Question

Xenon difluoride molecules crystallize in the body-centered tetragonal system. Pictures of the system are in the diagram of the 14 Bravais lattices (http://www.chm.bris.ac.uk/webprojects2003/cook/latticetypes.htm). In the crystal, the base of the unit cell is a square (lengths a and b) 432 pm on a side. The height of the unit cell (length c) is 699 pm. Assume that molecules occupy the atomic positions in the unit cell. What is the density of this compound?

Answer 1

As we know density is

here n = no. atoms in a unit cell ........as it is BCC the no. of atoms =2

N_{A = Avagadro's Number} = 6.022 X 10^22mol^-1

V = Volume = (axbxc)^3

M = molar mass ....................molar mass of XeF2 = 169.28g/mol

density = 2 X 169.28 x 10^-3 kg/mol / 6.022X10^23 mol^-1 X ( 432 X 10^-12 m X 432 X10^-12 m X 699X 10^-12m)

density = 338.56 X 10^-3 kg/mol / 785.55 X 10^-7 mol^-1 m^3

density = 0.4309 X 10^4 kg m^-3

density = 4.309 X 10^3 kg m^-3