Question

you are given a small bar of an unknown metal, x. you find the density of the metal to be 10.5 g/cm cubed. an x ray diffraction experiment measures the edge of the unit cell as 409 pm. assuming that the metal crystallizes in a face centered cubic lattice, what is XeF4non most likely to be? why
a Ag
b Rh
c Pt
do Pb
email none of these

Answer 1

1) Convert picometers to m to cm:

409 pm = 4.09 x 10^-10 m = 4.09 x 10^-8 cm

2) Determine the volume of the unit cube:

(4.09 x 10^-8 cm)³ = 6.84 x 10^-23 cm³

3) Determine the mass of the metal in the unit cube:

10.5 g/cm³ times 6.84 x 10^-23 cm³ = 7.18 x 10^-22 g

4) Determine atomic weight (based on 4 atoms per unit cell):

7.18 x 10^-22 g is to 4 atoms as x grams is to 6.022 x 10²³ atoms

x = 108.1 g/mol (to three significative figures)

This weight is close to that of Silver (Ag MW: 107.87).