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  4. An unknown metal is found to have a density of 10.2 g/cc at 25° C . It is found to crystallize in a body-centered cubic lattice with a unit cell edge length of 3.147 mathringA . Calculate the molar mass of the metal in grams. Give your answer as the nearest integer.

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Q. An unknown metal is found to have a density of $10.2\,g/cc$ 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.

NTA AbhyasNTA Abhyas 2022

Solution:

Solution
Solution
The relationship between density, edge length, number of atoms and the unit cell is:
$d=\frac{M \times Z}{a^{3} \times N_{0}} a=3.147 \,\mathring{A} =3.147 \times(10)^{-8} cm$
$Z =2 M=? d=10.2\, g / c c$
$ 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=95.7\, g$