Question

A metal crystallizes in a body-centered cubic unit cell. The radius of one atom = 2.30 x 10 -8 cm. The density of the metal is 0.867 g/cm^3 . What is molar mass of metal?

Answer 1

Answer:

25.41 g/mol is molar mass of metal.

Explanation:

Number of atom in BCC unit cell = Z = 2

Density of metal = $0.867 g/cm^3$

Edge length of cubic unit cell= a = ?

Radius  of the atom of metal = r = $2.30\times 10^{-8} cm$

$a=2\times r=2\times 2.30\times 10^{-8} cm=4.60\times 10^{-8} cm$

Atomic mass of metal =M

Formula used :  

$\rho=\frac{Z\times M}{N_{A}\times a^{3}}$

where,

$\rho$ = density

Z = number of atom in unit cell

M = atomic mass

$(N_{A})$ = Avogadro's number  

a = edge length of unit cell

On substituting all the given values , we will get the value of 'a'.

$0.867 g/cm^3=\frac{2\times M}{6.022\times 10^{23} mol^{-1}\times (4.60\times 10^{-8} cm)^{3}}$

$M = 25.41 g/mol$

25.41 g/mol is molar mass of metal.