Calculate the molar mass of an element having density 5.6 g cm − 3 that forms bcc structure. [ a 3 × N A = 75 cm 3 mol − 1 ]

Question

Calculate the molar mass of an element having density 5.6 g cm − 3 that forms bcc structure. [ a 3 × N A ​ = 75 cm 3 mol − 1 ]

TestHub · Accepted Answer

For a body-centered cubic (bcc) lattice, the number of atoms per unit cell is $Z = 2$ .

The density of the unit cell is given by the formula:

$d = \frac{Z \times M}{a ^{3} \times N _{A}}$

Rearranging the formula to solve for molar mass $M$ :

$M = \frac{d \times ( a ^{3} \times N _{A} )}{Z}$

Substituting the given values $d = 5.6 g cm^{- 3}$ , $a^{3} \times N_{A} = 75 cm^{3} mol^{- 1}$ , and $Z = 2$ :

$M = \frac{5.6 \times 75}{2}$

$M = 2.8 \times 75 = 210 g mol^{- 1}$

Answer: $210 g mol^{- 1}$

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