Ch.11 - Liquids, Solids & Intermolecular ForcesWorksheetSee 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
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
Sodium oxide (Na2O) adopts a cubic structure with Na atoms represented by green spheres and O atoms by red spheres. How many atoms of each type are there in the unit cell?
Imagine the primitive cubic lattice. Now imagine pushing on top of it, straight down. Next, stretch another face by pulling it to the right. All angles remain 90 . What kind of primitive lattice have you made?
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
Tausonite, a mineral composed o f Sr, O, and Ti, has the cubic unit cell shown in the drawing .What is the empirical formula of this mineral?
Determine the coordination number for each structure.
The density of diamond [Figure 11.41(a) in the textbook] is 3.5 g/cm3, and that of graphite [Figure 11.41(b) in the textbook] is 2.3 g/cm3. X-ray diffraction studies of buckminsterfullerene show that it has a face-centered cubic lattice of C60 molecules. The length of a side of the unit cell is 14.2 Å.Calculate the density of buckminsterfullerene.
Calculate the packing efficiency of the face-centered cubic unit cell.
Silicon has a face-centered cubic crystal structure with unit cell edge length of 5.43 Å and four atoms per unit cell.How many silicon atoms are there in 1 cm3 of material?
Silicon has a face-centered cubic crystal structure with unit cell edge length of 5.43 Å and four atoms per unit cell.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?
At room temperature and pressure RbI crystallizes with the NaCl-type structure.Use ionic radii to predict the length of the cubic unit cell edge.
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?
How many atoms are in the unit cell in the face-centered cubic structure?
Aluminum metal crystallizes in a cubic close-packed structure (face-centered cubic cell, as shown in the figure above).How many aluminum atoms are in a unit cell?
Aluminum metal crystallizes in a cubic close-packed structure (face-centered cubic cell, as shown in the figure above).What is the coordination number of each aluminum atom?
Aluminum metal crystallizes in a cubic close-packed structure (face-centered cubic cell, as shown in the figure above).Estimate the length of the unit cell edge, a, from the atomic radius of aluminum (1.43 Å).
Aluminum metal crystallizes in a cubic close-packed structure (face-centered cubic cell, as shown in the figure above).Calculate the density of aluminum metal.
Determine the number of atoms per unit cell for each of the following metals .Nickel
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.
Gold is a face-centered cubic structure that has a unit cell edge length of 4.08 Å. There are four gold atoms per unit cell.How many gold atoms are there in a sphere that is 16 nm in diameter? Recall that the volume of a sphere is r3.
A face-centered tetragonal lattice is not one of the 14 three-dimensional lattices. Show that a face-centered tetragonal unit cell can be redefined as a body-centered tetragonal lattice with a smaller unit cell.
Aluminum metal crystallizes in a face-centered cubic unit cell.How many Aluminum atoms are in a unit cell?
Aluminum metal crystallizes in a face-centered cubic unit cell.What is the coordination number of each Aluminum atom?
Aluminum metal crystallizes in a face-centered cubic unit cell.Estimate the length of the unit cell edge, a, from the atomic radius of Aluminum (1.43 Å).
Aluminum metal crystallizes in a face-centered cubic unit cell.Calculate the density of Aluminum metal.
Introduction of carbon into a metallic lattice generally results in a harder, less ductile substance with lower electrical and thermal conductivities.Explain why this might be so.
Silicon carbide, SiC, has the three-dimensional structure shown in the figure.Name another compound that has the same structure.
Sodium oxide (Na2O) adopts a cubic structure with Na atoms represented by green spheres and O atoms by red spheres. Determine the coordination number for the sodium ion.
Determine the coordination number for each structure.
An increase in temperature causes most metals to undergo thermal expansion, which means the volume of the metal increases upon heating.How does thermal expansion affect the unit cell length? What is the effect of an increase in temperature on the density of a metal?
Spinel is a mineral that contains 37.9% Al, 17.1% Mg, and 45.0% O, by mass, and has a density of 3.57 g/cm3. The unit cell is cubic, with an edge length of 809 pm.How many atoms of Al are in the unit cell?
Spinel is a mineral that contains 37.9% Al, 17.1% Mg, and 45.0% O, by mass, and has a density of 3.57 g/cm3. The unit cell is cubic, with an edge length of 809 pm.How many atoms of Mg are in the unit cell?
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?
Why are X-rays used fo