Ch.11 - Liquids, Solids & Intermolecular ForcesSee all chapters
All Chapters
Ch.1 - Intro to General Chemistry
Ch.2 - Atoms & Elements
Ch.3 - Chemical Reactions
BONUS: Lab Techniques and Procedures
BONUS: Mathematical Operations and Functions
Ch.4 - Chemical Quantities & Aqueous Reactions
Ch.5 - Gases
Ch.6 - Thermochemistry
Ch.7 - Quantum Mechanics
Ch.8 - Periodic Properties of the Elements
Ch.9 - Bonding & Molecular Structure
Ch.10 - Molecular Shapes & Valence Bond Theory
Ch.11 - Liquids, Solids & Intermolecular Forces
Ch.12 - Solutions
Ch.13 - Chemical Kinetics
Ch.14 - Chemical Equilibrium
Ch.15 - Acid and Base Equilibrium
Ch.16 - Aqueous Equilibrium
Ch. 17 - Chemical Thermodynamics
Ch.18 - Electrochemistry
Ch.19 - Nuclear Chemistry
Ch.20 - Organic Chemistry
Ch.22 - Chemistry of the Nonmetals
Ch.23 - Transition Metals and Coordination Compounds

Crystalline solids represent structures with well-organized patterns and shapes. 

Crystalline Solids vs. Amorphous Solids

Concept #1: Crystalline Solids

Unlike crystalline solidsamorphous solids represent structures that lack an organized patterns or shapes. 

When examining the particles within a crystal you may observe them tightly packed in an organized pattern. The smallest portion of which is termed the unit cell

Simple Cubic (SC) Unit Cell

There are 7 crystal systems and 14 types of unit cells that naturally occur. The simple cubic unit cell represents one of the simplest types. 

Concept #2: Simple Cubic Unit Cell

The Simple Cubic Unit Cell is composed of a cube with an atom at each corner. In the Lattice Diagram each of the unit cells are combined to form a crystal lattice. In the Space Filling Unit Cell Diagram we are shown that the unit cell uses only 1/8 of each of the 8 corner atoms. 

Body-Centered Cubic (BCC) Unit Cell 

The body-centered cubic unit cell is composed of a cube with one atom at each of its corners and one atom at the center of the cube. 

Concept #3: Body Centered Cubic Unit Cell

Face-Centered Cubic (FCC) Unit Cell 

The face-centered cubic unit cell is composed of a cube with one atom at each of its corners and one atom in the center of each cube face. 

Concept #4: Face Centered Cubic Unit Cell

Unit Cell Calculations

Example #1: Unit Cell Calculations 1

Example #2: Unit Cell Calculations 1

Example #3: Unit Cell Calculations 1

Example #4: Unit Cell Calculations

Example #5: Unit Cell Calculations 2

Example #6: Unit Cell Calculations 2

Example #7: Unit Cell Calculations 2

Example #8: Unit Cell Calculations 3

Example #9: Unit Cell Calculations 3

Example #10: Unit Cell Calculations 3

Additional Problems
Aluminum has a face-centered cubic unit structure and a density of 2.716 g/cm3. Calculate the edge length of the unit cell. a) 4.041 x 10 -8 cm b) 3.992 x 10 -8 cm c) 3.615 x 10 -8 cm d) 3.247 x 10 -8 cm e) 2.836 x 10 -8 cm
What is the number of nearest neighbors in a body-centered-cubic lattice? (A) 12 (B) 8 (C) 6 (D) 4
Determine the radius of an Al atom (in pm) if the density of aluminum is 2.71 g/cm 3. Aluminum crystallizes in a face centered cubic structure with an edge length of 2√2 r.  a) 143 pm b) 227 pm c) 96 pm d) 172 pm e) 193 pm
Gold crystallizes in a face-centered cubic structure. What is the edge length of the unit cell if the atomic radius of gold is 144 pm? a) 204 pm b) 288 pm c) 333 pm d) 407 pm
Which one of the following elements is considered an insulator? a. Fe b. Ga c. N d. Ge e. Si
Which of the following statements about crystalline and amorphous solids is TRUE? A) A crystalline solid is composed of atoms or molecules arranged with long-range repeating order. B) An example of a crystalline solid is glass. C) An example of an amorphous solid is table salt (NaCl). D) An amorphous solid is composed of atoms or molecules with a majority of its volume empty. E) All of the above statements are TRUE.
Rank the three cubic crystalline structures in order of increasing space between the particles of the crystal. Note: FCC = face-centered cubic, BCC = Body-centered cubic, and SC = simple cubic. a) SC < BCC = FCC b) FCC < BCC < SC c) BCC < FCC < SC d) FCC < SC < BCC e) SC = BCC < FCC
Sodium chloride, NaCl, crystallizes in a face-centered cubic lattice of chloride ions, with the smaller sodium ions occupying holes between the chloride ions. How many Cl – ions are in contact with any single Na+ ions? a) 4 b) 6 c) 8 d) 12
Which term describes the number of atoms surrounding an atom in a crystal lattice  a) Unit cell  b) Coordination number c) Crystalline solid d) Packing efficiency
   
