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deff fn [24]
3 years ago
7

A hypothetical metal crystallizes with the face-centered cubic unit cell. The radius of the metal atom is 234 picometers and its

molar mass is 195.08 g/mol. Calculate the density of the metal in g/cm3.

Chemistry
1 answer:
AleksAgata [21]3 years ago
6 0

Answer:

\delta=101.13 g/cm^3

Explanation:

As can be seen in the Figure in a face-centered cubic unit cell you have:

  • Six halves of atoms
  • Eight 1/8 of atom (1 in each corner)

In total:

n_{atom}=6*0.5+8*\frac{1}{8}=4 atoms

Now, each side of the cell is 234 picometers (2.34e-8 cm) long

V_{cell}=L^3=(2.34e^{-8} cm)^3

V_{cell}=1.28*10^{-23}cm^3

Atoms per cm3:

n=\frac{4 atoms}{1.28*10^{-23}cm^3}

n=3.12*10^{23} atoms/cm^3

Expressing in mass:

\delta=3.12*10^{23} atoms/cm^3* \frac{1 mol}{6.022*10^{23}}*195.08 g/mol

\delta=101.13 g/cm^3

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