Question #fde10

1 Answer
Dec 4, 2017

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:

http://web2.clarkson.edu/projects/nanomat/Chapter1html/chapters/fcc.htmlhttp://web2.clarkson.edu/projects/nanomat/Chapter1html/chapters/fcc.html
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.