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Question

(B) The density $(d)$ of a unit cell is given by the formula: $d = \frac{Z 	imes M}{a^3 	imes N_{A}}$ Given: $Z = 4$,$M = 27 \ g \ mol^{-1}$,$a = 40

Vedclass · Accepted Answer

$2.69$

Vedclass · Answer

(B) The density $(d)$ of a unit cell is given by the formula: $d = \frac{Z 	imes M}{a^3 	imes N_{A}}$ Given: $Z = 4$,$M = 27 \ g \ mol^{-1}$,$a = 405 \ pm = 4.05 	imes 10^{-8} \ cm$,$N_{A} = 6.022 	imes 10^{23} \ mol^{-1}$ Substituting the values: $d = \frac{4 	imes 27}{(4.05 	imes 10^{-8})^3 	imes 6.022 	imes 10^{23}}$ $d = \frac{108}{66.43 	imes 10^{-24} 	imes 6.022 	imes 10^{23}}$ $d = \frac{108}{40.01} \approx 2.699 \ g \ cm^{-3}$ Thus,the density is approximately $2.69 \ g \ cm^{-3}$.

Calculate the density of an element with molar mass $27 \ g \ mol^{-1}$ having $4$ atoms in a unit cell with edge length $405 \ pm$. (in $g \ cm^{-3}$)

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