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

To calculate the molar mass of a metal with a body-centered cubic unit cell, you need to calculate the edge length of the unit cell. Once you have the edge length and the density of the metal, you can determine the molar mass.

Step-by-step explanation:

The molar mass of a metal can be calculated using the formula:

Molar mass = (density × Avogadro's number) / (volume of one atom)

To calculate the volume of one atom, we need to know the type of unit cell and the edge length of the unit cell. Given that the metal crystallizes in a body-centered cubic unit cell, the edge length can be calculated using the formula:

Edge length = 4R / sqrt(3),

where R = radius of the atom.

Using the given radius of the atom (2.30 x 10-8 cm), we can calculate the edge length of the unit cell. With the edge length and the density of the metal (0.867 g/cm3), we can then calculate the molar mass of the metal.

Answer 2

25.41 g/mol is molar mass of metal.

Step-by-step 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* 10^(-8) cm`

`a=2* r=2* 2.30* 10^(-8) cm=4.60* 10^(-8) cm`

Atomic mass of metal =M

Formula used :

`\rho=(Z* M)/(N_(A)* 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=(2* M)/(6.022* 10^(23) mol^(-1)* (4.60* 10^(-8) cm)^(3))`

`M = 25.41 g/mol`

25.41 g/mol is molar mass of metal.