Calculate the molar mass of an element if it | vedclass

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Question

(A) For an $fcc$ unit cell,the number of atoms per unit cell $(Z)$ is $4$. The mass of a unit cell is given by the formula: $	ext{Mass of unit cell}

Vedclass · Accepted Answer

$27.0 \ g \ mol^{-1}$

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(A) For an $fcc$ unit cell,the number of atoms per unit cell $(Z)$ is $4$. The mass of a unit cell is given by the formula: $	ext{Mass of unit cell} = \frac{Z 	imes M}{N_A}$,where $M$ is the molar mass. Rearranging the formula to solve for $M$: $M = \frac{	ext{Mass of unit cell} 	imes N_A}{Z}$. Substituting the given values: $M = \frac{1.8 	imes 10^{-22} \ g 	imes 6.022 	imes 10^{23} \ mol^{-1}}{4}$. $M = \frac{108.396}{4} \ g \ mol^{-1} = 27.099 \ g \ mol^{-1} \approx 27.0 \ g \ mol^{-1}$.

Calculate the molar mass of an element if it forms $fcc$ unit cell structure. [Mass of unit cell $= 1.8 \times 10^{-22} \ g$,$N_A = 6.022 \times 10^{23} \ mol^{-1}$]

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