An element crystallises in a face-centred cubic (fcc) lattice with an edge length of $500 \text{ pm}$ . If the density of the element is $4.0 \text{ g cm}^{-3}$ , the molar mass of the element is _____ $\text{g mol}^{-1}$ . (Nearest integer)

(Given: $N_A = 6.0 \times 10^{23} \text{ mol}^{-1}$ )

Question

An element crystallises in a face-centred cubic (fcc) lattice with an edge length of

500 \text{ pm}

. If the density of the element is

4.0 \text{ g cm}^{-3}

, the molar mass of the element is _____

\text{g mol}^{-1}

. (Nearest integer)

(Given:

N_A = 6.0 \times 10^{23} \text{ mol}^{-1}

)

Quantrex Academy · Accepted Answer

Correct answer: 75

For a face-centred cubic (fcc) lattice, the number of atoms per unit cell,

Z = 4

.

Edge length,

a = 500 \text{ pm} = 5 \times 10^{-8} \text{ cm}

Density,

d = \dfrac{Z \times M}{N_A \times a^3}

Rearranging for molar mass,

M = \dfrac{d \times N_A \times a^3}{Z}

M = \dfrac{4.0 \times 6.0 \times 10^{23} \times (5 \times 10^{-8})^3}{4}

M = 6.0 \times 10^{23} \times 125 \times 10^{-24}

M = 6.0 \times 12.5 = 75 \text{ g mol}^{-1}

Answer:

75

An element crystallises in a face-centred cubic (fcc) lattice with...