Question

An unknown metal is found to have a density of $10.2g/cc$ at $25^{\circ }C$ . It is found to crystallize in a body-centered cubic lattice with a unit cell edge length of $3.147\mathring{A}$ . Calculate the molar mass of the metal in grams.
Give your answer as the nearest integer.

Answer 1

Answer: 96

The relationship between density, edge length, number of atoms and the unit cell is:
$d=\frac{M\times Z}{a^3\times N_0}a=3.147\mathring{A}=3.147\times (10{)}^{-8}cm$
$Z=2M=?d=10.2g/cc$
$N_0=6.023\times (10{)}^{23}$
$10.2=\frac{M\times 2}{{\left(3.147\times (10{)}^{-8}\right)}^3\times 6.023\times (10{)}^{23}}$
$M=\frac{{\left(3.147\times (10{)}^{-8}\right)}^3\times 6.023\times (10{)}^{22}\times 10.2}{2}$
$M=95.7g$