Question

KBr crystallizes in a NaCl (B1) structure with a lattice constant of a=0.65966nm.
Determine the bulk density of KBr and the distance between a K ion and a touching Br
ion in the structure. Rationalize your result with the sum of ionic radii for K and Br

Answer 1

Volume of KBr unit cell = a^3

                                     = (0.65966 x 10^-9)^3

                                     = 2.87 x 10^-22 cm^3

mass of 4 atoms in a unit cell = 4 x 119 g/mol/6.023 x 10^23

                                               = 7.90 x 10^-22 g

Bulk density = mass/volme

                      = 7.90 x 10^-22/2.87 x 10^-22

                      = 2.75 g/cm^3

ionic radii for K ion and a touching Br atom = a/2sq.rt.(2)

                                                                           = 6.5966 x 10^-8 cm/2 x sq.rt.(2)

                                                                           = 2.33 x 10^-8 cm

Result from ionic radii of K and Br = (1.52 + 182) pm

                                                       = 3.34 x 10^-8 cm

So the radii calculated and the theoretical radii are close to one another.