iron crystallizes in a body-centered cubic structure, shown in the figure. but small amounts of impurities can stabilize a facecentered cubic structure. Which form of iron has a higher density?

For each of the intermetallic compounds shown in Figure 12.17 determine the number of each type of atom in the unit cell. Do your answers correspond to the ratios expected from the empirical formulas: Ni3Al?

What type of lattice—primitive cubic, body-centered cubic, or face-centered cubic—does each of the following structure types possess: (e) ZnS?

Platinum nanoparticles of diameter 2 nm are important catalysts in carbon monoxide oxidation to carbon dioxide. Platinum crystallizes in a face-centered cubic arrangement with an edge length of 3.924 Å. (c) Using your results from (a) and (b), calculate the percentage of Pt atoms that are on the surface of a 2.0-nm nanoparticle.

Platinum nanoparticles of diameter 2 nm are important catalysts in carbon monoxide oxidation to carbon dioxide. Platinum crystallizes in a face-centered cubic arrangement with an edge length of 3.924 Å. (b) Estimate how many platinum atoms are on the surface of a 2.0-nm Pt sphere, using the surface area of a sphere 14pr22 and assuming that the 'footprint' of one Pt atom can be estimated from its atomic diameter of 2.8 A .

Sodium oxide (Na2O) adopts a cubic structure with Na atoms represented by green spheres and O atoms by red spheres.

(c) The unit cell edge length is 5.550 Å. Determine the density of Na2O.

(a) The density of diamond is 3.5 g>cm3, and that of graphite is 2.3 g>cm3. Based on the structure of buckminsterfullerene, what would you expect its density to be relative to these other forms of carbon?

Silicon has the diamond structure with a unit cell edge length of 5.43 Å and eight atoms per unit cell. (b) Suppose you dope that 1 cm3 sample of silicon with 1 ppm of phosphorus that will increase the conductivity by a factor of a million. How many milligrams of phosphorus are required?

The mineral wustite is a nonstoichiometric iron oxide with the empirical formula FexO, where x is a number slightly less than 1. Wustite can be regarded as an FeO in which some of the Fe sites are vacant. It has a density of 5.75 g>cm3, a cubic unit cell with an edge length of 431 pm, and a facecentered cubic arrangement of oxygen atoms. (c) Each Fe atom in wustite is in either the +2 or the +3 oxidation state. What percent of the Fe atoms are in the +3 oxidation state?

The alkali metal fulleride superconductors M3C60 have a cubic closest-packed (face-centered cubic) arrangement of nearly spherical C60 3- anions with M+ cations in the holes between the larger C603- ions. The holes are of two types: octahedral holes, which are surrounded octahedrally by six C603- ions; and tetrahedral holes, which are surrounded tetrahedrally by four C603- ions. (c) Specify fractional coordinates for all the octahedral and tetrahedral holes. (Fractional coordinates are fractions of the unit cell edge lengths. For example, a hole at the center of the cell has fractional coordinates 12, 12, 12.)