What is the edge length of a face-centered cubic unit cell made up of atoms having a radius of 128 pm?   A) 181 pm B) 362 pm C) 512 pm D) 1020 pm E) 81 pm
Vanadium crystallizes in a body centered cubic structure and has an atomic radius of 131 pm. Determine the density of vanadium, if the edge length of a bcc structure is 4r/√3. A) 3.06 g/cm3 B) 12.2 g/cm3 C) 6.11 g/cm3 D) 2.77 g/cm3 E) 8.46 g/cm3  
The edge of a body-centered-cubic unit cell (which contains two atoms per unit cell) of an element Y was found to be 3.16 x 10 –8 cm. The density of the metal is 19.35 g•cm –3. What is the approximate molar mass of Y? a) 65.4 g•mol –1  b) 92.0 g•mol –1 c) 184 g•mol –1 d) 238 g•mol –1
Which one of the following cannot form a solid with a lattice based on the sodium chloride structure? A. CuO        B. NaBr        C. LiF        D. CuCl2        E. RbI
Potassium metal crystallizes in a body-centered cubic structure with a unit cell edge length of 5.31 angstroms. The radius of a potassium atom is __________ angstroms. A. 2.30        B. 2.66         C. 5.31         D. 1.33          E. 1.88
For each of the cubic cells (simple cubic, body-centered cubic, and face-centered cubic) give the coordination number, edge length in terms of r, and number of atoms per unit cell.
Determine the number of atoms per unit cell for each of the following metals .Polonium
Polonium crystallizes with a simple cubic structure. It has a density of 9.3 g/cm3, a radius of 167 pm, and a molar mass of 209 g/mol.Use these data to estimate Avogadros number (the number of atoms in one mole).
Determine the coordination number for each structure.
Calculate the packing efficiency of the face-centered cubic unit cell.
A compound with the formula Rb3C60 has been shown to demonstrate superconductivity below 30.0 K.Given that the C60 molecules have a face-centered cubic arrangement, which of the tetrahedral and octahedral sites are occupied by Rb atoms?
You may want to reference (Pages 538 - 542) Section 12.3 while completing this problem.What is the coordination number of an atom in a face-centered unit cell?
You may want to reference (Pages 541 - 542) Section 12.3 while completing this problem.What is the packing efficiency of the face-centered cubic unit cell?
How many atoms are in the unit cell in the face-centered cubic structure?
Determine the number of atoms per unit cell for each of the following metals .Nickel
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.
Platinum crystallizes with the face-centered cubic unit cell. The radius of a platinum atom is 139 pm .Calculate the density of a platinum in g/cm3.
Consider the face-centered cubic structure shown below .What is the length of the line (labeled c) that runs diagonally across one of the faces of the cube in terms of r (the atomic radius)?
Consider the face-centered cubic structure shown below .Use the answer to part a and the Pythagorean theorem to derive the expression for the edge length (l) in terms of r.
You may want to reference (Pages 532 - 560)Chapter 12 while completing this problem.Calculate the fraction of empty space in cubic closest packing to five significant figures.
You may want to reference (Page 542) Section 12.3 while completing this problem.Rhodium crystallizes in a face-centered cubic unit cell. The radius of a rhodium atom is 135 pm.Determine the density of rhodium in g/cm3.
Rhodium has density of 12.41 g/cm3 and crystallizes with the face-centered cubic unit cell.Calculate the radius of a rhodium atom.
The unit cells for lithium oxide and silver iodide are shown. Identify the structure of each of the two unit cells shown below as the rock salt structure, zinc blende structure, fluorite structure, antifluorite structure, or none of these. lithium oxide
The unit cells for lithium oxide and silver iodide are shown. Identify the structure of each of the two unit cells shown below as the rock salt structure, zinc blende structure, fluorite structure, antifluorite structure, or none of these. silver iodide
Determine the coordination number for each structure.
The unit cells for cesium chloride and barium chloride are shown. Identify the structure of each of the two unit cells shown below as the rock salt structure, zinc blende structure, fluorite structure, antifluorite structure, or none of these. cesium chloride
The unit cells for cesium chloride and barium chloride are shown. Identify the structure of each of the two unit cells shown below as the rock salt structure, zinc blende structure, fluorite structure, antifluorite structure, or none of these. barium chloride
Consider the rock salt structure in the figure: What type of structure would result if all the anions were somehow removed, leaving only cations?
