Question

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.

Answer 1

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:

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

$\delta=101.13 g/cm^3$