Question

Question #fde10

Answer 1

`221.30 gmol^(-1)`

Explanation:

1. Calculate the volume of the unit cell

Convert pm to cm
1 pm = `1 * 10^(-10) cm`
419 pm = `4.19 * 10^(-8) cm`

Volume of unit cell = `(4.19 * 10^(-8) cm)^3`
Volume of unit cell = `7.36 * 10^(-23) cm^3`

2. Determine the mass of the metal in the unit cell
Mass of metal in unit cell = `20 gcm^(-3) xx 7.36 * 10^(-23) cm^3`
Mass of metal in unit cell = `1.47 * 10^(-21) g`

3. Determine number of atoms per unit cell

We have face-centered unit cell:

Lattice points on the corner count for an 1/8 because they are shared with 8 other unit cells. Lattice points on the face count for 1/2 as they are shared with one other unit cell.

1/8 x 8 corners = 1 lattice point
1/2 x 6 faces = 3 lattice points
Total number of lattice points (atoms) per unit cell = 4

4. Calculate molar mass of unknown metal

Mass per atom = Total mass of metal in unit cell / number of atoms in unit cell
Mass per atom = `(1.47 * 10^(-21) g) / 4`
Mass per atom = `3.68 * 10^(-22)g`

Use mass to determine molar mass by multiplying by Avogadro's number:

molar mass = `3.68 * 10^(-22)g xx 6.022 * 10^2 mol^(-1)`

molar mass = `221.30 gmol^(-1)`

Looking at the periodic table, this molar mass is the closest to radon.