Consider the rock salt structure in the figure: What type of structure would result if the remaining tetrahedral sites in the unit cell were also filled with cations?
Perovskite is a compound with a cubic unit cell and has a strontium atom at the center of the cell, titanium atoms at the corners of the unit cell, and oxygen atoms at the centers of each edge of the unit cell.What is the formula of perovskite?
Perovskite is a compound with a cubic unit cell and has a strontium atom at the center of the cell, titanium atoms at the corners of the unit cell, and oxygen atoms at the centers of each edge of the unit cell.What is the coordination number of strontium in the perovskite structure?
Perovskite is a compound with a cubic unit cell and has a strontium atom at the center of the cell, titanium atoms at the corners of the unit cell, and oxygen atoms at the centers of each edge of the unit cell.If the edge length of the unit cell is 3.905 g/cm3, calculate the density of perovskite in m g/cm^3.
Why are X-rays used for crystallography? Why not use some other, more accessible type of electromagnetic radiation such as ultraviolet light?
Platinum has a cubic crystalline lattice structure.Platinum has what type of cubic lattice structure?
Platinum has a cubic crystalline lattice structure.What is the coordination number of platinum?
Platinum has a cubic crystalline lattice structure.What is the packing efficiency of platinum?
Platinum has a cubic crystalline lattice structure.What is the edge length of platinum in terms of r?
Compare the crystal structure of diamond (C) and zinc blende (ZnS). What are the key similarities and differences between the two structures?
In X-ray crystallography, a small amount of oil is often used to mount the crystal sample on a glass fiber.Explain why neither the oil nor the glass fiber interferes with the diffraction pattern of the crystal.
You may want to reference (Pages 537 - 544) Section 12.3 while completing this problem. Identify the coordination number for each structure.
You may want to reference (Pages 537 - 544) Section 12.3 while completing this problem.Calculate the packing efficiency of the two-dimensional lattice shown here:
What is a crystalline lattice? How is the lattice represented with the unit cell?
What is the difference between hexagonal closest packing and cubic closest packing? What are the unit cells for each of these structures?
In an ionic compound, how are the relative sizes of the cation and anion related to the coordination number of the crystal structure?
Show how the cesium chloride, sodium chloride, and zinc blende unit cells each contain a cation-to-anion ratio of 1:1.
Show how the fluorite structure accommodates a cation-to-anion ratio of 1:2.
An oxide of titanium crystallizes with the following unit cell (titanium = gray; oxygen = red).What is the formula of the oxide?
The unit cells for cesium chloride and barium(II) chloride are shown below. Show that the ratio of cations to anions in each unit cell corresponds to the ratio of cations to anions in the formula of each compound.
The unit cells for lithium oxide and silver iodide are shown below.Show that the ratio of cations to anions in each unit cell corresponds to the ratio of cations to anions in the formula of each compound.
Copper iodide crystallizes in the zinc blende structure. The separation between nearest neighbor cations and anions is approximately 311 pm and the melting point is 606 oC. 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 is still higher (776 oC). Explain why the melting point of potassium chloride is higher than that of copper iodide.
A tetrahedral site in a close-packed lattice is formed by four spheres at the corners of a regular tetrahedron. This is equivalent to placing the spheres at alternate corners of a cube. In such a close-packed arrangement the spheres are in contact and if the spheres have a radius r, the diagonal of the face of the cube is 2r. The tetrahedral hole is inside the middle of the cube.Find the length of the body diagonal of this cube.
A tetrahedral site in a close-packed lattice is formed by four spheres at the corners of a regular tetrahedron. This is equivalent to placing the spheres at alternate corners of a cube. In such a close-packed arrangement the spheres are in contact and if the spheres have a radius r, the diagonal of the face of the cube is 2r. The tetrahedral hole is inside the middle of the cube.Find the radius of the tetrahedral hole.
Silver iodide crystallizes in the zinc blende structure. The separation between nearest neighbor cations and anions is approximately 325 pm and the melting point is 558 oC. Cesium chloride, by contrast, crystallizes in the cesium chloride structure shown in the figure. Even though the separation between nearest neighbor cations and anions is greater (348 pm), the melting point is still higher (645 oC). Explain
