Question

The edge of a body-centered-cubic unit cell (which contains two atoms per unit cell) of an element Y was found to be `3.16 x 10^-8` cm. The density of the metal is `19.35``g/(cm^3)`. What is the approximate molar mass of Y?

Answer 1

The approximate molar mass of `"Y"` is 184 g/mol.

Step 1. Calculate the volume of the unit cell

`V = l^3 = (3.16 × 10^"-8"color(white)(l) "cm")^3 = 3.155 × 10^"-23" color(white)(l)"cm"^3`

Step 2. Calculate the mass of a unit cell

`"Mass" = Vρ = 3.155 × 10^"-23" color(red)(cancel(color(black)("cm"^3))) × "19.35 g"/(1 color(red)(cancel(color(black)("cm"^3)))) = 6.106 × 10^"-22"color(white)(l) "g"`

Step 3. Calculate the mass of one atom

This is the mass of two atoms.

`"Mass of 1 atom" = (6.106 × 10^"-22" color(red)(cancel(color(black)("g"))))/"2 atoms" × "1 u"/(1.661 × 10^"-24" color(red)(cancel(color(black)("g")))) = "184 u/atom"`

The approximate molar mass of the element is 184 g/mol.