Calculate the density of an element having molar mass 225 g mol − 1 forming bcc structure [ a 3 × N A = 75 cm 3 mol − 1 ]

Question

Calculate the density of an element having molar mass 225 g mol − 1 forming bcc structure [ a 3 × N A ​ = 75 cm 3 mol − 1 ]

TestHub · Accepted Answer

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

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

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

Substituting the given values $Z = 2$ , $M = 225 g mol^{- 1}$ , and $a^{3} \times N_{A} = 75 cm^{3} mol^{- 1}$ :

$d = \frac{2 \times 225}{75}$

$d = \frac{450}{75} = 6.0 g cm^{- 3}$

Answer: $6.0$ g cm $^{- 3}$

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