Question

The density of a sample of metal was measured to be 8.91 g/cm3. An X-ray diffraction experiment measures the edge of a face-centered cubic cell as 352.4 pm. Part APart complete What is the atomic weight of the metal

Answer 1

The atomic weight of the metal is 58.7 g/mol

Step-by-step explanation:

Given;

density of the metal sample, ρ = 8.91 g/cm³

edge length of the face centered cubic cell, α = 352.4 pm = 352.4 x 10⁻¹⁰ cm

Volume of the unit cell of the metal;

V = α³

V = (352.4 x 10⁻¹⁰ cm)³

V = 4.376 x 10⁻²³ cm³

Mass of the metal in unit cell

mass = density x volume

mass = 8.91 g/cm³ x 4.376 x 10⁻²³ cm³

mass = 3.899 x 10⁻²² g

Atomic weight, based on 4 atoms per unit cell;

4 atoms = 3.899 x 10⁻²² g

6.022 x 10²³ atoms = ?

= (6.022 x 10²³atoms x 3.899 x 10⁻²² g) / (4 atoms)

= 58.699 g/mol

= 58.7 g/mol (this metal is Nickel)

Theerefore, the atomic weight of the metal is 58.7 g/mol