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 $c{m}^3$ ) of rhodium including the empty spaces. (Give answer after rounding off to the nearest integer value.)

Answer 1

Answer: 8

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 $1mole$ .
$Z=4forF.C.C.Volume=\frac{55.0\times 10^{-24}\times 6.023\times 10^{23}}{4}Volume=8.28c{m}^3$
The volume is $8.28c{m}^3\simeq 8c.c.$