Question

What is the molar mass of an element that crystallizes in a
body-centered cubic unit cell with a density equal to 0.971
g/cm^{3} and radius of 1.853 A?

Answer #1

edge length of the unit cell

Calculate the value for 4r (refer to the above diagram):

radius for barium = 1.853 A or 185.3 pm

4r = 741.2 pm

2) Apply the Pythagorean Theorem:

d^{2} + (d√2)^{2} = (741.2)^{2}

3d^{2} = 549377

d^{2} = 183125.813333. . .

d = 427.9 pm

Convert pm to cm:

427.9 pm x 1 cm/10^{10} pm = 330.6 x 10¯^{10} cm
= 4.279 x 10¯^{8} cm

Calculate the volume of the unit cell:

(4.279 x 10¯^{8} cm)^{3} = 7.8365 x
10¯^{23} cm^{3}

Calculate mass of the 2 atoms in the body-centered cubic unit cell:

0.971 g/cm^{3} times 7.8365 x 10¯^{23}
cm^{3} = 7.6075 x 10¯^{23} g

The mass of one atom :

7.6075 x 10¯^{23} g / 2 = 3.8037 x 10¯^{23}
g

5) The atomic weight in g/mol:

3.8037 x 10¯^{23} g times 6.022 x 10^{23}
mol¯^{1} = 22.91 g/mol

An element crystallizes in a body-centered cubic lattice. The
edge of the unit cell is 3.37 Å in length, and the density of the
crystal is 7.88 g/cm3 .
Calculate the atomic weight of the element.
Express the atomic weight in grams per mole to three significant
digits.

Chromium crystallizes in a body-centered cubic unit cell with an
edge length of 2.885 Å.
(a) What is the atomic radius (in Å) of chromium in this
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____ Å
(b) Calculate the density (in g/cm3) of chromium.
____ g/cm3

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A hypothetical metal crystallizes with the face-centered cubic
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Determine the density of rhodium in g/cm3. Which of the below is
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. Calculate the atomic radius of
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Determine the density of rhodium in g/cm3.
please show all work and units!

1. Unit Cells
i. A certain metal crystallizes in a face-centered cubic unit
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