The volume of a unit cell of diamond is 0.0454 nm3, and the density of diamond is 3.52 g/cm3.Find the number of carbon atoms in a unit cell of diamond.
Determine the coordination number for each structure.
Calculate the packing efficiency of the body-centered cubic unit cell.
You may want to reference (Pages 540 - 541) Section 12.3 while completing this problem.What is the edge length of a body-centered cubic unit cell made up of atoms that each has a radius of 168 pm?
You may want to reference (Pages 537 - 544) Section 12.3 while completing this problem.An atom has radius of 138 pm and crystallizes in a body-centered cubic unit cell. What is the volume of the unit cell?
Determine the number of atoms per unit cell for each of the following metals .Tungsten
Consider the body-centered cubic structure shown below: .What is the length of the line (labeled c) that runs from one corner of the cube diagonally through the center of the cube to the other corner in terms of r (the atomic radius)?
Consider the body-centered cubic structure shown below: .Use the Pythagorean theorem to derive an expression for the length of the line (labeled b) that runs diagonally across one of the faces of the cube in terms the edge length (l).
Consider the body-centered cubic structure shown below: .Use the answer to part (a) and (b) along with the Pythagorean theorem to derive the expression for the edge length (l) in terms of r.
An unknown metal is found to have a density of 7.8748 g/cm3 and to crystallize in a body-centered cubic lattice. The edge of the unit cell is found to be 0.28864 nm .Calculate the atomic mass of the metal.
You may want to reference (Pages 538 - 540) Section 12.2 while completing this problem.How many atoms are in the body-centered cubic unit cell?
You may want to reference (Pages 537 - 544) Section 12.3 while completing this problem. Chromium crystallizes with a body-centered cubic unit cell. The radius of a chromium atom is 125 pm. Calculate the density of solid crystalline chromium in grams per cubic centimeter.
The density of solid Ag is 10.5 g/cm3.a. How many atoms are present per cubic centimeter of Ag?b. As a solid, Ag adopts a face-centered cubic unit cell. How many unit cells are present per cubic centimeter of Ag?c. What is the volume of a unit cell of this metal?d. What is the edge length of a unit cell of Ag?
Consider a body-centered cubic unit cell as shown here.a. How many corner atoms (orange) are shown in this image?b. What fraction of each corner atom is inside the boundaries of the cube? c. How many body atoms shown in this image? d. What fraction of each body atom is inside the boundaries of the cube? e. If you sum all the fractions of atoms, how many atoms are actually inside a body-centered cubic unit cell?
How many atoms are in one body-centered cubic unit cell of a metal? A) 1 B) 2 C) 3 D) 4
Consider a simple cubic (a.k.a, primitive cubic) unit cell as shown here. (i) How many atoms are shown in this image? (ii) What fraction of each atom is inside the boundaries of the cube? (iii) If you sum all (the fractions of atoms, how many atoms are actually inside a simple cubic unit cell?
Rank the crystal lattice structures in order of decreasing efficiency of space in the structure.Simple cubic, Body centered cubic, Face centered cubic, Hexegonal close packed
The density of solid W is 19.3 g/cm3. a) How many atoms are present per cubic centimeter of W? b) As a solid, W adopts a body-centered cubic unit cell. How many unit cells are present per cubic centimeter of W? c) What is the volume of a unit cell of this metal? d) What is the edge length of a unit cell of W?
Consider a face-centered cubic unit cell as shown here.a. How many corner atoms are shown in this image?b. What fraction of each corner atom is inside the boundaries of the cube?c. How many face atoms are shown in this image?d. What fraction of each face atom is inside the boundaries of the cube?e. If you sum all the fractions of atoms, how many atoms are actually inside a face-centered cubic unit cell?
Lithium crystallizes in a body-centered cubic unit cell. What is the mass of one unit cell in grams?
a. The density of solid Fe is 7.87 g/cm3. How many atoms are present per cubic centimeter of Fe? b. As a solid, Fe adopts a body-centered cubic unit cell. How many unit cells are present per cubic centimeter of Fe? c. What is the volume of a unit cell of this metal? d. What is the edge length of a unit cell of Fe?
Lithium crystallizes in a body centered cubic unit cell. What is the mass of one unit cell? Report answer in grams.
  
