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Key concepts and summary

The structures of crystalline metals and simple ionic compounds can be described in terms of packing of spheres. Metal atoms can pack in hexagonal closest-packed structures, cubic closest-packed structures, body-centered structures, and simple cubic structures. The anions in simple ionic structures commonly adopt one of these structures, and the cations occupy the spaces remaining between the anions. Small cations usually occupy tetrahedral holes in a closest-packed array of anions. Larger cations usually occupy octahedral holes. Still larger cations can occupy cubic holes in a simple cubic array of anions. The structure of a solid can be described by indicating the size and shape of a unit cell and the contents of the cell. The type of structure and dimensions of the unit cell can be determined by X-ray diffraction measurements.

Key equations

  • n λ = 2 d sin θ

Chemistry end of chapter exercises

Describe the crystal structure of iron, which crystallizes with two equivalent metal atoms in a cubic unit cell.

The structure of this low-temperature form of iron (below 910 °C) is body-centered cubic. There is one-eighth atom at each of the eight corners of the cube and one atom in the center of the cube.

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Describe the crystal structure of Pt, which crystallizes with four equivalent metal atoms in a cubic unit cell.

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What is the coordination number of a chromium atom in the body-centered cubic structure of chromium?

eight

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What is the coordination number of an aluminum atom in the face-centered cubic structure of aluminum?

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Cobalt metal crystallizes in a hexagonal closest packed structure. What is the coordination number of a cobalt atom?

12

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Nickel metal crystallizes in a cubic closest packed structure. What is the coordination number of a nickel atom?

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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?

(b) Calculate the density of tungsten.

(a) 1.370 Å; (b) 19.26 g/cm

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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.

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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?

(b) Calculate the density of barium.

(a) 2.176 Å; (b) 3.595 g/cm 3

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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.

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The density of aluminum is 2.7 g/cm 3 ; that of silicon is 2.3 g/cm 3 . Explain why Si has the lower density even though it has heavier atoms.

The crystal structure of Si shows that it is less tightly packed (coordination number 4) in the solid than Al (coordination number 12).

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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?

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Questions & Answers

what is catenation
Oladuji Reply
The property of carbon to form long chain with other atom!
Lareb
hydrocarbons can be classified as..1.Aliphatic compounds 2.cyclic compounds.under aliphatic compounds there are two types saturated hydrocarbons(alkanes) and unsaturated hydrocarbons(alkenes and alkynes).
Niroshan Reply
thanks but i have also heard of aromatic hydrocarbons
emmanuel
so am kinda confused
emmanuel
hello i have big problems in understanding organic chemistry
emmanuel Reply
what are the main types of hydrocarbon
emmanuel
how many elements are in the periodic table
emmanuel Reply
118
daniel
please what are the main types of hydrocarbons
emmanuel
why Rutherford uses the gold foil instead of other metals?
Lareb Reply
Rutherford chose gold was because its extremely malleable. One can stretch gold foil until it is only a few atoms thick in places, which is not possible with aluminum. If the foil were too thick, there would be no transmission of particles at all; the whole point was to demonstrate that most alpha
daniel
wjat does Rutherford mean?
Asali
Ernest Rutherford was the scientist that preformed the experiment.
daniel
although other metals are also present which are more melleable!?so
Lareb
gold
daniel
what is a balanced equation 4 trioxonitrate (V)acid and sodium hydroxide?
Marcel Reply
proved ur Worth: If A is a of trioxonitrate(V)acid,HNO3' of unknown concentration .B is a standard solution of sodium hydroxide containing 4.00g per dm cube of solution.25cm cube portions solution B required an average of 24.00cm cube of solution A for neutralization,using 2 drops of methyl orange.
Marcel
calculate the concentration of solution B in moles per dm cube
Marcel
calculate the concentration of solution A and B in moles per DM cube
Marcel
finally calculate the concentration in g/dm cube of HNO3 in solution A (H=1,N=14,O=16,Na=23)
Marcel
calculate the standard enthalpy of formation for propane(C3H8) from the following data; 1), C3H8+5O2->3CO2+4H2O; -222.0kJ/mol 2), C+O2->CO2;-395.5kJ/mol 3),H2+O->H2O; 285.8kJ/mol
Josephine
let eventually of formation of propane = X X + (-222)=3×(-395.5)+4×(-286) rearrange to find X
Paul
wat is electrolysis?
Mgbachi Reply
it is the chemical decomposition of a substance when electric current is passed through it either in molten form or aqueous solution
Nuru
list the side effect of chemical industries
Chelsea Reply
how do you ionise an atom
Rabeka Reply
many ways ,but one of them is when the atom becomes heated to a certain temperature the surface electron becomes too energetic and leaves the atom because the attraction between the nucleus and the electron becomes overpowered by the energetic eletron
sunday
also hitting of two atoms can cause transfer of surface electrons
sunday
and when this transfers occur the atom becomes ionised
sunday
who is doing Cape chemistry tomorrow?
caramel Reply
What is hybridization
edmondnti Reply
the mix between different breeds of species in one
Jared
it is the blending of orbitals.
stanley
the mixing of orbital
caramel
are covalent bonds influenced by factors such as temperature and pressure?
patrick Reply
what is catalyst used for mirror test
Sanjay Reply
when an atom looses electron, what does it become?
Abdullahi Reply
it's oxidized and called an ion
Anora
thanks
Abdullahi
Now, I get it
Abdullahi
cation
Anora
can you give an example please, if you don't mind
Abdullahi
a positive ion,become positively charged/a cation.
Janis
sodium plus one is simple cation is exmpl
ajmal
Taking Sodium as example..... it carries a positive charge which means it is positively charged.....when it gains an electron, it is reduced cuz an electron is negatively charged.....also when an atom looses an electron, it becomes positively charged and when it gains, it becomes negatively charged.
Nuru
typically, ionization is the process where an atom looses or gains electron(s) to form ion(s) either a positively or negatively
Nuru
what is copper
Bryan Reply
just an element
Power
Cu
daniel

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Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
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