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) 20 g mol-1  (B) 40 g mol-1  (C) 30 g mol-1  (D) 27 g mol-1

Tardigrade Admin · Accepted Answer

Given, cell is fcc. So, Z=4 Edge length, a=404 pm =4.04 × 10-8 cm Density of metal, d=2.72 g / cm 3 NA=6.02 × 1023 mol -1 Molar mass of the metal, M= ? We know that density, d =(Z × M/a3 ⋅ NA) ⇒ M=(d ⋅ a3 NA/Z) =(2.72 ×(4.04 × 10-8)3 × 6.02 × 1023/4) =27 g / mol ∴ Atomic mass of copper (Cu)=63.1 u.

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

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

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

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

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

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

20gmol−1

40gmol−1

30gmol−1

27gmol−1

Given, cell is fcc. So, Z=4 Edge length, a=404pm=4.04×10−8cm Density of metal, d=2.72g/cm3 NA​=6.02×1023mol−1 Molar mass of the metal, M= ? We know that density, d=a3⋅NA​Z×M​ ⇒M=Zd⋅a3NA​​ =42.72×(4.04×10−8)3×6.02×1023​ =27g/mol ∴ Atomic mass of copper (Cu)=63.1u.

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

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

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

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

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