Copper crystallizes in a face-centered cubic lattice. If the edge of the unit cell is 351 pm, what is the radius of the copper atom?
Determine the number of atoms per unit cell for each of the following metals.a. Tungstenb. Nickel
Metallic copper crystallizes in a face-centered cubic lattice, with one Cu atom per lattice point. If the edge length of the unit cell is found to be 362 pm, what is the metallic radius of Cu in pm?
The substance lithium is found to crystallize in a cubic lattice, with an edge length of 346.0 pm. If the density of solid lithium is 0.5565 g/cm3, how many Li atoms are there per unit cell?
A compound of thallium and iodine crystallizes in a simple cubic array of iodide ions with thallium ions in all of the cubic holes. What is the formula of this iodide? Explain your answer.
Polonium, the Period 6 member of Group 6A(16), is a rare radioactive metal that is the only element with a crystal structure based on the simple cubic unit cell. If its density is 9.142 g/cm3, calculate an approximate atomic radius for polonium.
The coinage metals—copper, silver, and gold—crystallize in a cubic closest packed structure. Use the density of copper (8.95 g/cm3) and its molar mass (63.55 g/mol) to calculate an approximate atomic radius for copper.
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?
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?
The structure of manganese fluoride can be described as a simple cubic array of manganese ions with fluoride ions at the center of each edge of the cubic unit cell. What is the charge of the manganese ions in this compound?
The CsCl structure is a simple cubic array of chloride ions with a cesium ion at the center of each cubic array (see Exercise 69). Given that the density of cesium chloride is 3.97 g/cm3, 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 Cs+ and Cl- ions in the solid. Compare this value with the expected distance based on the sizes of the ions. The ionic radius of Cs+ is 169 pm, and the ionic radius of Cl - is 181 pm.
Calcium crystallizes in a cubic closest packed structure. If the atomic radius of calcium is 197 pm, find the density of the solid.
An element crystallizes in a face-centered cubic lattice, and it has a density of 1.45 g/cm3. The edge of its unit cell is 4.52 x 10 −8 cm. What is the mass of a unit cell?
An element crystallizes in a face-centered cubic lattice, and it has a density of 1.45 g/cm3. The edge of its unit cell is 4.52 x 10 −8 cm. Calculate an approximate atomic mass for the element.
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.
Aluminum has an atomic radius of 143 pm and forms a solid with a cubic closest packed structure. Calculate the density of solid aluminum in g/cm3.
The structure of the compound K 2O 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?
Calcium has a cubic closest packed structure as a solid. Assuming that calcium has an atomic radius of 197 pm, calculate the density of solid calcium.
Nickel has a face-centered cubic unit cell. The density of nickel is 6.84 g/cm 3. Calculate a value for the atomic radius of nickel.
A certain form of lead has a cubic closest packed structure with an edge length of 492 pm. Calculate the value of the atomic radius and the density of lead.
Iridium (Ir) has a face-centered cubic unit cell with an edge length of 383.3 pm. Calculate the density of solid iridium.
A metallic solid with atoms in a face-centered cubic unit cell with an edge length of 392 pm has a density of 21.45 g/cm3. Calculate the atomic mass and the atomic radius of the metal. Identify the metal.
Titanium metal has a body-centered cubic unit cell. The density of titanium is 4.50 g/cm3. Calculate the edge length of the unit cell and a value for the atomic radius of titanium. ( Hint: In a body-centered arrangement of spheres, the spheres touch across the body diagonal.)
The radius of gold is 144 pm, and the density is 19.32 g/cm3. Does elemental gold 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: Vsphere = 4/3 πr3.) What fraction of the total volume of a simple cubic structure is occupied by atoms? Compare the answers.
You may want to reference (Pages 532 - 560) Chapter 12 while completing this problem.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 compounds Na 2O, CdS, and ZrI4 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 1/8 of the tetrahedral holes and aluminum ions in 1/2 of the octahedral holes?
The unit cell of MgO is shown below.Does MgO have a structure like that of NaCl or ZnS? If the density of MgO is 3.58 g/cm3, estimate the radius (in centimeters) of the O2- anions and the Mg2+ cations.
In solid KCl the smallest distance between the centers of a potassium ion and a chloride ion is 314 pm. Calculate the length of the edge of the unit cell and the density of KCl, assuming it has the same structure as sodium chloride.
MnO has either the NaCl type structure or the CsCl type structure (see Exercise 69). The edge length of the MnO unit cell is 4.47 x 10-8 cm and the density of MnO is 5.28 g/cm 3. Does MnO crystallize in the NaCl or the CsCl type structure?
MnO has either the NaCl type structure or the CsCl type structure (see Exercise 69). The edge length of the MnO unit cell is 4.47 x 10-8 cm and the density of MnO is 5.28 g/cm 3. Assuming that the ionic radius of oxygen is 140. pm, estimate the ionic radius of manganese.
Palladium crystallizes with a face-centered cubic structure. It has a density of 12.0 g/cm3, a radius of 138 pm, and a molar mass of 106.42 g/mol.Use these data to calculate Avogadro's number.
KF has the same type of crystal structure as NaCl. The unit cell of KF has an edge length of 5.39 Å. Find the density of KF.
