An element crystallizes in a body-centered cubic (bcc) lattice with an edge length of $400$ pm. If the density of the element is $5.0$ g cm $^{-3}$ , the molar mass of the element is ________ g mol $^{-1}$ .

(Nearest integer)

[Given: $N_A = 6.0 \times 10^{23}$ mol $^{-1}$ ]

Question

An element crystallizes in a body-centered cubic (bcc) lattice with an edge length of

400

pm. If the density of the element is

5.0

g cm

^{-3}

, the molar mass of the element is ________ g mol

^{-1}

.

(Nearest integer)

[Given:

N_A = 6.0 \times 10^{23}

mol

^{-1}

]

Quantrex Academy · Accepted Answer

Correct answer: 96

For a bcc lattice, the effective number of atoms per unit cell,

Z = 2

.

Edge length,

a = 400

pm

= 400 \times 10^{-12}

m

= 4 \times 10^{-8}

cm.

The density of the unit cell is given by:

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

Rearranging for molar mass

M

:

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

Substituting the given values:

M = \dfrac{5.0 \times 6.0 \times 10^{23} \times (4 \times 10^{-8})^3}{2}

M = \dfrac{30.0 \times 10^{23} \times 64 \times 10^{-24}}{2}

M = \dfrac{30.0 \times 6.4}{2} = 96

g mol

^{-1}

.

Answer:

96

An element crystallizes in a body-centered cubic (bcc) lattice with...