Question

A metal has fcc lattice. The edge length of the unit cell is 404pm. The density of metal is 2.72 g/ cm. The molar mass of the metal is (N=6.02\times 10 mol)

• A. 30 g/ mol
• B. 27 g/ mol
• C. 20 g /mol
• D. 40 g /mol

Answer 1

Answer: (B)

27 g/ mol

$d=2.72gc{m}^{-3}$ density of crystal

z = no. of effective constituent particles in one unit cell

M = molecular weight

$a=404pm$ edge length of unit cell

$N_A=6.022\times {10}^{23}$

Density of cubic unit cell-

$d=\frac{ZM}{a^3{N}_A}$

For an FCC, $Z=4$

$M=\frac{d{a}^3{N}_A}{Z}$

$M=\frac{2.72\times (404\times {10}^{-10}{)}^3\times 6.02\times {10}^{23}}{4}$

$=27g/mol$