What is the number of atoms per unit cell for Silver, Ag?
When cadmium oxide reacts to form cadmium selenide, a change in unit cell occurs, as depicted below:What is the change in unit cell?
When cadmium oxide reacts to form cadmium selenide, a change in unit cell occurs, as depicted below:Does the coordination number of cadmium change? Explain.
Diamond has a face-centered cubic unit cell, with four more C atoms in tetrahedral holes within the cell. Densities of diamonds vary from 3.01 g/cm3 to 3.52 g/cm3 because C atoms are missing from some holes. Calculate the unit-cell edge length ofthe densest diamond.
Lead adopts the face-centered cubic unit cell in its crystal structure. If the edge length of the unit cell is 495 pm, find the atomic radius of lead.
Diamond has a face-centered cubic unit cell, with four more C atoms in tetrahedral holes within the cell. Densities of diamonds vary from 3.01 g/cm3 to 3.52 g/cm3 because C atoms are missing from some holes. Assuming the cell dimensions are fixed, how many C atoms are in the unit cell of the diamond with the lowest density?
Is it possible for a salt of formula AB3 to have a facecentered cubic unit cell of anions with cations in all eight of the available holes? Explain.
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?
A mineral crystallizes in a cubic closest packed array of oxygen ions with aluminum ions in some of the octahedral holes and magnesium ions in some of the tetrahedral holes. Deduce the formula of this mineral and predict the fraction of octahedral holes and tetrahedral holes that are filled by the various cations.
Zinc oxide adopts the zinc blende crystal structure (figure below). How many Zn  2+ ions are in the ZnO unit cell?
What is the coordination number of an aluminum atom in the face-centered cubic structure of aluminum?
Calcium sulfide adopts the sodium chloride crystal structure (figure below). How many S 2− ions are in the CaS unit cell?
One way of purifying gaseous H 2 is to pass it under high pressure through the holes of a metal’s crystal structure. Palladium, which adopts a cubic closest packed structure, absorbs more H2 than any other element and is one of the metals used for this purpose. How the metal and H2 interact is unclear, but it is estimated that the density of absorbed H 2 approaches that of liquid hydrogen (70.8 g/L). What volume (in L) of gaseous H2 (at STP) can be packed into the spaces of 1 dm3 of palladium metal?
Platinum (atomic radius = 1.38 Å) crystallizes in a cubic closely packed structure. Calculate the edge length of the face-centered cubic unit cell and the density of platinum.
Zinc selenide (ZnSe) crystallizes in the zinc blende structure and has a density of 5.42 g/cm3. How many Zn and Se ions are in each unit cell?
Aluminum (atomic radius = 1.43 Å) crystallizes in a cubic closely packed structure. Calculate the edge length of the face-centered cubic unit cell and the density of aluminum.
Zinc selenide (ZnSe) crystallizes in the zinc blende structure and has a density of 5.42 g/cm3. What is the mass of a unit cell?
Zinc selenide (ZnSe) crystallizes in the zinc blende structure and has a density of 5.42 g/cm3. What is the volume of a unit cell?
Zinc selenide (ZnSe) crystallizes in the zinc blende structure and has a density of 5.42 g/cm3. What is the edge length of a unit cell?
An element crystallizes in a face-centered cubic lattice, and it has a density of 1.45 g/cm3. The edge of its unit cell is 4.52 x 10 −8 cm. How many atoms are in each unit cell?
An element crystallizes in a face-centered cubic lattice, and it has a density of 1.45 g/cm3. The edge of its unit cell is 4.52 x 10 −8 cm. What is the volume of a unit cell?
Which of the following elements reacts with sulfur to form a solid in which the sulfur atoms form a closest packed array with all of the octahedral holes occupied: Li, Na, Be, Ca, or Al?
What is the percent by mass of titanium in rutile, a mineral that contains titanium and oxygen, if structure can be described as a closest packed array of oxide ions with titanium ions in one-half of the octahedral holes? What is the oxidation number of titanium?
Explain why the chemically similar alkali metal chlorides NaCl and CsCl have different structures, whereas the chemically different NaCl and MnS have the same structure.
Rubidium iodide crystallizes with a cubic unit cell that contains iodide ions at the corners and a rubidium ion in the center. What is the formula of the compound?
One of the various manganese oxides crystallizes with a cubic unit cell that contains manganese ions at the corners and in the center. Oxide ions are located at the center of each edge of the unit cell. What is the formula of the compound?
NaH crystallizes with the same crystal structure as NaCl. The edge length of the cubic unit cell of NaH is 4.880 Å.(a) Calculate the ionic radius of H−. (The ionic radius of Li+ is 0.0.95 Å.)
NaH crystallizes with the same crystal structure as NaCl. The edge length of the cubic unit cell of NaH is 4.880 Å(b) Calculate the density of NaH.
Thallium(I) iodide crystallizes with the same structure as CsCl. The edge length of the unit cell of TlI is 4.20 Å. Calculate the ionic radius of TI+. (The ionic radius of I− is 2.16 Å.)
A cubic unit cell contains manganese ions at the corners and fluoride ions at the center of each edge.(a) What is the empirical formula of this compound? Explain your answer.
A cubic unit cell contains manganese ions at the corners and fluoride ions at the center of each edge.(b) What is the coordination number of the Mn3+ ion?
A cubic unit cell contains manganese ions at the corners and fluoride ions at the center of each edge.(c) Calculate the edge length of the unit cell if the radius of a Mn3+ ion is 0.65 A.
