A metal has a fcc lattice. The edge length of the unit cell is 404 pm. The density of the metal is 2.72 g cm-3. The molar mass of the metal is

Question

A metal has a fcc lattice. The edge length of the unit cell is 404 pm. The density of the metal is 2.72 g cm-3. The molar mass of the metal is (A) 27 g mol-1 (B) 20 g mol-1 (C) 40 g mol-1 (D) 30 g mol-1

Tardigrade Admin · Accepted Answer

d = (ZM/NAa3) (Z = 4 for fcc) M = (d× NA× a3/Z) = (2.72× 6.023× 1023× (404× 10-10)3/4) M = 27 g mol-1

Q. A metal has a fcc lattice. The edge length of the unit cell is 404 pm. The density of the metal is $2.72 g c m^{- 3}$ . The molar mass of the metal is

$27 g m o l^{- 1}$

$20 g m o l^{- 1}$

$40 g m o l^{- 1}$

$30 g m o l^{- 1}$

$d = \frac{ZM}{N _{A} a ^{3}}$ ( $Z = 4$ for fcc)
$M = \frac{d \times N _{A} \times a ^{3}}{Z} = \frac{2.72 \times 6.023 \times 1 0 ^{23} \times ( 404 \times 1 0 ^{- 10} ) ^{3}}{4}$
$M = 27 g m o l^{- 1}$

Q. A metal has a fcc lattice. The edge length of the unit cell is 404 pm. The density of the metal is 2.72gcm−3. The molar mass of the metal is

27gmol−1

20gmol−1

40gmol−1

30gmol−1