13. Liquids, Solids & Intermolecular Forces

Face Centered Cubic Unit Cell

Gen Chem II - Lec 6 - Crystal Lattices of Solid Structures

Zinc selenide, ZnSe, crystallizes in a face-centered cubic unit cell has a density of 5.42 g/cm3. What is the volume of a unit cell?

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?

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

Titanium oxide crystallizes in the following cubic unit cell: 
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/277d28ee10e7ad41-1671132077069.jpg" alt="" /> 
(b) What is the formula of titanium oxide?

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?

Face Centered Cubic Crystal Structure

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?

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?

Aluminum has a face-centered cubic unit structure and a density of 2.716 g/cm3. Calculate the edge length of the unit cell.

Sodium oxide (Na2O) adopts a cubic structure with Na atoms
represented by green spheres and O atoms by red spheres.
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/586e30779c1fc4b0-1665669349470.jpg" alt="" />
(c) The unit cell edge length is 5.550 Å. Determine the density
of Na2O.

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.

Unit Cell Chemistry   Simple Cubic, Body Centered Cubic, Face Centered Cubic Crystal Lattice Structu

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?

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: 
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/c7303ae2175e62f6-1661361535337.jpg" alt="" /> 
(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?

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.

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.

(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?

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?<img src="https://lightcat-files.s3.amazonaws.com/problem_images/343a06bb5794cc9b-1667572866431.jpg" alt="" />

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? 
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/ef0999f825749c1e-1664549357120.jpg" alt="" />

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?
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/c128b3a268e6b1d7-1666015900819.jpg" alt="" />

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.)

Face Centered Cubic Unit Cell Example 1

An element crystallizes in a face-centered cubic lattice and has a density of 1.45 g/cm3. The edge of its unit cell is 4.52×10–8 cm. How many atoms are in each unit cell?

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.

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.

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 .

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 .

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?

Niobium oxide crystallizes in the following cubic unit cell:
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/a3a2b83154838ab8-1671121841875.jpg" alt="" />
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

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.)

The face centered cubic crystal structure and the theoretical density of metals

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?

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: 
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/567e19ce32cf1d32-1661361445792.jpg" alt="" /> 
(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).

An element crystallizes in a face-centered cubic lattice and has a density of 1.45 g/cm3. The edge of its unit cell is 4.52×10-8 cm. Calculate the atomic mass for the element.

11.3 Structures of Solids | General Chemistry

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? 
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/d07e305c1e71707b-1665662393158.jpg" alt="" />

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.)<img src="https://lightcat-files.s3.amazonaws.com/problem_images/1a7b083a2e43a766-1671472531338.jpg" alt="" />

Face Centered Cubic Unit Cell Concept 1

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?

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

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.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/b85825c8659038ba-1659627886319.jpg" alt="" />

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.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/c1ee483b551d2308-1666369503685.jpg" alt="" />

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?

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

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?

Learn the toughest concepts covered in Chemistry with step-by-step video tutorials and practice problems by world-class tutors

Jules

General Chemistry

https://static.studychannel-prd.pearsonprd.tech/courses/general-chemistry/thumbnails/general-chemistry

#FFFFFF

LearnWithManim

The Organic Chemistry Tutor

Jules Bruno

Scott Ramsay

Chad's Prep

Jeffrey A Tibbitt

1. Intro to General Chemistry

2. Atoms & Elements

3. Chemical Reactions

4. BONUS: Lab Techniques and Procedures

5. BONUS: Mathematical Operations and Functions

6. Chemical Quantities & Aqueous Reactions

7. Gases

8. Thermochemistry

9. Quantum Mechanics

10. Periodic Properties of the Elements

11. Bonding & Molecular Structure

12. Molecular Shapes & Valence Bond Theory

14. Solutions

15. Chemical Kinetics

16. Chemical Equilibrium

17. Acid and Base Equilibrium

18. Aqueous Equilibrium

19. Chemical Thermodynamics

20. Electrochemistry

21. Nuclear Chemistry

22. Organic Chemistry

23. Chemistry of the Nonmetals

24. Transition Metals and Coordination Compounds

[BOOK CHEM] Clutch Version

Body Centered Cubic Unit Cell

Body Centered Cubic Unit Cell contains 2 atoms total.

Phase Diagrams

Phase&nbsp;Diagrams show&nbsp;what&nbsp;effect&nbsp;temperature and pressure have&nbsp;on a pure substance in a closed system without any air.

Intermolecular Forces and Physical Properties

Intermolecular forces influence physical properties. &nbsp;We will look at direct and indirect relationships.

Face Centered Cubic Unit Cell contains 4 atoms in total.

Heating and Cooling Curves

Heating and Cooling Curves represent amount of heat (q) absorbed or released by a substance during phase changes.

Clausius-Clapeyron Equation

The Clausius-Clapeyron Equation establishes a quantitative relationship between vapor pressure and temperature.&nbsp;

Molecular Polarity

Polarity of chemical bonds happen in molecules when there is an unequal sharing of electrons.&nbsp;

Intermolecular Forces

Intramolecular Forces are the bonding forces within a molecule. Intermolecular Forces are the attractive forces between 2 molecules.

Simple Cubic Unit Cell

Simple Cubic Unit Cell is the least complex&nbsp;cubic unit cell and contains only 1 atom.

Atomic, Ionic, and Molecular Solids

<div dir="auto"><div contenteditable="true"dir="auto"spellcheck="true">Crystalline solids represent structures with well-organized patterns and shapes. Amorphous solids represent structures that lack an organized pattern or shape.&nbsp;</div></div>

Crystalline Solids

Crystalline Solids are composed of unit cells, crystal lattice and lattice point.