Question

Metallic rhodium crystallizes in a face-centered cubic lattice with a unit-cell edge length of $3.803\,\mathring{A}$ Calculate the molar volume ( in $cm^{3}$ ) of rhodium including the empty spaces. (Give answer after rounding off to the nearest integer value.)

Answer 1

In F.C.C. crystalline solid unit cell $Z=4$ .
If the edge length of the cube is. $a=3.803A^{0}a=3.803\times 10^{- 8}cm$
The volume of the cube is.
$a^{3}=\left(3 . 803 \times \left(10\right)^{- 8}\right)^{3}=55.0\times \left(10\right)^{- 24}\left(cm\right)^{3}$
The volume of cube including vacant space for F.C.C. with $1\,mole$ .
$Z=4forF.C.C.Volume=\frac{55 . 0 \times 10^{- 24} \times 6 . 023 \times 10^{23}}{4}Volume=8.28\,cm^{3}$
The volume is $8.28\,cm^{3}\simeq 8\,c.c.$