The volume of fcc unit cell is 5.6×10^ -23 \ cm^3 . Calculate the molar mass of metal if the density of metal is 20.4\ g cm^ -3 . [N_A=6.022×10^ 23 ]

Question

Quantrex Academy · Accepted Answer

Correct answer: A. 172\ g mol^ -1

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

d = \dfrac{Z \times M}{N_A \times V}

For an fcc unit cell, the number of atoms per unit cell is

Z = 4

.

Rearranging the formula to solve for molar mass

M

:

M = \dfrac{d \times N_A \times V}{Z}

Substituting the given values:

M = \dfrac{20.4 \times 6.022 \times 10^{23} \times 5.6 \times 10^{-23}}{4}

M = \dfrac{20.4 \times 6.022 \times 5.6}{4}

M = 171.98 \approx 172\ \text{g mol}^{-1}

Answer:

172\ \text{g mol}^{-1}

The volume of fcc unit cell is 5.6×10^ -23 \ cm^3 . Calculate the...