Boron nitride (BN) exists in two forms. The first is a slippery solid formed from the reaction of BCl 3 with NH 3, followed by heating in an ammonia atmosphere at 750 ˚C. Subjecting the first form of BN to a pressure of 85,000 atm at 1800 ˚C produces a second form that is the second hardest substance known. Both forms of BN remain solids to 3000 ˚C. Suggest structures for the two forms of BN.
A cubic unit cell contains manganese ions at the corners and fluoride ions at the center of each edge.(d) Calculate the density of the compound.
What is the spacing between crystal planes that diffract X-rays with a wavelength of 1.541 nm at an angle θ of 15.55° (first order reflection)?
What is the spacing between crystal planes that diffract X-rays with a wavelength of 1.541 nm at an angle θ of 15.55° (first order reflection)?
The free space in a metal may be found by subtracting the volume of the atoms in a unit cell from the volume of the cell. Calculate the percentage of free space in each of the three cubic lattices if all atoms in each are of equal size and touch their nearest neighbors. Which of these structures represents the most efficient packing? That is, which packs with the least amount of unused space?
Cadmium sulfide, sometimes used as a yellow pigment by artists, crystallizes with cadmium, occupying one half of the tetrahedral holes in a closest packed array of sulfide ions. What is the formula of cadmium sulfide? Explain your answer.
A compound of cadmium, tin, and phosphorus is used in the fabrication of some semiconductors. It crystallizes with cadmium occupying one-fourth of the tetrahedral holes and tin occupying one-fourth of the tetrahedral holes in a closest packed array of phosphide ions. What is the formula of the compound? Explain your answer.
What is the formula of the magnetic oxide of cobalt, used in recording tapes, that crystallizes with cobalt atoms occupying one-eighth of the tetrahedral holes and one-half of the octahedral holes in a closely packed array of oxide ions?
The structures of some common crystalline substances are shown below. Show that the net composition of each unit cell corresponds to the correct formula of each substance.
Assume the two-dimensional structure of an ionic compound, M xAy, isWhat is the empirical formula of this ionic compound?
A compound containing zinc, aluminum, and sulfur crystallizes with a closest-packed array of sulfide ions. Zinc ions are found in one-eighth of the tetrahedral holes and aluminum ions in one-half of the octahedral holes. What is the empirical formula of the compound?
What type of unit cell does Ni (4) use in its crystal lattice? (The number of atoms per unit cell is given in parentheses.)
Like most transition metals, tantalum (Ta) exhibits several oxidation states. Give the formula of the tantalum compound whose unit cell is depicted below:
What type of unit cell does Cr (2) use in its crystal lattice? (The number of atoms per unit cell is given in parentheses.)
Like most transition metals, tantalum (Ta) exhibits several oxidation states. Give the formula of the tantalum compound whose unit cell is depicted below:
What type of unit cell does Ca (4) use in its crystal lattice? (The number of atoms per unit cell is given in parentheses.)
As molten iron cools to 1674 K, it adopts one type of cubic unit cell; then, as the temperature drops below 1181 K, it changes to another, as depicted below:What is the change in unit cell?
As molten iron cools to 1674 K, it adopts one type of cubic unit cell; then, as the temperature drops below 1181 K, it changes to another, as depicted below:Which crystal structure has the greater packing efficiency?
You may want to reference (Pages 549 - 550)Section 12.5 while completing this problem.An oxide of rhenium crystallizes with the unit cell depicted here (where rhenium = gray and oxygen = red).What is the formula of the oxide?
Of the five major types of crystalline solid, which does the following form, and why: Ni?
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. Describe the unit cell for nitinol.
Of the five major types of crystalline solid, which does the following form, and why: F2?
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. What is the empirical formula of nitinol?
Of the five major types of crystalline solid, which does the following form, and why:CH3OH?
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. What are the coordination numbers (number of nearest neighbors) of Ni and Ti in nitinol?
Of the five major types of crystalline solid, which does the following form, and why: Sn?
Of the five major types of crystalline solid, which does the following form, and why: Si?
Of the five major types of crystalline solid, which does the following form, and why: Xe?
Of the five major types of crystalline solid, which does the following form, and why: SiC?
Materials containing the elements Y, Ba, Cu, and O that are superconductors (electrical resistance equals zero) at temperatures above that of liquid nitrogen were recently discovered. The structures of these materials are based on the perovskite structure. Were they to have the ideal perovskite structure, the superconductor would have the structure shown in part (a) of the following figure.What is the formula of this ideal perovskite material?
Of the five major types of crystalline solid, which does the following form, and why:Na2SO4?
Materials containing the elements Y, Ba, Cu, and O that are superconductors (electrical resistance equals zero) at temperatures above that of liquid nitrogen were recently discovered. The structures of these materials are based on the perovskite structure. Were they to have the ideal perovskite structure, the superconductor would have the structure shown in part (a) of the following figure.These materials, however, do not act as superconductors unless they are deficient in oxygen. The structure of the actual superconducting phase appears to be that shown in part (b) of the figure. What is the formula of this material?
Of the five major types of crystalline solid, which does the following form, and why: SF6?
Of the five major types of crystalline solid, which does the following form, and why: cholesterol (C27H45OH)?
The structures of another class of ceramic, high-temperature superconductors are shown in figures a-d.Determine the formula of each of these four superconductors.
Of the five major types of crystalline solid, which does the following form, and why: KCl?
Of the five major types of crystalline solid, which does the following form, and why: BN?
Describe the crystal structure of iron, which crystallizes with two equivalent metal atoms in a cubic unit cell.
Describe the crystal structure of Pt, which crystallizes with four equivalent metal atoms in a cubic unit cell.
Cobalt metal crystallizes in a hexagonal closest packed structure. What is the coordination number of a cobalt atom?
Nickel metal crystallizes in a cubic closest packed structure. What is the coordination number of a nickel atom?
Nickel metal crystallizes in a cubic closest packed structure. What is the coordination number of a nickel atom?
The density of aluminum is 2.7 g/cm3; that of silicon is 2.3 g/cm3. Explain why Si has the lower density even though it has heavier atoms.
The unit cell for a pure xenon fluoride compound is shown below. What is the formula of the compound?
One of the most important enzymes in the world—nitrogenase, the plant protein that catalyzes nitrogen fixation—contains active clusters of iron, sulfur, and molybdenum atoms. Crystalline molybdenum (Mo) has a body-centered cubic unit cell (d of Mo = 10.28 g/cm3). Determine the edge length of the unit cell.
One of the most important enzymes in the world—nitrogenase, the plant protein that catalyzes nitrogen fixation—contains active clusters of iron, sulfur, and molybdenum atoms. Crystalline molybdenum (Mo) has a body-centered cubic unit cell (d of Mo = 10.28 g/cm3). Calculate the atomic radius of Mo.
Tantalum (Ta; d = 16.634 g/cm3 and ℳ = 180.9479 g/mol) has a body-centered cubic structure with a unit-cell edge length of 3.3058 Å. Use these data to calculate Avogadro’s number.
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?
Barium is the largest nonradioactive alkaline earth metal. It has a body-centered cubic unit cell and a density of 3.62 g/cm3. What is the atomic radius of barium? [Volume of a sphere: V = 4/3(πr3).]
Barium has a body-centered cubic structure. If the atomic radius of barium is 222 pm, calculate the density of solid barium.
The radius of tungsten is 137 pm and the density is 19.3 g/cm3. Does elemental tungsten have a face-centered cubic structure or a body-centered cubic structure?
Iron has a density of 7.86 g/cm3 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.
You may want to reference (Pages 532 - 560) Chapter 12 while completing this problem.When spheres of radius r are packed in a body-centered cubic arrangement, they occupy 68 % of the available volume. Use the fraction of occupied volume to calculate the value of a, the length of the edge of the cube in terms of r.
The unit cell for nickel arsenide is shown below. What is the formula of this compound?
You may want to reference (Pages 537 - 544) Section 12.3 while completing this problem.Barium has a density of 3.59 g/cm3  and crystallizes with a body-centered cubic unit cell. Calculate the radius of a barium atom.
What is the number of atoms per unit cell for Polonium, Po?
What is the number of atoms per unit cell for Manganese, Mn?
Chromium adopts the body-centered cubic unit cell in its crystal structure. If the density of chromium is 7.14 g/cm3, find its atomic radius.
You may want to reference (Pages 537 - 544) Section 12.3 while completing this problem.Molybdenum crystallizes with a body-centered unit cell. The radius of a molybdenum atom is 136 pm. Calculate the edge length of the unit cell of molybdenum .
Potassium adopts the body-centered cubic unit cell in its crystal structure. If the atomic radius of potassium is 227 pm, find the edge length of the unit cell.
You may want to reference (Pages 537 - 544) Section 12.3 while completing this problem.Molybdenum crystallizes with a body-centered unit cell. The radius of a molybdenum atom is 136 pm. Calculate the density of molybdenum.
The crystal structure of sodium is based on the body-centered cubic unit cell. What is the mass of one unit cell of Na?
Perovskite is a mineral containing calcium, titanium, and oxygen. Two different representations of the unit cell are shown below. Show that both these representations give the same formula and the same number of oxygen atoms around each titanium atom.
What is the coordination number of a chromium atom in the body-centered cubic structure of chromium?
Tungsten crystallizes in a body-centered cubic unit cell with an edge length of 3.165 Å.(a) What is the atomic radius of tungsten in this structure?
Tungsten crystallizes in a body-centered cubic unit cell with an edge length of 3.165 Å.(b) Calculate the density of tungsten.
Barium crystallizes in a body-centered cubic unit cell with an edge length of 5.025 Å(a) What is the atomic radius of barium in this structure?
Barium crystallizes in a body-centered cubic unit cell with an edge length of 5.025 Å(b) Calculate the density of barium.
Arrange the three common unit cells in order from least dense to most dense packing.